← Legendre's Conjecture: The Base-Space Prime-Fitting Program
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Phase 1 · The canonical consecutive-square space
Legendre's Conjecture: The Base-Space Prime-Fitting Program
Phase 1 · The canonical consecutive-square space
Author line in the source: Neo.K × AI collaboration (no AI named)
Canonical Algebraic Consecutive-Square Base Space
Defines T_sq = {(n, k) : 1 ≤ k ≤ 2n} and E(n, k) = n² + k, proves that E is a bijection onto the non-square integers greater than 1; Legendre holds iff the prime pull-back projects onto every n iff a prime-valued section exists; a 'fitting graph' inside P_sq would give Legendre (conditionally).
An equivalent reformulation, not a proof of Legendre (the paper: 'Theorem 15.1 is an equivalent reformulation, not a proof of Legendre').
'Phase 1 verdict: CLOSED' in the closing block means the formalization is finished; the same block says 'Legendre proof status: OPEN'. The label is ambiguous for web readers: read every CLOSED / PROVED / PASS in this series as concerning a sub-lemma or one sector.
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.