Source authenticated

The periodicity conjecture for finite-dimensional algebras

False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 9, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. 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: The periodicity conjecture for finite-dimensional algebras · Periodicity conjecture

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

GPT-6 Astra
model · ai model contributor · OpenAI

Claude Opus 5
model · ai model contributor · Anthropic

Haruhisa Enomoto
human · human collaborator

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Named evidence

VibeMathed record: The periodicity conjecture for finite-dimensional algebras

specialist registry · passed

Checked here on 22 September 2026 against arXiv:2609.09732: the abstract states the conjecture and gives a 36-dimensional counterexample whose simple modules have period four and which carries a 2-dimensional nonperiodic module, so the algebra itself is not periodic. The reference list confirms the Erdmann-Skowroński attribution (Colloq. Math. 138 (2015) on the periodicity conjecture for blocks of group algebras; J. Algebra 505 (2018) on weighted surface algebras). The mathematics was not checked here; thirteen days old, no referee.

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The periodicity conjecture for finite-dimensional algebras

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 Claude Opus 5

The periodicity conjecture for finite-dimensional algebras parent of this event

The periodicity conjecture for finite-dimensional algebras evidence for this event

This event attributed to Haruhisa Enomoto

VibeMathed record: The periodicity conjecture for finite-dimensional algebras evidence for this event

This event attributed to GPT-6 Astra

False: an explicit 36-dimensional algebra whose simple modules all have period four, but which has a 2-dimensional nonperiodic module and so is not itself periodic. parent of this event

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