What was already known
Gurvits established the lower inequality, and Anari-Rezaei proved the sharp universal upper factor 2^(n/2), attained at 4-cycles. Anari conjectured the optimal girth-dependent factor 2^(2n/g); forest support was already exact.
AI involvement
Dong and Jain devised the initial strategy, then ChatGPT 5.6 Sol Pro developed a girth-dependent intermediate bound. Later model discussions contributed to the sharp proof; the authors wrote and explain the final argument, but the precise model-origin sharp step is not identified.
The authors document substantial model development of the central girth-dependent strategy and model interaction leading to the final proof; they retain leadership and final authorship. The precise sharp step remains unresolved.
Importance
Proves Anari's conjectured girth-dependent factor within the stated matrix setting.
Limitations
The upper factor assumes a nonnegative matrix with bipartite support girth at least even g≥4. Equality examples require g to divide 2n. A completed technical check of the final sharp proof is not documented, and attribution of its exact sharp step remains unresolved.
Technical verification
A full proof is published, but the AI-use statement assigns responsibility rather than recording a completed check of the final argument. No machine proof or explicit independent review was found.
Human understanding
The human authors explain their original strategy and the final good-vertex, information-flow and averaging mechanisms; no central reasoning gap is identified.
Correction and publication history
Proves Anari's conjectured girth-dependent factor within the stated matrix setting.
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