test(bpsk): #1363's three outstanding measurements, incl. the labelled ray split

[dc0sk]

Apparatus for #1363. Test-only; no production code changes. It lands the measurements behind
this comment so the
numbers stay reproducible, and it answers all three measurements that issue had outstanding.

mod carrier_dip_tiebreak gains:

• ray_split — the two Watterson rays as complex values, labelled, without private access.
• the_ray_split_agrees_with_the_envelope — default-run pin for it.
• measure_snr_axis_tap_split_and_bytes — #[ignore]d harness: SNR axis, payload-aligned byte
  counts, and the tap split.

The finding it produced

The cancellation costs 8 frames of 96 at every SNR, including noise-free, so no SNR-conditioned
mitigation can help. The harm localises to delayed-dominant mid-depth dips (noise-free,
|H| ∈ [0.05,0.20), err b0/b1):

dominant tap	soft	HARD
direct	0.295 / 0.303	0.333 / 0.242 — on par, better on b1
delayed	0.008 / 0.011	0.236 / 0.114

A far sharper fix target than "the cancellation hurts on fades".

The split was recorded as impossible, and is not

ray_envelopes draws env0 then env1 before any noise sample and reads neither
delay_spread_ms nor snr_db, so one seed gives identical rays under any delay. apply_complex at
delay 0 with a DC probe gives (e0+e1)/√2; at 1 ms with a complex 1500 Hz tone it gives (e0−e1)/√2
(1.5 cycles → e^{−j3π} = −1). Magnitudes alone really are insufficient — that half of my argument
held — but the complex values are available, which I had not considered.

Two defects in my own apparatus, both caught by assertions rather than by reading

1. The pin first asserted E[|e|²] ≈ 1 per seed. One frame is a single Rayleigh realisation and
seed 0 reads 1.561/0.747, so it failed at once. The property is population-level; it is now a ratio
across seeds, with the per-seed spread recorded in the comment so nobody re-tightens it.

2. The worse one — the self-consistent-checker archetype. The pin re-derived the demixed
difference inline and compared that to carrier_envelope. That exercises the algebra but never
ray_split, so a planted dif * 0.5 inside the helper passed. Measured, not theorised.

Fixed by routing the pin through the helper and making the harness call the same function instead
of keeping a private copy. Sabotage-verified in both directions:

control (unmodified)        -> ok
dif * 0.5 inside ray_split  -> FAILED
   "the rays recovered by `ray_split` depart from `carrier_envelope` by 1.1306 over 9992 symbols"

The harness's numbers are identical before and after that refactor, so it is behaviour-preserving.

Retractions, on the issue

• "Exactly 21 lost frames at all three SNRs" — a byte-alignment artefact. Grouping began 31
  bits before the payload's byte boundary and swept in preamble bytes; aligned it is 21/19/19/19,
  and the robust statement is the gap of 8.
• "Soft improves while hard is pinned" — false. Both drop by 2 from 16→24 dB and neither moves
  to noise-free.
• The deterministic deep-null limit is NOT refuted. Split by distance to the next true flip,
  d=1 rises 0.905 → 0.937 as noise is removed while d≥4 falls to 0.000 — the pooled plateau is the
  mechanism at finite |H|. "→ 1.0" was always a statement about H ≡ 0, which is measure zero.

Stated limits

The byte count covers 200 payload bytes of a 255-byte wire frame, so it is a lower bound for
both arms and is not a decode rate — do not equate 19/96 with the issue's opening 50/38. No
scrambler; RS is not actually run; deep-bin figures are clustered (nominal SE ≈ 0.03 per bit). The
next measurement is (lock × dominance) — dominance here is absolute, while the thread holds that
dominance relative to the timing lock is the real variable — and it is not done.

Test results

suites=339 tests_passed=2577 tests_failed=0
GATE: PASS 6b7d308e233585fa450d649b9c81af3077c74d79 clean 20260921T131458Z

All 13 steps ok. 2577 tests against main's 2576 — the one new default-run pin.

Refactors: CAP-12
Verification-objective: the apparatus behind a published measurement must be pinned by an assertion
that runs through the function the measurement calls

Review: none — this lands apparatus whose findings and write-up were reviewed before the issue
comment was posted; the review supplied the tap split, the alignment fix and the by-distance
breakdown, and its verdict is what this applies.

🤖 Generated with Claude Code

https://claude.ai/code/session_0188ATCj6DZ9aRVQ2vSirua6