Spec 01 1.4.6.5: the shipped rule's own rejection shares beside the class v2 census figures (adv-accept's 20,000-seed attempts census on sub-version 3, 8 October 2026: 68.1 percent rejected per candidate, (a') 83.5 percent of rejections, mean accepted attempt 2.1, 0 exhaustions)

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

docs/spec/01-lottery-hash.md

@@ -262,7 +262,7 @@ A load site is a load's ordinal within the iteration, 0 to 15, in instruction or
 
 (c'') The distinct-index ratio. The one test that runs past the 64 units: `ACCEPT_UNITS_DISTINCT_V4 = 4,096` units, the first 4,096 base nonces of the same stream (the 64 of (c) are its first 64), so every site is evaluated `N = 2^20` times. For each site `s`, `d_s` is the number of distinct `idx` values it computed over those evaluations, `W_s = 2^28 >> min(k_off_s, 2)` is its window in words, and the expectation of a uniform source on that window is `E_s = N - N^2 / (2 W_s)` (an integer at these constants: 2^20 - 2^11, 2^20 - 2^12, 2^20 - 2^13). The site's ratio `d_s / E_s` must reach `MIN_DISTINCT_RATIO_V4 = 0.98`; the first site under it, in order, rejects the program (`LowEntropySite`). The implementation compares in f64; the integer comparison `50 d_s >= 49 E_s` gives the same verdict for every value of `d_s` at these constants (the margin is at least 0.32 of a count; adv-accept-3 section 6.1), and an implementation MAY use it. The floor sits in a measured gap: the accepted population's minimum is 0.983 to 0.989 and the rejected population's maximum 0.966 over 20,275 draws of two lanes, so a floor anywhere in 0.967 to 0.988 gives the same verdicts on every program seen (adv-accept-3 section 6.4). `MAX_SOURCE_REPEAT_V4 = 8` exists in the file and is not part of the rule.
 
-What the parts catch: (a) the empty-list fallback of 1.4.3; (b) registers that saturate to all ones (2.4 percent of class v2 candidates); (c) zero-absorbing register sets, lane-constant load sites, output bias and value-level address repeats (2.1 percent); (a') the cross-hash hot set of a load fed by `or`, `mul` or `mulhi` through the iteration boundary (AP-F8-1); (c') the same set delivered any other way; (c'') a low-entropy index band the lineage rules cannot see (F8's p23, p18, p19, p15, p56). Why (c) uses the closed form: the test is a pure function of the program (no cache, no day), costs about 3 ms on one core for the 64 units and 2.8 s with (c'') on the chosen candidate, and the census checked on 100,000 class v2 programs that its verdict agrees with the memory-hard dataset's on all but 39 threshold-edge cases (section 7.3). Not in the rule, and why: a contraction as the last write (80 percent of programs) and the `or` count are too common and (c) already catches the cases that matter; the load critical path is a hash-rate question, not a weakness; a 2^24 stage of (c'') does not separate the open F8 tail (p4, p8, p10, p34 read the clean seeds' values there; ledger AP-F8-1).
+What the parts catch: (a) the empty-list fallback of 1.4.3; (b) registers that saturate to all ones (2.4 percent of class v2 candidates, the class v2 census); (c) zero-absorbing register sets, lane-constant load sites, output bias and value-level address repeats (2.1 percent of class v2 candidates); (a') the cross-hash hot set of a load fed by `or`, `mul` or `mulhi` through the iteration boundary (AP-F8-1); (c') the same set delivered any other way; (c'') a low-entropy index band the lineage rules cannot see (F8's p23, p18, p19, p15, p56). Under the shipped rule, measured on 20,000 seeds (adv-accept's attempts census on sub-version 3, 42,711 rejected candidates, 8 October 2026): 68.1 percent of candidates are rejected, flat across attempts; of the rejections (a') takes 83.5 percent, (a) 11.6, (b) 3.0, (c'') 1.1, (c) constant bits 0.4, (c) saturated finals 0.3, (c') 0.05 and (c) the distinct sum 0.04; the accepted attempt is 2.1 on average and 28 at most, 0 seeds of 20,000 reached the cap, and 256 consecutive rejections have probability about 2 x 10^-43. Why (c) uses the closed form: the test is a pure function of the program (no cache, no day), costs about 3 ms on one core for the 64 units and 2.8 s with (c'') on the chosen candidate, and the census checked on 100,000 class v2 programs that its verdict agrees with the memory-hard dataset's on all but 39 threshold-edge cases (section 7.3). Not in the rule, and why: a contraction as the last write (80 percent of programs) and the `or` count are too common and (c) already catches the cases that matter; the load critical path is a hash-rate question, not a weakness; a 2^24 stage of (c'') does not separate the open F8 tail (p4, p8, p10, p34 read the clean seeds' values there; ledger AP-F8-1).
 
 #### 1.4.6.6 Attempts, the cap, the last resort and the program id