Source authenticated

Thakur's Conjecture on Carlitz-Wieferich Primes

VibeMathed recorded: Thakur's Conjecture on Carlitz-Wieferich Primes. Consult the linked registry entry for the original report and scope.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 14, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: preprint. AI contribution: ai-discovered. Editorial metadata: CC BY 4.0; linked content retains its own rights.

Canonical aliases: Thakur's Conjecture on Carlitz-Wieferich Primes · Carlitz-Wieferich primes

Confidence: Not scored

Registry verification: site confirmed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

David Niedbala Giraudin
human · human collaborator

Claude Opus 4.8
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Thakur's Conjecture on Carlitz-Wieferich Primes

specialist registry · passed

Independently reproduced. We recomputed the claim from the definitions in arXiv:2607.15305, from scratch and with no computer-algebra dependency, so the check shares no code with the author's appendix. Confirmed: $x^3-8x^2-4x-11$ is irreducible over $\mathbb{F}_{19}$ , so $\mathbb{F}_{19^3}$ is a field; $P$ is monic of degree $5$ , irreducible over $\mathbb{F}_{19^3}$ , and genuinely uses the cubic extension; and $\rho_P(1) \equiv 1 \bmod P^2$ , which is the definition of a $c$ -Wieferich prime, computed through the Carlitz recursion inside $\mathbb{F}_q[T]/(P^2)$ . The Bamunoba-Bergstrom criterion the paper cites, $M_5(\theta) = 0$ , was computed by a separate route and agrees. We also confirmed that $\mu(X)$ divides $X + X^q + \cdots + X^{q^4}$ , which is what makes $G = \mu(T^q - T)$ divide $[5]$ . Since $19 \nmid 5$ , the counterexample stands. This matters more than usual here because the author states he cannot verify the mathematics directly. arXiv preprint (v2), not peer-reviewed.

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Thakur's Conjecture on Carlitz-Wieferich Primes

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lineage and corrections

This event attributed to David Niedbala Giraudin

This event attributed to Claude Opus 4.8

Registry resolution: resolved. Reported result type: disproved. The registry record and named primary source provide the statement and scope. parent of this event

Thakur's Conjecture on Carlitz-Wieferich Primes parent of this event

VibeMathed record: Thakur's Conjecture on Carlitz-Wieferich Primes evidence for this event

Thakur's Conjecture on Carlitz-Wieferich Primes evidence for this event

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