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Period-doubling prefix palindromic length is not 2-regular
The exact period-doubling conjecture is proved: d(n)=P(n+1)−P(n) is not 2-automatic and P is not 2-regular. The proof uses a marker C(n) recording a singleton 1 in some globally optimal factorization. A Gray-code independent-set bound gives nonnegative palindrome-edge slack. Uniform constructions and an all-path diagonal obstruction distinguish infinitely many binary prefixes for C. The sole computer-assisted lemma is an all-length local inclusion proved by complete reachable-state closure, independently implemented twice; finite value tests are not its proof. This does not provide a full closed formula for P or settle the separate Fibonacci conjecture. Classical palindrome structure, automatic-sequence closure and state distinguishability, and the source regularity/difference equivalence are credited. Worldwide priority remains unassessed.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Oct 4, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Period-doubling prefix palindromic length is not 2-regular · Period-doubling nonregularity
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
OpenAI assistant (dot; underlying model unspecified)
model · ai model contributor · OpenAI
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Compute record
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Period-doubling prefix palindromic length is not 2-regular evidence for this event
Original conjecture, arXiv v2 evidence for this event
The exact period-doubling conjecture is proved: d(n)=P(n+1)−P(n) is not 2-automatic and P is not 2-regular. The proof uses a marker C(n) recording a singleton 1 in some globally optimal factorization. A Gray-code independent-set bound gives nonnegative palindrome-edge slack. Uniform constructions and an all-path diagonal obstruction distinguish infinitely many binary prefixes for C. The sole computer-assisted lemma is an all-length local inclusion proved by complete reachable-state closure, independently implemented twice; finite value tests are not its proof. This does not provide a full closed formula for P or settle the separate Fibonacci conjecture. Classical palindrome structure, automatic-sequence closure and state distinguishability, and the source regularity/difference equivalence are credited. Worldwide priority remains unassessed. parent of this event
Period-doubling prefix palindromic length is not 2-regular parent of this event
This event attributed to OpenAI assistant (dot; underlying model unspecified)
VibeMathed record: Period-doubling prefix palindromic length is not 2-regular evidence for this event
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