docs: a design for a node editor whose wires can be drawn, deleted and navigated

The reported "cannot add edges" has a specific cause: the output port's hit
radius reaches past the box it belongs to, and the press handler re-derives the
owning node with a box test, so clicking the visible dot's outer half sets
pending_out to -1 and silently disarms. Edge deletion has no code path at all.

The design replaces the two-click protocol with a drag gesture, makes the list
order the editor's own invariant via a topological re-sort rather than a rule the
user must obey, adds a view transform with every hit test routed through its
inverse, and trades the modal alert on Apply for a live validation line. It also
records that the Cancel button still calls gtk_window_destroy -- the dangling
dialog pointer CLAUDE.md documents as fixed was only fixed on the Apply path.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -62,7 +62,11 @@ app's plain `GtkApplicationWindow` is supported and warning-free; it was checked
 
 `deps/plotter` is upstream's own repository and this app's figure support was added
 there rather than worked around here: `Figure::set_min_y_gutter()` (a floor under the
-common left gutter), and in the GTK4 adapter `PlotArea`'s **figure mode** —
+common left gutter), `Figure::set_right_gutter()` / `Plot::set_right_gutter()` (an empty
+band on the *other* side, which the layout had no concept of — `axes` reached the
+viewport's right edge, so the rightmost x tick label was centred on a line it had half of
+itself outside of; the guard is `figure_rows_share_one_right_gutter`), and in the GTK4
+adapter `PlotArea`'s **figure mode** —
 `set_figure()`, one `input::Controller` per row, nearest-row event routing, a
 figure-wide crosshair — plus `PlotArea::row_at()` for naming the row a pointer is over.
 
@@ -72,9 +76,14 @@ it, and `LineProgram::set_snap()` / `u_snap` rounds an axis-aligned segment's in
 whole pixels for the chrome that frames a plot (grid and axis lines), never for anything
 drawn at a data position. `generate_ticks()` also stores the tick at the origin as
 exactly `0.0` — the walk starts at `ceil(min/stride)*stride` and so never lands on zero
-when the stride is not a power of two, which labelled it `-139a`. All three carry
+when the stride is not a power of two, which labelled it `-139a`. `format_time()` picks its
+unit rung by the **rounded** mantissa (`t < u.scale * 0.9995`, and the same slack on the
+whole-second branch) — the `>= 999.5` spill guard `format_si()` in the same file always had —
+because a tick a hair under a rung's top rounds to 1000 at three significant figures and
+`%.3g` writes that `1e+03`, which is how a one-second tick read `1e+3ms`. All four carry
 upstream tests — `the_atlas_is_filtered_not_point_sampled`,
-`grid_hairlines_land_on_whole_pixels` and `the_tick_at_the_origin_reads_zero`. The minor
+`grid_hairlines_land_on_whole_pixels`, `the_tick_at_the_origin_reads_zero` and
+`format_time_never_lets_a_field_reach_its_radix`. The minor
 grid's look is set there too, not here: `grid_minor` carries 50% alpha, `grid_minor_width` is
 0.75 (sub-pixel, expressed as coverage at 1x) and `grid_minor_dash_on`/`_off` are 3/3 — a
 fragment discard, no extra geometry — so the subdivisions read as texture under the labelled
@@ -105,9 +114,18 @@ Two baselines every run is read against. A clean build emits **five** warnings a
 `-Woverlength-strings` on **both** generated GResource `.c` files — the help pages' and the
 icons', whose blob crossed C99's 4095-byte string-literal limit when the two app icons joined the
 four action ones (a note about a generated file, which GCC itself supports). And an exit-dump run
-emits exactly **two** `Gtk-CRITICAL`s, `gtk_widget_get_height` and `gtk_widget_get_width`, from
-the dump asking a destroyed widget for its size. A sixth warning, or a third critical, is a
-finding.
+emits **no** `Gtk-CRITICAL` at all. A sixth warning, or any critical, is a finding.
+
+That second baseline used to be "exactly two, `gtk_widget_get_height` and `gtk_widget_get_width`,
+from the dump asking a destroyed widget for its size", and tolerating them was a mistake: the dump
+runs from the destroy handler, so the widget pointer is **freed memory**, and a critical is only
+the lucky reading of it. A run that had built and destroyed other windows first —
+`UDPSCOPE_PROBE_HELP_MS`, which opens three — has had that memory reused, and the same two calls
+then **SIGSEGV in the middle of the dump**, which reads as a truncated dump rather than as a
+crash in a debug line. Every size the dump prints is therefore captured on the *tick*, while the
+window is alive (`App::dbg_*`), and **no `gtk_widget_*` call may appear in the dump** — the
+`panel controls:` line was already written that way for the same reason, and that comment is the
+precedent, not an exception.
 
 - `UDPSCOPE_EXIT_AFTER_MS` — run the trigger-on → go-live probe, close the window,
   then dump the whole pipeline state to stdout (frame/sample counts, per-plot painted
@@ -152,9 +170,12 @@ finding.
   waveform over a window of millions -- 0.1% is what the pyramid-backed walks give (see the
   measurement-cost invariant below). A `raw` near `covered` means the walks went back to reading
   the window, which at 1 MS/s is 19.7 ms per recompute and a third of the run's frames. It is
-  *legitimately* near `covered` for a window shorter than a bucket (64 samples) or a signal noisy
-  enough to straddle a level everywhere, so read it on the fast mock
+  *legitimately* higher for a window shorter than a bucket (64 samples) or a signal noisy
+  enough to cross a threshold everywhere, so read it on the fast mock
   (`tools/mock_udpstreamer.py --rate 1300000 --batch 2000`), where a window is ~2 M samples.
+  `--noise 0.1` there reads **2.0%** at 1.96 ms a recompute against the clean 0.1% at 1.41 ms, and
+  that is the interferer's own cost rather than a regression -- the figure to compare a change
+  against is the **clean** one.
   Note the **final** `measurements:` line and `[measure-trace]`'s last lines may read `--`:
   `UDPSCOPE_EXIT_AFTER_MS` arms the trigger before it dumps, so the dump can land in `Waiting`
   with nothing bound and the axis at its default. The race-free reading is an earlier
@@ -208,8 +229,8 @@ finding.
   since `set_time_window()` frames the newest span before the pin clamps it — both are expected.
 - `UDPSCOPE_PROBE_PAUSE_MS` — pause acquisition mid-run so layout numbers are
   measured on a still picture. It now also asserts what a pause *is*
-  (`[pause-probe] <action> paused=D ring_produced=N event_size=M frozen_x=[..] axis=[..]` on
-  stderr):
+  (`[pause-probe] <action> paused=D ring_produced=N event_size=M frozen_x=[..] axis=[..]
+  glance=[..]` on stderr):
   it presses the **button**, not `Acquisition::set_paused()`, because pausing is a display
   state as well as an acquisition one and the view snapshot and axis pin live in the
   handler. Across the three lines **`ring_produced` must grow** (the producer never
@@ -218,6 +239,17 @@ finding.
   the ring) and **`frozen_x` must not move between the pause and the resume**; after the
   resume `event_size` is 0 and the window is back on the newest data. Pausing used to stop
   the producer, which is why the counts grew by nothing and the resume left a hole.
+  `frozen_x` is the *rebased* snapshot — the pause view's own stamps are relative to the freeze
+  instant now, so the range reads `[-window..0]`-ish rather than stream seconds, and a
+  `frozen_x` in the thousands is the rebase gone.
+  **`glance=` is the assertion for the paused status field**, and this is the only line that can
+  make it: the exit dump's `status bar:` is read live and its two `mode …` lines are the live and
+  triggered states. While paused it must read `paused · <rate> · <window> · for <elapsed>`, with
+  the elapsed figure **growing between the two paused lines** and **absent on the resume line**.
+  It is **wall** time (`g_get_monotonic_time()`), not stream time, because the producer never
+  stops while paused and "how long have I been looking at this" is a question about the user, not
+  about the stream; it is written through `format_elapsed()` so the field steps to a coarser unit
+  instead of growing digits (see the layout rule).
 - `UDPSCOPE_EXPORT_MS` (+ optional `UDPSCOPE_EXPORT_PATH`, default
   `/tmp/udpscope-export`) — collect the export table and write it both ways, skipping
   only the file chooser.
@@ -235,10 +267,18 @@ Two lines of the self-check output are assertions in disguise:
   monotone (`plot_host.cpp`), its one-shot widest-label reservation can land a frame or
   two after the first measured frame, and the figure serves its floor out of the label
   strip (`y_width = max(measured, floor - y_title_w)`, `plot.cpp`) so the reservation
-  converges over two layouts rather than one. A `y-gutter 44..74` dragging
-  `axes.x 67..80`/`axes.w 546..559` with it is that settle, not a twitch — confirm it
+  converges over two layouts rather than one. A `y-gutter 88..104` dragging
+  `axes.x 88..104`/`axes.w 707..782` with it is that settle, not a twitch — confirm it
   with the `changes` line below. A range that keeps moving is the "twitching axis" bug:
-  the plot being re-measured every frame. **`x-desync` must read 0**: it counts frames
+  the plot being re-measured every frame. **A range that keeps *climbing* to 200 is the
+  other one**: `note_y_gutter()` is handed the gutter the row was laid out with, which
+  already includes the floor imposed last frame, so slack added to it is added again every
+  frame and the gutter ratchets to its own 200 px cap — `axes.x 88..200 / y-gutter 88..200
+  / axes.w changes: 17` on an 870 px viewport is what that reads as, and 17 changes looks
+  like a settle. The reservation's own padding is the only slack there may be.
+  `axes.w` also no longer reaches the viewport's right edge: `apply_gutters()` reserves an
+  empty band there (~59 px of 870), so `viewport.w - axes.x - axes.w` is a *constant*, not
+  a zero. **`x-desync` must read 0**: it counts frames
   in which any row's x range differed from row 0's by more than a pixel of data, i.e.
   frames the x link group did not reach. `x-ticks` is content, not layout, and
   legitimately varies by one as a live
@@ -258,7 +298,11 @@ Two lines of the self-check output are assertions in disguise:
   edge and `axis=` must stay at `[-pre..+post]` across consecutive probes while
   `data=`'s upper bound climbs towards `+post` — an axis that moves instead means the
   capture is being treated as a live view (`clamp_to_data()` reaching a pinned window).
-  `epoch=` must be back to `0.0000` in every other state. Note the probe reads
+  `epoch=` is **minus the newest acquired stamp** in `live` and `nothing` — it is what makes the
+  live axis `[-window, 0]`, so there it grows (in magnitude) with the stream and a `0.0000` is
+  the defect, not the healthy reading. It is back to `0.0000` only in `event(frozen)`, where the
+  snapshot carries its own origin (`EventSnapshot::x_offset`) and the display epoch has nothing
+  left to do. Note the probe reads
   `pending=` fresher than `display=` (which is last tick's decision), so a single
   `pending=0 display=live(capturing)` line is one frame of sampling skew, not a defect.
   And `snap=[a..b]` must equal `axis=[a..b]`, with `b` positive by roughly
@@ -305,19 +349,24 @@ Two lines of the self-check output are assertions in disguise:
   `events` does not move**: no event fired, so the partial publish deliberately leaves
   `trigger_latches()` alone — which is also what keeps the `trigger events: N total, M at
   the disarm` line in the dump meaning what it says.
-- `[export-probe] mode=.. axis=[a..b] rows=N cols=M time=[c..d] stream=[..]` (stderr,
+- `[export-probe] mode=.. axis=[a..b] rows=N cols=M time=[c..d] abs=[..]` (stderr,
   `UDPSCOPE_EXPORT_MS`) — **`time=` must equal `axis=`** and **`rows=` must be the
   span times the stream's real rate, plus one** (2 s at 10 kS/s is 20001). The export
   is the *visible* range at the *stored* rate, so a count far short of that is a table
   cut from the LOD pyramid, and a `time=` narrower than `axis=` is a window searched on
-  the wrong clock (the live branch subtracts `display_epoch()` before searching the
-  ring). In `mode=event`, `stream=` must be the edge ± the window; in `mode=live` it
-  equals `time=`.
-  The one exception to both: an export taken **mid-capture** reports `mode=live` with
-  `time=[-pre..e]` where `e` is how far the post window has filled, and `stream=` offset
-  from it by the edge (so `stream - time` reads the edge exactly) — the export is what is
-  on screen, and during a capture that is a partly filled window. Pin the probe outside a
-  capture when checking the `rows=` count.
+  the wrong clock (the live branch puts the window back on the stream's clock with
+  `stream_at_x0()` before searching the ring, and that offset is a whole window while
+  streaming — not the 0 it once was).
+  **`abs - time` must be a single constant across both ends of a line**, and that constant is
+  where the display's origin sits in the stream's own clock: `epoch()` plus the newest stamp in
+  `mode=live`, `epoch()` plus the accepted edge in `mode=event`. That is the one assertion on
+  the second column, and it replaces the old "`stream=` must be the edge ± the window" reading,
+  which only ever held because the display clock *was* the stream clock. A `mode=live` line
+  whose `abs - time` differs between the two ends is the two columns computed from different
+  epochs — the defect `abs_base` exists as a single `const` to prevent.
+  An export taken **mid-capture** reports `mode=live` with `time=[-pre..e]` where `e` is how far
+  the post window has filled — the export is what is on screen, and during a capture that is a
+  partly filled window. Pin the probe outside a capture when checking the `rows=` count.
   The two `bytes=` lines are the writers: the `.npy` is
   `64·⌈(10+len(header)+1)/64⌉ + rows·(16 + 4·cols)`, so a size that is not that is a
   mispacked record. Read it back with `pd.DataFrame(np.load(path))` after changing
@@ -392,7 +441,14 @@ Two lines of the self-check output are assertions in disguise:
   plottable signal and lets the tick compute them, so what it prints is what a user reads.
   On the test stream's 1 Hz ±1 sine the values must be: average ≈ 0, `top` ≈ 0.64 and
   `bottom` ≈ -0.64 (the mean of each half of a sine), max/min ≈ ±1, `pulse duration` ≈ 0.5 s
-  with `duty` ≈ 0.5, `period` ≈ 1 s and `frequency` ≈ 1 Hz. `marks=` lists each mark with its kind, and the **mix is the point**:
+  with `duty` ≈ 0.5, `period` ≈ 1 s and `frequency` ≈ 1 Hz. It needs **`UDPSCOPE_ENABLE_ALL_MS`
+  ahead of it** or it prints `no acquired signal to measure` and the dump reads `n=0`.
+  **Run it against `--noise 0.1 --freq 1` as well, and the three crossing types must still read
+  those figures** (measured: `period=1.000100 frequency=0.999900 pulse duration=0.504100`): the
+  hysteresis band is the only thing holding them there, a single level reads a 500 Hz interferer as
+  the signal, and the default `--noise 0` mock cannot see it. The band costs `raw`, not accuracy --
+  the clean fast mock reads `raw=0.1%` at 1.41 ms a recompute and the noisy one `raw=2.0%` at 1.96
+  ms, so read `measure cost:` on **both**. `marks=` lists each mark with its kind, and the **mix is the point**:
   `level:V` alone for average/top/bottom, `level:V,time:T` for min/max (a ruler at the value
   *and* a marker at the first sample that reached it — two level marks at both extremes was
   the bug), `time:A,time:B` for pulse/period/frequency. `text=` is the pane's own string with
@@ -401,11 +457,17 @@ Two lines of the self-check output are assertions in disguise:
   (a min/max showing both its marks counts two of its own). `measures window:` is the
   timeliness assertion -- the window the numbers were computed over against the one on screen.
   **The reading that must hold is `marks_in_window=K/K`**: every *time* mark inside the window
-  on screen. `drift` itself is a **single sample of a sawtooth** and is not an assertion on its
+  on screen. Both ranges are on the **stream's** clock, which is the space `measure_window` and
+  the time marks are stored in -- a live axis is a fixed `[-window, 0]`, so comparing display x
+  would read no drift whatever the data did.
+  `drift` itself is a **single sample of a sawtooth** and is not an assertion on its
   own: a live view scrolls between recomputes, so it rises to one `kMeasureRefreshUs` of scroll
-  and drops to zero at each pass. On a 2 s window at the 100 ms cadence the top of that sawtooth
-  is `drift=5%`, which is what a dump landing just before a scheduled pass reads -- a `0.0000%`
-  is a dump that landed just after one, not a better state. Read it against the recompute count:
+  and drops to zero at each pass. The figure is `(|Δmin| + |Δmax|) / span`, so a pure scroll
+  counts **twice** and the top of the sawtooth is `2 × refresh / window`: ~10 % on a 2 s window
+  at the 100 ms cadence, and a few *hundred* percent on a window shorter than the interval (a
+  50 ms window reads 254 % for 63.6 ms of scroll, and its ceiling is 400 %). Compute the ceiling
+  for the window the run actually used before calling a figure large. A `0.0000%`
+  is a dump that landed just after a pass, not a better state. Read it against the recompute count:
   *more* recomputes with a *higher* drift sample is the sawtooth, while a drift that exceeds one
   refresh interval of scroll, or marks outside the window, is the defect. A measurement is
   recomputed when the window moves (2 % of its span) or the held/live state changes, never on a
@@ -443,12 +505,17 @@ Two lines of the self-check output are assertions in disguise:
   row-level `set_time_window()` does nothing** (a probe that changes the window must use the
   app's path). **`distinct` must be 1 on every line, and that is the assertion** — it says no two
   major labels on the axis are the same string, which is the one thing the relative form exists to
-  buy and the only reading that holds whatever the stream's uptime is. `relative=D` deliberately
-  is *not* fixed per window: the form is decided by the tick step against the label resolution at
-  the axis' **magnitude** (see the invariant below), so the same 50 ms window reads absolute at
-  2 s of uptime (`2.13s, 2.14s, 2.15s`) and relative at 17 s (`100µs, 10.1ms, 20.1ms`, with the
-  caption) — both correct, and a probe pinned to one of them would assert the stream's clock
-  rather than the app. The **caption must be non-empty exactly when `relative=1`**. Run it after
+  buy and the only reading that holds whatever the stream's uptime is. `relative=D` is **expected
+  to read 0 on every line now**, and that is a consequence of the newest-relative axis rather than
+  a change to the rule: the form is decided by the tick step against the label resolution at the
+  axis' **magnitude** (see the invariant below), and no display mode carries a large magnitude any
+  more — live and waiting are `[-window, 0]`, a capture and a held event are edge-relative, a pause
+  is freeze-relative. The 50 ms window that used to read absolute at 2 s of uptime (`2.13s, 2.14s,
+  2.15s`) and relative at 17 s (`100µs, 10.1ms, 20.1ms`, with the caption) now reads
+  `-40ms, -30ms, -20ms, -10ms` at any uptime. The rule and the caption are kept because they are
+  the answer for *any* axis magnitude and nothing in them is mode-specific — do not delete them on
+  the strength of this reading — but what the probe asserts is `distinct`, not the form. The
+  **caption must be non-empty exactly when `relative=1`**, which here means empty throughout. Run it after
   `UDPSCOPE_ARM_TRIGGER_MS` as well, which is the case the span rule got wrong: a triggered 50 ms
   window must read `relative=0 note=[] ticks=[-20ms,-10ms,0,10ms]` — a `t0` caption on an axis
   that is already edge-relative re-anchors the ticks away from the trigger, which is the one
@@ -563,15 +630,25 @@ Two lines of the self-check output are assertions in disguise:
   first run's values, and the signals it names must come back *acquired* (a `row 0 slot 0
   -> channel ... samples=N` line). Delete the file before a run whose layout you did not
   mean to inherit (`127.0.0.1_9540.toml` and friends accumulate otherwise).
-- `[udpscope] starved: connected (config=D), reconnects=N, no new frames in the last
+- `[udpscope] starved: connected (config=1), reconnects=N, no new frames in the last
   second ...` (stderr, once per second while the state holds, plus a status-line notice) —
   "connected but nothing is arriving after a reconnect", which over unicast is the second
-  instance taking the source's single session. Two ways to see it without a second client:
-  point the app at a UDP port where nothing answers (the client CONNECTs, times out,
-  reconnects; `config=0`), and check it does **not** fire against a live source. The status
-  line carries ` | N reconnects` only when N > 0, which is the same counter without the
-  prose.
-- **The export's `time`/`stream_time` columns must be strictly increasing and evenly
+  instance taking the source's single session. Check it does **not** fire against a live
+  source. The status line carries ` | N reconnects` only when N > 0, which is the same
+  counter without the prose.
+  **The same stall test has two outcomes, split on `have_config`, and they are different
+  diagnoses.** With a signal list in hand, the above. With **no CONFIG at all** it prints
+  `[udpscope] connecting: connected (config=0), reconnects=N, no configuration from the
+  stream ...` and the notice reads *trying to connect* — nothing was taken away, because
+  with no signal list nothing can be enabled and no DATA frame is owed, and the old wording
+  blamed a second reader that does not exist. That state is also named *without* waiting for
+  the three-sample stall: the glance word is `connecting` and the badge is **yellow** from the
+  first frame (see `badge frames:`). The way to see it with no second client is to point the
+  app at a UDP port where nothing answers (the client CONNECTs, times out, reconnects), which
+  is now the `config=0` branch and no longer exercises the `starved:` one at all — a check of
+  the unicast-contention wording needs a real second reader, or a source that configures and
+  then goes quiet.
+- **The export's `time`/`abs_seconds` columns must be strictly increasing and evenly
   spaced.** Check the written file, not just the probe: `np.diff(t)` with no `<= 0` and
   `rows / (t[-1] - t[0])` equal to the stored rate (the `ch` line's figure). Duplicate or
   backwards stamps mean the recorded timeline holds two clocks or a collapsed cadence —
@@ -579,35 +656,92 @@ Two lines of the self-check output are assertions in disguise:
   README) and a per-sample step derived from the client's `lost` counter (now the
   stream's measured arrival cadence). A `rows=` count far below the span times the rate
   is the other signature, that of a table cut from the LOD pyramid.
-  **`set(np.diff(t))` must hold exactly one value**, and this is the check that needs a long
-  run at a high rate: a *plateau* of equal stamps, or a diff taking two or three values a few
-  hundred nanoseconds apart, is the time ring losing precision with uptime (see the `f64`
-  time-ring invariant below — the figure to compute is the ULP of `t[0]`, since the defect
-  grows with how long the app has run, not with the export's own length).
-- `badge frames: lit=L dim=D idle=I` — the activity badge's phase per frame. Over a run
-  that acquired anything **both `lit` and `dim` must be non-zero**: that is what "it
+  **The step must hold to a few ULP of the column's own magnitude**, and this is the check that
+  needs a long run at a high rate: the old form of this assertion was "`set(np.diff(t))` holds
+  exactly one value", and that was only true while `time` *was* the stored stamp. Both columns
+  are derived now — `time` is `stamp - stream_at_x0()` and `abs_seconds` is that plus a base of a
+  wholly different magnitude — so each subtraction costs a rounding and `set()` legitimately
+  holds a handful of neighbouring doubles. Measured: four values spanning ~1.5 ULP, 6.8e-16 s.
+  The thing that must not come back is the **plateau**: equal stamps, or a diff taking two or
+  three values a few *hundred nanoseconds* apart, is the time ring losing precision with uptime
+  (see the `f64` time-ring invariant below). The figure to compute is the ULP of `t[0]` and of
+  `abs_seconds[0]` — the defect that invariant guards is microseconds, nine orders of magnitude
+  above the arithmetic noise, so the two readings cannot be confused.
+- `badge frames: lit=L dim=D idle=I connecting=C` — the activity badge's phase per frame. Over
+  a run that acquired anything **both `lit` and `dim` must be non-zero**: that is what "it
   blinks" means, and a badge stuck lit is indistinguishable from a working one in a
   screenshot. One or two `idle` frames at the start are the frames before the socket
   connected; a large `idle` is correct only when the run paused or disarmed (a
-  `UDPSCOPE_PROBE_DISARM_MS` run should show hundreds). The `mode ...` lines carry the
-  rest of the status line, so `rate` and `last event ... ago` are checked there.
+  `UDPSCOPE_PROBE_DISARM_MS` run should show hundreds). **`connecting` must be 0 on a run
+  against a live source** — it is the steady *yellow* phase, "the socket answered but the
+  stream has sent no CONFIG", and a non-zero count against a working mock means a signal list
+  that arrived late or not at all. It is the *only* non-zero phase on a dead-port run
+  (measured: `lit=0 dim=0 idle=90 connecting=446`, the `idle` being the frames before the
+  first CONNECT), which is also the check that a source that has sent nothing never gets the
+  blinking green. The `mode ...` lines carry the rest of the status line, so `rate` and
+  `last event ... ago` are checked there.
 - `frame cost: tick A/B ms over N, draw C/D ms (max at frame F), paint E/G ms over M` and
-  `frame path: raw=R lod=L frames, segments S/T (mean/max), visible max V samples` — the
+  `frame path: raw=R lod=L columns=C graded=G frames, segments S/T (mean/max), visible max V samples`
+  — the
   drawing cost, split into the frame tick, `PlotArea`'s own draw (timed from the frame
   clock's `before-paint` to the end of the host's `render` handler) and the whole GTK
-  paint. **`segments` max must stay in the tens of thousands and `lod` must dominate `raw`
+  paint. **`segments` max must stay in the low thousands and `lod` must dominate `raw`
   on any run holding a large capture**: a max in the *millions* with `lod=0` is the
   empty-pyramid defect (see the `MinMaxPyramid` invariant below) — the renderer drawing
   every raw sample of a held event on every frame, which measured 6,000,073 segments and
   100–230 ms a frame at 1 MS/s. `raw` frames are expected and cheap below 64 samples per
-  pixel, which is where `level_for()`'s own gate puts the boundary. **`draw`'s max must sit
+  pixel, which is where `level_for()`'s own gate puts the boundary.
+  **`columns` must equal the frames that drew a trace at all on any run at a high rate**, and
+  it is the reading that says *why* `segments` is small: a dense gathered window is reduced
+  onto the pixel grid upstream (one snapped vertical segment per column — see the moiré
+  invariant below), so the geometry is bounded by `axes.w`, and a `columns=0` beside a large
+  `segments` is that reduction gone rather than a narrower window. Measured on
+  `--rate 1300000 --batch 2000 --freq 3000` over 20 s: `raw=2 lod=1198 columns=1200 frames,
+  segments 2041/2237` over 1201 painted frames, against `columns=0 ... segments
+  10960/216093` over 263 before it existed — the same run at 4.6× the frame rate.
+  **`graded` must equal `columns`**: this app turns `Style::intensity_grading` on, and grading is
+  a way of *drawing* the reduction rather than a third path, so a `graded` below `columns` is the
+  style not reaching a frame. **`UDPSCOPE_NO_PHOSPHOR=1` is the A/B** and the only way to read
+  either of these two lines against the ungraded path, since a frame mean cannot attribute its own
+  cost: measured on `--rate 1300000 --batch 2000`, `columns=1166 graded=1166` with
+  `draw 3.24/21.43 ms` and `segments 1340/4157` against `graded=0`, `draw 2.30/25.76 ms` and
+  `segments 131/4306` over the same `lod=453` frames. The segment rise *is* the gradient (alpha is
+  quantised into steps, one `LineBatch` and one draw call each, because the line pipeline's colour
+  is a uniform) and the ~1 ms is its cost; a `raw` that *grows* when the grading is on is the
+  level-floor invariant below gone, which measured `raw=1154 lod=0` and 6.36 ms.
+  **`draw`'s max must sit
   at a frame near 0** — that is the warm-up (glyph atlas, first vertex-buffer growth); a
   late `F` is a frame whose own geometry was expensive and worth tracing. `tick`'s max is
   the publish stall: `publish_event()` builds the snapshot's pyramids under `mutex()`, so a
   latch at over 1 MS/s costs one ~40 ms tick, which must not produce `gaps`. Both these
   lines and the disarm probe's `axis=`/`snap=` need a fast source to say anything —
-  `tools/mock_udpstreamer.py --rate 1300000 --batch 20000` — since at the default 10 kS/s a
-  whole window fits in the raw path and the publish is too short to lose a race.
+  `tools/mock_udpstreamer.py --rate 1300000 --batch 2000` — since at the default 10 kS/s a
+  whole window fits in the raw path and the publish is too short to lose a race. (Do not
+  raise `--batch` to chase the rate: a batch of 20000 exceeds the datagram limit and the mock
+  dies with `OSError: [Errno 90] Message too long`.)
+- `publish cost: N events, A/B ms (mean/worst, blocks the UI); M pauses, C/D ms (mean/worst,
+  blocks the producer)` — what *freezing a view* costs, and the line that attributes the stall
+  `frame cost:`'s `tick` max can only hint at. The two publishes are counted apart because they
+  stall **opposite threads**, and nothing else in the dump distinguishes them:
+  `publish_event()` runs on the producer with `mutex()` already held, so its cost lands on the UI
+  as a long tick; `publish_pause_view()` runs on the UI thread and takes the lock, so its cost
+  lands on the producer and can only surface as `gaps`. Read the event figure against `tick`'s max
+  and the pause figure against `gaps`. Both are **wide**: on the fast mock the event publish has
+  read **69, 89, 92 and 115 ms** and the pause publish **22 and 86 ms** across runs, so treat the
+  line as an order of magnitude and not a figure to compare a change against at the millisecond.
+  The event reading matters anyway because it is far above the ~40 ms the `frame cost:` entry above
+  quotes — treat that 40 as the old reading and this line as the authority.
+  It is also **the number to judge a second live ring against**, which is the one design question
+  it exists to answer: freezing a whole `BufferStore` copies nothing and inherits the pyramid a
+  `ChannelBuffer` already maintains incrementally, so both `worst` figures would go to **0** — at
+  the price of a second budget's worth of memory (README records that one live ring is why
+  `--buffer-mb 200` really is 200 MB) and a second per-sample write on the producer. What the line
+  says about that trade is that the stall is real but **costs no packets**: an A/B of the same run
+  with and without a pause read `gaps=0` both ways, the paused one with an 86 ms publish, so a
+  second ring would buy a smoother frame at a latch rather than recovered data. (An earlier run
+  reported `gaps=73` with a pause against 0 without, which is what made the stall worth measuring;
+  it has not reproduced and did not scale with the publish length — 79 gaps with the pyramid build
+  removed against 73 with it — so it was incidental load on one run. Do not quote it as a cost.)
 - `trace ink: N paints checked, C collapsed, S staircase, H short, worst cover P%, worst
   drawn-vs-quoted D px over R raw paints` plus a
   `[ink] paint N <flags> mode=.. axis=[..] n=.. idx=[..) spp=.. level=.. pts=.. kept=..
@@ -663,7 +797,7 @@ Two lines of the self-check output are assertions in disguise:
   so the panes the tick rewrites are measured directly. The `[width-probe]` lines are the
   per-change detail behind the `axes.w changes` count, and a step over 100 px dumps the widget
   tree's wide subtrees — that is what the documented, intermittent ~320 px step wants read.
-- `[help] pages=14 parsed=14 shortest='Pause and play' 1434 B; shortcuts: app=12 plot=13; about version=… commit=… built=… settings=… icon=org.udpscope.app; closed ok` (stderr, `UDPSCOPE_PROBE_HELP_MS`) — **`parsed` must equal `pages`** and no page may be empty: a missing resource or markup Pango rejects renders a one-line stand-in instead of failing, so the window *looks* fine and only this count notices. `settings=` must be a real path (the same one the About dialog shows). **`icon=` must read `org.udpscope.app`** — it is read back through `adw_about_dialog_get_application_icon()` while the dialog is open, so the dialog is asserted to *carry* the icon rather than merely to open (a `set_application_icon()` lost in an edit leaves a dialog that opens, looks almost right, and shows a generic placeholder). `closed ok` with **no `Gtk-CRITICAL`** is as much a crash test of three windows built, presented and closed in one run as it is a state check, and a stronger one than it was: the three are now closed by **two different calls**, so a mismatched pair crashes or leaks here. One of the three is a `GtkWindow` (the help window, `gtk_window_close()`); the About dialog and the shortcut overview are `AdwDialog`s and close with `adw_dialog_close()`, cleared on `::closed`. `shortest=` is the page title — a page whose body was never compiled into the binary is absent rather than empty, and a title alone is the stand-in's shape.
+- `[help] pages=14 parsed=14 shortest='Choosing a source' 1563 B; shortcuts: app=12 plot=13; about version=… commit=… built=… settings=… icon=org.udpscope.app; closed ok` (stderr, `UDPSCOPE_PROBE_HELP_MS`) — **`parsed` must equal `pages`** and no page may be empty: a missing resource or markup Pango rejects renders a one-line stand-in instead of failing, so the window *looks* fine and only this count notices. `settings=` must be a real path (the same one the About dialog shows). **`icon=` must read `org.udpscope.app`** — it is read back through `adw_about_dialog_get_application_icon()` while the dialog is open, so the dialog is asserted to *carry* the icon rather than merely to open (a `set_application_icon()` lost in an edit leaves a dialog that opens, looks almost right, and shows a generic placeholder). `closed ok` with **no `Gtk-CRITICAL`** is as much a crash test of three windows built, presented and closed in one run as it is a state check, and a stronger one than it was: the three are now closed by **two different calls**, so a mismatched pair crashes or leaks here. One of the three is a `GtkWindow` (the help window, `gtk_window_close()`); the About dialog and the shortcut overview are `AdwDialog`s and close with `adw_dialog_close()`, cleared on `::closed`. `shortest=` is the page title — a page whose body was never compiled into the binary is absent rather than empty, and a title alone is the stand-in's shape.
 - `[menu] N 'label' accel='key' h=P label_x=X accel_right=R/W order=D ok=O`, one line per row,
   then `[menu] rows=R expected=E order=D rows_bad=B popover_visible=V mapped=M button_mapped=B`
   and `[menu] status pos=top bubble=WxH button_top=T button_right=R fits=F` (stderr,
@@ -685,7 +819,7 @@ Two lines of the self-check output are assertions in disguise:
   it afterwards.
 - `[keys] a: armed 0->1 | space: paused 0->1 | t: trigger panel: 0->1 | … | editable focused: 'm' refused=1` (stderr, `UDPSCOPE_PROBE_KEYS_MS`) — **every `X->Y` pair must differ** and **`refused` must be 1**. The refusal is the whole reason the controller is in the bubble phase: every bare-letter accel is also a character, so an accel that fires while a `GtkEditable` has focus makes the window entry unusable. A pair reading `0->0` is an action whose dispatch does not reach the handler a click reaches. Note the format is `<key>: <widget-description>: <before>-><after>` — the name passed to `before_after()` includes the widget's description, so `t: trigger panel: 0->1` is the correct form (not `t: trigger panel 0->1` without the colon before the values).
 - `[zoomkeys] ctrl+plus x=[..]->[..] y_held=1 | alt+plus y=[..]->[..] x_held=1` (stderr, `UDPSCOPE_PROBE_ZOOMKEYS_MS`) — **both `_held` must be 1 and both zooms must still happen.** Run it inside a pinned state, where a frame cannot re-frame the other axis for its own reasons: `UDPSCOPE_PROBE_PAUSE_MS=1500 UDPSCOPE_PROBE_ZOOMKEYS_MS=2200`. A `_held=0` is the modifier not reaching the plotter's controller; an unchanged range on the *zoomed* axis is the opposite failure, the key doing nothing. Ctrl restricts to x and Alt to y; Ctrl+Alt zooms neither (no special case needed — neither flag alone fires).
-- `status bar: glance=[● live · 1.09 MS/s · 2 s window] max_glance_chars=53 detail_fields=11 popover_rebuilds=0` (exit dump) — **`max_glance_chars` must stay small** (under about 60) and **`popover_rebuilds` must be 0**. The status row is directly above the plot, so this is the "layout must not depend on content" rule read from the bar's own side: the state field is one word from a fixed set, the rate field is `%.3g` (so `10 kS/s`, never `10.0 kS/s`), and the only field trigger mode adds is the elapsed time, which steps units rather than growing digits. `detail_fields` is the popover's label count, a literal, so adding a label without thinking about layout shows up here. The glance rate format matters: `%.3g` drops the trailing zero that a `%.4g` or a fixed-precision format would keep — a rate that reads differently in the dump and in the help page is a format disagreement, and `14-status.txt`'s example must match it.
+- `status bar: glance=[● live · 1.09 MS/s · 2 s window] max_glance_chars=53 detail_fields=11 popover_rebuilds=0` (exit dump) — **`max_glance_chars` must stay small** (under about 60) and **`popover_rebuilds` must be 0**. The status row is directly above the plot, so this is the "layout must not depend on content" rule read from the bar's own side: the state field is one word from a fixed set (`connecting`, `live`, `paused`, `armed`, `capturing`, `event held`, `disarmed` — a word added to it must be **no wider than the widest already there**, which is what let `connecting` join at ten characters beside `event held`; the dead-port glance reads `max_glance_chars=51` against a live run's 54), the rate field is `%.3g` (so `10 kS/s`, never `10.0 kS/s`), and the two fields a *state* adds are both elapsed times — trigger mode's `last event … ago` and a pause's `for <elapsed>` — which step units rather than growing digits (`format_elapsed()`). A **paused** glance is not in the dump at all: it is read by `[pause-probe]`'s `glance=` field, since the dump's own line is taken live. `detail_fields` is the popover's label count, a literal, so adding a label without thinking about layout shows up here. The glance rate format matters: `%.3g` drops the trailing zero that a `%.4g` or a fixed-precision format would keep — a rate that reads differently in the dump and in the help page is a format disagreement, and `14-status.txt`'s example must match it.
 
 The probes are the regression net — when changing UI or plot-host behaviour, extend
 the probe/dump in `src/ui.cpp` rather than adding a separate harness.
@@ -721,13 +855,16 @@ immutable copy of the captured window; see README for why two live rings were dr
 What a trace binds to is `ScopeModel::display_mode()`, one of four states, and
 `RowSet::bind()` takes it as an argument rather than recomputing it:
 
-- `Live` — no trigger: the live ring on the stream clock.
+- `Live` — no trigger: the live ring, on the clock of the **newest sample**
+  (`display_epoch() == -newest`), so the axis is a fixed `[-window, 0]` and x reads as an age.
 - `Capturing` — an edge has been accepted (so the pre window was full) and the post
   window is still filling: the live ring, on the coming event's own clock
   (`display_epoch() == -edge`), inside an axis already pinned to `[-pre, +post]`. The
   post side fills in view and the marker sits at x = 0 throughout.
-- `Held` — the frozen `EventSnapshot` of the last event.
-- `Waiting` — armed, nothing captured yet: blank.
+- `Held` — the frozen `EventSnapshot` of the last event, whose stamps are already edge-relative,
+  so the display epoch is 0.
+- `Waiting` — armed, nothing captured yet: blank, with the live epoch (there is nothing bound,
+  but the axis is still a live one).
 
 **Disarm during a capture publishes what the capture got to**, then disarms: the producer
 cuts the window at the newest sample and that partial snapshot becomes the held event, so
@@ -750,6 +887,35 @@ and hands it to `bind()`). The producer can open or close a capture between any
 reads, and two reads in one frame put the bind, the epoch, the pin and the status line on
 different clocks.
 
+**The display clock is not the stream clock, and `ScopeModel::stream_at_x0()` is the only
+conversion.** `display_x = stream_t - stream_at_x0()` in **every** mode, and the offset lives in
+one of two places: a snapshot carries its own (`EventSnapshot::x_offset`, frozen with the
+picture) and a live view carries it as minus `display_epoch()`. Anything crossing between the
+two clocks goes through that one accessor rather than picking the branch itself — the export's
+`abs_seconds` column, the pause handler putting a display window back on the ring to cut it, the
+measurement marks — because there are four modes and picking the branch by hand gets one of them
+wrong. It reads atomics only, so it is safe to call inside an existing `mutex()` guard.
+Three things about the live epoch specifically:
+- **It is written after `bind()` and `acquire_all()`, not before.** It must be minus the newest
+  sample the *traces* can report, and asking before the acquire is one frame of production
+  stale — at 1 MS/s over a 50 ms window that is a third of the screen to the right of the axis.
+- **There is no feedback loop**, even though the newest stamp is read through the epoch that is
+  about to change: `RowSet::live_edge()` reports in the epoch currently in force, so
+  `display_epoch() - live_edge()` is minus the *raw* stamp and the fixed point is reached in one
+  frame rather than converged on.
+- **`Waiting` takes the live epoch too.** Nothing is bound, but the axis is still a live one, and
+  an epoch of 0 there would make the axis jump on the frame a capture closes.
+
+**A measurement mark is glued to its sample; a cursor stays on screen.** The two instruments move
+in opposite directions under a rolling axis and that is deliberate — a bench scope's cursors sit
+where the user put them while the waveform rolls under, and a measurement's mark names the sample
+it measured. The cursors need no code: their x *is* a display coordinate. The marks are stored in
+**stream** seconds and reconverted every frame by `place_measure_marks()`, since a mark left in
+display coordinates would crawl forward at one window per window. `App::measure_window` is
+stream-clocked for the same reason, and that one is load-bearing: the recompute trigger is "the
+window moved by 2 % of its span", and in display coordinates a live window is a fixed
+`[-window, 0]` — it never moves, so the measurements would never be recomputed again.
+
 Layers to keep straight:
 
 - `SignalInfo` — one signal as the CONFIG described it. The unit of enable/disable.
@@ -995,11 +1161,93 @@ far the largest file.
   is built once in `publish_event()` inside the `O(n)` pass that already computes the y
   bounds, and the same channel on two rows shares it. It costs ≈1 byte per sample per
   channel. `frame path:`'s `segments` is the guard.
+  **"Every" includes the pause**, and that is the half this invariant was written without and
+  which then went wrong for real: `publish_pause_view()` filled `stamps`, `values` and `y` and
+  left `pyramids` empty, so a *paused* view was re-gathered raw on every frame. Both halves of
+  the cost are readable, and the second is the one a performance line cannot show.
+  `frame path:` read `raw=21 lod=118` over a 1.6 s pause against `raw=1 lod=170` for the same run
+  live, with the draw mean 12.34 → 18.18 ms — and the **trace changed appearance**, which is what
+  gets reported. `stage_trace_density()` grades a column against *its own peak* from a `1/height`
+  deposit per segment, so a column fed ~660 raw inter-sample segments accumulates a far spikier
+  distribution, and a far larger peak to normalise against, than one fed the one or two bucket
+  envelopes the pyramid gives: the paused trace read as a hard bright core with its dwell tail
+  dimmed out. **A pause is not a cheaper case than a capture — it freezes the same rings**, so
+  anything `publish_event()` does to a snapshot, `publish_pause_view()` owes too. Building it is
+  not free (see `publish cost:` below): it took the pause publish from 6.15 ms to 22.31 ms, a
+  one-off producer stall against ~5 ms a frame of draw for the pause's whole length, which at
+  ~60 fps repays about thirty times over on a 1.6 s pause — and the producer absorbs it without
+  losing packets (`gaps=0` with and without a pause, the paused run at an 86 ms publish).
+  **The check that the look is restored is `frame path:` across the pause, not the cost line**:
+  a paused run must read the same path as a live one — measured `raw=1 lod=555 columns=555
+  graded=555` against `raw=0 lod=373 columns=373 graded=373`, same 24711-segment worst frame,
+  segment mean within 5 % — where the defect read `raw=21 lod=118`. A `raw` in the tens over a
+  pause is this returning, and it is the appearance as much as the cost.
 - **`EventSeries::gather()` emits a bucket's envelope, not every `2^level`-th sample.**
   Point decimation hides exactly the spike the capture was triggered on; a scope has to
   draw a bucket's extremes. It needs no index rebasing, unlike the ring: the snapshot's
   pyramid is built from sample 0 and nothing is ever dropped from it, so `window_base()` is
   0 and a window index *is* the absolute one.
+- **A trace denser than the axis is drawn one pixel column at a time, and that is what keeps
+  the plots free of moiré.** The envelope staged as a polyline banded visibly and *crawled*
+  under a pan on exactly the signals this app is pointed at — a high rate, a high frequency or
+  noise — and three things compound to produce it, none a bug alone: `level_for()` sizes a
+  bucket at one to two pixel columns, `Envelope` emits two points per bucket so each
+  contributes a near-vertical min→max hairline *and* a near-vertical connector (≈3.6 per
+  column per trace), and every one lands at a **fractional** x because a trace is deliberately
+  not snapped. Under src-alpha compositing a column's brightness is then a non-linear function
+  of the sub-pixel phases overlapping it, the pattern repeats at the beat between the bucket
+  pitch and the pixel pitch, and a pan sweeps the beat. `deps/plotter`'s
+  `Renderer::stage_trace_columns()` emits one snapped vertical segment per integer column
+  instead, so the trace has **one** phase and there is nothing left to beat. Four things to
+  know before touching it, all upstream in `docs/data-and-performance.md`: the gate is the
+  gathered **density** (≥2 points per column) and `Envelope`, never the LOD level — the raw
+  path at 1.5–64 spp beats the same way, and the density term is also what keeps the reduction
+  off a *sparse* window whose trace is the two segments entering and leaving the frame; a hole
+  stays a hole; disjoint neighbours are joined so a fast edge keeps its join; and it is the one
+  carve-out in `u_snap`'s "never anything drawn at a data position" rule, because a column *is*
+  a pixel column.
+  **It needs a thin ribbon to be visible at all** — a window whose buckets span several periods
+  paints a saturated block and hides the beat — so a screenshot of a slow sine at a whole-window
+  view says nothing either way. The guards are upstream's
+  `a_dense_trace_is_drawn_as_whole_pixel_columns`, which counts the **distinct coverage levels**
+  in the ink (4 against the polyline's 126; a count of *partially covered* pixels separates
+  nothing, 577 against 652, because a 1.5 px stroke's fringe always spills into the next
+  column), and `frame path:`'s `columns=` field here. `trace ink:` deliberately cannot see this
+  path: it recomputes the **gathered** points, which the reduction is downstream of, so its
+  `drawn-vs-quoted` reads 0.0000 either way and remains the guard for the gather origin alone.
+- **A reduced column is graded by dwell, and the grading may not undo the reduction.** The
+  column above is honest about *where* the signal went and silent about *how long it was there*
+  — a column's min and max are identical whether its samples fill the span or pile at its two
+  ends, so a ramp and a pulse are one flat band. `Style::intensity_grading` grades it instead
+  (bright where the signal sits, faint where it only passes through, the digital-phosphor look),
+  and **udpscope turns it on; the library's default is off**, so other hosts are not restyled by
+  an upgrade. The switch is a one-shot in `tick()` guarded by `App::style_stated`, not a line in
+  the window build: `PlotArea::renderer()` is null until the area is realized, so there is no
+  earlier place to state a style. Three things to know here, the rest upstream in
+  `docs/data-and-performance.md` (the `1/height` dwell weighting, the one-column accumulator, the
+  per-column-peak normalisation, the quantised alpha steps):
+  * **The finer gather level is floored at 1 whenever the flat path would have used the
+    pyramid.** Grading asks for `samples_per_pixel / intensity_sub_columns`, and
+    `MinMaxPyramid::level_for()` answers **0 — raw samples** — as soon as that falls under one
+    bucket (`kBucket` is 64). Unfloored, every moderately dense frame became an O(visible)
+    gather: at 1.3 MS/s over a 2 s window, 172 samples a pixel, `raw=1154 lod=0` against the flat
+    path's `raw=710 lod=453`, and 2.30 → 6.36 ms of draw mean. The floor degrades the *look*
+    (fewer sub-columns than asked for, down to what the coarsest buckets give — still two or
+    three per column at 64 samples a bucket) and never the path. It is also why
+    `intensity_sub_columns` past about 8 buys nothing: the bucket size is the limit.
+  * **`graded=` must equal `columns=`** in `frame path:`, and `UDPSCOPE_NO_PHOSPHOR=1` is the A/B
+    that makes either line readable against the ungraded path (see Verification).
+  * **The steps are draw calls, not per-segment alpha.** `LineInstance` is four floats of
+    geometry and the colour is a **uniform** (only `TextInstance` carries `a_colour`), so the
+    gradient is `intensity_steps` `LineBatch`es flushed at different alphas. That is why the
+    segment mean rises from 131 to 1340 on the same frames — the rise is the tiers, not extra
+    geometry per column, and the bound is still `axes.w` (measured 14.5 runs a column in the
+    library's own guard, 8303 segments over a 572 px axis).
+  The guard is upstream's `a_dense_trace_can_be_graded_by_dwell`, which draws one frame both ways
+  and profiles the band's outer fifths against its middle: flat reads **191/191**, graded
+  **191/131**. That 0.69 is a *tier* ratio, not the dwell ratio — `intensity_gamma` (0.45) and
+  `intensity_floor` (0.3) compress it deliberately, the floor so that a fast riser, one
+  sub-bucket deep everywhere, is never dimmed out of existence.
 - **The time ring is `f64` and the value rings are `f32`, and the asymmetry is the point.**
   A value's precision is a property of the signal (24 bits is plenty for a sample); a
   timestamp's is a property of *how long the scope has been running*, because the stamps are
@@ -1017,12 +1265,15 @@ far the largest file.
   the doubling against overflow); `live_window_locked()` compares its bounds in the ring's own
   type with **no rounding step**, the old `f32` round-trip having existed only so that a
   sample sitting exactly on a bound was kept whatever the stream's absolute time was; and
-  `EventSnapshot::stamps` is `f64` because a **pause** view is deliberately *not* rebased and
-  therefore carries full stream time (an event's own stamps are edge-relative and small — the
-  symmetry is not the reason). `RingBuffer<T>` stores slots as `std::atomic<T>` behind a
-  `static_assert(is_always_lock_free)`, which `double` satisfies on every supported target.
-  The guard is the **export**: `np.diff(t)` over a multi-million-row `.npy` must hold exactly
-  one distinct step. Three steps at 2, 2.5 and 3 ULP of the stamps' magnitude is this defect.
+  `EventSnapshot::stamps` is `f64` because it is cut from this ring and is therefore in the same
+  units, whatever a given snapshot's own origin is (both kinds are rebased now — an event's
+  stamps are edge-relative, a pause's freeze-relative — so neither is magnitude-bound the way the
+  ring is, and the width is for the cut rather than for the coordinate). `RingBuffer<T>` stores
+  slots as `std::atomic<T>` behind a `static_assert(is_always_lock_free)`, which `double`
+  satisfies on every supported target. The guard is the **export**: over a multi-million-row
+  `.npy`, `np.diff(t)` must hold one step to within a few ULP of the column's magnitude (see
+  the export guard above for why it is no longer exactly one value). Three steps at 2, 2.5 and
+  3 ULP of *the stream's uptime* — microseconds, not femtoseconds — is this defect.
 - **A dropped time slot is clamped, never answered with a sentinel.** `acquire()` pins
   the published window to the value ring's base and both rings keep sliding afterwards —
   their capacities are equal, so there is no slack — which means the oldest few samples
@@ -1082,8 +1333,18 @@ far the largest file.
   Its pan clamping is likewise gated on the data being wider than the view, or the empty
   left-hand side drags the live edge off the right-hand edge.
 - **Layout must not depend on content.** The y gutter is reserved at the widest label
-  `TickFormat::Si` can produce and only ever grows; the status label is ellipsized so
+  `TickFormat::Si` can produce *for an axis with no unit* — a sign, three significant
+  figures and a one-glyph prefix, measured and not counted in characters — and only ever
+  grows; the status label is ellipsized so
   its text cannot drive the paned divider. Both exist to stop per-frame relayout.
+  The reservation deliberately does **not** cover `format_si()`'s `%.3g` fallback
+  (`-1.23e-45`), which it used to: that form needs a value past 1e24, so it bought a third
+  of the gutter for a label no stream produces, and the floor being a monotone maximum over
+  the *measured* need means one that did appear widens the gutter for good anyway. Erring
+  wide is not free here — it is a third of the plot's width.
+  And **nothing may add slack to the gutter it is told**: `note_y_gutter()`'s argument is
+  `layout().y_axis_width`, which is `max(measured, floor)` — partly our own answer coming
+  back — so a constant added to it compounds. See the ratchet reading under Verification.
   The same rule is why the activity badge is one glyph in three colours rather than
   three glyphs, why the `rate` field collapses to one figure or a range instead of a
   per-channel list, and why `format_elapsed()` steps to a coarser unit instead of
@@ -1093,6 +1354,16 @@ far the largest file.
   plotter for this), not on the rows: `Figure::layout()` clears every row's
   `set_min_y_gutter()` to measure what its own labels need, so a floor written onto the
   rows survives exactly until the next layout.
+- **The right-hand band is a want, and the left gutter is a measurement.** The two sides of
+  the plot are not symmetric in kind: the left holds the y labels, so it is measured and
+  floored; the right holds nothing, so there is nothing to measure and `RowSet` simply asks
+  for half the widest time label plus the label padding (`right_gutter_px_`, reserved in the
+  same one-shot block). Half a label is the figure that matters: an x tick label is
+  *centred* on its tick and a live axis is `[-window, 0]`, so there is always a tick exactly
+  on the axes' right edge, and with `axes` flush to the viewport half of that label was
+  drawn outside the plot. Both go on the **figure** and for the same reason — the rows have
+  to end on one column as well as start on one — which is why `apply_gutters()` applies the
+  pair and `rebuild_all()` calls it: a new `Figure` carries neither.
 - **Signals start disabled** — enabling is what starts acquisition. A trigger on a
   signal nobody acquires can never fire, so selecting/arming enables it.
 - **The trigger's event window is separate from the display window**, and
@@ -1351,13 +1622,19 @@ far the largest file.
   level-0 buckets -- 64 samples each, carrying min, max an **exact** sum and a finite count -- and
   locates each extreme to a *bucket*; one raw `measure_scan()` of that bucket alone then pins it
   to a sample, two buckets at most whatever the window's size. Pass two
-  (`measure_accumulate_bucket()`) folds a bucket whole only when it lies **strictly** on one side
-  of its level (`k.lo > level` or `k.hi < level`): then every sample decides the same side, none
-  is *at* the level, and an entering edge is exactly the bucket's first sample -- which is where
-  the raw walk would have found it, so this is exact and not an approximation. It refuses a
-  bucket that straddles, and a bucket holding a non-finite sample, because the raw walk takes the
-  first *finite* sample of the new side and an aggregate cannot say which that is; the caller
-  then opens that bucket. Four things this rests on, each of which breaks it silently:
+  (`measure_accumulate_bucket()`) folds a bucket's **sums** only when it lies **strictly** on one
+  side of its level (`k.lo > level` or `k.hi < level`): then every sample falls in the same bin and
+  none is *at* the level, so the fold is exact and not an approximation. It asks **separately**
+  whether the bucket enters a side of the hysteresis band (see the invariant below), because a
+  single test against `level ± h` refuses exactly the buckets a crossing passes through. A bucket
+  wholly past a threshold holds that crossing at its first sample, exactly -- which is where the raw
+  walk would have found it. It refuses a bucket that straddles the level, one that enters a side
+  somewhere inside itself, and one holding a non-finite sample (the raw walk takes the first
+  *finite* sample of the new side and an aggregate cannot say which that is); the caller then opens
+  that bucket. **Nothing may be folded before a refusal** -- a refused bucket goes to
+  `measure_accumulate()`, which adds the same samples again, and sums added above the `return false`
+  double-counted every opened bucket, reading `top=0.614304` on a unit sine against the 2/pi it must
+  be. Four things this rests on, each of which breaks it silently:
   * **Exactness is the point, so nothing may stride or decimate.** `peak to peak` must still read
     exactly `2` on a unit sine and `top` exactly `0.636620` (2/pi). A bucket's sum is a sum.
   * **The bucket index space must be the window's.** `ChannelBuffer::acquire()` calls
@@ -1376,6 +1653,39 @@ far the largest file.
   `measure cost:`'s `covered`/`buckets`/`raw` is the guard, and it needs the fast mock to say
   anything.
 
+- **A crossing is counted with hysteresis, and the band moves the *edge decision* only.**
+  `MeasureLevel::hysteresis` is a Schmitt trigger about `level`: an edge is counted once the signal
+  has passed `level + h` going up or `level - h` going down, and a sample inside the band decides
+  nothing. Without it `period`, `frequency` and `pulse duration` are unusable on anything real --
+  the mid level is exactly where a waveform moves *fastest*, so an interferer faster than the
+  fundamental recrosses a single level several times per true crossing. Measured on a 5 Hz sine with
+  a 500 Hz tone at a tenth of the amplitude (`tools/mock_udpstreamer.py --noise 0.1`): 9 true
+  crossings counted as **79**, `period=0.025622 freq=39.029` for a true 0.2 s / 5 Hz, against
+  `period=0.200188` with the band. Four rules, each of which was wrong first:
+  * **`measure_set_level()` is the only place the band is sized**, and `src/ui.cpp` calls it rather
+    than assigning `.level` itself: two expressions for the width is how the raw walk and the bucket
+    path end up disagreeing about where a crossing was. `h = min(0.10 * (hi - lo), 0.5 * min(hi -
+    level, level - lo))`. The 0.10 is measured -- 5 % reads a 0.1 interferer and fails at 0.2
+    (`period=0.075`), 10 % holds to 0.3 and to white noise at sigma=0.05.
+  * **The clamp is load-bearing.** `PulseDuration` lets the user put the split near an extreme, and
+    a fixed tenth of the span there puts the upper threshold *above every sample*: the walk never
+    decides that side and the measurement reads nothing at all, which is worse than reading
+    something noisy. On a ringing 3.3 V logic signal at a 90 % split: `enters=0` with a fixed band,
+    `enters=4 period=0.200000` with the clamp.
+  * **The `sum`/`count` split stays at the bare `level`.** That split *is* `Top`/`Bottom` -- the mean
+    above and below the threshold -- so a band there changes a documented exact reading. `top` on a
+    unit sine must still be `0.636620`.
+  * **`h = 0` must reduce exactly to the single-level walk**, including the `v == level` skip, so the
+    band is a parameter of the engine rather than a mode of it.
+  The cost is the noise's, not the band's: the clean fast mock reads `raw=119412 (0.1%)` of 215 M at
+  1.41 ms a recompute and with the 0.1 interferer `raw=2.0%` at 1.96 ms. A
+  `/tmp/check_measure.cpp`-style check is how the walk itself was verified (`g++ -std=c++20 -O2 -I
+  src ... src/measure.cpp`): over a clean sine, sines with 0.1 and 0.3 interferers, 10 %/50 % duty
+  squares and a 90 % threshold, the **bucket walk must equal the raw walk exactly** -- same
+  `enters`, same `count[]`, identical `first_enter`/`last_enter` to 0.0 -- which is the assertion
+  that the fast path is a fast path and not an approximation. The app's reading is
+  `[measures-probe]` against `--noise 0.1`.
+
 - **The math channels' cost is the *producer's*, and the instrument must not be part of it.**
   `push_math_sample()` runs once per stored slot -- up to the wire rate -- so what a regression
   here looks like is `gaps`, never a frame time. Three things were taken off that path and must
@@ -1604,9 +1914,14 @@ far the largest file.
   Those two used to read the *label*, and the label no longer carries `packets`, `gaps`,
   `plot 1:` or the buffer figures — so a `gtk_label_get_text()` there would silently reduce
   every documented `mode …:` assertion to four fields. The glance line's state field is **one
-  word from a fixed set** (`live`, `paused`, `armed`, `capturing`, `event held`, `disarmed`) for
-  the layout reason above; a seventh word, or a field whose width tracks the stream, breaks the
-  row the plot is laid out under.
+  word from a fixed set** (`connecting`, `live`, `paused`, `armed`, `capturing`, `event held`,
+  `disarmed`) for the layout reason above; a word **wider than the widest already there**, or a
+  field whose width tracks the stream, breaks the row the plot is laid out under. The set may
+  grow — `connecting` was added for the no-CONFIG state — but only on that condition, and the
+  check is the dump's `max_glance_chars`. `connecting` is derived from `have_config` alone and
+  sits **ahead of every other branch**, including the display mode's: with no signal list, every
+  other word claims something that does not exist yet. The `mode` prose branches the same way for
+  the same reason, which is what keeps the two tiers from disagreeing.
 - **The ⓘ popover's widgets are built once and only their text is set.** It is visible when the
   tick updates it, so a rebuild is a per-frame relayout of a widget on screen.
   `update_status_popover()` only ever calls `gtk_label_set_text()`, and `popover_rebuilds` in

README.md

@@ -41,6 +41,15 @@ both states, the frame and per-channel sample counts, each plot's painted-frame
 count, which channel each trace slot holds, and the allocated size and reveal
 state of both side panels.
 
+Every size it prints is read from a value the frame tick captured while the window was alive, not
+from the widget: the dump runs from the destroy handler, where the widget pointer is already freed
+memory. It used to ask two of them directly, which is where the long-standing "an exit-dump run
+emits exactly two `Gtk-CRITICAL`s" baseline came from — and a critical was only the lucky reading.
+`UDPSCOPE_PROBE_HELP_MS` builds and destroys three windows of its own before the dump, so by then
+the memory had been reused and the same two calls **crashed in the middle of the dump**, which
+looks like a truncated log rather than like a segfault in a debug line. The dump now makes no
+`gtk_widget_*` call at all and a clean run carries no critical.
+
 ## Layout
 
 ```
@@ -63,16 +72,66 @@ frame and the GUI thread takes once per frame around binding the traces.
 Samples cross the boundary through `plot::data::RingBuffer` (single producer,
 single consumer), never through the lock.
 
-## Measurements
+## The x axis is relative to now
+
+**A live axis is fixed at `[-window, 0]`, with the newest sample at 0.** That is what a bench
+scope in roll mode shows and what the window control's figure means: a 2 s window reads `-2s` to
+`0` and keeps reading that for as long as the stream runs, with the trace flowing right to left
+under it. The axis used to carry the stream's own clock, so the labels counted the app's uptime
+upwards (`20:00`, `20:01`, …) and the one number a user actually wants — how long ago a feature
+happened — had to be worked out by subtraction.
+
+Every mode now expresses x as *seconds from the thing the view is about*, and the rule is one
+line: `display_x = stream_t - ScopeModel::stream_at_x0()`, where `stream_at_x0()` is the stream
+time of display x = 0.
+
+| display mode | x = 0 is | `stream_at_x0()` |
+| --- | --- | --- |
+| `Live`, `Waiting` | the newest acquired sample | the newest stamp |
+| `Capturing` | the accepted edge | the edge |
+| `Held` | the event's edge | the snapshot's `x_offset` |
+| `Paused` | the instant of the freeze | the snapshot's `x_offset` |
+
+The live answer is written by the frame tick **after** `bind()` and `acquire()`, because it has to
+be minus the newest sample the *traces* can report: asking the model before they are bound puts
+the newest data a frame's production to the right of the axis, which at 1 MS/s over a 50 ms window
+is a third of the screen. It converges in exactly one frame and cannot oscillate — `live_edge()`
+reports in the epoch currently in force, so `new = old - live_edge()` is `-raw_newest` whatever the
+old value was.
+
+A snapshot carries its own offset (`EventSnapshot::x_offset`) rather than leaning on the model's
+epoch, because its coordinates outlive the epoch that produced them. One consequence is a reversal
+of an earlier deliberate choice: **a pause snapshot is now rebased** like an event's. Leaving its
+stamps on the stream's clock would have thrown the frozen picture a whole uptime to the right of an
+axis that is now newest-relative. `x_offset` keeps the stream clock recoverable, which is what the
+export's second column reads — and it fixed a latent bug on the way, the export's snapshot branch
+having added `trigger_time()` to a *paused* view's stamps: an unrelated edge, or none at all before
+the first latch.
+
+Two things move in **opposite** directions under a rolling axis, and the asymmetry is deliberate.
+A **cursor** stays on screen: placed at -1.5 s it keeps meaning "1.5 s ago" and the data flows
+under it, which is a bench scope's roll behaviour and is free here, the cursors already being
+stored in display coordinates. A **measurement mark** is glued to the sample it measured, because
+a mark is a *result* rather than an instrument — so the marks are stored in stream seconds and
+reconverted every frame (`place_measure_marks()`), which is what makes them drift left with their
+own data between recomputes. `App::measure_window` is on the stream's clock for a related reason:
+"has the window moved" is the question that triggers a recompute, and a fixed `[-window, 0]` makes
+it invisible in display coordinates, so the pane would have computed once and never again.
 
 **Pause freezes the picture, not the acquisition.** The producer keeps writing the live ring
 while paused — the same thing it does when the trigger is off — and the plot binds a *snapshot*
 of the window that was on screen at the pause, with the axes pinned there. That is the same
-immutable-series path a held trigger event uses (`DisplayMode::Paused` sits beside `Held`); the
-difference is the anchoring: an event's stamps are edge-relative, a pause's are the stream's own,
-so the times on the axis do not change when the pause begins. Resuming drops the snapshot and
+immutable-series path a held trigger event uses (`DisplayMode::Paused` sits beside `Held`).
+Resuming drops the snapshot and
 re-frames on the newest data, so the seconds that passed while paused are *there*, not a hole —
-which is what pausing used to leave, because it stopped the producer outright.
+which is what pausing used to leave, because it stopped the producer outright. The status bar
+says how long it has been frozen (`paused · 10 kS/s · 2 s window · for 12 s`), in **wall**
+seconds: the producer never stopped, so the stream's own clock says nothing about how long the
+user has been looking at a still picture. It is written through `format_elapsed()`, which steps to
+a coarser unit instead of growing digits, because the status row sits directly above the plot and
+a field whose width tracks the wait would relayout it.
+
+## Measurements
 
 **The x ticks read relative when, and only when, they could not be written absolutely.** A
 `TickFormat::Time` label carries three significant digits, so the test is the tick **step**
@@ -103,8 +162,11 @@ annotation's anchor is a *data* coordinate, so the caption crawled across the pl
 drifted under a zoom, which is what it was reported as. The library test is
 `the_x_note_is_chrome_that_a_pan_or_a_zoom_does_not_move`: the footprint is measured as the pixels
 a frame with the caption differs from the same frame without one, and a pan to another decade plus
-a 64× zoom must produce the same box to the pixel. Everything a user copies out —
-the cursors' `T0`/`T1`/`dT`, a measurement, an export — stays in absolute stream seconds.
+a 64× zoom must produce the same box to the pixel. Everything a user reads off the screen is in
+the *display* coordinate the labels name — the cursors' `T0`/`T1`/`dT`, a measurement's time
+marks, the crosshair — so live they are negative ages and in trigger mode they are offsets from
+the edge. Only the **export** carries the stream's own clock as well, in a second column
+(`abs_seconds`); see *Export*.
 
 The anchor is taken by the *axis* on every layout (`Axis::origin_follows_range`), not written
 by the app: the window's edge is derived from the newest sample during the layout, so a value
@@ -139,13 +201,53 @@ measurement.
 
 `period` and `frequency` deliberately take **no options**: the engine counts *rising*
 crossings of the *mid* level, one edge per cycle, and a split or a side to choose from could
-only make that count wrong — a split near either extreme counts noise as crossings, and
-counting both edges halves the period.
+only make that count wrong — a split near either extreme leaves the hysteresis band below no room
+to reject noise with, and counting both edges halves the period.
 
 The split is a share of the **window's own** min..max, not volts: a measurement is about this
-signal in this window, and a level in volts would have to be typed for every signal. A
-crossing has to be *strict* — a sample exactly at the level is on neither side — so a signal
-that merely touches the level does not count every sample as an event.
+signal in this window, and a level in volts would have to be typed for every signal.
+
+### Why a crossing is counted with hysteresis
+
+A crossing is not read off a single level. It is read off a **band**: two thresholds a tenth of
+the window's peak-to-peak either side of the split, and an edge is counted only once the signal
+has passed the far one. Inside the band a sample decides nothing. That is a Schmitt trigger, and
+it is the difference between counting the waveform's cycles and counting its noise.
+
+Counting on one level was the first implementation and it fails on anything real, badly and
+silently. The mid level is exactly where a waveform moves *fastest* — on a sine the slope there
+is 2πf and the signal only clears a disturbance of amplitude *a* after a/2πf seconds — so any
+interferer faster than the fundamental recrosses the level several times per true crossing, and
+each recrossing is counted. Measured on a 5 Hz sine with a 500 Hz tone at a tenth of the
+amplitude (`tools/mock_udpstreamer.py --noise 0.1`): 9 true crossings read as **79**, giving
+`period=0.025622` and `frequency=39.029` for a true 0.2 s and 5 Hz. The number is not merely
+noisy, it is a different order. With the band the same window reads `period=0.200188`. The band
+holds to an interferer at **0.3** — a third of the waveform — where it reads `period=0.200688`,
+and to white noise at σ=0.05; at 5 % of peak-to-peak it already fails at 0.2.
+
+Three things about it are deliberate, and each was wrong first.
+
+- **The band moves the edge decision only.** The side the `sum`/`count` split uses stays the bare
+  level, because that split *is* `top` and `bottom` — the mean of the samples above and below the
+  threshold — and a band there changes a documented exact reading. `top` on a unit sine must still
+  be `0.636620`, 2/π.
+- **The band is clamped to stay inside the data**, to half the room between the level and the
+  nearer extreme. `pulse duration` lets the user put the split near an extreme (a 3.3 V logic
+  signal with ringing wants it nearer the top), and a fixed tenth of the span there puts the upper
+  threshold *above every sample in the window*: the walk never decides the upper side and the
+  measurement reads nothing at all, which is strictly worse than reading something noisy. Measured
+  on such a signal at a 90 % split: `enters=0` with a fixed band, `enters=4 period=0.200000` with
+  the clamp.
+- **The LOD fast path tests the band and the level separately.** Tightening the bucket-fold
+  condition to `level ± h` would refuse every bucket lying inside the band — and those are
+  precisely the buckets a crossing passes through, so the raw walk would get a *share of the
+  window* instead of a bucket or two per crossing. A bucket on one side of the **level** can always
+  be binned; only a side *change* whose position is inside the bucket is refused. The clean fast
+  mock still reads `raw=119412 (0.1%)` of a 215 M-sample total at 1.41 ms a recompute; with the
+  0.1 interferer it is `raw=2.0%` at 1.96 ms, which is the noise's own cost and not the band's.
+
+A sample exactly *at* a threshold is still on neither side, so a signal that merely touches one
+does not count every sample as an event.
 
 Each measurement's row carries **two badges**: its own colour (the same one its marks use on
 the plot) and the signal's chip, in the palette colour every other view names that signal
@@ -196,18 +298,20 @@ Both walks go through it:
   the window's size. The two stamps the scan needed are read at the end rather than at every
   chunk that moved an extreme, since a stamp is a ring read and an extreme moves many times.
 - **Pass two** (the threshold types: `top`, `bottom`, `pulse duration`, `period`, `frequency`)
-  folds a bucket whole whenever it lies *strictly* on one side of its level — then every sample
-  in it decides the same side, none is *at* the level, and an entering edge is exactly the
-  bucket's first sample, which is where the raw walk would have found it. Only the buckets that
-  **straddle** a level are opened, which on a clean waveform is one per crossing.
+  folds a bucket's sums whenever it lies *strictly* on one side of its level — then every sample
+  in it falls in the same bin and none is *at* the level, so the fold is exact. It then asks
+  separately whether the bucket *enters* a side of the hysteresis band: one wholly past a threshold
+  holds that crossing at its first sample, exactly, which is where the raw walk would have found
+  it. Only a bucket that straddles the level, or one that enters a side somewhere inside itself, is
+  opened — on a clean waveform a bucket or two per crossing.
 
 The raw path is still there and still exact, for the window's partial edge buckets, for the
 samples produced since this frame's `acquire_all()` (bounded by one frame of production), and
-for those straddling buckets. Nothing is decimated or strided: `peak to peak` still reads
+for those opened buckets. Nothing is decimated or strided: `peak to peak` still reads
 exactly `2` on a unit sine and `top` exactly `0.636620` — 2/π, the half-wave mean, which is the
 check that a threshold type is not merely plausible. A window shorter than a bucket, or a signal
-noisy enough to straddle everywhere, degrades back to the O(window) cost and nothing else
-changes. The dump's `measure cost:` line reports `covered`, `buckets` and `raw` for exactly
+noisy enough to cross a threshold everywhere, degrades back towards the O(window) cost and nothing
+else changes. The dump's `measure cost:` line reports `covered`, `buckets` and `raw` for exactly
 this: `raw` near `covered` means the pyramid bought nothing.
 
 ### What the math channels cost
@@ -355,7 +459,8 @@ ring per channel (N enabled signals -- see the limitation on multi-element signa
 below). The spec's second buffer is the latched `EventSnapshot`, which is already
 an immutable copy of the captured window (see "Trigger" below); a second live ring
 bought nothing and cost half the memory budget, so `--buffer-mb 200` really is
-200 MB.
+200 MB. What it *would* buy is priced in the dump's `publish cost:` line — see
+"There is one live buffer, not two" under the review findings.
 `plan_partition()` sizes the rings to cover `--max-window` seconds and then grows
 them with the rest of the budget. When a channel's declared sample rate is lower
 than the fastest channel's, it is decimated by the integer ratio
@@ -869,14 +974,109 @@ which hides exactly the spike a capture was triggered on, and since the level wa
 it never even ran. On the same repro: **138,078 segments** (43× fewer) and a 66 ms worst
 frame, with the steady-state draw around 2 ms. It costs about 1 byte per sample per
 channel (≈25 % on top of the snapshot's `f32` values) and one stall per latch, since the
-build runs under `ScopeModel::mutex()` — at 1.3 MS/s that is a ~40 ms tick, once, with no
-packet gaps.
+build runs under `ScopeModel::mutex()`. That stall is now measured rather than estimated —
+the dump's `publish cost:` line read **115 ms** for one event publish at 1.3 MS/s, against
+the ~40 ms this paragraph used to quote — and it produced no packet gaps.
+
+**A paused view carries one too**, and that half was missing until it was found by its
+*appearance*. `publish_pause_view()` filled `stamps`, `values` and `y` and left `pyramids`
+empty, so a frozen pause was drawn from every raw sample it held, on every frame — the same
+defect as above with the same cause, in the other snapshot. `frame path:` read
+`raw=21 lod=118` over a 1.6 s pause against `raw=1 lod=170` for the same run live, with the
+draw mean going 12.34 → 18.18 ms and its worst frame 30.35 → 86.92 ms. But the reason it was
+noticed is that the trace *looked* different: `Renderer::stage_trace_density()` grades each
+pixel column against that column's own peak, from a `1/height` dwell deposit per segment, so
+a column fed several hundred raw inter-sample segments accumulates a far spikier
+distribution — and a far larger peak to normalise against — than one fed the one or two
+bucket envelopes the pyramid gives. The paused trace read as a hard bright core with its
+dwell tail dimmed away. The rule the invariant was written without: **a pause is not a
+cheaper case than a capture — it freezes the same rings.**
+
+It is not free, and the trade is one-off against per-frame. Building the pause pyramid took
+that publish from 6.15 ms to 22.31 ms, and unlike the event publish this one runs on the
+**UI** thread and so blocks the *producer* — against ~5 ms a frame of draw for as long as the
+pause lasts, which over a 1.6 s pause at ~60 fps repays thirty times over. The producer
+absorbs it: an A/B of the same fast-mock run with and without a pause read `gaps=0` both
+ways, with the pause publish at 86 ms in the paused one. (One earlier run reported `gaps=73`
+with a pause against 0 without, which is why the stall was worth measuring at all — but it
+has not reproduced, it did not scale with the publish length, and an 86 ms publish costing
+nothing is the stronger reading. Treat that 73 as incidental load on one run.)
+
+The verification that the *look* is restored is the same A/B read through `frame path:`:
+`raw=0 lod=373 columns=373 graded=373` without a pause against `raw=1 lod=555 columns=555
+graded=555` with one — the same path, the same 24711-segment worst frame and a segment mean
+within 5 % — where before the fix the paused run read `raw=21 lod=118`.
 
 The self-check's two `frame cost:` / `frame path:` lines are the guard: they split a frame
 into the tick, the plot's own draw and the whole GTK paint, and report the segment counts
 and whether the LOD path was taken at all. A segment count in the millions is this defect
 returning.
 
+**A dense trace is drawn one pixel column at a time, which is what cured the moiré.** At a
+high sample rate, a high signal frequency or on a noisy signal the plots showed strong,
+*crawling* banding — and three things compounded to produce it, none of which is a bug on its
+own. `MinMaxPyramid::level_for()` sizes a bucket at one to two pixel columns; `Envelope`
+emits two points per bucket, so each bucket contributes a near-vertical min→max hairline
+*and* a near-vertical connector to the next, about 3.6 near-vertical hairlines per column per
+trace; and every one of them lands at a *fractional* x, because a trace is deliberately not
+snapped. With src-alpha compositing a column's brightness is then a non-linear function of
+the sub-pixel phases overlapping it, the phase pattern repeats at the beat between the bucket
+pitch and the pixel pitch, and a pan sweeps the beat. It needs a *thin ribbon* to be visible:
+a window whose buckets each span several periods paints a saturated block and hides it
+entirely, which is why it showed up on fast and noisy signals and not on a slow sine at a
+whole-window view.
+
+`deps/plotter`'s `Renderer::draw_traces` now reduces such a window onto the pixel grid: one
+exactly vertical segment per integer column, from the lowest to the highest screen y any
+gathered point put in it, flushed in framebuffer pixels with the snap on. The whole trace
+then has **one** sub-pixel phase, so there is nothing left to beat. See the upstream
+`docs/data-and-performance.md` for the four rules it keeps (a hole stays a hole, disjoint
+neighbours are joined so a fast edge keeps its join, a span under the stroke is drawn *as*
+the stroke, and the gate is the gathered density rather than the LOD level) and for why this
+is the one carve-out in `u_snap`'s rule that chrome may be snapped and data may not.
+
+It is also a large speed-up, because the geometry becomes O(axes.w) instead of O(buckets).
+Measured on the fast mock (`--rate 1300000 --batch 2000 --freq 3000`, a 20 s run): `frame
+path: raw=1 lod=262 columns=0 frames, segments 10960/216093` and **263 painted frames**
+before, `raw=2 lod=1198 columns=1200 frames, segments 2041/2237` and **1201 painted frames**
+after — the same run at 4.6× the frame rate, with `trace ink:` reading `0 collapsed, 0
+staircase, 0 short, worst drawn-vs-quoted 0.0000 px` either way. `frame path:`'s
+`columns=` field is the reading that separates "the segment count collapsed because the
+reduction ran" from "the window got narrower".
+
+**Those columns are then graded by dwell, which is the rest of the answer.** A reduced column
+is honest about *where* the signal went and silent about *how long it was there*: its min and
+max are the same whether its samples fill the span evenly or pile at its two ends, so a ramp
+and a pulse are one flat band. `Style::intensity_grading` — off in the library, which udpscope
+turns on at the first tick, since the renderer does not exist until the area is realized —
+draws each column graded instead: bright where the signal sits, faint where it only passes
+through, the way a digital-phosphor scope reads. The distribution cannot be recovered from the
+band, so the gather is asked at a level finer than the pixel grid and the dwell read from those
+sub-buckets; the measure is dwell *per row*, each segment depositing one unit spread over the
+rows it spans, and normalisation is against the column's own peak. See the upstream
+`docs/data-and-performance.md` for the five things that carry it and for the two that were
+wrong first (counting rows at +1 each inverts the pattern, grading a sine's fast middle as
+brightly as its rails; a frame-wide scale needs a 33 MB density image *and* fades the trace out
+exactly where it moves fastest).
+
+It costs about a millisecond a frame and the A/B is the only way to read that, because a frame
+mean cannot attribute its own cost: **`UDPSCOPE_NO_PHOSPHOR=1` puts the style back to the
+library's default**, and the same probe run on the fast mock (`--rate 1300000 --batch 2000`)
+reads `draw 3.24/21.43 ms` with the grading against `draw 2.30/25.76 ms` without, over the same
+`lod=453` frames. **`frame path:`'s `graded=` must equal `columns=`** — grading is a way of
+drawing the reduction and not a third path, so the two counts agreeing is what says the look
+reaches every reduced frame (`columns=1166 graded=1166` in that run, `graded=0` under the env
+var). The segment count rises with it, from a mean of 131 to 1340, which is the gradient's
+tiers: alpha is quantised into steps because the line pipeline's colour is a uniform and a
+per-segment alpha is inexpressible, and each step is its own draw call.
+
+The one performance trap here is worth stating because only the A/B found it. Asking for a
+finer level drops straight to **raw samples** once a sub-column falls under one pyramid bucket
+(64 samples), which at the run's 172 samples a pixel it did: `raw=1154 lod=0` and 6.4 ms a
+frame, i.e. grading undoing the very reduction it draws. The finer ask is floored at level 1
+whenever the flat path would have used the pyramid, so what degrades is the *look* — fewer
+sub-columns than asked for — and never the path.
+
 **The panels and the toolbar.** The header bar carries only what you reach for
 *while watching a signal*: the time window, pause/resume, the trigger toggle, the
 side-panel toggle and an overflow menu. Those
@@ -942,13 +1142,21 @@ connection, the measured rate, the packet/frame/gap counters, what plot 1 holds
 the buffer's size and span. Three of those are worth calling out:
 
 - **The badge blinks green at 1 Hz while the pipeline is actually running** — the
-  stream is connected, acquisition is not paused, and in trigger mode the trigger is
-  armed. Anything else leaves it a steady grey, with the reason on its tooltip
-  (`paused`, `trigger disarmed`, `waiting for the stream`). *Blinking* is the signal,
-  not the colour: a steady badge is a stopped pipeline, and that distinction survives
-  a screenshot. It is one glyph whose colour is all that changes, so blinking it
+  stream is connected, a CONFIG has arrived, acquisition is not paused, and in trigger
+  mode the trigger is armed. Anything else leaves it steady, with the reason on its
+  tooltip (`paused`, `trigger disarmed`, `waiting for the stream`). *Blinking* is the
+  signal, not the colour: a steady badge is a stopped pipeline, and that distinction
+  survives a screenshot. It is one glyph whose colour is all that changes, so blinking it
   cannot change its width — a badge that grew and shrank twice a second would move the
   label beside it and re-lay out the plot with it.
+  There are two steady colours, and the difference is how far the handshake got.
+  **Grey** is a socket with nothing behind it, or a pipeline the user stopped.
+  **Yellow** is a source that answered CONNECT but has sent **no CONFIG**: there is no
+  signal list, so nothing can be enabled and no DATA frame is owed. The glance line reads
+  `connecting` in both, because neither has the signal list every other state word claims;
+  the colour is what separates "no socket yet" from "a socket and no stream behind it". A
+  blinking green over a source that has sent nothing would claim a working pipeline, which
+  is the one reading the badge exists to prevent.
 - **`rate 9.99 kS/s` is the rate the buffer actually stored over the last second**, not
   the rate the CONFIG declared. The two agree unless the requested window is too long
   to hold at the wire rate, in which case the ingest resamples (see "A window longer
@@ -1022,13 +1230,40 @@ which is how the second one was found:
    what its labels need, so a floor written onto the rows would survive exactly
    until the next layout. The figure seeds its common gutter — the maximum over
    the rows, which is also what aligns their axes — with that reservation.
+   The reservation is the widest label `format_si()` writes for an axis with no
+   unit (a sign, three significant figures and a one-glyph prefix), not the
+   wider `%.3g` fallback it used to cover: that form needs a value past 1e24, so
+   it cost a third of the gutter for a label no real signal produces — and since
+   the floor is a monotone maximum over the *measured* need, one that did appear
+   would widen the gutter for good anyway.
 2. *The status line drove the pane width.* A `GtkLabel`'s minimum width is its
    text, and the status line is rewritten every frame; as its counters and
    messages changed width they moved the paned divider, which resized the plot,
    which re-laid out the axes and their ticks. The label is now ellipsized, so its
    minimum is “…”; the plot keeps the width it was given.
+3. *The gutter was a ratchet.* `note_y_gutter()` is handed the gutter the row was
+   **laid out with** — already the maximum of its labels and the floor imposed on
+   the frame before — and it added six pixels of slack to it. Those six pixels came
+   back next frame and were added again, so the left margin climbed a decade of
+   pixels a second until it hit the 200 px cap and stopped: 200 px of an 870 px
+   viewport, with `axes.w changes: 17` beside it, which reads as a settle and is a
+   runaway that ran out of room. The reservation's own padding is the slack, once;
+   nothing is added to a measurement that is partly our own answer.
 
-The self-check reports both. `viewport.w` must collapse to a single value, and
+**The two sides are balanced.** The axes rect used to reach the viewport's right
+edge, because that is all the library's layout had ever reserved — so the
+rightmost x tick label, *centred* on its tick, had half of itself outside the plot
+(a live axis is `[-window, 0]`, so there is always a tick exactly on that edge) and
+the newest sample's ink landed on the frame. `Plot::set_right_gutter()` and
+`Figure::set_right_gutter()` were added upstream for this: an empty band, served
+from the same half-viewport allowance as the label and title strips, set once on
+every row because the rows' axes have to end on a common column as well as start on
+one. `RowSet` asks for half the widest time label plus the label padding, which is
+exactly what the last label needs to be drawn whole. With the two fixes above the
+figure now sits in a 104 px left gutter holding the y labels and a 59 px empty band
+on the right, where it was 200 px and nothing.
+
+The self-check reports all of it. `viewport.w` must collapse to a single value, and
 `axes.x`, `axes.w` and `y-gutter` must settle: the one-shot label reservation
 lands a few frames after the first measured frame, and because the figure serves
 its floor out of the label strip the reservation converges over two layouts, so
@@ -1039,9 +1274,9 @@ bug. `x-ticks` is content, and varies by one as a live window slides over a roun
 number:
 
 ```
-layout over 952 frames: axes.x 67..80, axes.w 546..559, viewport.w 627..627,
-                        y-gutter 44..74, x-ticks 20..21, x-desync 0
-axes.w changes: 2 (last at frame 35, side panel up=1)
+layout over 583 frames: axes.x 88..104, axes.w 707..782, viewport.w 870..870,
+                        y-gutter 88..104, x-ticks 20..41, x-desync 0
+axes.w changes: 1 (last at frame 1, side panel up=1)
 ```
 
 Set `UDPSCOPE_PROBE_PAUSE_MS=<ms>` to pause the acquisition part-way through a
@@ -1107,6 +1342,16 @@ A third, found the same way, is in the tick generator rather than the shaders:
    — where the same residue read `3.19e-13ms`. A range whose ticks are *legitimately*
    that small keeps them.
 
+4. *One second was labelled `1e+3ms`.* `format_time()` picked its rung by comparing the raw
+   value against each unit's scale and then wrote the mantissa with `%.3g` — so a tick a hair
+   under a rung's top (a 1 s tick computed as 0.9999999 s, which is what differencing a live
+   axis gives) stayed on the rung below and its mantissa *rounded up to 1000*, which `%.3g`
+   writes in exponential form. The fix is to pick the rung by the **rounded** mantissa
+   (`t < u.scale * 0.9995`), which is exactly the `>= 999.5` spill guard `format_si()` in the
+   same file already had; the whole-second branch takes the same slack. The test is
+   `format_time_never_lets_a_field_reach_its_radix`, extended with the boundary of every rung
+   from seconds down to nanoseconds and its negative.
+
 **The minor grid is texture, the labelled grid is structure.** The subdivisions used to be
 drawn exactly like the labelled lines — same width, same opacity — so a plot dense enough to
 need them read as two competing sets of ticks. They are now three things the style states
@@ -1133,6 +1378,7 @@ so it is one path, and it costs what the crosshair's own lookup costs.
 
 Each carries a test upstream (`the_atlas_is_filtered_not_point_sampled`,
 `grid_hairlines_land_on_whole_pixels`, `the_tick_at_the_origin_reads_zero`,
+`format_time_never_lets_a_field_reach_its_radix`,
 `a_sparse_window_between_samples_still_inks_both_margins`), and each
 was verified to fail with its own fix reverted.
 
@@ -1358,7 +1604,7 @@ them all with nothing to propagate by hand. The live follow is the *group's*
 (`set_x_link_follow`), not each row's — `Figure::link_x()` refuses a member whose
 own axis still follows, because a following axis would reinterpret the pushed
 range as its own span and offset behind its own edge, which is per-row drift by
-construction. The figure also owns the left gutter and the crosshair, so a
+construction. The figure also owns both gutters and the crosshair, so a
 vertical feature lands in the same pixel column in every row.
 
 The self-check's layout line carries `x-desync N`, the number of frames in which
@@ -1409,16 +1655,30 @@ division.
 over the shared x window, at the **stored** sample rate — never the LOD pyramid's
 buckets, which are the envelope the renderer drew rather than the acquisition. A
 signal on several rows is one column; the columns come out in channel order, so the
-file reads in the same order as the signal panel. The table has two time columns:
-`time` is the axis as displayed (stream seconds live, `[-pre, +post]` while an event
-is held) and `stream_time` is always the stream's own clock, so two exports taken in
-different modes line up.
+file reads in the same order as the signal panel.
+
+The table has **two time columns**, which is the whole answer to "relative or absolute":
+
+- **`time`** is the axis exactly as it was displayed — negative ages ending at 0 live, offsets
+  from the edge in trigger mode — so a row's `time` is the x the user read a value at.
+- **`abs_seconds`** is the stream's own clock for the same sample: `epoch() + stream_at_x0() +
+  time[i]`, one expression correct in all four display modes (see *The x axis is relative to
+  now*). Two exports taken in different modes therefore line up on this column, and
+  `abs - time` is a constant per file naming where the display's origin sat in the stream.
+
+Both are `f64` seconds and not the wire's integer, because the wire's integer never exists in
+this process: `udps_frame_t::values` is a `const double*`, so the time signal has already been
+widened by the client before udpscope sees it. One caveat follows from that and from `time`
+being a *derived* coordinate: `abs_seconds` is a sum of two numbers of very different
+magnitudes, so consecutive differences wobble by a few ULP of the stream's uptime
+(femtoseconds at any plausible uptime — note that the `f32` defect this used to guard against
+was *microseconds*, four orders of magnitude up).
 
 Two formats, picked by the extension the save dialog ends up with:
 
 | file | what it is |
 |---|---|
-| `.npy` | one NumPy structured array, `time`/`stream_time` as `<f8` and every signal as `<f4` — the width the ring stores, so the file invents no precision and is about half an all-`f8` one. `pd.DataFrame(np.load(path))` is the whole reader. |
+| `.npy` | one NumPy structured array, `time`/`abs_seconds` as `<f8` and every signal as `<f4` — the width the ring stores, so the file invents no precision and is about half an all-`f8` one. `pd.DataFrame(np.load(path))` is the whole reader. |
 | `.csv` | the same table as text, `%.17g` for the times and `%.9g` for the values: the shortest widths that round-trip each type exactly. |
 
 Parquet (the original ask) would have meant linking Arrow — tens of megabytes of
@@ -1487,7 +1747,8 @@ fails validation renders a one-line stand-in so the window always opens rather t
 no `Gtk-CRITICAL`.
 
 **The status bar is two tiers.** The bar itself shows one glance line: the activity badge, the
-display state (one word from a fixed set), the stored rate and the window. Everything else —
+display state (one word from a fixed set — `connecting`, `live`, `paused`, `armed`, `capturing`,
+`event held`, `disarmed`, none wider than ten characters), the stored rate and the window. Everything else —
 packet and frame counts, gaps, buffer size and span, per-plot trace counts — is behind the ⓘ
 button at the bar's right-hand end, opening a popover. The two moved there because a bar that
 carried all of them was too wide to read while watching a signal, and because the bar sits
@@ -1508,7 +1769,16 @@ now — they are listed so they are not mistaken for anything else:
   latched `EventSnapshot` — an immutable copy of the captured window, which is
   exactly what "the buffer the view is frozen on" needs to be. Two live rings would
   also mean acquisition had to follow the trigger state, which is what left the first
-  latch after arming with no pre-trigger history.
+  latch after arming with no pre-trigger history. What a second ring would buy is the
+  publish: freezing a whole `BufferStore` copies nothing and inherits the pyramid the
+  producer already maintains, so both figures in the dump's `publish cost:` line would
+  go to zero. They are worth knowing before pricing that — at 1.3 MS/s an event publish
+  measured **69–115 ms of blocked UI tick** and a pause publish **22–86 ms of blocked
+  producer** — but they do not pay for a second budget's worth of memory, a second
+  per-sample write on the producer, and a single frozen slot where the app today holds
+  an event, a pause and an export's window at once. The *observable* cost is also
+  smaller than the stall: an A/B with and without a pause read `gaps=0` both ways, so
+  what a second ring would buy is a smoother frame at a latch, not recovered packets.
 - **The buffer is allocated at the first CONFIG, not at initialisation.**
   The spec's "N+1 split" needs N, which only a CONFIG gives; `--buffer-mb` is the
   *budget*, and the power-of-two ring rounding means the final
@@ -1572,6 +1842,17 @@ status line as `N reconnects` once it is nonzero) it says so in the status line
 leaving an empty plot to be puzzled over, and prints a `starved:` line to stderr while the
 state holds.
 
+That notice is **split on whether a CONFIG ever arrived**, because the two states are
+different diagnoses and only one of them is about another reader. With a signal list in
+hand, a stream that stops is the fight above: something took the session away, and the
+notice says so (`starved:` on stderr). With **no CONFIG at all** nothing was ever taken —
+there is no signal list, so nothing can be enabled and no DATA frame is owed — and the app
+says `trying to connect` instead (`connecting:` on stderr), with the glance line reading
+`connecting` and the badge yellow from the first frame rather than after the three-second
+stall test. Calling that one "connected, but no data is arriving" blamed a second reader
+that does not exist; the usual cause is a streamer that is not running, or one serving a
+different port.
+
 ## Limitations
 
 - **Multi-element (vector/matrix) signals are acquired with a zero-order hold.**

docs/superpowers/specs/2026-10-06-math-node-editor-design.md

@@ -0,0 +1,452 @@
+<!-- SPDX-License-Identifier: MIT -->
+<!-- SPDX-FileCopyrightText: 2026 Martino Ferrari -->
+
+# The math node editor: wires you can draw and delete, and a canvas you can navigate
+
+The math channel editor works as a *form* and fails as a *graph editor*. Three things were
+reported — edges cannot be added, edges cannot be deleted, and the canvas cannot be zoomed or
+panned — and all three are true. The first is a defect with a specific cause, the second has no
+code path at all, and the third is an absence. Beyond them the editor asks the user to obey a
+rule the data structure has (a node may only read nodes above it in the list) rather than
+maintaining that rule itself, and it reports an invalid graph in a modal alert at the end
+instead of on the canvas as it is being built.
+
+This redesigns the canvas interaction. Nothing below changes `MathNode`, `MathChannel`, the
+evaluator in `src/math_channel.cpp`, the session format, or the producer's path.
+
+## Scope
+
+In: the canvas view transform, the port and wire hit tests, the gesture state machine
+(node drag / wire drag / background pan / wheel zoom), edge creation and deletion, a
+topological re-sort that lets a wire be drawn in either direction, an op picker on the add
+button, a live validation line that replaces the modal alert, a tidy/auto-layout pass, the
+`Cancel` button's close path, and the `[math-probe]` assertions for all of it.
+
+Out: parameters drawn on the node boxes (explicitly declined — the form beside the canvas is
+where a node's values live). No new ops. No change to `math_channel_valid()`'s rules, to the
+evaluator, to `MathRuntime`, or to how a derived channel is acquired. No node *library* panel,
+no copy/paste, no undo.
+
+## Why edges cannot be added today
+
+`math_canvas_pressed` (`src/ui.cpp:3455`) handles an output-port hit like this:
+
+```cpp
+const int port = math_port_at(d, x, y, which);
+if (port == -2) {
+  const int node = math_node_at(d, x, y);
+  d->pending_out = (node >= 0 && d->pending_out == node) ? -1 : node;
+  ...
+}
+```
+
+`math_port_at` throws away *which* node's output was hit — it returns the sentinel `-2` — and
+the handler recovers the node with `math_node_at()`, which matches only **inside the box**. The
+output square is drawn at `x = n.x + kNodeW`, i.e. straddling the right edge: half of it is
+outside. Its hit radius is `kPort` (±10) while it is drawn at `±kPort * 0.5` (±5), so the
+clickable region extends 10 px past the edge and `math_node_at()` answers `-1` for every pixel
+of it beyond the first. `pending_out` is then set to `-1` — a *silent disarm*. Clicking the
+visible dot's outer half, which is most of what the eye aims at, arms nothing, and the input
+squares never light up. That is the whole of "it is not possible to add edges": the mechanism
+exists and the first click of the two-click sequence usually fails.
+
+It is worth fixing the cause and not only the symptom, because the same re-derivation would
+break again under the view transform below.
+
+Edge *deletion* needs no diagnosis: no path in the file ever writes `-1` back into `in_a` or
+`in_b` except `on_math_node_deleted`, which is deleting the whole node.
+
+## The view transform
+
+`MathDialog` gains three doubles:
+
+```cpp
+double view_scale = 1.0;   ///< canvas pixels per graph unit
+double view_x = 0.0;       ///< canvas pixels: where graph (0,0) is drawn
+double view_y = 0.0;
+```
+
+Graph coordinates are what `MathNode::x`/`y` already are and what the session file stores, so a
+view change is never persisted — reopening the editor shows the graph at 1:1, which is the
+right default for a window whose size the user did not choose either.
+
+Two conversions, and **every** hit test goes through the second:
+
+```cpp
+// canvas <- graph: applied once to the cairo context, never per item.
+cairo_translate(cr, d->view_x, d->view_y);
+cairo_scale(cr, d->view_scale, d->view_scale);
+
+// graph <- canvas: the inverse, for a pointer position.
+void math_to_graph(const MathDialog* d, double cx, double cy, double& gx, double& gy) {
+  gx = (cx - d->view_x) / d->view_scale;
+  gy = (cy - d->view_y) / d->view_scale;
+}
+```
+
+Applying the transform to the context rather than to each item is what keeps the drawing code
+unchanged: `math_canvas_draw` keeps every coordinate it has today, and the line widths and font
+sizes scale with the graph, which is what a zoom should do to a diagram.
+
+**A hit tolerance is a screen distance, not a graph distance.** A port is aimed at with a
+pointer, so its clickable radius must be the same number of *canvas* pixels at every zoom —
+which in graph units is `kPort / view_scale`. The same for the wire tolerance below. Getting
+this backwards makes the ports unhittable when zoomed out, which is exactly when a user is
+looking for them.
+
+**Scale is clamped to `[0.25, 4.0]`.** Below a quarter the op names are unreadable and the
+boxes are smaller than the pointer tolerance; above four a single node fills the canvas. The
+clamp lives in one place, a `math_set_scale()` helper, because three callers reach it (wheel,
+Fit, reset).
+
+### Wheel zoom about the pointer
+
+A `GtkEventControllerScroll` with `GTK_EVENT_CONTROLLER_SCROLL_VERTICAL`. The anchor is the
+graph point under the pointer, and it must not move:
+
+```cpp
+double gx = 0.0, gy = 0.0;
+math_to_graph(d, px, py, gx, gy);                 // before
+d->view_scale = clamp(d->view_scale * (dy < 0 ? 1.1 : 1.0 / 1.1), 0.25, 4.0);
+d->view_x = px - gx * d->view_scale;              // restore the anchor
+d->view_y = py - gy * d->view_scale;
+```
+
+The pointer position comes from the controller's own `GtkEventController` current event rather
+than from a tracked motion position: a scroll event carries one, and tracking motion to supply
+it is a second source of truth that can be stale.
+
+No modifier is involved. The canvas has no other use for the wheel, so a bare wheel zoom is
+unambiguous here — unlike the plot, where the wheel's modifiers are already spoken for.
+
+### Pan, Fit, and reset
+
+Dragging the empty background pans: `view_x = pan_x0 + dx`, from a `pan_x0` recorded at
+`drag-begin`, for the same total-offset reason the node drag already documents at
+`src/ui.cpp:3507`.
+
+A **Fit** button frames every node:
+
+```
+bbox over all math_node_rect()  (empty graph -> identity view)
+scale = clamp(min(w_canvas / (bbox.w + 2*pad), h_canvas / (bbox.h + 2*pad)), 0.25, 4.0)
+view_* = centre the scaled bbox in the canvas
+```
+
+`Ctrl+0` resets to `scale = 1`, `view_x = view_y = 0`. Both are one call to a shared
+`math_fit_view()` / `math_reset_view()` so the button and the accelerator cannot drift apart.
+
+## The port and wire hit tests
+
+`math_port_at` is replaced by one that **names the node it found**:
+
+```cpp
+/// The port under a *graph* position. Returns the node index, with `which` set to
+/// `kPortOut` (-1) for its output or 0/1 for an input; `-1` when no port is under it.
+int math_port_at(const MathDialog* d, double gx, double gy, double tol, int& which);
+```
+
+Two changes beyond the signature. It scans **backward**, topmost first, so it agrees with
+`math_node_at()` about which of two overlapping nodes owns a shared pixel — a disagreement
+between the two searches is how a click lands on one node and a drag on another. And the
+caller never re-derives the owner, which is the defect above made structurally impossible.
+
+The hit radius stays *larger* than the drawn square: ±`kPort` canvas pixels around the port's
+centre, against a square drawn at ±`kPort * 0.5` — a 20 px target for a 10 px mark. That is
+deliberate and, once the owner is no longer re-derived, harmless: a generous radius is the
+difference between a diagram that can be wired and one that cannot. The asymmetry is written
+down in a comment at the hit test, because it is what the old defect fed on.
+
+A wire is picked by distance to the curve it is drawn as. The curve is the same cubic the
+renderer uses (`src/ui.cpp:3401`), so the pick and the ink cannot disagree:
+
+```cpp
+/// The wire under a graph position, as (consumer node, which input), or {-1, 0}.
+/// The bezier is sampled at 24 points and the nearest segment measured; a curve 40 units of
+/// tread wide over a node pitch of 160 is smooth at that sampling, and the tolerance is 6
+/// canvas pixels, so a miss by a pixel is not a wrong edge deleted.
+MathWireRef math_wire_at(const MathDialog* d, double gx, double gy, double tol);
+```
+
+Sampling rather than solving: the exact distance to a cubic is a fifth-degree root-find, and 24
+samples of a curve whose control points are 40 units out is well inside a 6 px tolerance. The
+sample count is a named constant so a future wider tread can raise it.
+
+**Order of precedence on a press**: port, then wire, then node body, then background. A port
+sits on a node's edge and a wire ends on a port, so each later test must only see what the
+earlier ones refused.
+
+## The gesture state machine
+
+One `GtkGestureDrag` serves four gestures, decided entirely by what the press landed on. A
+`GtkGestureClick` is kept for the selection-only cases, because a click is a drag of zero
+length and GTK delivers both; `drag-begin` records the mode and `pressed` only ever *selects*.
+
+```cpp
+enum class MathDrag { None, Node, Wire, Pan };
+MathDrag drag_mode = MathDrag::None;
+int wire_from = -1;        ///< Wire: the node whose output the live wire leaves
+int wire_detach = -1;      ///< Wire: the consumer whose input was detached to start it, or -1
+int wire_detach_which = 0;
+double wire_x = 0.0;       ///< Wire: the pointer, in graph units, for the preview
+double wire_y = 0.0;
+double pan_x0 = 0.0;
+double pan_y0 = 0.0;
+MathWireRef selected_wire{-1, 0};
+```
+
+`drag-begin`, in precedence order:
+
+- **An output port** → `Wire`, `wire_from = node`, `wire_detach = -1`.
+- **A wired input port** → `Wire`, `wire_from = <the node it was wired from>`,
+  `wire_detach = node`, `wire_detach_which = which`, and the input is cleared *immediately*.
+  Dragging an existing wire off its input and dropping it elsewhere is one gesture, and
+  clearing on begin is what makes the preview show the truth: the wire the user is holding.
+  Dropping it on nothing therefore *detaches*, which is the agreed detach gesture, and needs
+  no separate case.
+- **An unwired input port** → `None` (select the node; there is nothing to drag from an empty
+  input). Wiring is always output→input, so this is not a connect gesture.
+- **A node body** → `Node`, exactly as today.
+- **Anything else** → `Pan`.
+
+`drag-update` moves the node, the live wire's endpoint, or the view, by mode.
+
+`drag-end` resolves `Wire`:
+
+- Released on an **input port** of a node that is not `wire_from` → `math_connect()`.
+- Released on an **input port of `wire_from` itself** → refused, with "a node cannot read
+  itself" on the validation line. A self-edge is the one cycle a topological sort cannot
+  break, and refusing it by name reads better than "the graph has a cycle".
+- Released anywhere else → nothing further. If the drag began by detaching, the detachment
+  stands.
+
+`Escape` during a `Wire` drag cancels and **restores** a detached input: a cancel must undo the
+clear-on-begin, or Escape would be a way to delete an edge by accident.
+
+A `GtkEventControllerKey` on the canvas handles `Delete`/`BackSpace` (clear `selected_wire`),
+`Escape` (cancel a drag, else clear the wire selection) and `Ctrl+0` (reset the view). It is
+added to the canvas and the canvas is given `gtk_widget_set_focusable(TRUE)` plus focus on
+press, because a drawing area is not focusable by default and a key controller on an unfocused
+widget never fires. **The key controller must not swallow text**: the dialog's name and unit
+entries are `GtkEditable`s, and the controller is on the *canvas*, so a key only reaches it
+while the canvas has focus — the same reasoning as the app-level accelerators' bubble phase,
+reached by a narrower route.
+
+## The edge model
+
+One function owns connection:
+
+```cpp
+/// Wire `from`'s output into `to`'s input `which`. Re-sorts the node list when the wire runs
+/// backwards. Returns false and sets `why` when the wire would make a cycle.
+bool math_connect(MathDialog* d, int from, int to, int which, std::string* why);
+```
+
+and deletion is a one-liner at the call site (`in_a`/`in_b` back to `-1`), because there is
+nothing to validate in removing an edge: a disconnected input is a state the validation line
+already names.
+
+### Backwards wires re-sort the list
+
+`MathChannel::nodes` is a list walked in order, and the evaluator's correctness rests on a node
+reading only nodes before it. Today that rule is the *user's* problem: the input ports of nodes
+above the armed output are not even drawn as armed, so a wire that would run backwards cannot
+be drawn at all. In a two-column auto-placed graph that is a real obstruction — the node you
+want to feed is frequently the one that happens to sit earlier in the list.
+
+The rule becomes the editor's invariant instead. `math_connect()` on a backwards wire
+(`from > to`) builds the new edge set, runs a topological sort, and commits only if it is
+acyclic:
+
+1. Trial edge set = every node's existing inputs, plus the new one.
+2. Kahn's algorithm over it. Ties broken by **current list index**, so a sort that changes
+   nothing leaves the list alone and a sort that must move something moves as little as
+   possible. (A stable order matters: the node positions on the canvas do not change, so a
+   gratuitous renumber would silently re-point `output` and `selected` for no reason the user
+   can see.)
+3. On a cycle: nothing is written, `why` is set, and the validation line shows it. The edge is
+   *not* created — this is the one refusal left, and it is the honest one.
+4. On success: permute `nodes`, then remap through the permutation **everything that holds an
+   index** — `output`, `selected`, every `in_a`/`in_b`, `drag_node`, `selected_wire.node`. A
+   forgotten one is a silent mis-wire, so they are remapped in a single block with a comment
+   naming the set.
+
+The session format is untouched: what is written is still a list in evaluation order. A file
+written by an older build still loads, because the sort is an editor operation and an
+already-ordered list sorts to itself.
+
+`math_canvas_draw` stops gating a wire on `from < i` once this holds — but keeps the gate as a
+**defensive skip**, because a `MathChannel` loaded from a file the editor did not write could
+hold a forward reference, and drawing it would be drawing an edge the evaluator ignores.
+
+### The armed-port highlight goes away
+
+`pending_out` and the "input ports of later nodes light up" highlight are both deleted. They
+exist to serve the two-click protocol and the list-order rule, and neither survives: with a
+drag gesture the feedback is the live wire following the pointer, and with the re-sort every
+input is a legal target. What replaces the highlight is a hover accent on the port under the
+pointer during a `Wire` drag, which says the one thing that still matters — whether releasing
+here will connect.
+
+## The live validation line
+
+`on_math_apply` validates in two steps today (`math_channel_valid()`, then an acquired-source
+check the validator cannot make) and reports each in a modal `GtkAlertDialog`. A modal alert at
+the end of a build is the worst time and place to be told; the graph is right there and can say
+so continuously.
+
+One extraction:
+
+```cpp
+/// Why the graph as it stands could not be saved, or "" when it could. Both checks the Apply
+/// path made: `math_channel_valid()`'s graph rules and the dialog's own "a Source must name an
+/// acquired channel", which the validator cannot make because only the dialog sees that list.
+std::string math_dialog_problem(const MathDialog* d);
+```
+
+`math_dialog_sync()` — already the one place that rewrites the form from the model, and already
+called from every mutation — sets the line's text and `gtk_widget_set_sensitive(apply, problem
+.empty())`. An insensitive Apply with the reason beside it is a better refusal than a dialog
+that must be dismissed.
+
+`on_math_apply` keeps the check and loses the **dialogs**: it calls `math_dialog_problem()` and
+returns on a non-empty answer, with no `GtkAlertDialog`. The guard has to stay even though the
+button cannot be clicked while it would fire, because the probe calls `on_math_apply()` directly
+and must not be able to save a broken graph through it. That `d->apply` pointer is new on
+`MathDialog`; the button is built after the canvas today, so `math_dialog_sync()`'s first call
+(at `src/ui.cpp:3972`, after the whole tree) already runs late enough to set it.
+
+The line is a `GtkLabel` under the canvas, `error` CSS class when non-empty, and
+`gtk_label_set_ellipsize(END)` with a tooltip carrying the full text — **the layout-must-not-
+depend-on-content rule applies here as much as to the status bar**: this label sits in a dialog
+whose canvas is `hexpand`, and a wrapping error message would otherwise widen the dialog on a
+mere change of graph.
+
+## The op picker on add
+
+`add node` always makes a `MathOp::Gain` (`src/ui.cpp:3516`), so adding a low pass is two
+actions and a dropdown hunt. It becomes a `GtkMenuButton` labelled `add` whose popover holds a
+flat button per op, built once from `math_op_count()` / `math_op_at(i)` — the accessor order,
+not the enum order, for the reason `CLAUDE.md` already records about writing an op's index.
+Each button carries its op index with `g_object_set_data`, so there is no action-name plumbing
+and nothing to parse.
+
+The two behaviours that already work are kept: the new node becomes the output when the graph
+`was_linear`, and placement is the existing grid. Placement gains one thing — a node is placed
+at the **first free grid cell** rather than at `nodes.size()`, so the slot left by a deletion is
+reused instead of the grid growing for ever. The overlap rule stands (`CLAUDE.md`: boxes must
+not overlap, or `math_node_at()`'s topmost-first search returns the wrong one).
+
+## Tidy / auto-layout
+
+A `tidy` button lays the graph out left to right by dependency depth:
+
+```
+depth(i) = 0 for a Source or an unwired node
+         = 1 + max(depth of its wired inputs)      // well-defined: inputs precede i
+x = 24 + depth * (kNodeW + 48)
+y = 20 + row_within_depth * (kNodeH + 22)
+```
+
+It needs no recursion and no visited set: the list is in evaluation order — the invariant the
+re-sort now maintains — so the depth of node `i` depends only on nodes before it and a single
+forward pass computes every depth. Then `math_fit_view()`, because a tidied graph that is off
+screen is not tidy.
+
+The column pitch is `kNodeW + 48`, which is 180 against the 160 the current grid uses: 160
+leaves 28 units for the wire's 40-unit tread, so the curve doubles back on itself between
+adjacent columns.
+
+## The `Cancel` button closes rather than destroys
+
+`src/ui.cpp:3962` connects `Cancel` to `gtk_window_destroy`:
+
+```cpp
+g_signal_connect_swapped(cancel, "clicked", G_CALLBACK(gtk_window_destroy), window);
+```
+
+This is the defect `CLAUDE.md` documents under the math channel invariants — "a Cancel that
+*destroyed* the window left `app.math_dialog` pointing at a dead widget: every later
+`open_math_dialog()` took the 'already open' branch and presented it" — and it is still live.
+The fix for it reached the Apply path (`src/ui.cpp:3731`) and the probe (`src/ui.cpp:6672`) and
+never reached the button. It is `gtk_window_close`, one word, and the probe must assert it,
+which it does not today: it only ever closes programmatically.
+
+## What `[math-probe]` must assert
+
+Every gesture above is reachable from the probe, because the handlers take the `MathDialog*`
+and plain coordinates — which is already how the drag test at `src/ui.cpp:6694` works. The
+probe is extended with one line per claim; each is an assertion stated as a `want` beside the
+reading, in the style of the existing lines.
+
+- `[math-probe] hit: output at edge+1 -> node N which=-1, at edge+9 -> node N which=-1
+  (want N N)` — the silent-disarm defect, read at two offsets inside the hit radius and outside
+  the box. Both must name the node. **This is the one line that would have caught the reported
+  bug**, and it is the reason the hit test returns the node rather than a sentinel.
+- `[math-probe] wire: connect 0->1.a wired=W (want 0)` then a backwards
+  `[math-probe] wire: backwards connect 2->0.a order=[..] wired=W reordered=D (want 1)` — the
+  re-sort, with the permuted op order printed so a wrong remap is visible as a wrong list.
+- `[math-probe] wire: self refused=D problem=[..] (want 1)` and
+  `[math-probe] wire: cycle refused=D problem=[..] (want 1)` — the two refusals, with the
+  cycle built by wiring a two-node pair both ways. `refused=1` **and** the edge absent.
+- `[math-probe] wire: pick at (x,y) -> (node,which)=(N,K) delete -> in=-1 (want -1)` — the
+  pick samples the curve at its midpoint, which is the one place a wrong tolerance or a wrong
+  curve shows.
+- `[math-probe] detach: drag from in 1.a to empty -> in=-1 (want -1)`, and
+  `[math-probe] detach: escape restores in=F (want F)` — the clear-on-begin and its undo, which
+  is the half that silently deletes an edge if Escape is forgotten.
+- `[math-probe] view: zoom scale=S anchor kept dx=.. dy=.. (want 0.0 0.0)` — the graph point
+  under the pointer before and after a wheel step, which is the only reading that distinguishes
+  "zoomed about the pointer" from "zoomed about the origin". Both must be zero to a rounding.
+- `[math-probe] view: fit scale=S box=[..] all_inside=D (want 1)`, and
+  `[math-probe] view: reset scale=S offset=(..) (want 1.000 (0,0))`.
+- `[math-probe] view: pan dx=.. dy=.. offset=(..) (want ..)` plus a hit test **after** a pan and
+  a zoom — `port at the same screen point -> node N` — because a hit test that forgot the
+  inverse transform passes every test taken at the identity view.
+- `[math-probe] tidy: depths=[..] columns=[..] overlaps=D (want 0)` — the overlap count is the
+  assertion (`CLAUDE.md`'s own rule), and the depths say the layout followed the graph.
+- `[math-probe] validate: problem=[..] apply_sensitive=D` before and after wiring the missing
+  input: `(want non-empty 0)` then `(want empty 1)`.
+- `[math-probe] cancel: dialog=cleared` — the `Cancel` button's `::clicked` emitted directly,
+  then `app.math_dialog` read back. `STILL SET` is the regression.
+
+Two things the probe deliberately cannot assert, and which are therefore stated as design
+constraints rather than checks: that the canvas takes **focus** on press (a synthetic press
+does not run GTK's focus machinery), and that the live wire *looks* like it follows the pointer
+(a draw is not readable from a probe). The second is bounded by the first assertion set — the
+endpoint it is drawn from is `wire_x`/`wire_y`, which the drag test writes and can print.
+
+The existing lines are all kept. `drag:` in particular stays as it is: the total-offset rule is
+unchanged by any of this, and the gesture that exercises it is still a node-body drag.
+
+## Documentation
+
+Three places, following the project's existing split:
+
+- **`CLAUDE.md`** — the `[math-probe]` bullet under Verification gains the new readings and
+  their `want`s; the math channel invariants gain the **hit-test-names-its-own-node** rule (a
+  port hit must not be re-derived with a box test), the **tolerance-is-a-screen-distance** rule,
+  the **list order is the editor's invariant, maintained by a topological re-sort** rule with
+  the index-remap set named, and a note that the `Cancel` path is now asserted.
+- **`README.md`** — a subsection under the math channels describing the editor as it now
+  behaves, and the diagnosis of the silent disarm, since README is where "what was actually
+  built and why" lives.
+- **`src/help/11-math.txt`** gains the four canvas gestures (drag a port to wire, drag a wired
+  input away to detach, click a wire and press Delete, wheel to zoom and drag the background to
+  pan) and the two buttons. It is an edit to an existing page, so `pages` stays 14 and
+  `[help] pages=14 parsed=14` must still hold — the markup is Pango and a page that fails to
+  parse renders a stand-in.
+
+## Risks
+
+- **The re-sort touching an index nothing remapped.** The mitigation is that the remap is one
+  block, the probe prints the permuted op order, and `selected`/`output` are both read back.
+- **The key controller stealing a keystroke from the name entry.** It is on the canvas, which
+  must have focus; the probe cannot see this, so it is checked by hand once, by typing in the
+  name field with a wire selected.
+- **The wheel controller fighting a future scrolled window.** There is none and this design
+  removes the reason for one, which is worth stating so a later "wrap the canvas in a
+  `GtkScrolledWindow`" is recognised as undoing the zoom rather than adding to it.
+- **`GtkGestureDrag` and `GtkGestureClick` on one widget both claiming a press.** They already
+  coexist on this canvas; the change is that `pressed` now only selects and never mutates the
+  graph, which removes the ordering question rather than answering it.

src/event_series.hpp

@@ -26,14 +26,24 @@ using plot::u64;
 /// live ring buffers switched by a pending flag, plus a display-epoch shift)
 /// could not stop.
 struct EventSnapshot {
-  /// Seconds, monotonic -- edge-relative for a trigger event, the stream's own for a
-  /// pause view. **f64, like the live ring it is cut from** (see `BufferStore::time()`):
-  /// an event's stamps are small enough that f32 would nearly do, but a *pause* is
-  /// deliberately not rebased, so its stamps carry the full stream time and quantise at
-  /// the same 3.8 us per 32 s of uptime the live ring did. Keeping the two the same type
-  /// also makes the cut in `publish_event()`/`publish_pause_view()` a straight copy.
+  /// Seconds, monotonic, and **in the coordinates the axis reads**: a trigger event's
+  /// stamps are edge-relative and a pause view's are relative to the instant it froze,
+  /// which is what `x_offset` below records. **f64, like the live ring it is cut from**
+  /// (see `BufferStore::time()`), which also makes the cut in `publish_event()`/
+  /// `publish_pause_view()` a straight copy.
   std::vector<f64> stamps;
   std::vector<std::vector<f32>> values;  ///< one array per channel, same length
+  /// The stream time of this snapshot's x = 0, so `x_offset + stamps[i]` is the clock the
+  /// data arrived on: the edge for a trigger event, the newest sample at the moment of the
+  /// freeze for a pause view.
+  ///
+  /// It exists because a snapshot is the one thing on screen whose coordinates outlive the
+  /// `display_epoch()` that produced them, and `ScopeModel::stream_at_x0()` is what reads
+  /// it: an export has to name the stream's own clock whatever is on screen, and the pause
+  /// handler has to put a *display* window back on the ring to cut it. Before it, the
+  /// export added `trigger_time()` to a pause view's stamps -- an unrelated edge, or none
+  /// at all -- for want of anywhere to record which clock a snapshot was on.
+  double x_offset = 0.0;
   double pre_s = 0.0;                    ///< seconds of pre-trigger data kept
   double post_s = 0.0;                   ///< seconds of post-trigger data kept
   std::vector<plot::Range> y;            ///< per-channel value bounds, precomputed

src/export.cpp

@@ -38,7 +38,7 @@ std::string sanitise(const std::string& name) {
 /// two time columns, with a `_2`, `_3` suffix. Two elements of one vector signal can
 /// easily sanitise to the same string.
 std::vector<std::string> column_labels(const ExportTable& table) {
-  std::vector<std::string> taken{"time", "stream_time"};
+  std::vector<std::string> taken{"time", "abs_seconds"};
   std::vector<std::string> out;
   out.reserve(table.columns.size());
   for (const ExportTable::Column& col : table.columns) {
@@ -106,6 +106,14 @@ ExportTable collect_export(ScopeModel& model, RowSet& rows) {
   // What is on screen: a pause's frozen view, or the trigger's held event. Both are immutable
   // snapshots, so the export is the picture the user is looking at either way.
   std::shared_ptr<const EventSnapshot> snap = model.display_snapshot();
+  // The absolute clock of display x = 0, so `abs_base + time[i]` is the number the stream
+  // stamped sample i with -- **one expression, correct in all four display modes**, which is the
+  // whole reason `stream_at_x0()` exists. `epoch()` is the stream time of the first sample ever
+  // seen (the rings store stamps relative to it) and `stream_at_x0()` is the offset of the
+  // display's origin within that, whether it comes from a snapshot or from the live epoch. The
+  // snapshot branch used to add `trigger_time()` here, which named an unrelated edge on a
+  // *paused* export, or none at all before the first latch.
+  const f64 abs_base = model.epoch() + model.stream_at_x0();
   if (snap != nullptr) {
     // The snapshot is immutable and already index-aligned, so the visible window is two
     // binary searches over its stamps and the same index range for every channel.
@@ -115,15 +123,11 @@ ExportTable collect_export(ScopeModel& model, RowSet& rows) {
     if (hi <= lo) return table;
     const std::size_t first = static_cast<std::size_t>(lo - st.begin());
     const std::size_t n = static_cast<std::size_t>(hi - lo);
-    // The event's x = 0 is the edge, so the stream clock has to be added back for the
-    // second column -- the one case where the visible x is not the stream's own.
-    const f64 edge = model.trigger_time().load(std::memory_order_relaxed);
-
     table.time.resize(n);
-    table.stream_time.resize(n);
+    table.abs_seconds.resize(n);
     for (std::size_t i = 0; i < n; ++i) {
       table.time[i] = st[first + i];
-      table.stream_time[i] = edge + table.time[i];
+      table.abs_seconds[i] = abs_base + table.time[i];
     }
     for (const int c : chans) {
       const std::size_t ch = static_cast<std::size_t>(c);
@@ -141,12 +145,12 @@ ExportTable collect_export(ScopeModel& model, RowSet& rows) {
   // the same window hold the same samples. The lock is against a structural change
   // dropping the rings under the copy, which is what the UI thread has to fear here.
   std::lock_guard<std::mutex> lock(model.mutex());
-  // The axis reads `display_epoch + stamp`, so the window has to be put back on the
-  // stream's clock before the ring is searched. It is 0 in live mode, but reading it is
-  // what keeps this correct rather than merely true today.
-  const f64 epoch = model.display_epoch();
+  // The axis reads `stamp - stream_at_x0()`, so the window has to be put back on the stream's
+  // clock before the ring is searched -- and that offset is a whole window while streaming now,
+  // not the 0 it once was: the live axis is `[-window, 0]` about the newest sample.
+  const f64 s0 = model.stream_at_x0();
   u64 first = 0, last = 0;
-  model.live_window_locked(view.min - epoch, view.max - epoch, first, last);
+  model.live_window_locked(view.min + s0, view.max + s0, first, last);
   const u64 n = last - first;
   if (n == 0) return table;
 
@@ -154,10 +158,10 @@ ExportTable collect_export(ScopeModel& model, RowSet& rows) {
   std::vector<f64> stamps(static_cast<std::size_t>(n));
   store.time().copy_from(first, n, stamps.data());
   table.time.resize(static_cast<std::size_t>(n));
-  table.stream_time.resize(static_cast<std::size_t>(n));
+  table.abs_seconds.resize(static_cast<std::size_t>(n));
   for (std::size_t i = 0; i < stamps.size(); ++i) {
-    table.stream_time[i] = stamps[i];
-    table.time[i] = epoch + table.stream_time[i];
+    table.time[i] = stamps[i] - s0;
+    table.abs_seconds[i] = abs_base + table.time[i];
   }
   for (const int c : chans) {
     const std::size_t ch = static_cast<std::size_t>(c);
@@ -179,7 +183,7 @@ bool write_npy(const std::string& path, const ExportTable& table, std::string& e
   // `descr` as a list of (name, format) pairs is a *packed* structured dtype -- NumPy
   // only inserts alignment padding when asked to (`align=True`) -- so the records below
   // are field widths back to back with no gaps.
-  std::string descr = "[('time', '<f8'), ('stream_time', '<f8')";
+  std::string descr = "[('time', '<f8'), ('abs_seconds', '<f8')";
   for (const std::string& label : labels) descr += ", ('" + label + "', '<f4')";
   descr += "]";
   std::string header = "{'descr': " + descr + ", 'fortran_order': False, 'shape': (" +
@@ -211,7 +215,7 @@ bool write_npy(const std::string& path, const ExportTable& table, std::string& e
     std::size_t at = 0;
     std::memcpy(record.data() + at, &table.time[i], sizeof(f64));
     at += sizeof(f64);
-    std::memcpy(record.data() + at, &table.stream_time[i], sizeof(f64));
+    std::memcpy(record.data() + at, &table.abs_seconds[i], sizeof(f64));
     at += sizeof(f64);
     for (const ExportTable::Column& col : table.columns) {
       const f32 v = i < col.values.size() ? col.values[i] : 0.0f;
@@ -239,7 +243,7 @@ bool write_csv(const std::string& path, const ExportTable& table, std::string& e
   if (!opened(out, path, error)) return false;
 
   const std::vector<std::string> labels = column_labels(table);
-  std::string line = "time,stream_time";
+  std::string line = "time,abs_seconds";
   for (const std::string& label : labels) line += "," + label;
   line += "\n";
   std::fwrite(line.data(), 1, line.size(), out.f);
@@ -252,7 +256,7 @@ bool write_csv(const std::string& path, const ExportTable& table, std::string& e
     line.clear();
     std::snprintf(buf, sizeof(buf), "%.17g", table.time[i]);
     line += buf;
-    std::snprintf(buf, sizeof(buf), "%.17g", table.stream_time[i]);
+    std::snprintf(buf, sizeof(buf), "%.17g", table.abs_seconds[i]);
     line += ",";
     line += buf;
     for (const ExportTable::Column& col : table.columns) {

src/export.hpp

@@ -24,13 +24,22 @@ struct ExportTable {
     std::vector<f32> values;  ///< `rows()` long, the ring's own `f32`
   };
 
-  /// The x the plot shows and the crosshair reads: stream seconds in live mode,
-  /// edge-relative seconds in `[-pre, +post]` while an event is held.
+  /// The x the plot shows and the crosshair reads, which is **relative** in every mode: seconds
+  /// before now while streaming (so the newest sample is 0 and the window is `[-window, 0]`),
+  /// seconds from the edge in `[-pre, +post]` while an event is held, and seconds from the
+  /// instant of the freeze on a paused view.
   std::vector<f64> time;
-  /// The stream's own clock, so two exports taken in different modes line up. Equal to
-  /// `time` in live mode; `time + trigger_time` while an event is held, which is the one
-  /// case where the visible x is not the stream's.
-  std::vector<f64> stream_time;
+  /// The stream's own absolute clock -- the number the time signal carried, which is what the
+  /// source stamped the samples with -- so two exports taken in different modes, or from
+  /// different runs, line up on one timeline.
+  ///
+  /// `f64 seconds` rather than the wire's integer, because the integer does not exist in this
+  /// process: `udps_frame_t::values` is a `const double*`, so the client has already widened
+  /// every value by the time acquisition sees it. At Unix-epoch magnitudes an `f64` resolves
+  /// about 240 ns, which is coarser than a 1 MS/s sample period -- so this column is the
+  /// *provenance* of a row and `time` is the column to difference. Its own `np.diff` is
+  /// legitimately not single-valued for that reason.
+  std::vector<f64> abs_seconds;
   std::vector<Column> columns;
 
   std::size_t rows() const noexcept { return time.size(); }
@@ -45,7 +54,7 @@ struct ExportTable {
 /// model access. In trigger mode nothing is locked: the `EventSnapshot` is immutable.
 ExportTable collect_export(ScopeModel& model, RowSet& rows);
 
-/// Writes a NumPy `.npy` file holding one structured array: `time` and `stream_time` as
+/// Writes a NumPy `.npy` file holding one structured array: `time` and `abs_seconds` as
 /// `<f8`, every signal as `<f4` -- the width the ring actually stores, so the file is
 /// about half the size of an all-`f8` one and invents no precision.
 ///

src/help/01-overview.txt

@@ -6,9 +6,15 @@ Acquisition runs on its own thread and writes a ring buffer sized from <tt>--buf
 the drawing thread reads whatever that ring holds when a frame starts, which is why a trace
 never makes the window stutter.
 
-The stream is the clock. Every time you read on screen is a timestamp the source sent, never
-your machine's, so a stalled source freezes the view instead of scrolling it -- and a source
-whose clock steps still gets the window you asked for.
+The stream is the clock. Every interval you read on screen is measured between timestamps the
+source sent, never your machine's, so a stalled source freezes the view instead of scrolling it
+-- and a source whose clock steps still gets the window you asked for.
+
+The time axis is <i>relative to now</i>. While streaming it is a fixed <tt>[-window .. 0]</tt>
+with the newest sample at 0, so x reads as an age: <tt>-1.5s</tt> is a sample a second and a half
+old. In trigger mode 0 is the event's edge instead, and a paused view keeps the ages it was
+frozen with. The source's own clock is still there when you need it -- an export writes it as a
+second column.
 
 <b>How to reach it</b>
 

src/help/04-layout.txt

@@ -1,7 +1,10 @@
 <b>Rows, layout and drag &amp; drop</b>
 
 The figure is a stack of rows, 1 to 8 of them, each holding up to 4 traces. Rows share one
-time axis and one left gutter, so their y labels line up and their windows cannot drift apart.
+time axis and one pair of side margins, so their y labels line up, their data areas start and
+end on the same two columns, and their windows cannot drift apart. The left margin holds the y
+labels; the right one is empty, and is there so the newest tick's label and the newest sample's
+ink have somewhere to land instead of sitting on the frame.
 
 <b>How to reach it</b>
 

src/help/06-navigate.txt

@@ -24,12 +24,30 @@ The full table is in the shortcut overview (<tt>Ctrl+/</tt>).
   zoom, so a 2 s window zoomed into reads 2 s again. The window is more than the axis: it is also
   the trigger's event span and how the samples are stored, so a wheel notch that redefined it
   would re-plan the buffer and drop your history.
+• The axis does not scroll — the <i>data</i> does. A live axis is a fixed <tt>[-window .. 0]</tt>
+  with the newest sample at 0, so the labels stand still and the trace rolls under them. The
+  cursors stand still with the labels (they are positions on screen, so a cursor you placed stays
+  where you put it, over newer data each frame), while a measurement's marks travel with the
+  sample they measured and leave the view when it does.
 • A live view is clamped to the window you asked for, not to what the ring happens to hold.
   That is why a buffer that has only just started filling leaves its left-hand side empty
   instead of squeezing the window down to the first few samples.
 • Zooming hard into a held capture is exact. The renderer finds the visible samples by binary
   search over the real timestamps, never over a nominal sample grid, so a capture whose clock
   wandered does not drift away from its axis as you zoom.
+• A trace holding far more samples than the plot has pixels is drawn <i>one pixel column at a
+  time</i>: each column is a single vertical line from the lowest to the highest value that falls
+  in it. Drawn as a polyline instead, such a window puts three or four near-vertical lines in
+  every column at slightly different sub-pixel positions, and how they overlap beats against the
+  pixel grid — which reads as bands of light and dark that <i>crawl</i> as you pan. One line per
+  column removes the beat, and it is also much faster: a 1 MS/s view costs a couple of thousand
+  line segments a frame instead of a couple of hundred thousand.
+• Those columns are <i>graded by brightness</i>, the way a digital-phosphor scope reads: bright
+  where the signal spent its time, faint where it only passed through. A column's highest and
+  lowest value are the same whether the samples in it are spread evenly or piled at its two ends,
+  so the grading is what tells the two apart — the flat parts of a square wave come out solid and
+  the edges between them faint. It is read from a finer division of each column rather than from
+  the line that is drawn, and it costs about a millisecond a frame.
 
 <b>Example</b>
 

src/help/07-pause.txt

@@ -20,6 +20,8 @@ live ring and puts the window back on the newest data.
   zoom out is clamped to the snapshot's data.
 • Pausing is the easiest way to measure a layout or read a cursor precisely, because nothing
   under the pointer moves between frames.
+• The status bar says how long you have been paused — wall time, since the stream itself never
+  stopped. It is there so a frozen picture cannot be mistaken for a live one that went quiet.
 
 <b>Example</b>
 

src/help/09-cursors.txt

@@ -37,6 +37,11 @@ owns a <b>Reset</b> button. Drag a marker to move it. The mode dropdown offers f
   is drawn larger than a trace's sample dots so it does not read as one more sample.
 • The time row exists only in the modes that show the vertical pair. <tt>horizontal</tt> has no
   time row, by design.
+• A cursor <i>stays where you put it</i> while a live view rolls under it, which is what a bench
+  scope does: its <tt>T0</tt> is an age, so a marker left at <tt>-1.5s</tt> keeps reading the
+  sample a second and a half old as the stream advances. A measurement's marks do the opposite —
+  they travel with the sample they measured — because a cursor is a question you asked and a mark
+  is an answer about one particular sample.
 
 <b>Example</b>
 

src/help/10-measurements.txt

@@ -24,6 +24,17 @@ set, with <b>Save</b> and <b>Delete</b>.
 • An invalid pass keeps its <i>level</i> marks and drops its <i>time</i> marks. A level is a
   property of the signal and outlives the window; a position inside the window does not. That is
   what stops the rulers blinking off at a mode change.
+• A crossing is counted with <i>hysteresis</i>, not on a bare level: the thresholds are a tenth of
+  the window's peak to peak either side of the share, and an edge is counted only once the signal
+  has passed the far one. Period, frequency and pulse duration all depend on it. The mid level is
+  exactly where a waveform moves fastest, so any interferer faster than the fundamental recrosses a
+  single level several times per real crossing — a 5 Hz sine with a 500 Hz tone at a tenth of the
+  amplitude reads 39 Hz without the band and 5 Hz with it. The band holds to an interferer a third
+  of the waveform's own size.
+• The band is clamped to stay inside the data, which is what keeps a threshold set near an extreme
+  usable: a fixed band there would sit above every sample and the measurement would read nothing.
+  A share near an extreme still leaves the band little room, so it rejects less — which is one
+  reason period and frequency offer no share to set.
 • A window with too few crossings reads <tt>invalid</tt> / <tt>--</tt> rather than a plausible
   invented number. Frequency over a window holding one edge is the usual case.
 • <tt>frequency</tt> is reported in Hz and <tt>period</tt>/<tt>pulse duration</tt> in seconds;

src/help/12-export.txt

@@ -17,15 +17,17 @@ the format follows the path's extension.
 • The stored rate is not always the wire rate. A window long enough to need decimation is stored
   averaged at a lower rate, and the export carries <i>that</i> — read the status bar's ⓘ popover
   for the figure before trusting a sample count.
-• Two time columns. <tt>time</tt> is the display timeline (relative to the trigger edge while an
-  event is held) and <tt>stream_time</tt> is the source's own clock. Both are strictly increasing
-  and evenly spaced; duplicate or backwards stamps would mean the file held two clocks.
+• Two time columns. <tt>time</tt> is the display timeline — negative ages ending at 0 while
+  streaming, offsets from the trigger edge while an event is held — so it is the x you read a
+  value at on screen. <tt>abs_seconds</tt> is the source's own clock for the same sample, which
+  is what lets two exports taken in different modes line up. Both are strictly increasing and
+  evenly spaced; duplicate or backwards stamps would mean the file held two clocks.
 • An export taken <i>mid-capture</i> writes the partly filled window that is on screen, which is
   shorter than the event span. Export outside a capture if you want the whole event.
 
 <b>Example</b>
 
 A 2 s window at 10 kS/s over 3 traces writes 20001 rows and 5 columns
-(<tt>time</tt>, <tt>stream_time</tt>, three signals). The <tt>.npy</tt> is
+(<tt>time</tt>, <tt>abs_seconds</tt>, three signals). The <tt>.npy</tt> is
 <tt>64·⌈(10+len(header)+1)/64⌉ + rows·(16 + 4·cols)</tt> bytes. Read it back with
 <tt>pd.DataFrame(np.load(path))</tt>.

src/help/14-status.txt

@@ -9,11 +9,19 @@ The bar is always visible under the plot. Click <b>ⓘ</b> for the detail popove
 
 <b>Worth knowing</b>
 
-• The badge is one glyph in three colours: lit and dim alternating means data is arriving, and a
-  steady idle colour means it is not. A badge that never blinks is not a working badge.
-• The state field is one word from a fixed set: <tt>live</tt>, <tt>paused</tt>, <tt>armed</tt>,
-  <tt>capturing</tt>, <tt>event held</tt>, <tt>disarmed</tt>. In trigger mode the bar adds
-  exactly one more field, how long ago the last event was.
+• The badge is one glyph in four colours: green <i>alternating</i> lit and dim means data is
+  arriving, and a steady colour means it is not. A badge that never blinks is not a working badge.
+  Of the two steady colours, <i>grey</i> is no stream at all or a pipeline you stopped (the
+  tooltip says which), and <i>yellow</i> is a source that answered but has sent no configuration.
+• The state field is one word from a fixed set: <tt>connecting</tt>, <tt>live</tt>,
+  <tt>paused</tt>, <tt>armed</tt>, <tt>capturing</tt>, <tt>event held</tt>, <tt>disarmed</tt>. Two
+  states add one field each: in trigger mode, how long ago the last event was; while paused, how
+  long you have been paused.
+• <tt>connecting</tt> means there is no <i>signal list</i> yet — either no session or a session
+  with no configuration behind it. Every other word claims a signal list, so until one arrives
+  there is nothing for them to describe: nothing can be enabled and no data is owed.
+• The paused figure is <i>wall</i> time, not stream time — the producer never stops while paused,
+  so it answers "how long have I been looking at this picture".
 • Nothing on the bar may change width with the stream, because the bar sits directly above the
   plot and a wider label would relayout it. That is why the rate collapses to one figure or a
   range rather than listing per channel, and why an elapsed time steps to a coarser unit instead
@@ -22,9 +30,11 @@ The bar is always visible under the plot. Click <b>ⓘ</b> for the detail popove
   non-zero count means samples are absent from the buffer, not merely late.
 • <tt>reconnects</tt> counts sessions re-established with the source. Over unicast a climbing
   count usually means a second client is taking the source's single session.
-• The starvation notice — <i>connected, but no new frames in the last second</i> — is that same
-  situation seen from the other side. Pointing the app at a port where nothing answers produces
-  it too.
+• The starvation notice — <i>connected, but no data is arriving</i> — is that same situation seen
+  from the other side: the signal list is here, so something took the stream away. A source that
+  has sent <i>no</i> configuration gets a different notice, <i>trying to connect</i>, because
+  nothing was taken away — pointing the app at a port where nothing answers is that case, and the
+  usual cause is a streamer that is not running or is serving another port.
 • <tt>stored</tt> versus <tt>wire</tt> in the popover is the decimation. They differ exactly
   when the window is too long to store at full rate.
 

src/measure.cpp

@@ -28,8 +28,27 @@ void enter_side(MeasureLevel& acc, std::size_t e, double t) {
   acc.open[e] = true;
 }
 
+/// The hysteresis band's half-width, as a share of the window's peak-to-peak. Measured rather than
+/// chosen: 5 % reads the mock's 0.1 interferer correctly and fails at 0.2 (`period=0.075` for a
+/// true 0.2), while 10 % holds to an interferer amplitude of 0.3 -- a third of the waveform -- and
+/// to white noise at sigma=0.05. Above that the band starts eating a real waveform's own extremes
+/// on anything less square than a sine.
+constexpr double kHysteresisFrac = 0.10;
+
 }  // namespace
 
+void measure_set_level(MeasureLevel& acc, const MeasureStats& s, double pct) {
+  const double span = s.hi - s.lo;
+  acc.level = s.lo + pct * span;
+  // Half the room to the nearer extreme is the clamp. A threshold at 90 % has a tenth of the span
+  // above it, so a fixed 10 % band would put `level + h` *above every sample*: the walk then never
+  // decides the upper side and the measurement reads nothing at all, which is strictly worse than
+  // a noisy reading. Measured on a 3.3 V logic signal with ringing at thr=90 %: `enters=0` with a
+  // fixed band, `enters=4 period=0.200000` with the clamp.
+  const double room = std::min(s.hi - acc.level, acc.level - s.lo);
+  acc.hysteresis = std::max(0.0, std::min(kHysteresisFrac * span, 0.5 * room));
+}
+
 void measure_scan(const MeasureChunk& chunk, MeasureStats& s) {
   // The chunk's own extremes first, in a loop that touches nothing but the values: *where* an
   // extreme is costs an index, and the caller turns the two that survive into stamps once at the
@@ -130,17 +149,27 @@ void measure_accumulate(const MeasureChunk& chunk,
     for (std::size_t i = 0; i < chunk.count; ++i) {
       const double v = static_cast<double>(chunk.value[i]);
       if (!std::isfinite(v)) continue;
+      // The *sums* split at the bare level: `Top` and `Bottom` are defined as the mean above and
+      // below the threshold, and a band here would move a documented exact reading.
       const int s = v > acc.level ? 1 : 0;
       acc.sum[static_cast<std::size_t>(s)] += v;
       ++acc.count[static_cast<std::size_t>(s)];
-      // A sample *at* the level is on neither side, so it decides no crossing and the walk keeps
-      // the side it last decided. That is what stops a signal which merely touches the level from
-      // counting every sample as an edge.
-      if (v == acc.level) continue;
-      if (acc.have_side && s != (acc.side ? 1 : 0)) {
-        enter_side(acc, static_cast<std::size_t>(s), time_of(chunk.offset + i));
+      // The *edge* decision reads the band instead. A sample inside it is on neither side, so it
+      // decides no crossing and the walk keeps the side it last decided -- which is what stops a
+      // signal that merely wobbles about the level from counting every wobble as an edge. With
+      // `hysteresis == 0` this is the single-level test, `v == level` skip included.
+      int d;
+      if (v > acc.level + acc.hysteresis) {
+        d = 1;
+      } else if (v < acc.level - acc.hysteresis) {
+        d = 0;
+      } else {
+        continue;
       }
-      acc.side = s != 0;
+      if (acc.have_side && d != (acc.side ? 1 : 0)) {
+        enter_side(acc, static_cast<std::size_t>(d), time_of(chunk.offset + i));
+      }
+      acc.side = d != 0;
       acc.have_side = true;
     }
   }
@@ -153,21 +182,40 @@ bool measure_accumulate_bucket(const MeasureBucket& k,
   // A non-finite sample in the bucket would make the edge's position a guess: the raw walk takes
   // the first *finite* sample of the new side, and an aggregate cannot say which that is.
   if (k.count != k.span) return false;
-  // Strictly on one side, so every sample decides the same side and none is *at* the level --
-  // which is what makes this exact rather than an approximation of the walk.
+  // The *sums* need only the bare level: strictly on one side of it, so every sample decides the
+  // same bin and none is *at* it, which is what makes the fold exact rather than an approximation.
   const bool above = k.lo > acc.level;
   const bool below = k.hi < acc.level;
   if (!above && !below) return false;
   const std::size_t e = above ? 1u : 0u;
+  // The band is deliberately *not* folded into the test above. Tightening the whole condition to
+  // `level +/- h` refuses every bucket lying inside the band -- a tenth of the amplitude either side
+  // of the mid level is where a waveform moves fastest, so those are exactly the buckets a crossing
+  // passes through -- which hands the raw walk a share of the window rather than a bucket or two per
+  // crossing, and breaks the "`raw` stays at a fraction of a percent of `covered`" invariant.
+  // Instead: a bucket on one side of the level can always be *binned*, and only a *side change*
+  // whose position is inside the bucket is refused.
+  const double top = acc.level + acc.hysteresis;
+  const double bot = acc.level - acc.hysteresis;
+  // Does the bucket reach past the band at all? One wholly inside it decides no side, exactly as a
+  // raw sample inside it decides none, so the walk state is left alone.
+  const bool reaches = above ? (k.hi > top) : (k.lo < bot);
+  const bool change = reaches && acc.have_side && e != (acc.side ? 1u : 0u);
+  // A bucket that *enters* a side while straddling its own threshold holds the crossing somewhere
+  // inside itself, and only the raw walk can say where. One wholly past the threshold holds it at
+  // the bucket's first sample, exactly, which is where the raw walk would have found it.
+  const bool fully_outside = above ? (k.lo > top) : (k.hi < bot);
+  // Nothing may be folded before this point: a refusal hands the bucket to `measure_accumulate()`,
+  // which adds the same samples again. Sums added above the refusal double-counted every opened
+  // bucket, which read as `top` 0.614304 on a unit sine against the 2/pi it must be.
+  if (change && !fully_outside) return false;
   acc.sum[e] += k.sum;
   acc.count[e] += k.count;
-  if (acc.have_side && e != (acc.side ? 1u : 0u)) {
-    // The edge is the bucket's *first* sample: everything before it was on the other side and
-    // everything in the bucket is on this one, so that is where the raw walk would have found it.
-    enter_side(acc, e, time_of(k.offset));
+  if (change) enter_side(acc, e, time_of(k.offset));
+  if (reaches) {
+    acc.side = e != 0;
+    acc.have_side = true;
   }
-  acc.side = e != 0;
-  acc.have_side = true;
   return true;
 }
 

src/measure.hpp

@@ -152,6 +152,20 @@ void measure_scan_buckets(const MeasureBucket* buckets, std::size_t count, Measu
 /// must adding a second measurement of the same type at the same level.
 struct MeasureLevel {
   double level = 0.0;
+  /// Half-width of the hysteresis band about `level`: a crossing is counted only once the signal
+  /// has passed `level + hysteresis` going up or `level - hysteresis` going down, and a sample
+  /// inside the band decides nothing. It is a Schmitt trigger, and it is what makes an edge count
+  /// a count of the *waveform's* cycles rather than of its noise: a single level is recrossed
+  /// several times per true crossing by any interferer faster than the fundamental, because near
+  /// the mid level the fundamental's own slope is at its smallest. Measured on a 5 Hz sine with a
+  /// 500 Hz interferer at a tenth of the amplitude: 9 true crossings counted as 79, reading
+  /// `period=0.025622 freq=39.029` for a true 0.2 s / 5 Hz. With the band, `period=0.200188`.
+  ///
+  /// It moves the *edge decision* only. The `sum`/`count` split below stays at the bare `level`,
+  /// because that is what `Top`/`Bottom` are -- the mean of the samples above/below the threshold --
+  /// and a band there would change a documented exact reading (`top` on a unit sine is 2/pi).
+  /// `measure_set_level()` is what sizes it; zero reduces the walk exactly to a single level.
+  double hysteresis = 0.0;
   /// Index 0 is the side below the level (a sample exactly *at* it counts here, which is what
   /// `bottom` has always reported), index 1 the side above it.
   double sum[2] = {0.0, 0.0};
@@ -170,6 +184,14 @@ struct MeasureLevel {
   bool open[2] = {false, false};
 };
 
+/// Fill a level accumulator's `level` and `hysteresis` from the window's extremes and the share
+/// `measure_level_pct()` gave. The one place the band is sized, so every caller gets the same rule:
+/// a tenth of the window's peak-to-peak, *clamped* to half the room between the level and the
+/// nearer extreme. The clamp is what keeps a threshold near an extreme usable -- `PulseDuration`
+/// lets the user put one at 90 %, and a fixed band there puts the upper threshold above every
+/// sample in the window, which reads as nothing measured at all rather than as a noisy reading.
+void measure_set_level(MeasureLevel& level, const MeasureStats& stats, double pct);
+
 /// Pass two: one chunk into every level at once. The usual case is a single level -- every
 /// crossing type reads the mid level and `Top`/`Bottom` default to it too -- so a pane full of
 /// measurements on one signal costs two walks, not two per measurement.
@@ -182,10 +204,14 @@ void measure_accumulate(const MeasureChunk& chunk,
 /// fold in whole and the walk's side is decided by the bucket rather than by 64 samples. An edge
 /// *into* such a bucket lands on its first sample, exactly, which is why that is the stamp taken.
 ///
-/// False means the bucket straddles the level -- or holds a non-finite sample, which would make
-/// the edge's position a guess -- and the caller must feed its raw samples to
-/// `measure_accumulate()` for this level instead. That is the only place a measurement still
-/// reads raw samples in bulk, and on a clean waveform it is a bucket per crossing.
+/// False means the caller must feed the bucket's raw samples to `measure_accumulate()` for this
+/// level instead. That is the only place a measurement still reads raw samples in bulk, and on a
+/// clean waveform it is a bucket or two per crossing. Three things make it happen: the bucket
+/// straddles the level (so the sums cannot be binned); it holds a non-finite sample, which would
+/// make the edge's position a guess; or it is where the signal passes `level +/- hysteresis` and the
+/// *position* of that crossing is inside the bucket. The band is deliberately not folded into the
+/// first test -- see the comment in the implementation for why refusing every bucket inside the band
+/// costs a share of the window rather than a bucket.
 bool measure_accumulate_bucket(const MeasureBucket& bucket,
                                const std::function<double(std::size_t)>& time_of,
                                MeasureLevel& level);

src/model.cpp

@@ -515,8 +515,12 @@ void ScopeModel::reset_live_history_locked() {
   }
 }
 
-void ScopeModel::publish_pause_view(double lo_s, double hi_s) {
+void ScopeModel::publish_pause_view(double lo_s, double hi_s, double x_offset) {
+  // Timed from before the lock: the wait for it is part of what freezing a view costs the thread
+  // doing it, and this one is the UI's.
+  const std::uint64_t t0 = now_ns();
   auto snap = std::make_shared<EventSnapshot>();
+  snap->x_offset = x_offset;
   std::lock_guard<std::mutex> lock(mutex_);
   BufferStore& src = live();
   u64 first = 0;
@@ -525,13 +529,18 @@ void ScopeModel::publish_pause_view(double lo_s, double hi_s) {
   const u64 n = last - first;
   snap->stamps.resize(static_cast<std::size_t>(n));
   if (n > 0) {
-    // The stamps go in *as the ring holds them*: the stream's own seconds, which is the
-    // coordinate the axis was already reading. Nothing is rebased, so a pause does not move the
-    // dates under the reader the way a trigger event's edge-relative axis deliberately does.
+    // The stamps come out of the ring on the stream's own clock and are rebased onto
+    // `x_offset`, which is the coordinate the axis was *already* reading: a live view is
+    // newest-relative, so leaving them absolute would throw the frozen picture a whole uptime
+    // to the right of the axis at the instant the user pressed pause. Nothing is lost by the
+    // shift -- `x_offset` is exactly what makes the stream's time recoverable, which is what
+    // `stream_at_x0()` reads it for.
     src.time().copy_from(first, n, snap->stamps.data());
+    for (f64& t : snap->stamps) t -= x_offset;
   }
   snap->values.resize(channels_.size());
   snap->y.resize(channels_.size(), plot::Range{0.0, 0.0});
+  snap->pyramids.resize(channels_.size());
   for (std::size_t c = 0; c < channels_.size(); ++c) {
     const u64 stride = std::max<u64>(1, part_.stride[c]);
     auto& vals = snap->values[c];
@@ -540,17 +549,44 @@ void ScopeModel::publish_pause_view(double lo_s, double hi_s) {
     if (take > 0) src.values(c).copy_from(first + n - take, take, vals.data());
     f32 lo = vals.empty() ? 0.0f : vals.front();
     f32 hi = lo;
+    // The LOD index, folded into the bounds pass exactly as `publish_event()` folds it, and for
+    // the same reason: a snapshot that answers `pyramid()` with an empty one has `level_for()`
+    // descend to level 0, so the frozen view is re-gathered from every raw sample it holds on
+    // every frame it is on screen. A pause is not a cheaper case than a capture -- it freezes the
+    // *same* rings -- and leaving it out was visible twice over. The cost: `frame path:` read
+    // `raw=21 lod=118` over a 1.6 s pause against `raw=1 lod=170` for the same run live, with the
+    // draw mean 12.34 -> 18.18 ms. And the *look* changed, which is the half a cost figure does
+    // not show: `stage_trace_density()` grades a column against its own peak from a `1/height`
+    // deposit per segment, so a column fed ~660 raw inter-sample segments accumulates a far
+    // spikier distribution -- and a far larger peak to normalise against -- than one fed the one
+    // or two bucket envelopes the pyramid gives. The paused trace read as a hard bright core with
+    // its dwell tail dimmed out, i.e. the trace changed appearance on pause.
+    //
+    // It is not free, and the trade is one-off against per-frame: building it took the pause
+    // publish from 6.15 ms to 22.31 ms (`publish cost:`), which blocks the *producer* -- against
+    // ~5 ms a frame of draw for as long as the pause lasts, which at ~60 fps a 1.6 s pause repays
+    // thirty times over. The producer absorbs the stall: `gaps=0` with and without a pause, the
+    // paused run having published in 86 ms.
+    auto& pyr = snap->pyramids[c];
+    pyr.reserve(take);
     for (f32 v : vals) {
       lo = std::min(lo, v);
       hi = std::max(hi, v);
+      pyr.append(v);
     }
     snap->y[c] = plot::Range{lo, hi};
   }
   pause_view_.store(std::move(snap), std::memory_order_release);
+  note_publish(publish_pause_count_, publish_pause_us_total_, publish_pause_us_worst_,
+               (now_ns() - t0) / 1000u);
 }
 
 void ScopeModel::publish_event(double pre_s, double post_s, double edge) {
+  // The caller is the producer and already holds `mutex()`, so every microsecond counted here is a
+  // microsecond the UI tick is blocked for -- which is what the documented `tick` max is made of.
+  const std::uint64_t t0 = now_ns();
   auto snap = std::make_shared<EventSnapshot>();
+  snap->x_offset = edge;  // the stream time x = 0 means, for everything that has to cross back
   BufferStore& src = live();
   plot::data::RingBuffer<f64>& tsrc = src.time();
 
@@ -599,6 +635,8 @@ void ScopeModel::publish_event(double pre_s, double post_s, double edge) {
   // Bumped after the snapshot is in place, so a consumer that sees the new sequence
   // number sees the snapshot it counts.
   event_seq_.fetch_add(1, std::memory_order_release);
+  note_publish(publish_event_count_, publish_event_us_total_, publish_event_us_worst_,
+               (now_ns() - t0) / 1000u);
 }
 
 void BufferStore::set_epoch(f64 epoch) noexcept {

src/model.hpp

@@ -224,6 +224,37 @@ class ScopeModel {
   std::uint64_t math_cost_ns() const noexcept {
     return math_cost_ns_.load(std::memory_order_relaxed);
   }
+  /// What freezing a view costs, and *which thread it costs it to*. The two publishes are stalls on
+  /// opposite sides of `mutex()` and so are counted apart: `publish_event()` runs on the **producer**
+  /// with the lock already held, so its cost lands on the UI as a long tick (the documented `tick`
+  /// max); `publish_pause_view()` runs on the **UI** thread and takes the lock, so its cost lands on
+  /// the producer and can only surface as `gaps`. Neither is attributable in a frame mean, which is
+  /// why they are counted rather than inferred. Each counter is written by one thread and read by the
+  /// dump, so a relaxed store of a value already in hand is enough.
+  ///
+  /// This is the number to judge a second live ring against: freezing a whole `BufferStore` would
+  /// make both figures zero, since a `ChannelBuffer` maintains its pyramid incrementally and there
+  /// would be nothing to copy -- but it costs a second budget's worth of memory and a second
+  /// per-sample write on the producer, so it is worth paying only if the worst figures here are
+  /// large enough to matter.
+  std::uint64_t publish_event_count() const noexcept {
+    return publish_event_count_.load(std::memory_order_relaxed);
+  }
+  std::uint64_t publish_event_us_total() const noexcept {
+    return publish_event_us_total_.load(std::memory_order_relaxed);
+  }
+  std::uint64_t publish_event_us_worst() const noexcept {
+    return publish_event_us_worst_.load(std::memory_order_relaxed);
+  }
+  std::uint64_t publish_pause_count() const noexcept {
+    return publish_pause_count_.load(std::memory_order_relaxed);
+  }
+  std::uint64_t publish_pause_us_total() const noexcept {
+    return publish_pause_us_total_.load(std::memory_order_relaxed);
+  }
+  std::uint64_t publish_pause_us_worst() const noexcept {
+    return publish_pause_us_worst_.load(std::memory_order_relaxed);
+  }
   const std::vector<SignalInfo>& signals() const noexcept { return signals_; }
   const std::vector<ChannelInfo>& channels() const noexcept { return channels_; }
 
@@ -290,16 +321,17 @@ class ScopeModel {
   void live_window_locked(double lo_s, double hi_s, u64& first, u64& last);
   /// The frozen view taken when the user paused, or null while running. A pause is a
   /// snapshot of the *visible window* in exactly the sense a trigger event is -- an immutable
-  /// series the plot binds to -- and the difference is the anchoring: an event's stamps are
-  /// edge-relative, a pause's are the stream's own, so the axis does not move when the pause
-  /// begins and the reader keeps the times they were already reading.
+  /// series the plot binds to -- and both are anchored the same way: the stamps are the
+  /// coordinates the axis was already reading, with `x_offset` recording which instant that
+  /// x = 0 was. So the axis does not move when the pause begins.
   std::shared_ptr<const EventSnapshot> pause_view() const noexcept {
     return pause_view_.load(std::memory_order_acquire);
   }
-  /// Snapshots the live ring over `[lo_s, hi_s]` (stream seconds, the display epoch already
-  /// removed) as the pause view. The acquisition thread keeps writing, so this is a copy: what
-  /// is frozen is the picture, not the data.
-  void publish_pause_view(double lo_s, double hi_s);
+  /// Snapshots the live ring over `[lo_s, hi_s]` (stream seconds, i.e. the display window put
+  /// back on the stream's clock) as the pause view, rebased onto `x_offset` so its stamps are
+  /// the x the axis is already showing. The acquisition thread keeps writing, so this is a
+  /// copy: what is frozen is the picture, not the data.
+  void publish_pause_view(double lo_s, double hi_s, double x_offset);
   void clear_pause_view() noexcept { pause_view_.store(nullptr, std::memory_order_release); }
 
   /// Whether the user paused acquisition. Lives here rather than on `Acquisition` because the
@@ -378,12 +410,30 @@ class ScopeModel {
     return event() != nullptr ? DisplayMode::Held : DisplayMode::Waiting;
   }
 
-  /// The x origin the plot uses: 0 for "seconds since the stream started", or minus
-  /// the trigger instant while in trigger mode, so the axis reads seconds from the
-  /// event. Applied to the live store's channels.
+  /// The offset the **live** channels report their x with: `display_x = stream_t + epoch`.
+  /// Minus the newest stored sample's stamp while streaming, so the axis reads
+  /// `[-window, 0]` and the newest data is at 0; minus the trigger instant while a capture
+  /// is filling, so the axis reads seconds from the event. It is 0 while a *snapshot* is on
+  /// screen (a held event, a paused view), because then the live channels are bound to
+  /// nothing and the snapshot's own `x_offset` is what says which clock x = 0 is --
+  /// `stream_at_x0()` is the accessor that does not have to know which of the two it is.
   f64 display_epoch() const noexcept { return display_epoch_.load(std::memory_order_relaxed); }
   void set_display_epoch(f64 e) noexcept;
 
+  /// The stream time of the display's x = 0, so `stream_t = display_x + stream_at_x0()` and
+  /// `display_x = stream_t - stream_at_x0()` in **every** display mode.
+  ///
+  /// One accessor for the two places the offset can live: a snapshot carries its own
+  /// (`EventSnapshot::x_offset`, frozen with the picture), and a live view carries it as
+  /// minus the display epoch. Everything that has to cross between the two clocks goes
+  /// through here -- the export's absolute column, and the pause handler putting a display
+  /// window back on the ring to cut it -- rather than picking the branch itself and getting
+  /// one of the four modes wrong.
+  f64 stream_at_x0() const noexcept {
+    if (std::shared_ptr<const EventSnapshot> snap = display_snapshot()) return snap->x_offset;
+    return -display_epoch();
+  }
+
   // --- stream state ---------------------------------------------------------
   StreamStats& stats() noexcept { return stats_; }
   const StreamStats& stats() const noexcept { return stats_; }
@@ -472,6 +522,22 @@ class ScopeModel {
   std::atomic<std::uint64_t> math_slots_{0};
   std::atomic<std::uint64_t> math_timed_{0};
   std::atomic<std::uint64_t> math_cost_ns_{0};
+  /// See `publish_event_count()`. Single-writer each: the first three are the producer's, the last
+  /// three the UI thread's.
+  std::atomic<std::uint64_t> publish_event_count_{0};
+  std::atomic<std::uint64_t> publish_event_us_total_{0};
+  std::atomic<std::uint64_t> publish_event_us_worst_{0};
+  std::atomic<std::uint64_t> publish_pause_count_{0};
+  std::atomic<std::uint64_t> publish_pause_us_total_{0};
+  std::atomic<std::uint64_t> publish_pause_us_worst_{0};
+  /// Fold one publish's elapsed microseconds into a counter triple. Called by the one thread that
+  /// owns the triple, so the load/store pairs need no read-modify-write.
+  static void note_publish(std::atomic<std::uint64_t>& count, std::atomic<std::uint64_t>& total,
+                           std::atomic<std::uint64_t>& worst, std::uint64_t us) noexcept {
+    count.store(count.load(std::memory_order_relaxed) + 1, std::memory_order_relaxed);
+    total.store(total.load(std::memory_order_relaxed) + us, std::memory_order_relaxed);
+    if (us > worst.load(std::memory_order_relaxed)) worst.store(us, std::memory_order_relaxed);
+  }
   std::vector<bool> enabled_;
 
   Partition part_;

src/plot_host.cpp

@@ -125,9 +125,9 @@ bool RowSet::remove_row(int at) {
 void RowSet::install(Row& r, int /*row_index*/, plot::Plot& p) {
   r.plot = &p;
   r.axis_x = r.plot->add_x_axis(
-      {"time", {-1.0, 1.0}, true, plot::AxisPlace::Bottom, false, plot::TickFormat::Time});
+      {"", {-1.0, 1.0}, true, plot::AxisPlace::Bottom, false, plot::TickFormat::Time});
   r.axis_y = r.plot->add_y_axis(
-      {"value", {-1.0, 1.0}, true, plot::AxisPlace::Left, false, plot::TickFormat::Si});
+      {"", {-1.0, 1.0}, true, plot::AxisPlace::Left, false, plot::TickFormat::Si});
   for (int s = 0; s < kSlotsPerRow; ++s) {
     const std::size_t i = static_cast<std::size_t>(s);
     r.plot->add_trace(
@@ -199,7 +199,7 @@ void RowSet::rebuild_all() {
     }
     figure_->link_x(static_cast<plot::u32>(i), x_group_);
   }
-  if (y_gutter_px_ > 0.0) apply_y_gutter();
+  apply_gutters();
   // A new figure starts with no window at all, so the one the rows were showing has to
   // be restated -- as the pin it was, if an event is on screen: assigning a trace or
   // changing the row count while a capture is displayed must not throw the view back
@@ -844,10 +844,16 @@ void RowSet::fit_all() {
 }
 
 void RowSet::note_y_gutter(double need_px) {
-  double want = std::min(need_px + 6.0, 200.0);
+  // No slack added here, and that is load-bearing: `need_px` is the gutter the row was
+  // *laid out with*, which is already the maximum of its labels and the floor imposed last
+  // frame -- so a few pixels added to it are added again next frame. The `+ 6.0` this used
+  // to carry made the gutter a ratchet that climbed 6 px a frame until it hit the cap
+  // below, which is the whole reason the left margin was `200` of an 870 px viewport (and
+  // the `axes.w changes: 17` beside it). The label padding the reservation below adds is
+  // the slack, once.
+  double want = std::min(need_px, 200.0);
   // Reserve room for the widest label the formatter can produce, once, with the
-  // font the labels are actually drawn in (the embedded font is monospaced, so a
-  // character count is an exact width).
+  // font the labels are actually drawn in.
   if (!y_gutter_reserved_) {
     for (int i = 0; i < rows_; ++i) {
       Row& r = row(i);
@@ -855,10 +861,19 @@ void RowSet::note_y_gutter(double need_px) {
       const plot::render::TextBackend* text = r.plot->text_backend();
       if (text == nullptr) continue;
       const plot::render::Style& style = r.plot->style();
-      const double advance = double(text->measure("0123456789")) / 10.0;
       const double pad = double(style.device(style.grid_label_pad));
-      // "-1.23e-45" is the longest label `format_si()`'s fallback can print.
-      want = std::max(want, 9.0 * advance + 2.0 * pad + 2.0);
+      // A sign, three significant figures and a one-glyph SI prefix: the widest label
+      // `format_si()` writes for an axis with no unit, measured rather than counted in
+      // characters. Its `%.3g` fallback is wider (`-1.23e-45`) and was what this reserved,
+      // which cost a *third* of the gutter for a label no signal on a `Si` axis produces --
+      // it needs a value past 1e24, and `note_y_gutter()` is a monotone maximum over the
+      // measured need, so one that did appear widens the gutter for good anyway.
+      want = std::max(want, double(text->measure("-1.23m")) + 2.0 * pad + 2.0);
+      // The other side, from the same metrics. An x tick label is *centred* on its tick and
+      // the newest tick sits on the axes' right edge (a live axis is [-window, 0]), so half
+      // the widest time label is what the rightmost one needs to be drawn at all -- and that
+      // is also the band which keeps the newest sample's ink off the frame.
+      right_gutter_px_ = 0.5 * double(text->measure("-1.23ms")) + pad;
       y_gutter_reserved_ = true;
       break;
     }
@@ -866,9 +881,10 @@ void RowSet::note_y_gutter(double need_px) {
   if (want > y_gutter_px_) y_gutter_px_ = want;
 }
 
-void RowSet::apply_y_gutter() {
-  if (!figure_ || !(y_gutter_px_ > 0.0)) return;
-  figure_->set_min_y_gutter(static_cast<f32>(y_gutter_px_));
+void RowSet::apply_gutters() {
+  if (!figure_) return;
+  if (y_gutter_px_ > 0.0) figure_->set_min_y_gutter(static_cast<f32>(y_gutter_px_));
+  figure_->set_right_gutter(static_cast<f32>(right_gutter_px_));
 }
 
 void RowSet::set_trigger_marker(double x, bool visible) {

src/plot_host.hpp

@@ -178,6 +178,14 @@ class RowSet {
   void set_time_window(double seconds);
   double time_window() const noexcept { return window_s_; }
 
+  /// The newest x any row's live traces hold, which is what the link group follows -- and, since
+  /// it is reported in the display epoch currently in force, also what the frame tick subtracts
+  /// from that epoch to park the newest sample at x = 0. It must be read **after** `bind()` and
+  /// `acquire()`: it asks the bound series, so before them it answers for the previous frame's
+  /// window, and a frame's production at 1 MS/s over a 50 ms view is a third of the screen.
+  /// False when no row holds a streaming trace.
+  bool live_edge(double& newest) const;
+
   void set_y_auto(int row, bool on);
   void set_y_range(int row, double lo, double hi);
 
@@ -191,7 +199,13 @@ class RowSet {
   void place_crossings();
   CursorMode cursor_mode() const noexcept { return cursor_mode_; }
 
-  /// The two vertical cursors' stream times; shared by every row.
+  /// The two vertical cursors' positions, in the **display** x the axis reads -- not stream
+  /// seconds, which they coincided with only while `display_epoch()` was always 0. A live view
+  /// is newest-relative now, so a cursor left at -1.5 s keeps meaning "1.5 s ago" and the data
+  /// flows under it, which is what a bench scope's roll mode does and is the behaviour that was
+  /// asked for. They are read back out of the plots and written to them unchanged, so there is
+  /// nothing to convert; anything that needs the stream's own clock goes through
+  /// `ScopeModel::stream_at_x0()`. Shared by every row.
   double cursor_a_x() const noexcept { return cursor_a_x_; }
   double cursor_b_x() const noexcept { return cursor_b_x_; }
   /// One row's ruler values, or 0 for a row that does not exist.
@@ -359,18 +373,22 @@ class RowSet {
   /// left and right by a few pixels every frame. Since `set_min_y_gutter()` is a
   /// floor and the library still takes the larger of the two, a floor smaller than
   /// the labels cannot stop that; the reservation therefore covers the widest label
-  /// `format_si()` can produce (three significant digits, a sign and a prefix, or the
-  /// `%.3g` fallback) plus the label padding, measured once with the plot's own font.
-  /// Both reservations only ever grow, so the gutter is constant in practice.
+  /// `format_si()` writes for an axis with no unit -- a sign, three significant figures
+  /// and a one-glyph prefix -- plus the label padding, measured once with the plot's own
+  /// font. Both reservations only ever grow, so the gutter is constant in practice.
+  ///
+  /// The same metrics fix the **right** gutter, which is a want and not a measurement:
+  /// see `apply_gutters()`.
   void note_y_gutter(double need_px);
 
-  /// Applies the stable gutter as the figure's floor. Call once per frame, before the
-  /// frame is drawn.
+  /// Applies the stable left gutter as the figure's floor, and the right gutter beside
+  /// it. Call once per frame, before the frame is drawn.
   ///
-  /// It has to be the *figure's* floor and not each row's: `Figure::layout()` clears
-  /// every row's `set_min_y_gutter()` to measure what its own labels need, so a floor
-  /// written onto the rows survives exactly until the next layout.
-  void apply_y_gutter();
+  /// Both have to be the *figure's* and not each row's: `Figure::layout()` clears every
+  /// row's `set_min_y_gutter()` to measure what its own labels need, so a floor written
+  /// onto the rows survives exactly until the next layout, and the rows have to end on
+  /// one column as well as start on one.
+  void apply_gutters();
 
   /// The palette entry `index`, wrapped. Keyed by the *signal*, so that the colour a
   /// trace is drawn in is the colour the signal list's chip shows, on every row the
@@ -399,8 +417,6 @@ class RowSet {
   /// at the end of the gesture (`Controller::end_drag()`), and a value read out of the plot
   /// mid-drag has already been through that act.
   void place_cursors(Row& r, plot::CursorPlacement placement = plot::CursorPlacement::Snapped);
-  /// The newest x any row's live traces hold, which is what the group follows.
-  bool live_edge(double& newest) const;
 
   std::unique_ptr<plot::Figure> figure_;
   /// The one x link group every visible row belongs to. Groups are numbered from 1.
@@ -419,6 +435,9 @@ class RowSet {
   /// gesture to be honoured; one that matches it is just the clamp's own answer arriving back.
   plot::Range pinned_stated_{0.0, 0.0};
   double y_gutter_px_ = 0.0;
+  /// The empty band kept to the right of the data, device pixels. Nothing is drawn in it,
+  /// so it is reserved once from the font's metrics and never measured or grown.
+  double right_gutter_px_ = 0.0;
   bool y_gutter_reserved_ = false;
   std::array<Row, static_cast<std::size_t>(kMaxRows)> storage_{};
   CursorMode cursor_mode_ = CursorMode::Vertical;

src/status_text.cpp

@@ -48,6 +48,11 @@ std::string format_glance(const StatusSnapshot& s) {
   out += " · ";
   out += s.window_text;
   out += " window";
+  if (s.paused) {
+    // Directly after the state word's own field rather than at the end, because it qualifies
+    // *that* word: "paused · 10 kS/s · 2 s window · for 12 s" reads as one statement.
+    out += " · for " + format_elapsed(s.paused_for_s);
+  }
   if (s.trigger_on) {
     out += " · ";
     if (s.have_event) {
@@ -74,6 +79,7 @@ std::string format_detail(const StatusSnapshot& s) {
                 s.plot1_traces, s.plot1_samples, s.buffer_mb, s.span_s,
                 static_cast<unsigned long long>(s.time_stride));
   std::string out = buf;
+  if (s.paused) out += " | paused for " + format_elapsed(s.paused_for_s);
   if (s.trigger_on) {
     out += s.have_event ? " | last event " + format_elapsed(s.since_event_s) + " ago"
                         : " | no event yet";

src/status_text.hpp

@@ -11,9 +11,12 @@ namespace udpscope {
 /// two cannot disagree. No GTK here on purpose: this is the one part of the status bar that
 /// can be reasoned about as text.
 struct StatusSnapshot {
-  /// One word from the fixed set: "live", "paused", "armed", "capturing", "event held",
-  /// "disarmed". It is a word from a *fixed* set because the bar sits directly above the plot
-  /// and a field whose width tracked the stream would relayout it every frame.
+  /// One word from the fixed set: "connecting", "live", "paused", "armed", "capturing",
+  /// "event held", "disarmed". It is a word from a *fixed* set because the bar sits directly
+  /// above the plot and a field whose width tracked the stream would relayout it every frame --
+  /// so a word added here must be no wider than the widest already in it ("connecting" and
+  /// "event held" are both ten characters). "connecting" is the state before a CONFIG has
+  /// arrived, in which there is no signal list and so nothing any other word here can describe.
   const char* state_word = "live";
   /// The long prose the old single-line bar carried, kept for the detail string and the dump.
   std::string state_detail;
@@ -44,10 +47,20 @@ struct StatusSnapshot {
   bool have_event = false;
   double since_event_s = 0.0;
   int reconnects = 0;
+
+  /// How long the view has been frozen, in **wall** seconds, and whether it is. The producer
+  /// never stops while paused -- it keeps filling the live ring, which is what makes the resume
+  /// seamless -- so the stream's own clock says nothing about how long the user has been looking
+  /// at a still picture. Written through `format_elapsed()` like the event age, for the same
+  /// reason: it steps to a coarser unit instead of growing digits, and the bar is directly above
+  /// the plot.
+  bool paused = false;
+  double paused_for_s = 0.0;
 };
 
-/// The bar: "live · 10 kS/s · 2 s window", plus " · event 4.2 s ago" in trigger mode and
-/// nothing else ever. The badge glyph is a separate widget and is not part of this string.
+/// The bar: "live · 10 kS/s · 2 s window", plus " · event 4.2 s ago" in trigger mode, " · for
+/// 12 s" while paused, and nothing else ever. The badge glyph is a separate widget and is not
+/// part of this string.
 std::string format_glance(const StatusSnapshot& s);
 
 /// The popover's prose and the exit dump's line, field for field as the old single-line bar

src/ui.cpp

@@ -137,6 +137,12 @@ struct App {
   GtkWidget* trigger_holdoff_spin = nullptr;
   GtkWidget* signal_list = nullptr;
   GtkWidget* pause_button = nullptr;
+  /// When the pause began, on the **monotonic wall clock**, or 0 while running. The elapsed time
+  /// the status bar shows has to be wall time rather than stream time: the producer never stops
+  /// while paused (it keeps filling the live ring, which is what makes the resume seamless), so
+  /// the stream's own clock advances whether the view is frozen or not and would say nothing
+  /// about how long the user has been looking at a still picture.
+  gint64 pause_started_us = 0;
   GtkWidget* menu_button = nullptr;
   GtkWidget* cursors_toggle = nullptr;
   /// Where the panel controls ended up, decided once at build time: the dump runs after the window
@@ -198,6 +204,12 @@ struct App {
   std::vector<std::string> measure_text;
   /// The window the current results were computed over, and whether a capture was held then:
   /// a recomputation is owed when either moves (see `update_measures`).
+  ///
+  /// It is kept in **stream** seconds (through `ScopeModel::stream_at_x0()`), not in the display x
+  /// it was read as, because a live view is newest-relative: the axis there is a fixed
+  /// `[-window, 0]` whatever arrives, so "the window moved" is invisible in display coordinates
+  /// and the pane would compute once and then never again -- the readout frozen on the samples
+  /// that happened to be on screen when the pane opened.
   plot::Range measure_window{};
   bool measure_window_valid = false;
   bool measure_was_held = false;
@@ -245,13 +257,30 @@ struct App {
   std::vector<MeasureResult> measure_last_valid;
   /// The marks the last computation produced: re-placed every frame, which is what makes the
   /// measurement cursors read-only.
+  ///
+  /// A **time** mark's `value` is held in stream seconds, like `measure_window`, and converted to
+  /// the axis' own x by `place_measure_marks()` on the frame it is placed. That is what keeps a
+  /// mark glued to the sample it measured while a live view rolls the data leftwards under it --
+  /// a mark is a *result*, so it travels with its datum, which is the opposite of a cursor (an
+  /// instrument the user put at a position and that stays there). A level mark's `value` is a y
+  /// and has nothing to do with either clock.
   std::vector<RowSet::MeasureMark> measure_marks;
+  /// `measure_marks` with the time marks converted to display x, rebuilt in place each frame
+  /// rather than allocated: this is on the frame tick's path.
+  std::vector<RowSet::MeasureMark> measure_marks_display;
   /// What the dump prints for the header and the panels. Captured while the window is alive:
   /// the dump runs from the destroy handler, where every widget call is a GTK-CRITICAL and
   /// reads nothing.
   int dbg_win_btn_w = -1;
   int dbg_win_label_w = -1;
   int dbg_bar_w = -1;
+  /// The measurements pane's allocation, for the same reason and more urgently: the dump used
+  /// to ask the widget itself, which is where the two documented `Gtk-CRITICAL`s came from --
+  /// and a critical is the lucky outcome. The pointer is freed memory by then, so a run that
+  /// built and destroyed other windows first (`UDPSCOPE_PROBE_HELP_MS`, three of them) has had
+  /// that memory reused and the read is a **SIGSEGV** in the middle of the dump.
+  int dbg_measures_pane_w = -1;
+  int dbg_measures_pane_h = -1;
   bool measures_revealed = false;
   /// The measurement dialog while one is open (null otherwise). A probe needs a handle on it:
   /// it is a window of its own, so the main window's widget tree does not reach its buttons.
@@ -282,6 +311,9 @@ struct App {
   unsigned signal_generation = ~0u;
   bool updating_panels = false;  ///< guards signal handlers during a rebuild
   bool relayout_pending = false;
+  /// True once the renderer's `Style` has been stated (see `tick()`): the renderer does not
+  /// exist until the area is realized, so the one-shot has to be a tick's job.
+  bool style_stated = false;
   bool signals_panel_initialised = false;
   /// Set once the user edits the trigger level, so the panel stops defaulting it
   /// into the middle of the declared range.
@@ -382,6 +414,17 @@ struct App {
   std::uint64_t dbg_visible_max = 0;
   int dbg_raw_frames = 0;
   int dbg_lod_frames = 0;
+  /// Frames on which at least one trace's geometry was reduced onto the pixel grid (one
+  /// vertical segment per column). It is orthogonal to `raw`/`lod` on purpose -- the
+  /// reduction is gated on the *density* of the gathered points, not on which level
+  /// produced them -- and it is the only reading that distinguishes "the segment count
+  /// collapsed because the reduction ran" from "the window got narrower".
+  int dbg_column_frames = 0;
+  /// Frames on which at least one reduced column was drawn **graded by dwell** rather than
+  /// as one flat band (`Style::intensity_grading`, which this app turns on). A subset of
+  /// `columns`: grading is a way of drawing the reduction, not a third path, so the two
+  /// counts being equal is what says the look is reaching every reduced frame.
+  int dbg_graded_frames = 0;
   /// Painted frames on which `draw_traces` drew **no trace at all**, and the last one's index.
   /// This is the observable for "the plot flickers as if there were no data": `staged_segments`
   /// cannot see it, because the grid and the instruments stage geometry of their own, so a frame
@@ -430,7 +473,7 @@ struct App {
   /// Frames the badge spent in each `BadgePhase`. Both `lit` and `dim` have to be non-zero
   /// over a run that acquired anything -- that is what "it blinks" means, and a badge
   /// stuck lit looks identical to a working one in a screenshot.
-  int dbg_badge_frames[3] = {0, 0, 0};
+  int dbg_badge_frames[4] = {0, 0, 0, 0};
   int dbg_reset_visible = -1;
   std::vector<std::uint64_t> last_stored;
   std::uint64_t dbg_latches_at_disarm = 0;
@@ -904,10 +947,14 @@ std::string format_window(double s) {
 
 /// What the activity badge is saying. `Lit`/`Dim` are the two halves of the blink, so
 /// the badge is only *blinking* while the pipeline is actually running; a steady badge is
-/// a stopped one, which is the state worth noticing on a glance.
-enum class BadgePhase { Lit = 0, Dim = 1, Idle = 2 };
+/// a stopped one, which is the state worth noticing on a glance. `Connecting` is the
+/// half-way state -- the socket answered but the stream has sent no CONFIG, so there is no
+/// signal list and nothing to acquire -- and it is steady yellow rather than green,
+/// because a blinking green badge over a source that has sent nothing claims a working
+/// pipeline.
+enum class BadgePhase { Lit = 0, Dim = 1, Idle = 2, Connecting = 3 };
 
-/// The badge is one glyph in one of three colours. It must stay the *same glyph*: the
+/// The badge is one glyph in one of four colours. It must stay the *same glyph*: the
 /// status row sits above the plot, and a badge that changed width as it blinked would
 /// move the label beside it and re-lay out the plot twice a second.
 const char* badge_markup(BadgePhase phase) {
@@ -916,6 +963,8 @@ const char* badge_markup(BadgePhase phase) {
       return "<span foreground=\"#45E045\">\u25CF</span>";
     case BadgePhase::Dim:
       return "<span foreground=\"#1C5A1C\">\u25CF</span>";
+    case BadgePhase::Connecting:
+      return "<span foreground=\"#E0B020\">\u25CF</span>";
     case BadgePhase::Idle:
       break;
   }
@@ -1212,6 +1261,8 @@ int on_render_probe(GtkGLArea*, GdkGLContext*, gpointer user) {
       app->dbg_seg_last = s.staged_segments;
       if (s.raw_traces > 0) ++app->dbg_raw_frames;
       if (s.lod_traces > 0) ++app->dbg_lod_frames;
+      if (s.column_traces > 0) ++app->dbg_column_frames;
+      if (s.graded_traces > 0) ++app->dbg_graded_frames;
       if (s.raw_traces > 0 || s.lod_traces > 0) check_frame_ink(*app);
       if (s.raw_traces == 0 && s.lod_traces == 0) {
         ++app->dbg_notrace_frames;
@@ -1978,8 +2029,16 @@ void on_pause_toggled(GtkToggleButton* button, gpointer user) {
     // arrived while paused instead of a hole.
     if (RowSet::Row& r0 = app->rows->row(0); r0.plot != nullptr) {
       const plot::Range view = r0.plot->x_range(r0.axis_x);
-      const double epoch = app->model->display_epoch();
-      app->model->publish_pause_view(view.min - epoch, view.max - epoch);
+      // The axis is in display x and the ring is on the stream's clock, so the window has to be
+      // put back on that clock to be cut -- `stream_at_x0()` is the one accessor that is right in
+      // every mode, including a pause taken while an event is *held*, where the axis is
+      // edge-relative and the old `- display_epoch()` form searched the ring with event
+      // coordinates. The same offset is handed to the snapshot as its `x_offset`, so its stamps
+      // come back rebased onto the x the axis is already showing and the frozen picture does not
+      // move at the instant of the pause.
+      const double s0 = app->model->stream_at_x0();
+      app->model->publish_pause_view(view.min + s0, view.max + s0, s0);
+      app->pause_started_us = g_get_monotonic_time();
       // Pin on what the snapshot *got*: the cut is clamped to the ring, so it can be narrower than
       // the view, and pinning the request left the shortfall as an empty left margin.
       plot::Range pin = view;
@@ -1994,6 +2053,7 @@ void on_pause_toggled(GtkToggleButton* button, gpointer user) {
   } else {
     app->model->clear_pause_view();
     app->rows->unpin_pause_window();
+    app->pause_started_us = 0;
   }
   gtk_button_set_icon_name(GTK_BUTTON(button), paused ? "media-playback-start-symbolic"
                                                      : "media-playback-pause-symbolic");
@@ -2016,7 +2076,12 @@ void on_trigger_toggled(GtkToggleButton* button, gpointer user) {
   app->capturing = false;
   if (!on) {
     app->model->trigger_time_valid().store(false, std::memory_order_relaxed);
-    app->model->set_display_epoch(0.0);  // back to seconds since the stream started
+    // The epoch is *not* written here: the frame tick owns it and states the live answer -- minus
+    // the newest acquired sample -- after it has bound and acquired, which is the only moment the
+    // right number is knowable. This used to set it to 0 ("seconds since the stream started"),
+    // which is no longer a display coordinate anything uses. Nothing is left stale in the
+    // meantime: the group follows the live edge again from here, and `Figure::layout()` re-derives
+    // the range from it on every frame.
     app->rows->set_time_window(app->rows->time_window());  // and follow the live edge
   }
   if (on && signal >= 0) {
@@ -2876,6 +2941,19 @@ void open_measure_dialog(App& app, int edit_index) {
   gtk_window_present(GTK_WINDOW(window));
 }
 
+/// Puts `App::measure_marks` on the plots, converting each **time** mark from the stream seconds
+/// it is stored in to the x the axis is reading this frame. Called every frame -- that is what
+/// makes the marks read-only (a gesture moves one, and this puts it back) and, since a live axis
+/// is newest-relative, also what rolls each mark leftwards with the sample it measured.
+void place_measure_marks(App& app) {
+  const double s0 = app.model->stream_at_x0();
+  app.measure_marks_display = app.measure_marks;
+  for (RowSet::MeasureMark& mk : app.measure_marks_display) {
+    if (!mk.level) mk.value -= s0;
+  }
+  app.rows->set_measure_marks(app.measure_marks_display);
+}
+
 /// Recomputes every measurement over the visible window and writes the results into the pane,
 /// collecting the marks the ones asking to be shown need.
 ///
@@ -2890,12 +2968,17 @@ void update_measures(App& app, bool force) {
   if (app.measure_labels.size() != app.measures.size()) return;  // mid-rebuild
   const RowSet::Row& r0 = app.rows->row(0);
   if (r0.plot == nullptr) return;
+  // The window on the **stream's** clock, which is the only space in which "it moved" is a
+  // question with an answer: a live axis is newest-relative, so `view` itself is a fixed
+  // `[-window, 0]` that never changes while the data under it does.
+  const double s0 = app.model->stream_at_x0();
   const plot::Range view = r0.plot->x_range(r0.axis_x);
+  const plot::Range swin{view.min + s0, view.max + s0};
   const bool held = app.model->display_mode() == DisplayMode::Held;
   const bool moved = app.measure_window_valid && !held &&
-                     std::fabs(view.min - app.measure_window.min) +
-                             std::fabs(view.max - app.measure_window.max) >
-                         0.02 * std::max(1.0e-12, view.span());
+                     std::fabs(swin.min - app.measure_window.min) +
+                             std::fabs(swin.max - app.measure_window.max) >
+                         0.02 * std::max(1.0e-12, swin.span());
   // A measurement is a statistic of the visible window, and *a live view moves that window every
   // frame* -- so "recompute when the window moves" is "recompute every frame", at O(visible
   // samples) per measurement. That is what stalled the frame tick (0.4 ms -> 13.7 ms, a third of
@@ -2918,16 +3001,16 @@ void update_measures(App& app, bool force) {
   // lag on it is not readable.
   const bool changed = !app.measure_window_valid || held != app.measure_was_held || moved;
   if (!force && !changed) {
-    app.rows->set_measure_marks(app.measure_marks);
+    place_measure_marks(app);
     return;
   }
   if (!force && moved && held == app.measure_was_held && !due) {
     // Nothing to recompute -- but the marks are still re-placed below, which is what makes
     // them read-only: a gesture moves one on the plot, and this is what puts it back.
-    app.rows->set_measure_marks(app.measure_marks);
+    place_measure_marks(app);
     return;
   }
-  app.measure_window = view;
+  app.measure_window = swin;
   app.measure_window_valid = true;
   app.measure_was_held = held;
   app.measure_stamp_us = now_us;
@@ -3042,7 +3125,10 @@ void update_measures(App& app, bool force) {
     if (w.ok && !w.pct.empty()) {
       w.level.assign(w.pct.size(), MeasureLevel{});
       for (std::size_t k = 0; k < w.pct.size(); ++k) {
-        w.level[k].level = w.stats.lo + w.pct[k] * (w.stats.hi - w.stats.lo);
+        // The level *and* its hysteresis band, in the engine: how wide the band is is a property of
+        // how an edge is counted, not of the pane, and two expressions for it is how the walk and
+        // the bucket fast path end up disagreeing about where a crossing was.
+        measure_set_level(w.level[k], w.stats, w.pct[k]);
       }
       const auto accumulate = [&](const MeasureChunk& c) {
         measure_accumulate(c, time_of, w.level.data(), w.level.size());
@@ -3131,11 +3217,15 @@ void update_measures(App& app, bool force) {
     const plot::u32 color = measure_color(i);
     for (const MeasureMarkSpec& spec : mk->marks) {
       if (!spec.level && !r.valid) continue;
-      marks.push_back({row, spec.level, spec.value, color});
+      // A time mark is stored on the **stream's** clock -- the walks report display x, so `s0`
+      // puts it back -- and `place_measure_marks()` converts it again on every frame it draws.
+      // That is what keeps the mark on its own sample as a live view rolls underneath it; a level
+      // mark is a y and is stored as it comes.
+      marks.push_back({row, spec.level, spec.level ? spec.value : spec.value + s0, color});
     }
   }
   app.measure_marks = std::move(marks);
-  app.rows->set_measure_marks(app.measure_marks);
+  place_measure_marks(app);
 }
 
 /// The measurements panel: a header with the `[+]`, and one row per measurement.
@@ -4794,6 +4884,22 @@ gboolean tick(gpointer user) {
     }
   }
 
+  // The trace look, stated on the first tick that finds a renderer -- there is none until
+  // the area is realized, and this is the same "claim it when it exists" shape as the frame
+  // clock above. `intensity_grading` is off in the library by default (it is a change of
+  // look, not a correction, and other hosts must not be restyled by an upgrade); an
+  // oscilloscope is exactly the host it is for, so udpscope turns it on. A one-shot rather
+  // than a per-frame write because `Style` is plain data and nothing else touches it.
+  if (!app->style_stated && app->area != nullptr) {
+    if (plot::Renderer* r = app->area->renderer()) {
+      // `UDPSCOPE_NO_PHOSPHOR` puts it back to the library's default, which is the only way
+      // to read `frame cost:` and `frame path:` against the ungraded path -- a frame mean
+      // cannot attribute its own cost, so the A/B is the measurement.
+      r->style().intensity_grading = g_getenv("UDPSCOPE_NO_PHOSPHOR") == nullptr;
+      app->style_stated = true;
+    }
+  }
+
   if (app->relayout_pending) {
     app->relayout_pending = false;
     relayout_areas(*app);
@@ -4814,6 +4920,11 @@ gboolean tick(gpointer user) {
       std::fflush(stderr);
     }
   }
+  // Captured every frame so the dump has the last live value: see `dbg_measures_pane_w`.
+  if (app->measures_list != nullptr) {
+    app->dbg_measures_pane_w = gtk_widget_get_width(app->measures_list);
+    app->dbg_measures_pane_h = gtk_widget_get_height(app->measures_list);
+  }
   if (model.generation() != app->signal_generation) rebuild_signal_panels(*app);
   // A gesture moves the *plot's* cursor; adopting it here is what makes the two
   // vertical markers one time across every row, and what the pane then reads.
@@ -4865,16 +4976,37 @@ gboolean tick(gpointer user) {
     // UI's own structural changes: the bind takes shared handles into the live
     // store, and acquire() reads it.
     std::lock_guard<std::mutex> lock(model.mutex());
-    // Mid-capture the live ring is drawn on the coming event's clock, so its edge sits at
-    // x = 0 exactly as a snapshot's does and the pinned [-pre, +post] axis means the same
-    // thing in both. Every other mode reads stream seconds. The epoch is a consumer-side
-    // offset on the live channels, so it has to be in place before the bind that hands
-    // them to the traces -- and it is written here, under the lock, because a rebuild can
-    // replace the store.
-    const double want_epoch = display == DisplayMode::Capturing ? -cap_edge : 0.0;
-    if (model.display_epoch() != want_epoch) model.set_display_epoch(want_epoch);
     app->rows->bind(model, display);
     app->rows->acquire(model);
+    // What x = 0 means, written *after* the bind and the acquire on purpose: the live answer
+    // is minus the newest sample the traces can now report, and asking before they were bound
+    // would put the newest data a frame's production to the right of the axis -- a third of
+    // the screen at 1 MS/s over a 50 ms window. The epoch is only read on the consumer side
+    // (it offsets the live channels' x), so nothing between here and the next frame's bind
+    // depends on it having been set earlier. It is written under the lock because a rebuild
+    // can replace the store it is pushed into.
+    //
+    // Three cases, one rule -- `display_x = stream_t + epoch`:
+    //  * streaming, the newest stored sample sits at x = 0, so the axis is a fixed
+    //    [-window, 0] and the data flows leftwards through it. A scope's time base is "how
+    //    long ago", and the stream's own clock is an uptime nobody reads off an axis.
+    //  * mid-capture, the coming event's edge sits at x = 0 exactly as the published
+    //    snapshot's will, so the pinned [-pre, +post] means the same thing in both and the
+    //    picture does not jump at the latch.
+    //  * with a *snapshot* on screen (a held event, a paused view) the live channels are
+    //    bound to nothing and the snapshot carries its own `x_offset`, so the epoch is 0 and
+    //    `ScopeModel::stream_at_x0()` is what crosses between the clocks.
+    double want_epoch = 0.0;
+    if (display == DisplayMode::Capturing) {
+      want_epoch = -cap_edge;
+    } else if (model.display_snapshot() == nullptr) {
+      // `live_edge()` reports in the epoch currently in force, so subtracting it is minus the
+      // raw stamp: the fixed point is reached in one frame rather than converged on.
+      double newest = 0.0;
+      want_epoch = app->rows->live_edge(newest) ? model.display_epoch() - newest
+                                                : model.display_epoch();
+    }
+    if (model.display_epoch() != want_epoch) model.set_display_epoch(want_epoch);
   }
 
   // The gesture probe's verdicts, one frame after the ask and after this frame's clamp: a
@@ -5158,7 +5290,7 @@ gboolean tick(gpointer user) {
     if (r.plot) gutter = std::max(gutter, double(r.plot->layout().y_axis_width));
   }
   app->rows->note_y_gutter(gutter);
-  app->rows->apply_y_gutter();
+  app->rows->apply_gutters();
 
   // The editor's buttons are placed from the rects this frame was laid out with, so they
   // follow a resize and the gutter settling without being told.
@@ -5361,7 +5493,12 @@ gboolean tick(gpointer user) {
   }
   StreamStats& st = model.stats();
   const char* mode = "live";
-  if (trigger_on) {
+  if (!st.have_config.load()) {
+    // Ahead of every other branch for the reason the glance word is: with no CONFIG there is no
+    // signal list, so "live" (or "armed", which cannot happen without one) would name a pipeline
+    // that has not been described yet.
+    mode = "trying to connect: no configuration, and so no signal list, from the stream yet";
+  } else if (trigger_on) {
     if (app->capturing) {
       mode = "trigger: CAPTURING (post-trigger window filling)";
     } else if (app->event_held) {
@@ -5386,14 +5523,26 @@ gboolean tick(gpointer user) {
   // green light over a dead socket is the one reading that must not happen. The blink is
   // a 1 Hz square wave off the monotonic clock rather than its own timer, so it cannot
   // drift away from the frame it is drawn on.
+  // A source that answered CONNECT but has sent no CONFIG is *connecting*, not acquiring:
+  // there is no signal list, so nothing can be enabled and no DATA frame can arrive. It gets
+  // the steady yellow rather than the blinking green, because the green says "the pipeline is
+  // running end to end" and here it has not started.
   const bool paused = app->acq->paused();
-  const bool active = st.connected.load() && !paused && (!trigger_on || armed);
+  const bool connecting = st.connected.load() && !st.have_config.load();
+  const bool active =
+      st.connected.load() && !connecting && !paused && (!trigger_on || armed);
   const bool lit = ((g_get_monotonic_time() / (G_TIME_SPAN_SECOND / 2)) & 1) == 0;
-  const BadgePhase phase =
-      !active ? BadgePhase::Idle : (lit ? BadgePhase::Lit : BadgePhase::Dim);
-  const int reason = active ? 0 : !st.connected.load() ? 1 : paused ? 2 : 3;
+  const BadgePhase phase = connecting ? BadgePhase::Connecting
+                           : !active  ? BadgePhase::Idle
+                                      : (lit ? BadgePhase::Lit : BadgePhase::Dim);
+  const int reason = active                 ? 0
+                     : !st.connected.load() ? 1
+                     : connecting           ? 4
+                     : paused               ? 2
+                                            : 3;
   static const char* const kWhy[] = {"acquiring", "waiting for the stream", "paused",
-                                     "trigger disarmed"};
+                                     "trigger disarmed",
+                                     "trying to connect: no configuration from the stream yet"};
   // Keyed on the reason as well as the phase: three of the reasons share the Idle phase,
   // so a pause that becomes a disarm has to reach the tooltip.
   ++app->dbg_badge_frames[static_cast<int>(phase)];
@@ -5430,8 +5579,16 @@ gboolean tick(gpointer user) {
 
   // Derive the one-word state for the glance line from the same conditions the mode prose
   // branches on, so the two cannot disagree.
+  //
+  // `connecting` is first and covers both halves of the handshake -- no socket yet, and a
+  // socket with no CONFIG behind it -- because in neither is there a signal list, and every
+  // other word here claims one. The badge is what distinguishes them (grey against yellow):
+  // the word says what the app is doing, the colour says how far it got. It is no wider than
+  // `event held`, which is what lets it join a set the plot's layout is measured against.
   const char* state_word = "live";
-  if (display == DisplayMode::Capturing) {
+  if (!st.have_config.load()) {
+    state_word = "connecting";
+  } else if (display == DisplayMode::Capturing) {
     state_word = "capturing";
   } else if (display == DisplayMode::Held) {
     state_word = "event held";
@@ -5468,6 +5625,12 @@ gboolean tick(gpointer user) {
                            ? double(g_get_monotonic_time() - app->last_latch_us) / 1.0e6
                            : 0.0;
   snap.reconnects = static_cast<int>(st.reconnects.load(std::memory_order_relaxed));
+  // Paused *and* with a recorded start: the button's handler is what stamps it, so a pause
+  // arriving any other way (there is none today) reports the state without a duration rather
+  // than counting from the epoch.
+  snap.paused = paused && app->pause_started_us != 0;
+  snap.paused_for_s =
+      snap.paused ? double(g_get_monotonic_time() - app->pause_started_us) / 1.0e6 : 0.0;
 
   const std::string glance = udpscope::format_glance(snap);
   app->dbg_glance_last = glance;
@@ -5600,9 +5763,6 @@ void note_starvation(App& app) {
   const std::uint64_t reconnects = st.reconnects.load(std::memory_order_relaxed);
   const bool connected = st.connected.load(std::memory_order_relaxed);
 
-  // No `have_config` here: the losing client of a single-client source need never see a
-  // CONFIG at all (the server answered the first one), and "connected, kicked, nothing
-  // arriving" is the state worth naming either way.
   // "Connected, but nothing is arriving" is a *rate* fact, not a reconnect one: a source that
   // answers CONNECT and then goes quiet -- the unicast case where another client took the session --
   // never reconnects while it is silent, so requiring a reconnect made the notice invisible in
@@ -5621,16 +5781,28 @@ void note_starvation(App& app) {
     // stream was arriving perfectly well.
     return;
   }
+  // Two diagnoses, split on `have_config`, because they are not the same situation. A source
+  // that sent a CONFIG and then went quiet is the unicast fight: the signal list is here, so
+  // something took the stream away. One that has sent no CONFIG at all never had the stream to
+  // lose -- there is no signal list, so nothing can be enabled and no DATA frame is owed -- and
+  // naming that "connected, but no data is arriving" blamed a second reader that does not exist.
+  // It is still the same stall test: a CONFIG that arrives promptly leaves no notice at all.
+  const bool have_config = st.have_config.load(std::memory_order_relaxed);
   app.notice =
-      "connected, but no data is arriving: another reader may hold the source (a unicast "
-      "source serves one client at a time) -- use --multicast to watch from several UIs";
+      have_config
+          ? "connected, but no data is arriving: another reader may hold the source (a unicast "
+            "source serves one client at a time) -- use --multicast to watch from several UIs"
+          : "trying to connect: the source answered, but has sent no configuration, so there is "
+            "no signal list yet -- check that the streamer is running and serving this port";
   app.notice_until_us = g_get_monotonic_time() + 3 * G_TIME_SPAN_SECOND;
   if (!app.starve_reported) {
     app.starve_reported = true;
     std::fprintf(stderr,
-                 "[udpscope] starved: connected (config=%d), reconnects=%llu, no new frames "
-                 "in the last second -- a unicast source serves one client at a time\n",
-                 st.have_config.load(std::memory_order_relaxed) ? 1 : 0,
+                 have_config
+                     ? "[udpscope] starved: connected (config=1), reconnects=%llu, no new frames "
+                       "in the last second -- a unicast source serves one client at a time\n"
+                     : "[udpscope] connecting: connected (config=0), reconnects=%llu, no "
+                       "configuration from the stream -- there is no signal list to acquire\n",
                  static_cast<unsigned long long>(reconnects));
     std::fflush(stderr);
   }
@@ -6625,8 +6797,11 @@ gboolean measure_trace(gpointer user) {
     line += " " + std::string(measure_type_name(a->measures[i].type)) + "=" +
             (r.valid ? std::to_string(r.primary) : std::string("--"));
   }
-  line += " marks=" + std::to_string(a->measure_marks.size());
-  for (const RowSet::MeasureMark& m : a->measure_marks) {
+  // The marks as *placed*, not as stored: a time mark is kept on the stream's clock and converted
+  // for the axis each frame (see `place_measure_marks()`), and it is the converted value that is
+  // comparable with the `view=` printed beside it.
+  line += " marks=" + std::to_string(a->measure_marks_display.size());
+  for (const RowSet::MeasureMark& m : a->measure_marks_display) {
     line += " " + std::string(m.level ? "level" : "time") + ":" + std::to_string(m.value);
   }
   std::fprintf(stderr, "%s\n", line.c_str());
@@ -7039,11 +7214,14 @@ void pause_probe_report(App& a, const char* what) {
     const RowSet::Row& r0 = a.rows->row(0);
     axis = r0.plot->x_range(r0.axis_x);
   }
+  // The bar's own string, because "how long have I been paused" is a *status* field and the
+  // elapsed figure is the one part of it that no other line can show: the exit dump's
+  // `status bar:` is read live and the two `mode ...` lines are the live and triggered states.
   std::fprintf(stderr,
                "[pause-probe] %-9s paused=%d ring_produced=%zu event_size=%zu "
-               "frozen_x=[%.6f..%.6f] axis=[%.6f..%.6f]\n",
+               "frozen_x=[%.6f..%.6f] axis=[%.6f..%.6f] glance=[%s]\n",
                what, a.model->paused() ? 1 : 0, ring_produced, event_size, bounds_lo, bounds_hi,
-               double(axis.min), double(axis.max));
+               double(axis.min), double(axis.max), a.dbg_glance_last.c_str());
   std::fflush(stderr);
 }
 
@@ -7115,13 +7293,13 @@ gboolean export_probe(gpointer user) {
   const ExportTable table = collect_export(*a->model, *a->rows);
   std::fprintf(stderr,
                "[export-probe] mode=%s axis=[%.6f..%.6f] rows=%zu cols=%zu time=[%.6f..%.6f] "
-               "stream=[%.6f..%.6f]\n",
+               "abs=[%.6f..%.6f]\n",
                a->model->trigger_enabled() && a->model->event() != nullptr ? "event" : "live",
                axis.min, axis.max, table.rows(), table.columns.size(),
                table.rows() != 0 ? table.time.front() : 0.0,
                table.rows() != 0 ? table.time.back() : 0.0,
-               table.rows() != 0 ? table.stream_time.front() : 0.0,
-               table.rows() != 0 ? table.stream_time.back() : 0.0);
+               table.rows() != 0 ? table.abs_seconds.front() : 0.0,
+               table.rows() != 0 ? table.abs_seconds.back() : 0.0);
   for (const ExportTable::Column& col : table.columns) {
     std::fprintf(stderr, "[export-probe] column '%s' n=%zu\n", col.name.c_str(), col.values.size());
   }
@@ -7587,10 +7765,13 @@ gboolean measures_probe_step(gpointer user) {
       // A gesture on a measurement's own cursor, placed through the plot exactly as the
       // controller would: the next frame has to put it back, which is what "read-only" means
       // here (the library has no flag the hit test would respect).
-      if (!a->measure_marks.empty()) {
+      // The marks as *placed* throughout: the drag writes a plot cursor and the check below reads
+      // one back, so both sides have to be in the plot's own coordinates -- and a time mark is
+      // stored on the stream's clock (see `place_measure_marks()`).
+      if (!a->measure_marks_display.empty()) {
         RowSet::Row& r0 = a->rows->row(0);
         if (r0.plot != nullptr) {
-          const RowSet::MeasureMark& mk = a->measure_marks.front();
+          const RowSet::MeasureMark& mk = a->measure_marks_display.front();
           if (mk.level) {
             r0.plot->set_cursor_y(r0.measure_h[0], mk.value + 3.0, plot::CursorPlacement::Free);
           } else {
@@ -7603,9 +7784,13 @@ gboolean measures_probe_step(gpointer user) {
     default: {
       double restored = -1.0;
       double want = 0.0;
-      if (!a->measure_marks.empty()) {
+      // Both read *now*: a time mark rolls leftwards with its sample on a live axis, so the value
+      // placed on the most recent frame is the only one the plot's cursor can be expected to hold
+      // -- comparing against the value the drag was launched from would read 300 ms of scroll as a
+      // failure to restore.
+      if (!a->measure_marks_display.empty()) {
         const RowSet::Row& r0 = a->rows->row(0);
-        const RowSet::MeasureMark& mk = a->measure_marks.front();
+        const RowSet::MeasureMark& mk = a->measure_marks_display.front();
         want = mk.value;
         if (r0.plot != nullptr) {
           restored = mk.level ? r0.plot->cursor(r0.measure_h[0]).y
@@ -7614,7 +7799,7 @@ gboolean measures_probe_step(gpointer user) {
       }
       std::fprintf(stderr,
                    "[measures-probe] %-14s marks=%zu first=%.6f plot_now=%.6f restored=%d\n",
-                   "after drag", a->measure_marks.size(), want, restored,
+                   "after drag", a->measure_marks_display.size(), want, restored,
                    std::fabs(restored - want) < 1.0e-9 ? 1 : 0);
       std::fflush(stderr);
       measure_dialog_report(*a, "final");
@@ -8062,9 +8247,10 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
                 app.dbg_draw_ms_max, app.dbg_draw_max_frame,
                 app.dbg_paint_n > 0 ? app.dbg_paint_ms_sum / app.dbg_paint_n : 0.0,
                 app.dbg_paint_ms_max, app.dbg_paint_n);
-    std::printf("[udpscope]   frame path: raw=%d lod=%d frames, segments %llu/%u "
-                "(mean/max), visible max %llu samples\n",
-                app.dbg_raw_frames, app.dbg_lod_frames,
+    std::printf("[udpscope]   frame path: raw=%d lod=%d columns=%d graded=%d frames, segments "
+                "%llu/%u (mean/max), visible max %llu samples\n",
+                app.dbg_raw_frames, app.dbg_lod_frames, app.dbg_column_frames,
+                app.dbg_graded_frames,
                 static_cast<unsigned long long>(app.dbg_paint_n > 0
                                                     ? app.dbg_seg_sum / app.dbg_paint_n
                                                     : 0),
@@ -8197,6 +8383,28 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
                     per_slot * static_cast<double>(app.model->math_slots()) / 1.0e6);
       }
     }
+    // What freezing a view costs, counted apart for the two publishes because they stall opposite
+    // threads (see `ScopeModel::publish_event_count()`). This is the figure a second live ring would
+    // buy: freezing a whole `BufferStore` copies nothing and inherits the pyramid the producer
+    // already maintains, so both `worst` figures would be 0 -- at a second budget's worth of memory
+    // and a second per-sample write on the producer. Read `event worst` against `frame cost:`'s
+    // `tick` max (the same stall, seen from the UI) and `pause worst` against `gaps`.
+    {
+      const auto ev = app.model->publish_event_count();
+      const auto pa = app.model->publish_pause_count();
+      std::printf("[udpscope]   publish cost: %llu events, %.2f/%.2f ms (mean/worst, blocks the UI);"
+                  " %llu pauses, %.2f/%.2f ms (mean/worst, blocks the producer)\n",
+                  static_cast<unsigned long long>(ev),
+                  ev > 0 ? static_cast<double>(app.model->publish_event_us_total()) /
+                               static_cast<double>(ev) / 1000.0
+                         : 0.0,
+                  static_cast<double>(app.model->publish_event_us_worst()) / 1000.0,
+                  static_cast<unsigned long long>(pa),
+                  pa > 0 ? static_cast<double>(app.model->publish_pause_us_total()) /
+                               static_cast<double>(pa) / 1000.0
+                         : 0.0,
+                  static_cast<double>(app.model->publish_pause_us_worst()) / 1000.0);
+    }
     // Unconditional, unlike the pane's own lines below: this is about the instruments the app
     // *created*, which exist whether or not any measurement was added.
     std::printf("[udpscope]   readout instruments locked: %d (trigger marker + measurement marks)\n",
@@ -8244,8 +8452,9 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
                         : 0.0);
       }
     }
-    std::printf("[udpscope]   badge frames: lit=%d dim=%d idle=%d\n", app.dbg_badge_frames[0],
-                app.dbg_badge_frames[1], app.dbg_badge_frames[2]);
+    std::printf("[udpscope]   badge frames: lit=%d dim=%d idle=%d connecting=%d\n",
+                app.dbg_badge_frames[0], app.dbg_badge_frames[1], app.dbg_badge_frames[2],
+                app.dbg_badge_frames[3]);
     std::printf("[udpscope]   trigger panel revealed before the probe toggled it: %d; "
                 "signal list items=%d selected=%d; column visible after sidebar "
                 "toggle off=%d\n",
@@ -8384,8 +8593,13 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
       // `results_for` is the window the numbers describe, `win` the one on screen now: the
       // drift between them is the assertion that a measurement is a statistic of the *current*
       // window -- a timer-decoupled recomputation is what used to leave a marker outside it.
+      // Both on the **stream's** clock, which is the space `measure_window` and the time marks
+      // are stored in: a live axis is a fixed `[-window, 0]`, so comparing display x would read
+      // no drift whatever the data did (see `App::measure_window`).
+      const double s0 = model.stream_at_x0();
       const RowSet::Row& r0 = rows.row(0);
-      const plot::Range win = r0.plot != nullptr ? r0.plot->x_range(r0.axis_x) : plot::Range{};
+      const plot::Range view = r0.plot != nullptr ? r0.plot->x_range(r0.axis_x) : plot::Range{};
+      const plot::Range win{view.min + s0, view.max + s0};
       const double span = app.measure_window.span();
       int in_window = 0;
       int marks = 0;
@@ -8422,8 +8636,7 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
                   "pane_w=%d pane_h=%d\n",
                   app.measures.size(), app.measures_revealed ? 1 : 0,
                   rows.measure_marks_placed(), app.measure_labels.size(),
-                  app.measures_list != nullptr ? gtk_widget_get_width(app.measures_list) : -1,
-                  app.measures_list != nullptr ? gtk_widget_get_height(app.measures_list) : -1);
+                  app.dbg_measures_pane_w, app.dbg_measures_pane_h);
     }
     std::printf("[udpscope]   header: window_button_w=%d window_label_w=%d (bar_w=%d)\n",
                 app.dbg_win_btn_w, app.dbg_win_label_w, app.dbg_bar_w);

tools/mock_udpstreamer.py

@@ -55,8 +55,9 @@ def build_config(rate, time_mode=TIME_FULL_ARRAY, unit="V"):
         # The stream's clock: referenced by every data signal, so udpscope treats
         # it as the time base rather than a plottable channel. Its *own* time_mode
         # is what udpscope switches on, so `--time-mode first` has to land here.
-        signal_desc("time", rate=0.0, time_mode=time_mode,
-                    time_idx=NO_TIME_SIGNAL, unit="s"),
+        signal_desc(
+            "time", rate=0.0, time_mode=time_mode, time_idx=NO_TIME_SIGNAL, unit="s"
+        ),
         signal_desc("sine", rate=rate, time_mode=time_mode, time_idx=0, unit=unit),
         signal_desc("square", rate=rate, time_mode=time_mode, time_idx=0, unit=unit),
         signal_desc("ramp", rate=rate, time_mode=time_mode, time_idx=0, unit=unit),
@@ -66,10 +67,25 @@ def build_config(rate, time_mode=TIME_FULL_ARRAY, unit="V"):
     return header(PKT_CONFIG, 0, len(payload)) + payload
 
 
-def build_data(counter, t0, dt, batch, freq, time_mode=TIME_FULL_ARRAY):
+def build_data(counter, t0, dt, batch, freq, time_mode=TIME_FULL_ARRAY, noise=0.0):
     stamps = [t0 + i * dt for i in range(batch)]
-    sine = [math.sin(2.0 * math.pi * freq * t) for t in stamps]
-    square = [1.0 if math.sin(2.0 * math.pi * freq * 0.5 * t) >= 0.0 else -1.0 for t in stamps]
+    # The interferer is a tone at 100x the fundamental with a randomly scaled amplitude, which
+    # is the shape that is hardest on anything counting crossings: near the sine's own mid level
+    # the fundamental's slope is 2*pi*f while the interferer's is 100x that, so the signal
+    # recrosses the level several times per true crossing. `--noise 0` is the ideal waveform, and
+    # it is the default because the documented probe assertions are *exact* (`peak to peak=2`,
+    # `top=0.636620`) and any interferer moves the extremes.
+    if noise > 0.0:
+        sine = [
+            math.sin(2.0 * math.pi * freq * t)
+            + random.random() * noise * math.sin(2.0 * math.pi * 100.0 * freq * t)
+            for t in stamps
+        ]
+    else:
+        sine = [math.sin(2.0 * math.pi * freq * t) for t in stamps]
+    square = [
+        1.0 if math.sin(2.0 * math.pi * freq * 0.5 * t) >= 0.0 else -1.0 for t in stamps
+    ]
     ramp = [(freq * t) % 1.0 * 2.0 - 1.0 for t in stamps]
     # In FIRST_SAMPLE mode only element 0 of the time signal is meaningful: the producer
     # stamps the first sample of the batch and says nothing about the rest. A scalar
@@ -90,30 +106,58 @@ def main():
     ap.add_argument("--batch", type=int, default=100, help="samples per packet")
     ap.add_argument("--freq", type=float, default=5.0, help="waveform frequency, Hz")
     ap.add_argument("--duration", type=float, default=0.0, help="0 = forever")
-    ap.add_argument("--stream-scale", type=float, default=1.0,
-                    help="stream seconds per wall second: 0.1 mimics a producer whose own "
-                         "clock advances ten times slower than the wire delivers samples")
-    ap.add_argument("--declared-rate", type=float, default=-1.0,
-                    help="sampling_rate to put in CONFIG; -1 = the real rate, 0 = 'unknown'")
-    ap.add_argument("--time-mode", choices=("full", "first"), default="full",
-                    help="how the stream carries its clock: 'full' stamps every sample "
-                         "(UDPS_TIME_FULL_ARRAY), 'first' stamps only the batch's first "
-                         "sample (UDPS_TIME_FIRST_SAMPLE) and leaves the viewer to space the "
-                         "rest by the declared cadence -- the shape a real MARTe2-style "
-                         "producer with a single u64 clock has")
-    ap.add_argument("--unit", default="V",
-                    help="the unit the data signals declare in CONFIG; '' declares none, which "
-                         "is an ordinary stream (and what every math channel looks like) and is "
-                         "the only way a probe can see the unitless readout formatting")
-    ap.add_argument("--clock-jitter", type=float, default=0.0,
-                    help="per-packet stamp jitter, as a fraction of one packet's span: a device "
-                         "that stamps each batch from its own clock does not land on a perfect "
-                         "grid, so the stream's timestamps wobble about one. Non-cumulative "
-                         "(the mean rate is unchanged); 0 = the ideal grid")
+    ap.add_argument(
+        "--stream-scale",
+        type=float,
+        default=1.0,
+        help="stream seconds per wall second: 0.1 mimics a producer whose own "
+        "clock advances ten times slower than the wire delivers samples",
+    )
+    ap.add_argument(
+        "--declared-rate",
+        type=float,
+        default=-1.0,
+        help="sampling_rate to put in CONFIG; -1 = the real rate, 0 = 'unknown'",
+    )
+    ap.add_argument(
+        "--time-mode",
+        choices=("full", "first"),
+        default="full",
+        help="how the stream carries its clock: 'full' stamps every sample "
+        "(UDPS_TIME_FULL_ARRAY), 'first' stamps only the batch's first "
+        "sample (UDPS_TIME_FIRST_SAMPLE) and leaves the viewer to space the "
+        "rest by the declared cadence -- the shape a real MARTe2-style "
+        "producer with a single u64 clock has",
+    )
+    ap.add_argument(
+        "--unit",
+        default="V",
+        help="the unit the data signals declare in CONFIG; '' declares none, which "
+        "is an ordinary stream (and what every math channel looks like) and is "
+        "the only way a probe can see the unitless readout formatting",
+    )
+    ap.add_argument(
+        "--noise",
+        type=float,
+        default=0.0,
+        help="amplitude of an interferer added to `sine`: a tone at 100x the fundamental, "
+        "scaled by a fresh uniform random factor per sample. 0 = the ideal sine, which is "
+        "what the exact probe assertions (peak to peak = 2, top = 2/pi) are read against; "
+        "0.1 is the figure the measurement hysteresis is sized against",
+    )
+    ap.add_argument(
+        "--clock-jitter",
+        type=float,
+        default=0.0,
+        help="per-packet stamp jitter, as a fraction of one packet's span: a device "
+        "that stamps each batch from its own clock does not land on a perfect "
+        "grid, so the stream's timestamps wobble about one. Non-cumulative "
+        "(the mean rate is unchanged); 0 = the ideal grid",
+    )
     args = ap.parse_args()
 
-    dt = args.stream_scale / args.rate          # stream seconds per sample
-    period = args.batch / args.rate             # wall seconds per packet
+    dt = args.stream_scale / args.rate  # stream seconds per sample
+    period = args.batch / args.rate  # wall seconds per packet
     declared = args.rate if args.declared_rate < 0.0 else args.declared_rate
     time_mode = TIME_FIRST_SAMPLE if args.time_mode == "first" else TIME_FULL_ARRAY
 
@@ -121,9 +165,19 @@ def main():
     sock.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)
     sock.bind(("0.0.0.0", args.port))
     sock.settimeout(0.001)
-    print("mock udpstreamer: waiting for CONNECT on :%d (%.0f S/s wire, %d per packet, "
-          "stream clock x%.3g, declared %.0f S/s, time-mode %s)"
-          % (args.port, args.rate, args.batch, args.stream_scale, declared, args.time_mode), flush=True)
+    print(
+        "mock udpstreamer: waiting for CONNECT on :%d (%.0f S/s wire, %d per packet, "
+        "stream clock x%.3g, declared %.0f S/s, time-mode %s)"
+        % (
+            args.port,
+            args.rate,
+            args.batch,
+            args.stream_scale,
+            declared,
+            args.time_mode,
+        ),
+        flush=True,
+    )
 
     peer = None
     counter = 1
@@ -143,7 +197,10 @@ def main():
                     started = time.monotonic()
                     next_send = started
                     sock.sendto(build_config(declared, time_mode, args.unit), peer)
-                    print("mock udpstreamer: CONNECT from %s:%d, CONFIG sent" % peer, flush=True)
+                    print(
+                        "mock udpstreamer: CONNECT from %s:%d, CONFIG sent" % peer,
+                        flush=True,
+                    )
                 elif magic == MAGIC and ptype == PKT_DISCONNECT:
                     print("mock udpstreamer: DISCONNECT", flush=True)
                     peer = None
@@ -166,11 +223,20 @@ def main():
         pdt = dt
         if args.clock_jitter > 0.0:
             pdt = dt * (1.0 + random.uniform(-args.clock_jitter, args.clock_jitter))
-        sock.sendto(build_data(counter, t_stream, pdt, args.batch, args.freq, time_mode), peer)
+        sock.sendto(
+            build_data(
+                counter, t_stream, pdt, args.batch, args.freq, time_mode, args.noise
+            ),
+            peer,
+        )
         counter += 1
         t_stream += args.batch * pdt
         next_send += period
-        if args.duration > 0.0 and started is not None and now - started > args.duration:
+        if (
+            args.duration > 0.0
+            and started is not None
+            and now - started > args.duration
+        ):
             print("mock udpstreamer: done (%d packets)" % counter, flush=True)
             return