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adv-accept report: Q2 stand-in gap first bound (plant fires, four programs agree to 2e-4)

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Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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docs/analysis/cryptanalysis/report-acceptance-rule.md
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@ -165,6 +165,29 @@ programs gave X_0.1% = 0.155%. If the tail scales as the extreme of the populati
times that, still under 1% of reads. The census over consecutive seeds (random accepted programs) says how
often the hot-set test fires in the population; that number lands below.
### Q2, the stand-in gap: first bound (box 2, 18:46Z, `adv-accept gap`)
Tool: a mirror interpreter with per-site index capture, run on the rule's own base nonces (seed-keyed
acceptance stream) with init words = seed words, once on the closed-form dataset and once on the LIVE
memory-hard dataset (day 20730, the kit's day). Validation on every program: the mirror's 32 hashes equal
the library's hash_warp on 8 units on both datasets, and the mirror's closed-form per-site distinct counts
equal the library's distinct_indices_v4 on all 4096 units. Known-failed shape `--plant zero-dataset`
(every live word 0): live min ratio 0.9733, verdict live REJECT against closed accept, live distinct
mean 115.99 against 128.00: the tool reports a gap when there is one. Logs adv/gap-plant.log, gap-first.log.
| Seed | id | min per-site ratio closed (2^20) | min live (2^20) | largest site gap | (c) on 64 units: distinct mean, saturated, bias max (closed / live) | verdict closed / live |
|---|---|---|---|---|---|---|
| 100767 (the finding) | 9d68e6286fc817d4 | 0.9919 | 0.9920 | +0.0002 | 127.714, 0, 82 / 127.730, 1, 53 | accept / accept |
| 2 (control) | 8a0047b2eb071ade | 0.9999 | 0.9999 | -0.0002 | 128.000, 1, 56 / 128.000, 0, 57 | accept / accept |
| 100211 | d07885a437e237c7 | 0.9907 | 0.9908 | +0.0002 | 128.000, 0, 61 / 128.000, 0, 57 | accept / accept |
| 100064 | 2442abf9d56f6611 | 0.9832 | 0.9831 | +0.0002 | 128.000, 11, 64 / 128.000, 6, 51 | accept / accept |
Reading. The per-site index distribution is set by the program and the register init, and the dataset words
it folds in act as fresh randomness on both sides: the closed form and the live set give the same ratio to
2 parts in 10,000 at 2^20 evaluations, and the same (c) verdicts. No stand-in gap to steer into on these four;
the 50-program widening is running (gap-50.log). Also: the cheap 256-unit proxy did rank real tail programs,
and 100064 sits 0.0032 above the 0.98 floor at 2^20, so the floor is live in the population tail, not idle.
### Live hot-set census (RUNNING)
- box 2, 18:5xZ: `adv-live census --programs 2..201 --nonces 1000000 --threads 32` (200 consecutive accepted