Marton's inner bound shown not to reach the broadcast channel capacity region
There are discrete memoryless broadcast channels whose capacity region is strictly larger than Marton's inner bound, settling in the negative a question open since 1979.
- Lab
- Independent
- Model
- GPT-5.6 Sol, Claude Fable 5 and Claude Opus 5
- Field
- Computer science
- Date
- 2026-08-20
- Human collaborators
- Mian Huang, Yanxiao Liu, Yi Liu
- Problem posed
- 1979 · open 47 yrs
Sources
Original work
What was found
Marton's inner bound has been the best known achievable region for the general two-receiver discrete memoryless broadcast channel since 1979, and whether it is tight has been the central open question of the area. The paper exhibits channels whose capacity strictly exceeds it. The route ran through a related conjecture: the authors first found counterexamples to the Markovity conjecture of Gohari, Liu and Nair, then built a local tensorization test for a ternary-component broadcast channel, developed that into a counterexample to the additivity conjecture, and finally into an unconstrained counterexample to Marton's region. The violation gaps are small, of order ten to the minus six, and are certified with interval arithmetic.
Novelty check
Marton posed the inner bound in 1979 and its tightness is the standing open problem of broadcast-channel capacity, restated in the network information theory literature and in the Gohari-Liu-Nair line of work the paper builds on and partly refutes. The paper records that the Markovity conjecture had survived an experiment over more than ten thousand random channels in earlier work, which fixes the prior state of the art: no counterexample to either conjecture had been found. No prior demonstration of sub-optimality appears. The result is a new construction rather than a retrieval.
Caveats and known objections
A preprint one day old at entry, unrefereed and not formalized. The gaps are of order ten to the minus six, so the claim rests on the authors' interval-arithmetic certification rather than on anything visible by inspection, and no independent rerun is recorded. Autonomy graded ai-assisted rather than collaborative or ai-led: the acknowledgement credits each contribution individually and the recurring verb is assisted. Chandra Nair asked Yanxiao Liu to search using AI; GPT-5.6 Sol assisted Liu to a Markovity counterexample and, independently, assisted Mian Huang via the human-devised method of elimination geometry; Claude Fable 5 assisted the tensorization test; Claude Fable 5 and Opus 5 assisted a fixed-input-distribution example after Amin Gohari and Nair suggested that constraint; and Yanxiao Liu then modified that example into the unconstrained counterexample. Humans chose the method, set each search target and did the final construction. The weaker defensible reading applies.
Also recorded at
vibemathedmarton-inner-bound-capacity-region
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Entry history (1 event)
- AddedEntered the registry graded Author verified and AI-assisted.
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Cite this entry
whataifound.org. (2026). Marton's inner bound shown not to reach the broadcast channel capacity region. whataifound.org: A Registry of AI Scientific and Mathematical Discoveries. https://whataifound.org/finding/2026-08-20-marton-inner-boundBibTeX
@misc{whataifound-independent-2026-bound,
title = {Marton's inner bound shown not to reach the broadcast channel capacity region},
author = {{whataifound.org}},
year = {2026},
howpublished = {whataifound.org: A Registry of AI Scientific and Mathematical Discoveries},
note = {Result by Independent. Verification: Author verified. Autonomy: AI-assisted.},
url = {https://whataifound.org/finding/2026-08-20-marton-inner-bound}
}