GPT-5.6 Sol-Assisted Counterexamples Disprove the Markovity Conjecture
Yanxiao Liu and Mian Huang give two independently discovered, GPT-5.6 Sol-assisted counterexamples showing that an optimizer of the dual functional associated with Marton's inner bound need not satisfy the conjectured Markov structure; the paper certifies strict objective gaps while leaving Marton's region and the separate Additivity Conjecture intact.
In a manuscript dated August 12, 2026, Yanxiao Liu and Mian Huang present two counterexamples to the Markovity Conjecture for the two-receiver broadcast channel. The conjecture asserted that the dual functional associated with Marton's inner bound always has an optimizer satisfying the additional conditional-independence structure .
Both examples use ternary-input broadcast channels with strictly positive transition probabilities and the same nonrectangular auxiliary pattern. In each case, the authors exhibit an explicit non-Markov construction and certify that its objective value is strictly larger than the best value attainable by any construction with the conjectured Markov structure. The first example has a certified gap of about nats; the second uses exact-rational channel data and outward-rounded MPFR interval calculations to certify a smaller positive gap. The two examples were discovered independently by Liu and Huang at approximately the same time.
The authors state that both examples were obtained with assistance from GPT-5.6 Sol. They also acknowledge human checking of the counterexamples. The result disproves the structural Markovity Conjecture, but it does not invalidate Marton's achievable region and does not resolve the separate Additivity Conjecture.