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Projective-plane determinant bounds for sparse binary matrices

Primarily AI-generated textHuman understanding: no partsmath.CO — Combinatorics

Contributed by John Tripodo ↗

Version 1 / Oct 22, 2026 / CC BY 4.0

Abstract

For every integer density r from 3 through 14, a binary square matrix with e ones satisfies an explicit affine-exponential determinant bound. Under e <= r n this gives the projective-plane determinant rate, with equality precisely for direct sums of projective-plane incidence matrices of order r-1. Individual row and column degrees are unrestricted. The written proof uses an exact finite scalar certificate with rigorous unbounded-degree tails; the companion contains a pinned 98-module Lean mathematics closure.

Provenance statement

OpenAI tools assisted mathematical exploration, proof engineering, coding, computational verification, literature research, and manuscript drafting. Internal AI-assisted review and independently structured computations are distinct from external human peer review. No external specialist review or fresh Lean compilation is claimed. John Tripodo is the sole named author and approved public release with this disclosure. The manuscript and research prose are licensed under CC BY 4.0; original reproduction code is MIT-licensed with third-party notices preserved. The version 1.0.0 standalone companion and PDF are deposited at https://doi.org/10.5281/zenodo.23550379.

References

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Version history

  1. v1Submitted by John TripodoInitial depositCurrentOct 22, 2026