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Dittert's conjecture in dimension 16 via a joint-deficit scaling lemma

Boris Kafidov

Kafidov claims that, for every nonnegative 16-by-16 matrix with total entry sum 16, the Dittert functional (product of row sums plus product of column sums minus permanent) is at most 2-16!/16^16, with equality only at the constant matrix. The new joint-deficit scaling lemma makes a near maximizer doubly superstochastic after a sharper dilation and excludes a boundary maximizer at dimension 16.

Sources for this record

What was already known

The cases n=2 and n=3 were classical. Pang's 2026 preprint proved n at least 17 and left n=4 through 16 open. The earlier boundary-exclusion framework bounded row and column deficits separately and did not reach n=16.

AI involvement AI-led

Kafidov credits GPT-5.6 Sol with the strategy, joint-deficit lemma and most proof text. He chose the problem, directed revisions and submitted the paper; a completed independent check is not reported.

The model is credited with the central lemma and proof strategy, while a human directed the problem and final manuscript.

Importance Notable

Adds dimension 16 through a new joint-deficit scaling argument.

Limitations

The proof covers n=16. Together with Pang's prior n≥17 result it covers n≥16, but dimensions 4 through 15 remain outside this result. A completed check of the submitted proof is not documented.

Technical verification Reported

The manuscript gives a full argument but expressly says its AI disclosure is no substitute for independent expert mathematical review. No completed check is documented.

Human understanding Few

The manuscript explains the joint budget algebra, but most original proof text was model-produced and the author does not document his own explanation of the central reasoning. Few is the evidence-gap default, not a claim that he lacks understanding.

Correction and publication history