← Phase 1 / 15 · Removed 13 First-Failure Closure

Phase 1 · 15 v0.3 · 08 2026-08-12 First Document of Today's Third Round

Removed 13 First-Failure Closure

Directly addresses the problem left by document 08 yesterday: v0.2 conservatively tagged 13 removed curves as VERSION_REGRESSION_REMOVED, reason = OPEN, not daring to guess the reason. This document uses the one-commit diff precisely located in document 14, combined with the official old/current fixture mapping, LMFDB/Cremona primary curve/isogeny data, and an exact finite-field count, to calculate the precise first-failure criterion for each of the 13 curves, completing the closure. Histogram statistics: $9\times$ P_ISOGENY_3, $2\times$ P_ISOGENY_5, $1\times$ P_ISOGENY_7, $1\times$ A3_ABS_3. The document attaches a complete table listing the Cremona labels, LMFDB labels, and first failure criteria for all 13 curves. Among them, 26b1 is somewhat special: it simultaneously has the secondary condition $a_3=-3$, but the production pipeline executes the strict isogeny gate first, so its first failure is still recorded as P_ISOGENY_7, not A3_ABS_3 — this is a concrete demonstration of "first failure depends on gate execution order." Finally, the document encapsulates the conclusion in a box: the small-sample $25\to12$ is no longer a black-box version drift; the 13 removed curves are fully explained by the new Algorithm 1 criteria.

All 13 removed curves are explained by the new Algorithm 1 criteria (9×P_ISOGENY_3, 2×P_ISOGENY_5, 1×P_ISOGENY_7, 1×A3_ABS_3); no longer a black-box version drift. — The phased status self-reported by the documents in the package, reproduced as is.

Connections · Connections

Relationship with other documents, try to use the words from its own document, not my interpretation.

"The small-sample 25→12 is no longer a black-box version drift: 13 removed curves are fully explained by the new Algorithm1 predicates." — Excerpt from Section "Key Conclusions" of this document.

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