Whether Marton's Inner Bound Achieves the Broadcast Channel Capacity Region
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Precise statement
Marton's inner bound, proposed in 1979, is the best known achievable region for a general discrete memoryless broadcast channel, and whether it always achieves the capacity region had been open ever since. It does not: there is a finite two-receiver discrete memoryless broadcast channel whose two-letter Marton value strictly exceeds twice its one-letter value, so the complete one-letter Marton region is strictly contained in the capacity region.
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fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Sol, Claude Fable 5, Claude Opus 5
The paper's statement: "The numerical search relied heavily on the assistance of AI models." It credits each contribution individually - GPT-5.6 Sol assisted Yanxiao Liu in finding a counterexample to the Markovity conjecture of Gohari, Liu and Nair and, independently, assisted Mian Huang via elimination geometry; Claude Fable 5 assisted in finding a counterexample to the local tensorization test and a fixed-input counterexample; Opus 5 assisted in the fixed-input construction. The theory that turns a numerical gap into an unconditional theorem, gradient shaping and constraint removal, is the authors'.
Checked by this site on 21 August 2026 against the paper (arXiv:2608.19869v1): the AI statement and the per-author credits are as quoted, and the result is unconditional rather than resting on the Markovity conjecture, which the paper shows fails and then works around. The authors certify the gap with interval arithmetic and outward-rounded MPFR at more than 1.88e-6 nats; that computation was not re-run here. Days-old preprint, no independent review.
Sub-optimality of Marton's Inner Bound for the Two-Receiver Broadcast Channel
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Known method families
computation (source-reported)
Source-reported tools: computation.
Independent: unknown · difference confidence: 0
What remains uncertain
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The source status is candidate and must not be represented as solved.
VibeMath has not independently verified the mathematical claim.
AI-attempt independence and training-data exposure are unknown unless explicitly documented.
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.