Černý Conjecture for One-Cluster Automata
Does every synchronizing one-cluster automaton on $n$ states admit a reset word of length at most $(n-1)^2$? The new bound $(m-1)(n-1) + m\ell \le (n-1)^2$ settles the one-cluster case of the Černý conjecture.
Exact FrontierDelta
Scope and record
Occurred: Jul 25, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Černý Conjecture for One-Cluster Automata · Černý, one-cluster
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Yinfeng Zhu
human · human collaborator
OpenAI Codex (GPT-5.6 Sol Ultra)
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Yinfeng Zhu
This event attributed to OpenAI Codex (GPT-5.6 Sol Ultra)