What does this research mean for the field?

The unresolved gap for the asymptotic value of Delsarte's linear program for binary codes is strictly bounded by a certified uniform ceiling of 0.0864 bits per dimension. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The research aims to certify an upper limit for the Delsarte LP gap concerning binary codes of relative distance.

August 12, 2026Open Access

A certified 0.0864 ceiling for the asymptotic binary Delsarte LP gap

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The research aims to certify an upper limit for the Delsarte LP gap concerning binary codes of relative distance.
Proved uniform ceiling ϱ* ≤ 0.0864 for binary codes
Analysed Hamming and constant-weight projection kernels as Delsarte dual solutions
Conducted independent evaluations certifying gap limits with distinct rational implementations
Established that the quantity R_LP(δ) − B(δ) has its ceiling at 0.0864
Certified 1264 leaves in 1428 evaluations and independently confirmed the result with a distinct method in 1281 evaluations
Demonstrated the current limitations of AI in fully resolving complex mathematical problems without human verification

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Implication

Randomized trial demonstrates a ceiling for the asymptotic Delsarte gap in binary codes, suggesting implications for mathematical proofs.

Cite This Study

Frisina Giovanni (2026) studied this question.

synapsesocial.com/papers/6a7c208206a85aed514b74dd https://doi.org/10.5281/zenodo.21867679

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A certified 0.0864 ceiling for the asymptotic binary Delsarte LP gap

Key Points

Discussion

Implication

Cite This Study

A certified 0.0864 ceiling for the asymptotic binary Delsarte LP gap

Key Points

Discussion

Implication

Cite This Study

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