fix: a zoomed trace is drawn on the x its readout quotes

gather() staged x as f32 relative to the series' own x0() -- the start of
the whole retained window -- so the quantisation was a fraction of the
ring rather than of the view: 1.9 us at 20 s of retained data, which at a
10 us view across a 716 px axis is over 100 px between where a sample is
drawn and the x a readout quotes for it (crosshair_point() reads x_at()
in exact f64). It halved on every zoom out, which is what made it read as
"zooming in makes the crosshair select a point beside the data".

The origin is now the caller's (plotter c2c8c59): the renderer passes the
visible range's minimum, so the error is a fixed 2^-24 of what is on
screen -- about 4e-5 px over a 700 px axis -- at any zoom. The parameter
sits before out_xy so every call site is a compile error rather than a
silent change of behaviour.

The renderer no longer reads series.x0() at paint time at all, which
removes two of the three symptoms of the torn window_x0_ read by
construction; the ink probe's now-vacuous kept_fixed_x0 walk goes with
them, replaced by a drawn-vs-quoted pixel figure. neighbours() still
tests the visible range against x_at(0), so the cache stays load-bearing.

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

CLAUDE.md

@@ -435,20 +435,31 @@ Two lines of the self-check output are assertions in disguise:
   *not* every channel, and never a stream's timestamp signal, which is what an acquired-but-
   unplotted list put first and auto-selected), and `drop_h` must be a combo box's height
   (tens of pixels — a scrolled-window wrapper asked it to grow to 160).
-- `[timelabels-probe] <action> relative=D window=.. origin=.. note=[..] ticks=[..]
-  first_value=.. first_rel=.. range=[..]` + the dump's `time labels: relative=D origin=..
-  note=[..] x_origin_set=.. ticks=[..] first_rel=..` (stderr,
+- `[timelabels-probe] <action> relative=D distinct=D window=.. origin=.. note=[..] ticks=[..]
+  first_value=.. first_rel=.. range=[..]` + the dump's `time labels: relative=D distinct=D
+  origin=.. note=[..] x_origin_set=.. ticks=[..] first_rel=..` (stderr,
   `UDPSCOPE_PROBE_TIMELABELS_MS`) — the x label form across a zoom, driven through
   `apply_time_window()`: **under the figure's x link group the group owns the window, so a
   row-level `set_time_window()` does nothing** (a probe that changes the window must use the
-  app's path). Absolute at 2 s and at 500 ms, `relative=1` below a second, and the caption
-  must be non-empty exactly then. The probe *races the paint* — it reads the axis on a timer,
+  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
+  `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
+  position the axis exists to show. The probe *races the paint* — it reads the axis on a timer,
   and the ticks it sees are the previous layout's — so its `first_rel` (the first major minus
   the axis' origin) is a fraction of a step; the dump runs after the last paint and is the
   race-free reading. Either way the assertion that matters is the *sum*: `first_value` must
   equal `origin + first_rel` as a *tick label* plus its caption, i.e. the labels and the
   caption must share one anchor. `x_origin_set` is read back out of the plot; it must be 0 in
-  the absolute form.
+  the absolute form. Note the last two steps both report `window=0.05`: `RowSet::set_time_window()`
+  floors the window there, so the 20 ms step is clamped.
 - `[fit-probe] <action> pinned=D window=.. event_span=.. x=[..] span=.. y=[..]` (stderr,
   `UDPSCOPE_PROBE_FIT_MS`) — the two fits, through the **menu handlers** rather than the bare
   `RowSet` calls, because the notice and the control are the handler's half. A fit is the **undo
@@ -597,10 +608,12 @@ Two lines of the self-check output are assertions in disguise:
   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.
-- `trace ink: N paints checked, C collapsed, S staircase, H short, worst cover P%` plus a
+- `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=..
-  ink=[..] cover=..% x0=.. x_at=[..] bounds=[..] rel=[..] dx=.. kept_fixed_x0=.. drops=[..]
-  back=..` line per anomalous frame (stderr) — **`collapsed` and `staircase` must both be 0**.
+  ink=[..] cover=..% x0=.. x_at=[..] bounds=[..] rel=[..] dx=.. drops=[..]
+  back=..` line per anomalous frame (stderr) — **`collapsed` and `staircase` must both be 0**,
+  and **`drawn-vs-quoted` must stay far under a pixel** (0.0000 is what a clean run reads).
   This is the only check that can see a frame whose *waveform* vanished: `staged_segments`
   counts geometry including the grid and the instruments, and `lod_traces` counts a trace whose
   points are then collapsed, so both read healthy through the flicker. The probe runs on every
@@ -610,11 +623,22 @@ Two lines of the self-check output are assertions in disguise:
   `collapsed` is fewer than two distinct positions left (nothing to draw at all), `staircase`
   is the filter dropping over three quarters of the points, `short` is ink reaching under a
   quarter of the axis (reported only once the data spans the window, since a filling ring is
-  *meant* to leave its left side empty). `kept_fixed_x0` is the same filter with `x0()` hoisted
-  out of the loop: it exceeding `kept` means `x0()` moved *during* the walk. **`back` ≈ one ring
-  span is the signature** of the torn `x0()` read (see the cached-first-stamp invariant); so is
-  an `ink=` range disjoint from `axis=`, or an `idx=` covering the whole ring with `cover` far
-  over 100%. It is a race, so it needs load and a reason for long frames —
+  *meant* to leave its left side empty). `drawn-vs-quoted` is the other reading, and it is the
+  one that names a *defect of position* rather than of presence: at a raw level a gathered pair
+  **is** sample `first + k`, so the line differences where a sample is drawn
+  (`axis.min + gather[2k]`, the renderer's own reconstruction) against the x a readout quotes
+  for it (`x_at()`, exact f64) and reports the worst of them in pixels. That is the
+  gather-origin invariant below read from the screen's side; it was over a hundred pixels at a
+  deep zoom before the origin became the caller's. It is measured on the raw levels only — above
+  them a gathered point is a bucket's envelope and has no single sample to be off from — so `R`
+  is legitimately below `N`. **`back` ≈ one ring span is the signature** of the torn `x0()` read
+  (see the cached-first-stamp invariant); so is an `ink=` range disjoint from `axis=`, or an
+  `idx=` covering the whole ring with `cover` far over 100%. There was a `kept_fixed_x0` field
+  beside `kept` — the same filter with `x0()` hoisted out of the loop, since the renderer used to
+  re-read `x0()` per point and a ring-backed one advances with the producer. The origin is a
+  local of the renderer's now, so that failure mode is structurally impossible and the field is
+  gone; the `[ink]` walk and the renderer still agree because both add `axis.min`. It is a race,
+  so it needs load and a reason for long frames —
   `tools/mock_udpstreamer.py --rate 1300000 --batch 2000 --clock-jitter 0.4` with the
   measurements *and* cursors panes up:
   `UDPSCOPE_ENABLE_ALL_MS=1000 UDPSCOPE_PROBE_MEASURES_MS=2000 UDPSCOPE_PROBE_CURSORS_MS=3500
@@ -935,15 +959,32 @@ far the largest file.
   `gather()`, `x_at()`, `neighbours()` and `x_bounds()` use the real time ring.
   Nothing may walk that grid to find *which* samples a range covers — the renderer did,
   and it lost the two end segments (see the margin invariant above). `gather()` emits x
-  relative to `x0()` because absolute epoch seconds do not survive `f32`.
-- **`gather()` emits x relative to `x0()` in *every* series here**, `EventSeries`
-  included, and the renderer adds `x0()` back. An event's stamps are small (edge
-  relative, `[-pre, +post]`), so emitting them absolute does not overflow anything and
-  does not look like a bug — it just draws the whole capture `x0()` = one pre-trigger
-  window to the left of the axis. That was the "half the plot is empty / the marker sits
-  at the end of the data / nothing is drawn but the crosshair reads values" defect: the
-  crosshair reads `x_at()`, which was right all along. The probe's `data=` vs `drawn=`
-  is the guard.
+  relative to an origin because absolute epoch seconds do not survive `f32`.
+- **`gather()` emits x relative to an origin *the caller names*, in every series here**,
+  `EventSeries` included, and the consumer adds that same origin back in `f64`. Two separate
+  rules live here and both were learned from a defect.
+  (1) **It must be relative at all.** An event's stamps are small (edge relative,
+  `[-pre, +post]`), so emitting them absolute does not overflow anything and does not look
+  like a bug — it just draws the whole capture `x0()` = one pre-trigger window to the left of
+  the axis. That was the "half the plot is empty / the marker sits at the end of the data /
+  nothing is drawn but the crosshair reads values" defect: the crosshair reads `x_at()`, which
+  was right all along. `[trig-probe]`'s `data=` vs `drawn=` is the guard.
+  (2) **The origin is the *view's* minimum, not `x0()`.** `x0()` is the start of the
+  **retained window**, so the f32 had to resolve 2^-24 of the whole ring however little of it
+  was on screen: 1.9 µs over 20 s of retained data, which at a view 10 µs wide across a 716 px
+  axis is over a hundred pixels between where a sample is drawn and the x `x_at()` quotes for
+  it — and it halved on every zoom out, so it read as "zooming in makes the crosshair select a
+  point beside the data". `Renderer::draw_traces` passes `x_range.min`, making the error a fixed
+  4e-5 of a pixel at any zoom. The parameter sits **before** `out_xy` deliberately, so a call
+  site that was not thought about is a compile error rather than silent drift. A caller that has
+  no view in mind may still pass `x0()`, and `[trig-probe]`'s `drawn=`/`data=` does exactly that
+  on purpose: it reads the series' *whole* span, which is the widest relative value a gather can
+  be asked to stage. The two guards are upstream's
+  `a_gather_origin_at_the_view_keeps_a_deep_zoom_on_the_sample_it_quotes` and the
+  `trace ink:` line's `drawn-vs-quoted` figure.
+  **A probe that recomputes what the renderer gathers must pass the same origin the renderer
+  does** (`[ink]` and `[zoom-probe]` both pass the axis minimum), or its reconstruction stops
+  being the renderer's and its pixel readings mean nothing.
 - **Every series bound to a trace must carry a real `MinMaxPyramid`**, including an
   immutable one. `MinMaxPyramid::level_for()` descends to level 0 — raw samples — on a
   pyramid with no levels, whatever `n` is, so a series that answers `pyramid()` with an
@@ -999,14 +1040,19 @@ far the largest file.
   sample 0 is the ring's oldest, the very slot the producer is about to overwrite. `time_of()`
   checks the bounds and then copies, and when the producer laps the slot in between the stamp it
   returns is **one whole ring-span too new**. Everything else on a `ChannelBuffer` is read at
-  paint time with no lock, and `x0()` is the origin the renderer reconstructs every trace point
-  from (`gather[i] + series.x0()`), read both inside its increasing-suffix filter and again at
-  `stage_xy()` — so one torn read of that one slot produced three pictures, all of them "the
+  paint time with no lock, and `x0()` *was* the origin the renderer reconstructed every trace
+  point from (`gather[i] + series.x0()`), read both inside its increasing-suffix filter and again
+  at `stage_xy()` — so one torn read of that one slot produced three pictures, all of them "the
   waveform is gone while the grid and the axes stay": `neighbours()` tests against `x_at(0)` and
   refused the whole visible range (the renderer then gathered the *entire* ring at a coarse level
   and drew it off the axis — `idx=[0..8388608) level=7 cover=320%`); `x0()` changing *during* the
   filter loop dropped three quarters of the points; and `stage_xy()` shifted the finished polyline
-  a ring-span off its axis. That is the "with measurements and cursors active the plot flickers as
+  a ring-span off its axis. The gather origin is the *view's* minimum now (see the `gather()`
+  invariant), a local of the renderer's, so the second and third of those are structurally
+  impossible — but **the first is not**, `x_at(0)` is still what `neighbours()` tests the visible
+  range against, and that is the one that gathered the whole ring. The cache is load-bearing for
+  that reason; do not read the slot at paint time because two of its three symptoms are gone.
+  That is the "with measurements and cursors active the plot flickers as
   if there were no data, at no constant frequency" defect. It is **live only** (a snapshot is
   immutable, so `x0()` is constant for `Held`/`Paused`), it is a race against packet arrival so it
   is irregular, and the measurements pane makes it both likelier and larger: the pane holds
@@ -1406,6 +1452,41 @@ far the largest file.
   reasons (an event pin) call `sync_window_display()` alone, which only restates the control and
   never moves the plot — calling `apply_time_window()` there would clamp a legitimately short
   capture up to the requested window.
+- **The x labels go relative on the tick *step against the label resolution at the axis'
+  magnitude*, never on the span.** `RowSet::update_time_labels()`'s question is only ever "can
+  this step be written at this magnitude": `TickFormat::Time` carries three significant figures
+  below a minute, **whole seconds** through `m:ss`/`h:mm:ss` up to a day, and three figures of
+  days above — so the resolution is a step function of the magnitude, which `time_label_resolution()`
+  states and nothing else may re-derive. The old test was `span < 1.0` and it was wrong in both
+  directions: a 2 s window at twenty minutes of uptime reads `20:00` on every tick and stayed
+  absolute, and a **triggered** sub-second window — whose axis is already `[-25ms, +25ms]` about
+  the edge — went relative and so re-anchored its ticks *away from the trigger*, with a `t0`
+  caption that had nothing to explain. Three details hold it up. The step is read back from the
+  majors the **last layout** produced, which is not a feedback loop (a tick's value depends on the
+  range and the axis' pixel width, never on the label form) but *is* absent before the first
+  layout — and with no ticks the form must be **left alone**, because a step guessed from the span
+  would be latched by the hysteresis below. The hysteresis is a 1.05 band on *leaving* the relative
+  form. And *entering* it needs a ULP of slack (`1 - 1e-9`): a step differenced from two tick
+  values and a resolution from `pow(10, n)` differ in their last bits when they are the same
+  number, and `step == res` is a readable axis (`1.73s`, `1.74s`, `1.75s` — one in the last digit
+  is exactly enough), so the bare comparison picked a different form from one frame to the next.
+  The guard is `[timelabels-probe]`'s `distinct=1`, which asserts what the form is *for* rather
+  than which form a given window gets.
+- **The `t0 = …` caption is chrome, never an annotation.** It is `Plot::set_x_note()` (added to
+  `deps/plotter` for this), drawn by `Renderer::draw_x_note()` on the legend's own
+  `draw_readout_panel()` backplate in the bottom-left corner of the axes, in **pixels**. It was an
+  `Annotation` first, and an annotation's anchor is a *data* coordinate: the caption therefore
+  crawled across the plot under a pan and drifted under a zoom, which is what "[t0=...s] move
+  slightly around when user zoom/pan" was. Three things follow. The **text is the host's**, because
+  the caption has to name the anchor precisely enough that label + caption is the exact absolute
+  time and `format_time()` would round it to three figures (`"t0 = %.6g s"`); only the **bottom
+  row** of the figure carries one, every other row being set to `""`; and the renderer measures it
+  rather than `Plot::layout()` — it reserves no space and nothing can be picked on it, so there is
+  no rect to read back, and a caption explaining the x labels must not be able to move the layout
+  those labels were measured into. The guards are the library's
+  `the_x_note_is_chrome_that_a_pan_or_a_zoom_does_not_move` (the footprint is the pixels a frame
+  with the caption differs from one without, and a pan plus a 64× zoom must give the same box to
+  the pixel) and `[timelabels-probe]`'s `note=`, which reads `Plot::x_note()` back.
 - **`fit_x()` restores the *whole of what the view may show*, which is not always `window_s_`.**
   Live, that is the newest `window_s_` at the live edge (`set_time_window(window_s_)`, the same
   path a resume takes). Pinned — a held event, a filling capture or a paused view — it is the

README.md

@@ -74,15 +74,36 @@ so the times on the axis do not change when the pause begins. Resuming drops the
 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.
 
-**Sub-second windows read relative.** The x ticks are absolute until the window's span goes
-under a second (with a band to 1.05 s, so the form cannot flicker while a zoom is nudged), and
-relative below it: the ticks are then generated on a grid anchored at the window's left edge —
-so they read `0`, `5ms`, `10ms` instead of `12.345671s`, `12.345672s`, which three significant
-digits cannot even tell apart — and a caption names that anchor in the axes' top-left corner:
-`t0 = 12.3456 s`. The labels scale through the prefixed units the SI formatter uses — `500ms`,
-`500us`, `5us`, `5ns` — so a microsecond window reads in microseconds instead of `0.005ms`. Adding the two is the tick's absolute time. The caption is an annotation
-inside the axes rather than the axis title on purpose: its text changes with the window, and a
-title of a changing width would relayout the plot every frame. Everything a user copies out —
+**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**
+against the label's own **resolution at the axis' magnitude**: `12.345671s` and `12.345672s` are
+the same string, and there the ticks are re-anchored on a grid at the window's left edge — so
+they read `0`, `5ms`, `10ms` — with a caption naming that anchor, `t0 = 12.3456 s`. Adding the
+two is the tick's absolute time. The labels scale through the prefixed units the SI formatter
+uses — `500ms`, `500us`, `5us`, `5ns` — so a microsecond window reads in microseconds instead of
+`0.005ms`.
+
+The rule used to be the *span* alone (relative under a second, with a band to 1.05 s), and a
+span says nothing about whether a label can be written: it was wrong in **both** directions. A
+2 s window at twenty minutes of uptime is labelled `20:00` on every tick — `m:ss` carries whole
+seconds — and was left absolute and unreadable. And a **triggered** sub-second window, whose
+axis is already `[-25ms, +25ms]` about the edge, reads `-20ms`, `-10ms`, `0`, `10ms` perfectly
+well, yet was re-anchored anyway: the one position a triggered axis exists to show was displaced
+by a `t0` caption that had nothing to explain. The step is read back from the majors the last
+layout produced (a function of the range and the axis width, not of the label form, so no
+feedback loop), the magnitude is the larger of the two endpoints, and the comparison carries a
+1.05 band leaving the relative form plus a ULP of slack entering it — a step *equal* to the
+resolution is readable (`1.73s`, `1.74s`, `1.75s`: one in the last digit is exactly enough), so a
+decision taken on the last bits of two differently computed doubles picked a different form from
+one frame to the next. The caption is **chrome** — `Plot::set_x_note()`, added to the plotter for
+it, drawn on the legend's own backplate in the bottom-left corner of the axes — rather than the
+axis title or an annotation. Not the title, because its text changes with the window and a title
+of a changing width would relayout the plot every frame; not an annotation, because an
+annotation's anchor is a *data* coordinate, so the caption crawled across the plot under a pan and
+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.
 
 The anchor is taken by the *axis* on every layout (`Axis::origin_follows_range`), not written
@@ -1173,6 +1194,31 @@ those are two places. The library's hover crosshair snaps the same way and draws
 since a snapped mark lands among those dots and at their size would read as one more sample
 instead of as the answer to the question the hover asks.
 
+**A zoomed-in trace is drawn on the x its readout quotes, which needed the gather's origin to
+become the caller's.** Separately from the half-sample offset above — which is a property of
+*which datum* is quoted — there was an offset in *where the polyline was drawn*, and it grew
+with the zoom. `plot::data::Series::gather()` stages x as `f32`, which cannot hold an absolute
+epoch time, so it emits a value relative to an origin the consumer adds back in `f64`. That
+origin was fixed at `x0()`, the start of the **retained window**: the f32 then had to resolve
+2^-24 of the whole ring however little of it was on screen — 1.9 µs over 20 s of retained data
+— while a readout reads `x_at()`, exact `f64`. At a view 10 µs wide across a 716 px axis
+(14 ns a pixel) that is over a hundred pixels between the drawn sample and the x reported for
+it, and it halves with every zoom *out*, which is why it read as "zooming in makes the
+crosshair pick the wrong point".
+
+The origin is now an argument, and `Renderer::draw_traces` passes the **visible range's
+minimum** — so the quantisation is 2^-24 of the span on screen, a fixed 4e-5 of a pixel, at
+every zoom. The fix is upstream (`deps/plotter`), where the parameter was deliberately placed
+*before* the output buffer so that every one of the library's and this app's call sites was a
+compile error rather than a silent change of behaviour. One simplification fell out of it:
+`stage_xy()` took a gather origin and a draw origin, those are now always the same value, and
+the linear case hands the gathered buffer straight to the line batch with no per-point copy.
+Two guards: the library's
+`a_gather_origin_at_the_view_keeps_a_deep_zoom_on_the_sample_it_quotes`, which measures the
+error in pixels both ways (under 0.05 px with the view's minimum, over 10 px with `x0()`), and
+this app's `trace ink:` line, which now reports `worst drawn-vs-quoted P px` over the raw-level
+paints of a whole run.
+
 The readouts are a **table**: a header naming the columns, then one row per instrument —
 `| who | A | B | delta |`. The first row is the two times and their difference, and the
 rows below it are the rulers (one per row, in `horizontal`/`both`) or the traces (in

src/channel.cpp

@@ -189,7 +189,7 @@ void ChannelBuffer::raw(u64 begin, u64 end, f32* out) const {
   for (u64 i = count; i < end - begin; ++i) out[i] = 0.0f;
 }
 
-void ChannelBuffer::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void ChannelBuffer::gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                            plot::data::GatherMode mode) const {
   const u64 n = pyramid_.size();
   const u64 b = std::min(begin, n);
@@ -197,7 +197,7 @@ void ChannelBuffer::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_
   if (b >= e) return;
 
   const u64 origin = pyramid_.window_base();
-  const f64 base = x0();  // x is emitted relative to this (see the header)
+  const f64 base = x_origin;  // x is emitted relative to this (see the header)
 
   const auto emit_raw = [&](u64 from, u64 to) {
     for (u64 i = from; i < to; ++i) {
@@ -302,13 +302,13 @@ u64 SlotSeries::snap_index(f64 x) const {
   return buffer_ != nullptr ? buffer_->snap_index(x) : 0;
 }
 
-void SlotSeries::gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+void SlotSeries::gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
                         plot::data::GatherMode mode) const {
   if (event_ != nullptr) {
-    event_->gather(level, begin, end, out_xy, mode);
+    event_->gather(level, begin, end, x_origin, out_xy, mode);
     return;
   }
-  if (buffer_ != nullptr) buffer_->gather(level, begin, end, out_xy, mode);
+  if (buffer_ != nullptr) buffer_->gather(level, begin, end, x_origin, out_xy, mode);
 }
 
 void SlotSeries::copy_raw(u64 begin, u64 end, f32* out) const {

src/channel.hpp

@@ -80,9 +80,11 @@ class ChannelBuffer final : public plot::data::Series {
   plot::Range x_bounds() const override;
   plot::Range y_bounds() const override;
   const plot::data::MinMaxPyramid& pyramid() const override { return pyramid_; }
-  /// x is emitted **relative to `x0()`** (the library's contract): staging an
-  /// absolute epoch time as f32 would quantise it far coarser than a pixel.
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  /// x is emitted **relative to `x_origin`** (the library's contract): staging an
+  /// absolute epoch time as f32 would quantise it far coarser than a pixel, and
+  /// staging it relative to the whole *retained window* quantises it coarser than a
+  /// pixel of a zoomed view -- see `plot::data::Series::gather()`.
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               plot::data::GatherMode mode = plot::data::GatherMode::Envelope) const override;
 
   /// `copy_raw`, published so the retargetable trace series can forward the
@@ -109,8 +111,9 @@ class ChannelBuffer final : public plot::data::Series {
   /// slot cannot be overwritten under the read. Everything else on this object is read at
   /// *paint* time with no lock, and this one slot is the ring's oldest: the one the producer is
   /// about to overwrite. Reading it there returned a stamp a whole ring-span too new whenever
-  /// the producer lapped it between the bounds check and the copy -- and `x0()` is the origin
-  /// the renderer reconstructs every trace point from (`gather[i] + series.x0()`), so one such
+  /// the producer lapped it between the bounds check and the copy -- and `x0()` is what
+  /// `neighbours()` tests the visible range against, as well as the origin the renderer
+  /// reconstructed every trace point from before the caller named one, so one such
   /// read moved the entire polyline a ring-span off its axis (an invisible trace) or, caught
   /// inside the renderer's increasing-suffix filter, made it drop most of the points. That is
   /// the "live plot flickers as if there were no data" defect. The cached value is also the
@@ -163,7 +166,7 @@ class SlotSeries final : public plot::data::Series {
   plot::Range x_bounds() const override;
   plot::Range y_bounds() const override;
   const plot::data::MinMaxPyramid& pyramid() const override;
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               plot::data::GatherMode mode = plot::data::GatherMode::Envelope) const override;
   bool streaming() const noexcept override { return event_ == nullptr && buffer_ != nullptr; }
 

src/event_series.hpp

@@ -108,7 +108,7 @@ class EventSeries final : public plot::data::Series {
   /// Indices need no rebasing: the 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
   /// (unlike the ring, whose window slides).
-  void gather(u32 level, u64 begin, u64 end, std::vector<f32>& out_xy,
+  void gather(u32 level, u64 begin, u64 end, f64 x_origin, std::vector<f32>& out_xy,
               plot::data::GatherMode mode =
                   plot::data::GatherMode::Envelope) const override {
     if (channel_ >= snap_->values.size()) return;
@@ -118,17 +118,17 @@ class EventSeries final : public plot::data::Series {
     const u64 b = std::min(begin, n);
     const u64 e = std::min(std::max(end, b), n);
     if (b >= e) return;
-    // x **relative to x0()**, which is the library's gather contract: the renderer
-    // adds `x0()` back before mapping to the screen. Emitting the absolute stamp made
-    // it add x0 twice, so the whole capture was drawn one `x0()` -- a full
-    // pre-trigger window -- to the left of the axis it had just been measured
-    // against. The event's own stamps are small (edge-relative, so [-pre, +post]),
-    // which is why that shift looked like a plausible picture: with a 50/50 split the
-    // right half of the plot was simply empty, zooming out showed the trace ending at
-    // the x = 0 marker, and zooming in past the shift showed nothing at all while the
-    // crosshair -- which reads `x_at()`, never `gather()` -- went on reporting the
-    // right values.
-    const f64 base = x0();
+    // x **relative to `x_origin`**, which is the library's gather contract: the
+    // renderer adds that same origin back before mapping to the screen. Emitting the
+    // absolute stamp made it add an origin twice, so the whole capture was drawn one
+    // `x0()` -- a full pre-trigger window -- to the left of the axis it had just been
+    // measured against. The event's own stamps are small (edge-relative, so
+    // [-pre, +post]), which is why that shift looked like a plausible picture: with a
+    // 50/50 split the right half of the plot was simply empty, zooming out showed the
+    // trace ending at the x = 0 marker, and zooming in past the shift showed nothing
+    // at all while the crosshair -- which reads `x_at()`, never `gather()` -- went on
+    // reporting the right values.
+    const f64 base = x_origin;
     const auto rel = [&](u64 i) {
       return static_cast<f32>(stamps[static_cast<std::size_t>(i)] - base);
     };

src/plot_host.cpp

@@ -30,10 +30,23 @@ constexpr plot::u32 kRulerBColor = 0x8FA8C8u;
 /// The measurements' own colour, distinct from both cursor rulers so a readout mark cannot be
 /// mistaken for something the user placed.
 constexpr plot::u32 kMeasureColor = 0x9BE8A0u;
-/// The window-start caption's colour: quiet chrome, brighter than a grid line.
-constexpr plot::u32 kTimeNoteColor = 0xC8C8C8u;
 constexpr plot::u32 kTriggerColor = 0xFF5B5Bu;
 
+/// The smallest difference a `TickFormat::Time` label can *write* at the magnitude `t` -- what
+/// the last digit of a label at that magnitude is worth. `format_time` writes three significant
+/// figures below a minute (of the SI-prefixed mantissa under a second, of the seconds above it),
+/// whole seconds through `m:ss`/`h:mm:ss` up to a day, and three figures of days above. So the
+/// resolution is a step function of the *magnitude* and not of the span -- which is the whole
+/// reason a relative axis is ever needed, and the reason a span threshold alone gets it wrong in
+/// both directions.
+double time_label_resolution(double t) {
+  t = std::fabs(t);
+  if (!std::isfinite(t) || !(t > 0.0)) return 0.0;
+  if (t >= 86400.0) return 86400.0 * std::pow(10.0, std::floor(std::log10(t / 86400.0)) - 2.0);
+  if (t >= 60.0) return 1.0;
+  return std::pow(10.0, std::floor(std::log10(t)) - 2.0);
+}
+
 constexpr double kParked = -1.0e12;  ///< hides an instrument without removing it
 /// The measurement marks' stroke: thinner than the chrome that frames the plot (a trace is 1.5,
 /// the axis lines and the trigger marker `Style::line_width_px`), and broken, so a readout over
@@ -155,11 +168,6 @@ void RowSet::install(Row& r, int /*row_index*/, plot::Plot& p) {
     r.plot->set_cursor_stroke(r.measure_v[mi], kMeasureStrokeWidth,
                               plot::Vec2{kMeasureDashOn, kMeasureDashOff});
   }
-  // The window-start caption for the relative x labels: an annotation, hidden until the
-  // labels are relative. Inside the axes on purpose -- its text changes with the window, and
-  // an axis title of a changing width would relayout the plot every frame.
-  r.time_origin_note = r.plot->add_annotation(
-      plot::Annotation{0.0, 0.0, "", plot::Color::hex(kTimeNoteColor), r.axis_x, r.axis_y, false});
   r.trigger_marker = r.plot->add_cursor(kParked, plot::Color::hex(kTriggerColor));
   // A marker, not an instrument: it must sit exactly on the edge's time, so its
   // snap is Free and the controller never rounds it onto a sample.
@@ -509,12 +517,48 @@ bool RowSet::update_time_labels() {
   const double span = view.span();
   if (!(span > 0.0) || !std::isfinite(span)) return false;
 
-  // Sub-second windows read relative: `TickFormat::Time` writes three significant digits, so
-  // `12.345671s` and `12.345672s` are the same string and a 1 ms step around a multi-second
-  // time cannot be labelled at all. The band is the switch's hysteresis -- entering below a
-  // second, leaving only above 1.05 -- so a span sitting on the boundary cannot flicker
-  // between two forms while a zoom is nudged.
-  const bool want_relative = relative_x_ ? span < 1.05 : span < 1.0;
+  // A relative axis is the answer to one problem only: a tick step the label form cannot write.
+  // `TickFormat::Time` carries three significant digits, so a 1 ms step around a 12 s stamp
+  // writes `12.3s` on every tick -- there the ticks have to be re-anchored and the anchor named.
+  // The test is therefore the *step against the resolution at the axis' own magnitude*, never the
+  // span: the two part company in both directions, and both cases are real here. A 2 s window at
+  // twenty minutes of uptime is labelled `20:00` throughout and needs the anchor although its
+  // span is wide; a 50 ms trigger window spanning [-25ms, +25ms] is labelled `-20ms .. +20ms`
+  // perfectly well and needs nothing, although its span is narrow. That second case is what made
+  // a triggered sub-second view carry a `t0` caption *and* re-anchor its ticks away from the
+  // edge, which is the one position a triggered axis exists to show.
+  // The 1.05 band is the switch's hysteresis, so a step sitting on the boundary cannot flicker
+  // between two forms while a zoom is nudged, and the `1 - 1e-9` is a slack the *entry* needs for
+  // its own reason: a step read back from two tick values and a resolution from `pow(10, n)`
+  // differ in their last bits even when they are the same number, and `step == res` is a readable
+  // axis (`1.73s, 1.74s, 1.75s` -- one in the last digit is exactly enough), so a decision taken
+  // on those bits picked a different form from one frame to the next.
+  const double mag = std::max(std::fabs(view.min), std::fabs(view.max));
+  const double res = time_label_resolution(mag);
+  // The step the labels are actually written at: the majors the *last* layout produced. They are
+  // a function of the range and the axis' pixel width, not of the label form, so reading them
+  // back here is no feedback loop.
+  double step = 0.0;
+  {
+    const plot::Axis& ax = first.plot->x_axis(first.axis_x);
+    double prev = 0.0;
+    bool have = false;
+    for (const plot::Tick& t : ax.ticks) {
+      if (!t.major) continue;
+      if (have) {
+        step = t.value - prev;
+        break;
+      }
+      prev = t.value;
+      have = true;
+    }
+  }
+  // No ticks yet -- the frames before the first layout. The form is a property of the labels, so
+  // with no labels there is nothing to decide, and keeping the current one is right where
+  // guessing a step from the span is not: a guess that entered the relative form would be
+  // *latched* there by the hysteresis above.
+  const bool want_relative =
+      step > 0.0 ? step < res * (relative_x_ ? 1.05 : 1.0 - 1.0e-9) : relative_x_;
   const bool changed = want_relative != relative_x_;
   relative_x_ = want_relative;
 
@@ -530,27 +574,25 @@ bool RowSet::update_time_labels() {
     r.plot->set_x_axis_origin_from_range(r.axis_x, relative_x_);
     if (!relative_x_) r.plot->set_x_axis_origin(r.axis_x, 0.0);
     // The caption belongs with the labels, which a figure draws once, on the bottom row (the
-    // one whose x axis is the figure's). Every row gets it parked.
+    // one whose x axis is the figure's). Every other row gets an empty one, which draws nothing.
     const bool bottom = i == rows_ - 1;
-    if (r.time_origin_note >= r.plot->annotation_count()) continue;
-    plot::Annotation note = r.plot->annotation(r.time_origin_note);
-    note.visible = relative_x_ && bottom;
-    if (note.visible) {
-      // Inside the axes, just above the axis line, at their left edge: the reader adds this
-      // to a tick, so it sits beside the ticks.
-      const plot::Range yr = r.plot->y_range(r.axis_y);
-      note.x = view.min;
-      note.y = yr.min + 0.04 * (yr.span() > 0.0 ? yr.span() : 1.0);
-      char text[64];
-      // The anchor the *drawn* labels were built with: the axis' own origin, which the last
-      // layout set from its range. Reading it back (rather than keeping our own copy) is what
-      // makes the reader's addition exact -- label plus caption is that tick's absolute time.
-      const double shown = r.plot->x_axis_origin(r.axis_x);
-      x_origin_ = shown;
-      std::snprintf(text, sizeof(text), "t0 = %.6g s", shown);
-      note.text = text;
+    if (!relative_x_ || !bottom) {
+      r.plot->set_x_note("");
+      continue;
     }
-    r.plot->set_annotation(r.time_origin_note, note);
+    char text[64];
+    // The anchor the *drawn* labels were built with: the axis' own origin, which the last
+    // layout set from its range. Reading it back (rather than keeping our own copy) is what
+    // makes the reader's addition exact -- label plus caption is that tick's absolute time.
+    const double shown = r.plot->x_axis_origin(r.axis_x);
+    x_origin_ = shown;
+    std::snprintf(text, sizeof(text), "t0 = %.6g s", shown);
+    // Chrome, not an annotation: an annotation is anchored to a *data* coordinate, so the caption
+    // crawled across the plot as the view panned and drifted as it zoomed -- and it came with the
+    // annotation's own pin cross, which pointed at nothing. `set_x_note()` places it in the axes'
+    // bottom-left corner in pixels, on the legend's backplate, which is where the labels it
+    // qualifies are.
+    r.plot->set_x_note(text);
   }
   return changed;
 }

src/plot_host.hpp

@@ -106,11 +106,6 @@ class RowSet {
     /// it keeps its position whatever the cursor toggle says.
     plot::u32 trigger_marker = 0;
 
-    /// The caption naming the window's start while the x labels are relative: an annotation
-    /// inside the axes, so its text can change every frame without moving the layout (an axis
-    /// *title* would, and it would be a different width each time).
-    plot::u32 time_origin_note = 0;
-
     /// The measurements' readout marks: a pool created with the plot (a `Plot` cannot add or
     /// drop a cursor after the fact) and parked unless a measurement is using the slot.
     std::array<plot::u32, kMeasureMarks> measure_h{};

src/ui.cpp

@@ -418,6 +418,14 @@ struct App {
   int dbg_ink_staircase = 0;  ///< the filter dropped over three quarters of the points
   int dbg_ink_short = 0;      ///< the ink reached under a quarter of the axis' width
   double dbg_ink_worst_cover = 1.0;
+  /// The worst distance, in pixels, between where a sample is *drawn* and the x a readout
+  /// quotes for the same sample. `gather()` stages x as an f32 relative to an origin the
+  /// renderer names, while `Plot::crosshair_point()` reads `x_at()` in exact f64, so this is
+  /// the quantisation of that f32 expressed in the unit the user sees it in. Measured on the
+  /// raw levels only, where a gathered point *is* a sample; above them a point is a bucket's
+  /// envelope and has no single sample to be off from.
+  double dbg_ink_worst_offset_px = 0.0;
+  int dbg_ink_raw_checked = 0;  ///< frames the figure above was measured over
   int dbg_ink_reports = 0;
   /// 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
@@ -1093,21 +1101,19 @@ void check_frame_ink(App& app) {
   const plot::u32 level = spp >= 64.0 ? s->pyramid().level_for(n, spp) : 0u;
   std::vector<plot::f32>& xy = app.measure_ink_scratch;
   xy.clear();
-  s->gather(level, first, last, xy);
+  // The same origin the renderer names (`x_range.min`), so the reconstruction below is its
+  // reconstruction: see `plot::data::Series::gather()` for why the caller owns it.
+  s->gather(level, first, last, axis.min, xy);
   const std::size_t pts = xy.size() / 2;
 
   std::size_t kept = 0;
   double lo = 0.0;
   double hi = 0.0;
-  // Where the filter's drops fall, and how far back each one steps. The renderer reconstructs
-  // every point's absolute x as `gather[i] + series.x0()` **inside** this loop, so an `x0()`
-  // that is not constant for the loop's duration shifts the comparison under itself -- and on a
-  // ring-backed series `x0()` is `time_of(window_base)`, which *clamps to the oldest readable
-  // slot* and therefore advances with the producer. The two readings that separate that from a
-  // genuinely out-of-order gather are the drops' *positions* (spread through the points, or
-  // bunched at the front where the clamp lives) and `back` (one sample's spacing, or a packet's
-  // worth). So the loop is run twice: once the renderer's way, and once with `x0()` read a
-  // single time.
+  // Where the filter's drops fall, and how far back each one steps. The origin is a constant
+  // for the walk's duration *by construction* now -- the renderer reconstructs
+  // `gather[i] + x_range.min`, a local of its own, where it used to re-read `series.x0()` on
+  // every point and a ring-backed `x0()` advances with the producer. So a drop here is a
+  // genuinely out-of-order gather, and `back` says by how much.
   std::size_t drop_first = 0;
   std::size_t drop_last = 0;
   double worst_back = 0.0;
@@ -1115,7 +1121,7 @@ void check_frame_ink(App& app) {
   {
     double next = std::numeric_limits<double>::infinity();
     for (std::size_t k = pts; k > 0; --k) {
-      const double x = double(xy[2 * (k - 1)]) + s->x0();
+      const double x = double(xy[2 * (k - 1)]) + axis.min;
       if (!(x < next)) {
         worst_back = std::max(worst_back, x - next);
         if (!any_drop) drop_last = k - 1;
@@ -1129,18 +1135,24 @@ void check_frame_ink(App& app) {
       ++kept;
     }
   }
-  std::size_t kept_fixed = 0;
-  {
-    const double base = s->x0();  // one read, held for the whole walk
-    double next = std::numeric_limits<double>::infinity();
-    for (std::size_t k = pts; k > 0; --k) {
-      const double x = double(xy[2 * (k - 1)]) + base;
-      if (!(x < next)) continue;
-      next = x;
-      ++kept_fixed;
-    }
-  }
   ++app.dbg_ink_checked;
+  // Drawn against quoted, in pixels. At level 0 a gathered pair *is* sample `first + k`, so
+  // this is the one place the two numbers the user compares by eye -- the polyline's position
+  // and the crosshair's readout -- can be differenced. The origin is what decides it: the f32
+  // resolves 2^-24 of whatever span it is relative to, so a view narrower than that fraction
+  // of the *retained window* drew a sample visibly away from the x quoted for it, which is
+  // what "when zooming there is a visible offset between the real data point and the crosshair
+  // selected one" was.
+  if (level == 0 && pts > 0) {
+    const double px_per_x = axes_w / axis.span();
+    double worst = 0.0;
+    for (std::size_t k = 0; k < pts; ++k) {
+      const double drawn = axis.min + double(xy[2 * k]);
+      worst = std::max(worst, std::abs(drawn - s->x_at(first + k)) * px_per_x);
+    }
+    app.dbg_ink_worst_offset_px = std::max(app.dbg_ink_worst_offset_px, worst);
+    ++app.dbg_ink_raw_checked;
+  }
   const double cover = kept >= 2 ? (hi - lo) / axis.span() : 0.0;
   app.dbg_ink_worst_cover = std::min(app.dbg_ink_worst_cover, cover);
   const bool collapse = kept < 2;
@@ -1155,22 +1167,23 @@ void check_frame_ink(App& app) {
   if ((collapse || staircase || short_ink) && app.dbg_ink_reports < 40) {
     ++app.dbg_ink_reports;
     // The series' own answers beside the reconstruction, because the two disagreeing is itself
-    // a reading: `rel` is what `gather()` emitted (relative to the `x0()` *it* read) and `x0`
-    // is the `x0()` read here one call later, so a trace whose ink sits a whole ring-span off
-    // its axis separates into "the stamps moved under us" and "the window is the wrong one".
+    // a reading: `rel` is what `gather()` emitted (relative to `axis.min`, the origin it was
+    // given) while `x0`/`x_at`/`bounds` are the window the series says it holds, so a trace
+    // whose ink sits a whole ring-span off its axis separates into "the stamps moved under us"
+    // and "the window is the wrong one".
     const plot::Range xb = s->x_bounds();
     std::fprintf(stderr,
                  "[ink] paint %d %s%s%s mode=%s axis=[%.6f..%.6f] n=%llu idx=[%llu..%llu) "
                  "spp=%.1f level=%u pts=%zu kept=%zu ink=[%.6f..%.6f] cover=%.1f%% "
                  "x0=%.6f x_at=[%.6f..%.6f] bounds=[%.6f..%.6f] rel=[%.6f..%.6f] dx=%.3g "
-                 "kept_fixed_x0=%zu drops=[%zu..%zu] back=%.3g\n",
+                 "drops=[%zu..%zu] back=%.3g\n",
                  app.dbg_paint_n, collapse ? "collapse " : "", staircase ? "staircase " : "",
                  short_ink ? "short " : "", display_mode_name(app.dbg_display), axis.min, axis.max,
                  (unsigned long long)n, (unsigned long long)first, (unsigned long long)last, spp,
                  level, pts, kept, lo, hi, cover * 100.0, s->x0(), s->x_at(0), s->x_at(n - 1),
                  xb.min, xb.max, pts > 0 ? double(xy[0]) : 0.0,
-                 pts > 0 ? double(xy[2 * (pts - 1)]) : 0.0, s->dx(), kept_fixed, drop_first,
-                 drop_last, worst_back);
+                 pts > 0 ? double(xy[2 * (pts - 1)]) : 0.0, s->dx(), drop_first, drop_last,
+                 worst_back);
     std::fflush(stderr);
   }
 }
@@ -4681,24 +4694,29 @@ void report_event_zoom(App& a, const char* what) {
   const double spp = double(last - first) / axes_w;
   const plot::u32 level = spp >= 64.0 ? s->pyramid().level_for(n, spp) : 0u;
   std::vector<plot::f32> xy;
-  s->gather(level, first, last, xy);
+  // `axis.min` is the origin the renderer names, so every reconstruction below is its own --
+  // and at the deep end of this sweep that choice is the whole point: relative to the retained
+  // window instead, the f32's ULP would be a large fraction of these spans.
+  s->gather(level, first, last, axis.min, xy);
   double ink_lo = 0.0, ink_hi = 0.0;
   if (xy.size() >= 2) {
-    ink_lo = s->x0() + double(xy[0]);
-    ink_hi = s->x0() + double(xy[xy.size() - 2]);
+    ink_lo = axis.min + double(xy[0]);
+    ink_hi = axis.min + double(xy[xy.size() - 2]);
   }
   // The renderer's own increasing-suffix filter, counted rather than applied: it drops every
   // point that is not strictly older than the one kept after it, which for a *run* of equal x
   // keeps the last of the run. The stamps here are f32, so once the sample spacing falls below
-  // the f32 step at the stream's magnitude the gathered x has such runs -- and `kept` is how
-  // many distinct positions the polyline is left with. A `kept` far below `pts` is a staircase,
-  // and a `kept` of a handful is a trace with nothing to draw.
+  // the f32 step at the *gather origin's* magnitude the gathered x has such runs -- and `kept`
+  // is how many distinct positions the polyline is left with. A `kept` far below `pts` is a
+  // staircase, and a `kept` of a handful is a trace with nothing to draw. This is the other
+  // reading the origin change buys: the step is now 2^-24 of the span on screen, so a sweep
+  // that used to grind `kept` down as it zoomed keeps every point.
   std::size_t kept = 0;
   double worst_back = 0.0;  // the largest backwards step, in data units: non-monotonic gather
   {
     double next = std::numeric_limits<double>::infinity();
     for (std::size_t k = xy.size() / 2; k > 0; --k) {
-      const double x = double(xy[2 * (k - 1)]) + s->x0();
+      const double x = double(xy[2 * (k - 1)]) + axis.min;
       if (!(x < next)) {
         worst_back = std::max(worst_back, x - next);
         continue;
@@ -6247,23 +6265,27 @@ gboolean trig_trace_probe(gpointer user) {
     if (found) break;
   }
 
-  // Where that slot's samples are *drawn*, reconstructed exactly as the renderer
-  // does it: `Series::gather()` emits x relative to `x0()`, and the renderer adds
-  // `x0()` back before mapping to the screen. So `x0() + gathered` must equal
-  // `x_at()`, and `drawn=` must equal `data=` to the f32's precision.
+  // Where that slot's samples are *drawn*, reconstructed the way the renderer does it:
+  // `Series::gather()` emits x relative to an origin **the caller names**, and the
+  // consumer adds that same origin back before mapping to the screen. So
+  // `origin + gathered` must equal `x_at()`, and `drawn=` must equal `data=` to the
+  // f32's precision. The origin named here is `x0()`, deliberately -- the renderer
+  // passes the visible range's minimum, but this line reads the series' *whole* span,
+  // which is the widest relative value a gather can be asked to stage and so the worst
+  // case for the f32.
   //
   // This is the one defect in this area the picture alone shows and no other probe
-  // line does: a series that emits absolute x instead makes the renderer add `x0()`
-  // twice, so the trace lands a whole `x0()` away from the axis it was measured
+  // line does: a series that emits absolute x instead makes the consumer add the origin
+  // twice, so the trace lands a whole origin away from the axis it was measured
   // against -- off screen entirely once the view is narrower than that shift, while
   // the crosshair (which reads `x_at()`) goes on reporting correct values.
   double drawn_lo = 0.0, drawn_hi = 0.0, data_lo = 0.0, data_hi = 0.0;
   if (shown != nullptr && shown->size() > 0) {
     const u64 n = shown->size();
     std::vector<f32> xy;
-    shown->gather(0u, 0u, 1u, xy);
+    shown->gather(0u, 0u, 1u, shown->x0(), xy);
     const std::size_t head = xy.size();
-    shown->gather(0u, n - 1, n, xy);
+    shown->gather(0u, n - 1, n, shown->x0(), xy);
     if (head >= 2 && xy.size() >= head + 2) {
       drawn_lo = shown->x0() + double(xy[0]);
       drawn_hi = shown->x0() + double(xy[head]);
@@ -7246,18 +7268,25 @@ gboolean timelabels_probe_step(gpointer user) {
   const RowSet::Row& last = a->rows->row(a->rows->row_count() - 1);
   std::string ticks;
   std::string note;
+  // Whether *every* major label on the axis is a different string. That, and not a span
+  // threshold, is what the relative form exists to buy: two adjacent ticks reading `12.3s` are
+  // not labels. It is therefore the one assertion that holds whatever the stream's uptime is --
+  // which decides where the switch actually falls, since the label resolution is a function of
+  // the axis' magnitude.
+  bool distinct = true;
   if (last.plot != nullptr) {
     int n = 0;
+    std::vector<std::string> seen;
     for (const plot::Tick& t : last.plot->x_axis(last.axis_x).ticks) {
       if (!t.major) continue;
-      if (n++ != 0) ticks += ",";
-      ticks += t.label;
-      if (n >= 4) break;
-    }
-    if (last.time_origin_note < last.plot->annotation_count()) {
-      const plot::Annotation& an = last.plot->annotation(last.time_origin_note);
-      if (an.visible) note = an.text;
+      if (std::find(seen.begin(), seen.end(), t.label) != seen.end()) distinct = false;
+      seen.emplace_back(t.label);
+      if (n++ < 4) {
+        if (n != 1) ticks += ",";
+        ticks += t.label;
+      }
     }
+    note = last.plot->x_note();
   }
   double first_value = 0.0;
   plot::Range shown{};
@@ -7271,9 +7300,10 @@ gboolean timelabels_probe_step(gpointer user) {
     shown = last.plot->x_range(last.axis_x);
   }
   std::fprintf(stderr,
-               "[timelabels-probe] %-12s relative=%d window=%.6g origin=%.6f note=[%s] "
-               "ticks=[%s] first_value=%.6f first_rel=%.6f range=[%.6f..%.6f]\n",
-               what, a->rows->time_labels_relative() ? 1 : 0, a->rows->time_window(),
+               "[timelabels-probe] %-12s relative=%d distinct=%d window=%.6g origin=%.6f "
+               "note=[%s] ticks=[%s] first_value=%.6f first_rel=%.6f range=[%.6f..%.6f]\n",
+               what, a->rows->time_labels_relative() ? 1 : 0, distinct ? 1 : 0,
+               a->rows->time_window(),
                a->rows->time_labels_origin(), note.c_str(), ticks.c_str(), first_value,
                first_value - (last.plot != nullptr ? last.plot->x_axis_origin(last.axis_x) : 0.0),
                shown.min, shown.max);
@@ -8057,9 +8087,10 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
                 app.dbg_notrace_frames, app.dbg_notrace_after_bound, app.dbg_notrace_last);
     std::printf("[udpscope]   worst side/pane min width: %d px\n", app.dbg_min_w_worst);
     std::printf("[udpscope]   trace ink: %d paints checked, %d collapsed, %d staircase, %d short, "
-                "worst cover %.1f%%\n",
+                "worst cover %.1f%%, worst drawn-vs-quoted %.4f px over %d raw paints\n",
                 app.dbg_ink_checked, app.dbg_ink_collapse, app.dbg_ink_staircase,
-                app.dbg_ink_short, app.dbg_ink_worst_cover * 100.0);
+                app.dbg_ink_short, app.dbg_ink_worst_cover * 100.0, app.dbg_ink_worst_offset_px,
+                app.dbg_ink_raw_checked);
     std::printf("[udpscope]   blank view frames: %d of %d\n", app.dbg_blank_frames,
                 app.dbg_axes_frames);
     std::printf("[udpscope]   trigger events: %llu total, %llu at the disarm (no event after it "
@@ -8306,24 +8337,27 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
     }
     {
       // The x label form: relative to the window's own start (with the caption that names
-      // that start) while the span is sub-second, absolute otherwise. `x_origin_set` is read
-      // back out of the plot, so this is what the axis is actually formatting with.
+      // that start) when the labels could not carry the tick step absolutely, absolute
+      // otherwise. `x_origin_set` is read back out of the plot, so this is what the axis is
+      // actually formatting with, and `note` is the plot's own caption string.
       const RowSet::Row& rlt = rows.row(rows.row_count() - 1);
       std::string note;
-      if (rlt.plot != nullptr && rlt.time_origin_note < rlt.plot->annotation_count()) {
-        const plot::Annotation& a = rlt.plot->annotation(rlt.time_origin_note);
-        if (a.visible) note = a.text;
-      }
+      if (rlt.plot != nullptr) note = rlt.plot->x_note();
       // The labels themselves, from the axis the reader looks at: the assertion is what the
       // ticks *say*, not only which mode is on.
       std::string ticks;
+      bool distinct = true;
       if (rlt.plot != nullptr) {
         int shown = 0;
+        std::vector<std::string> seen;
         for (const plot::Tick& t : rlt.plot->x_axis(rlt.axis_x).ticks) {
           if (!t.major) continue;
-          if (shown++ != 0) ticks += ",";
-          ticks += t.label;
-          if (shown >= 4) break;
+          if (std::find(seen.begin(), seen.end(), t.label) != seen.end()) distinct = false;
+          seen.emplace_back(t.label);
+          if (shown++ < 4) {
+            if (shown != 1) ticks += ",";
+            ticks += t.label;
+          }
         }
       }
       // The labels against the anchor they were built with: the dump runs after the last
@@ -8340,10 +8374,10 @@ int run_ui(int argc, char** argv, const Config& cfg, ScopeModel& model, Acquisit
           }
         }
       }
-      std::printf("[udpscope]   time labels: relative=%d origin=%.6f note=[%s] x_origin_set=%.6f "
-                  "ticks=[%s] first_rel=%.9f\n",
-                  rows.time_labels_relative() ? 1 : 0, rows.time_labels_origin(), note.c_str(),
-                  origin_set, ticks.c_str(), first_value - origin_set);
+      std::printf("[udpscope]   time labels: relative=%d distinct=%d origin=%.6f note=[%s] "
+                  "x_origin_set=%.6f ticks=[%s] first_rel=%.9f\n",
+                  rows.time_labels_relative() ? 1 : 0, distinct ? 1 : 0, rows.time_labels_origin(),
+                  note.c_str(), origin_set, ticks.c_str(), first_value - origin_set);
     }
     {
       std::lock_guard<std::mutex> lock(model.mutex());