mock: the square's edges ring, and the one probe that wants a step asks for it

The square was the mock's only ideal step, which is the one shape a real producer
does not put on the wire. It is now the truncated Fourier series of the step --
`--square-harmonics N` odd harmonics, default 30 -- so each edge overshoots by the
Gibbs constant (about 9% of the 2 V swing, y = +/-1.179) and then rings, and
`--square-harmonics 0` is the ideal +/-1 step as before.

Odd harmonics only, so the series keeps the ideal wave's edge instants and its
polarity: the level-0 trigger, the glitch's inverted pulse and the buffer search
land where they did. Re-run in pairs (`--square-harmonics 0` against the default),
search, condition legs 0/1, trigrenum, disarm, trig trace, measures and events all
read exactly what they read before, with only `t0` moving. The reading that moved
is the noise probe's group-delay leg, whose `want` is the analytic `tau*ln2` of a
step: a band-limited edge reads `delay=0.002770 ratio=1.255`, the same figure on
every run. That recipe now asks for the ideal step, so its documented number stays
exact; probe-readings says why.

The series is vectorised: as a per-sample Python sum it cost ~15 sin() calls a
sample, which at the fast mock's 1.3 MS/s made the producer the bottleneck and
halved the rate the app saw (the noise probe's span-dependent counts read 22
against 48). Vectorised it adds ~0.5 ms to a 2000-sample packet, so the fast mock
runs at about nine tenths of its declared pace and those counts read within a few
percent.

docs/claude/verification.md

@@ -631,13 +631,24 @@ same run).
 ```bash
 cd /home/martino/Projects/tools/udpscope
 python3 tools/mock_udpstreamer.py --port 8108 --rate 1300000 --batch 1000 --duration 20 \
-  --spike-every 0.005 --spike-amp 0.5 --spike-width 2 > /tmp/noise-mock.log 2>&1 &
+  --spike-every 0.005 --spike-amp 0.5 --spike-width 2 --square-harmonics 0 \
+  > /tmp/noise-mock.log 2>&1 &
 sleep 1.5
 xvfb-run -a env UDPSCOPE_EXIT_AFTER_MS=18000 UDPSCOPE_ENABLE_ALL_MS=1000 \
   UDPSCOPE_PROBE_NOISE_MS=4000 \
   ./build/udpscope --server 127.0.0.1 --port 8108 2>&1 | grep -E 'noise-probe|CRITICAL'
 ```
 
+`--square-harmonics 0` is the one flag in that command that is not about the sine, and it is what keeps the
+probe's last reading exact: the group-delay leg measures a one-pole's *step* response on `square`, and the
+mock's square rings by default (see [build-and-run.md](build-and-run.md)). A band-limited edge moves that
+crossing off `tau*ln2` — measured `delay=0.002770 ratio=1.255` against the ideal step's `0.002206 / 1.000`,
+and the same figure on every run, so it is a property of the shape and not of the run. The leg's assertion is
+the `0.7..1.4` band, which the ripple keeps, but the ideal step is what keeps the *number* the line prints
+beside `want` as well. The other legs measure event counts on the sine, which the ripple does not touch; the
+counts do read a few percent lower under the ripple at this rate, for the producer-cost reason
+[build-and-run.md](build-and-run.md) gives.
+
 `UDPSCOPE_PROBE_NOISE_MS` is **not the time its readings are taken**. It times the probe's first stage, which
 installs a math graph through `apply_math_channels()` -- and that is a *structural rebuild* that replaces the
 buffer and drops its history. Every reading the probe takes is over retained history, so the rebuild has to