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Program · v0.1 · 2026-09-30
Legendre's Conjecture: The Base-Space Prime-Fitting Program
Program · v0.1 · 2026-09-30
Author line in the source: Neo.K × AI collaboration (no AI named)
Legendre Base-Space Prime-Fitting Program
Recasts Legendre's conjecture as the existence of one global 'prime-fitting operator' F_P whose restriction to every square cell B_n = (n², (n+1)²) is the same operator and whose image is a prime inside the cell; lists certificate obligations C0–C8, failure conditions F1–F7 and a Phase 1–9 plan.
A methodological reconstruction and research program; the paper says it does not claim to complete Legendre's conjecture, and its closing block reads 'Legendre proof status: NOT PROVEN'.
'Quantifier descent' (∀n ∃p → ∃F ∀n) is called 'the most important logical reconstruction' but is a re-expression, not a reduction (§25 of the paper itself hedges). The program's own Phase 1–9 roadmap was not followed after Phase 4, and the program itself was never revised.
Connections · Connections
This is a full-text translation of the Chinese source, which remains authoritative for its research claims. Translation is not independent mathematical verification and does not upgrade the original evidence level.