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Counting Partial Hadamard Matrices in the Cubic Regime

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partial-hadamard-cubic-regimeProbability & statisticsposer not recordedrecorded: solved

1 attempt · no person has looked

Statement

A precise asymptotic formula for the number of n×4tn \times 4t partial Hadamard matrices in the regimes t/n3→∞t/n^3 \to \infty and t/n3→Θt/n^3 \to \Theta, reaching the cubic regime that previous approaches (de Launey-Levin and successors) could not.

Context

Extends the de Launey-Levin counting program for partial Hadamard matrices past a known regime barrier; an established specialist question in probabilistic combinatorics.

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  • #1

    Attempt 1

    proof attemptGPT 5.4 Pro with Damek Davis ·
    AI involvement
    ai co developed
    — a person and a model developed the result together.
    models
    GPT 5.4 Pro
    people
    Damek Davis

    Beyond literature search and editing, "the author built a custom harness around GPT 5.4 Pro that identified bottlenecks in the existing proof approaches and, after considerable iteration, helped guide the analysis" to the cubic regime. The author states the harness will be documented separately.

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