← Phase 1 / 18 · 500K One-Commit Global Impact

Phase 1 · 18 v0.4 · 11 2026-08-12

500K One-Commit Global Impact

Amplifies the "exactly one commit" effect discovered in the small <150 sample in Document 14 directly onto the official full-scale conductor<500,000 dataset for measurement. The paper reports that out of 3,064,705 curves, 1,170,876 have analytic rank 0; narrowing down to semistable/optimal/conductor with at least two prime factors leaves 178,364 pre-candidates, and the current Algorithm 1 accepts 36,687 (about 20.5686%). Git compare shows that the same commit caused a net change of +2/-4064 in ec_labels_500k.txt; after deducting metadata lines, this exactly corresponds to 4062 curve rows being removed, reconstructing the old accepted count of 40,749—a removal rate of 9.9683%, dropping the pre-candidate acceptance rate from 22.8460% to 20.5686% (a drop of about 2.28 percentage points), with an impact on all curves of about 0.1325 percentage points. Because Algorithm 1 in this commit has only two theorem-level changes (strict $3/5/7$ isogeny exclusion + independent $a_3\ne\pm3$), every removed curve must fall into the union of these two—this is set-level closure, but the exact per-gate histogram at the 500K scale remains unknown, and the document explicitly warns against directly extrapolating the $9/2/1/1$ ratio from <150.

The same commit caused 4062/40749 (≈9.97%) accepted curves to be removed at the 500K scale; set-level closure ⊆ isogeny-failure ∪ {|a3|=3}, but the exact histogram is unknown and cannot be extrapolated to the <150 ratio. — 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.

"A seemingly minor correction to the theorem predicate can change about 10% of the old accepted base-curve universe... semantic versioning is not an add-on engineering task, but a part of mathematical soundness." — Excerpt from Section "Research Interpretation" of this document.

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