What was already known
The weighted k=3 gap was already exactly two; for general k≥4 the previous upper bound was k. The conjectured k−1 factor remains open.
AI involvement
Cong and Zhao say GPT-5.6 Sol materially assisted the central gap proof and local-ratio algorithm. They formulated and explained the polyhedral argument and verified the manuscript.
The authors report material model assistance in the central gap proof and local-ratio derivation, but do not claim model leadership or autonomy.
Importance
Improves the general weighted LP gap below k for k≥4 and gives a matching algorithmic guarantee.
Limitations
The authors report checking all content, but do not assign specific proof steps to GPT-5.6 Sol. The p-matchoid extension and tight examples retain separate human author credit.
Technical verification
The named authors explicitly report verifying correctness of all content. This is a source-reported completed human check of the assessed theorem and algorithm; no machine check is documented.
Formal checking
Author verification of correctness and originality of all manuscript content
- Checker
- Yu Cong and Yajie Zhao, paper authors
- Scope
- Theorem 1.1 weighted k-matroid intersection gap k-1+1/k and the associated LP-relative algorithm
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors explain the closure inequality, aggregation with fractional marginals, and local-ratio construction in §§3–4.
Correction and publication history
Improves the general weighted LP gap below k for k≥4 and gives a matching algorithmic guarantee.
Read this published revision