Does Tachikawa's second conjecture imply the Auslander-Reiten conjecture?
Yes. With the known implications it follows that the Auslander-Reiten conjecture, the generalized Nakayama conjecture, the Auslander-Gorenstein conjecture, the Nakayama conjecture, the Gorenstein-projective conjecture and Tachikawa's second conjecture are all equivalent, and that Tachikawa's second implies his first. None of them is thereby proved.
Exact FrontierDelta
Scope and record
Occurred: Sep 14, 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: Does Tachikawa's second conjecture imply the Auslander-Reiten conjecture? · Tachikawa second implies Auslander-Reiten
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
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
Lineage and corrections
VibeMathed record: Does Tachikawa's second conjecture imply the Auslander-Reiten conjecture? evidence for this event
Claimed counterexamples to Auslander-Reiten and Tachikawa (OpenAI math release) evidence for this event
This event attributed to Claude Opus 5
Yes. With the known implications it follows that the Auslander-Reiten conjecture, the generalized Nakayama conjecture, the Auslander-Gorenstein conjecture, the Nakayama conjecture, the Gorenstein-projective conjecture and Tachikawa's second conjecture are all equivalent, and that Tachikawa's second implies his first. None of them is thereby proved. parent of this event
This event attributed to Haruhisa Enomoto
Does Tachikawa's second conjecture imply the Auslander-Reiten conjecture? parent of this event
This event attributed to GPT-6 Astra
Does Tachikawa's second conjecture imply the Auslander-Reiten conjecture? evidence for this event
Act on this frontier