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/build-and-run.md

@@ -106,6 +106,19 @@ belongs with `todo.md` item 3, alongside the relative-time toggle.
 
 `tools/mock_udpstreamer.py` has waveform-injection options used by the probes:
 
+- `--square-harmonics N` shapes `square`: `N` odd harmonics of the ideal step's Fourier
+  series, so each edge overshoots by the Gibbs constant (about 9 % of the 2 V swing at the
+  default 30, i.e. `y = ±1.179`) and then rings — a band-limited edge, which is what a
+  crossing count or a pulse-width test has to survive. The series is deterministic and the
+  odd harmonics keep the ideal wave's edge instants and its polarity, so the level-0 trigger,
+  the search and the glitch's inverted pulse still read where they did on the step; the
+  *extremes* are what move. `0` (or negative) is the ideal ±1 step, which is what a probe
+  asserting an exact extreme or an exact width asks for — the noise probe's group-delay leg is
+  the one that does, because its `want` is the analytic `tau*ln2` of a step
+  (see [verification.md](verification.md)). It costs the producer about 0.5 ms per
+  2000-sample packet on top of the ideal branch, so at the fast mock's 1.3 MS/s the mock
+  delivers at roughly nine tenths of its declared pace — a reading that scales with the
+  retained span reads that much lower, and nothing else does.
 - `--glitch-at S` / `--glitch-width W` invert the `square` signal for `W` seconds at the
   start of every square period from stream second `S` onwards — a runt pulse of a known
   width, which is what a `<` pulse-width trigger and a glitch search are checked against.