test: the noise probe reads the de-noise node, and the math probe builds one

The probe gains a staged chain rather than one phase, and the schedule moves with it:
`UDPSCOPE_PROBE_NOISE_MS` now times the *setup* stage, which installs the de-noise graph through
`apply_math_channels()` -- a structural rebuild that replaces the buffer and drops its history --
five seconds before anything scans it. The legs and the five measurements then run at about
10.5 s, and the reading that says the median rejected every impulse at 15.5 s, so the documented
run needs a 20 s mock and an 18 s exit.

The de-noise channel is installed **disabled** and enabled only at 13 s, for its own reading. An
acquired channel is a share of the ring, so a fifth one shortens every channel's retained span --
and the six `BufferSearch` leg counts and `pkpk bare` are all peaks and counts *of that window*.
Installing it enabled (as the plan had it) moved `bare` from 49 to 21, `ratio` from 7.00 to 3.00
and `pkpk bare` from 2.988 to 2.488, i.e. it would have rewritten the older feature's documented
proof to record a regression that is not one. With it enabled only at the end, every reading from
Tasks 4 and 8 is bit-for-bit what the doc records, and the new line reads
`denoise raw=2.987696/1 denoised=2.000000/1 ratio=0.669 channels=1` -- `denoised` exactly the
clean sine's 2.0, which is the claim the node makes.

Two other findings, both folded in: a derived channel whose source is switched off through the
panel's checkbox follows it off and does *not* come back when the source returns (the enable-all
probe's last act switches `sine` off at ~3 s), and the probes reload leftover math channels from
`$XDG_CONFIG_HOME/udpscope`, which is why a `setup channels=` count above 1 means an earlier run's
session, not a defect.

`math_probe` gains a third channel with a `DeNoise` node so the editor's median row is built and
synced on a baseline run: `3 math channels on 'sine' and 'noise'`, every other line as before,
`math cost: 103.3 ns/slot` (one reading of the same path).

verification.md: the recipe, and why the two stages may not be collapsed -- a probe that rebuilt
the buffer under its own legs reads `bare=0` and looks like a broken comparator. Also that the
noise and math probes may not share a run: both write `app.math`.

docs/claude/invariants-math-channels.md

@@ -26,9 +26,10 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   drag pans, `f` fits, `Ctrl+0` resets**.
   Its widgets are created once and only shown, hidden and set by `math_dialog_sync()`, so no rebuild
   can invalidate a live callback handle -- the same shape the measurements dialog uses.
-  `UDPSCOPE_PROBE_MATH_MS` defines two graphs and opens the editor (a construction crash test
-  as much as a state check), and the dump prints each derived channel's extremes beside the
-  source's. Read it on the fast mock, where the two assertions that matter are **`gaps=0`** (the
+  `UDPSCOPE_PROBE_MATH_MS` defines three graphs -- the third a `Source` of the first channel into a
+  `DeNoise` node, so the editor's median row is built and synced on a baseline run -- and opens the
+  editor (a construction crash test as much as a state check), and the dump prints each derived
+  channel's extremes beside the source's. Read it on the fast mock, where the two assertions that matter are **`gaps=0`** (the
   math is on the producer thread, so what it can break is packet capture, never the frame rate)
   and each `math '<name>': ... N samples vs M time slots` being **equal**, with `math x2` at
   `y=[-2, 2]`, `math lp` at `y=[-0.998, 0.998]` and `math3` at `y=[-2, 2]`. The `0 visible
@@ -61,7 +62,8 @@ Part of [CLAUDE.md](../../CLAUDE.md). These are rules that cost a defect to lear
   which is why the fix is in the push and not in the loader.
   `math cost: S slots, N ns/slot (T timed), X ms total est` is the per-slot cost; see the
   math-cost invariant below for why it is sampled, why it is an upper bound, and why a figure
-  anywhere in 78--101 ns/slot is one reading of the same thing.
+  anywhere in 78--101 ns/slot is one reading of the same thing; the three-graph run reads **103**, the
+  de-noise channel's per-sample median being the difference.
   The probe also asserts the new editor mechanics. `dialog build:` reads the identity row back as well --
 `name='math3' unit=''` -- which is the pair the `.ui` holds the widgets for and the code fills from the
 channel being edited, so a row that stopped being the one the code writes shows there.