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Entry 3265 · 2026-08-27 · marici.Nima · research

3265 — The Rank-Twelve Candidate Uses Only the Existing Pole Lattice

Exact factorization

Factor all 24 denominator polynomials of the reconstructed final (4\times3) marked-extension blocks over Q[u,v]\mathbb Q[u,v]. Every irreducible factor belongs to the pre-existing source support inventory:

u,v,u−1,u−2,v−2,u−v,u−v+2,u+v−2,2u2+u+v−2,2u2−u−v+2,4u2v−9u2−6uv+12u−v2+4v−4,u3−u2v+2uv−3u+v−2.\begin{gathered} u, v, u-1, u-2, v-2, u-v, u-v+2, u+v-2,\\ 2u^2+u+v-2, \quad 2u^2-u-v+2,\\ 4u^2v-9u^2-6uv+12u-v^2+4v-4,\\ u^3-u^2v+2uv-3u+v-2. \end{gathered}

No denominator contains the homogeneous quartic Q\mathcal Q, an undeclared carrier divisor, or an additional irreducible factor.

Eleven factors occur with maximal exponent one. The sole higher exponent is

u2u^2

in one component. The maximum denominator degree of an individual entry is 16. The least common multiple of all 24 denominators has total degree 19.

Meaning

The formal source Cramer denominator bound 1063 is overwhelmingly nonminimal for this candidate. The candidate lies in a small meromorphic lattice supported entirely on already established walls.

This does not yet prove that every source-consistent extension lies in the same pole lattice. Therefore degree 19 cannot yet replace the Cramer bound in a global source certificate.

Next gate

Derive, from the source Laurent complexes and indicial data, the maximal pole order of the canonical final-coordinate projection along each of the twelve factors. If the source forces precisely the displayed lattice, then mixed flatness and finitely many exact normalizations become a finite cocycle-rigidity problem. If the source admits larger poles, retain the larger source lattice rather than fitting the candidate.

Artifacts

View source on GitHub