Whether Marton's Inner Bound Achieves the Broadcast Channel Capacity Region
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.
- Result
- Disproved
- Status
- Candidate (review pending)
- AI contribution
- AI co-developed
- Method
- Computation
- Field
- Network information theory
- Posed by
- Katalin Marton
- Year posed
- 1979
- Years open
- 47y
- Solved
- 2026-08-20
- Model
- GPT-5.6 Sol, Claude Fable 5, Claude Opus 5
- Vendor
- OpenAI, Anthropic
- Collaborators
- Mian Huang, Yanxiao Liu, Yi Liu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 50 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
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'.
Verification
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.