The Liu-Morin Extension Conjecture
Han's conjecture predicts that a finite-dimensional algebra with eventually vanishing Hochschild homology has finite global dimension. Within the tau-Hochschild framework it splits into persistence and survival, and the Liu-Morin extension conjecture concerns when the property passes to extensions. A protected corner theorem bounding Ext at a surviving vertex settles it beyond the monomial and special biserial cases, and yields a trichotomy for failures on three strongly connected vertices.
- Result
- Proved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Homological algebra
- Posed by
- Liu, Morin
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-23
- Model
- Claude Fable 5
- Vendor
- Anthropic
- Collaborators
- Marco Armenta
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Han's conjecture itself remains open; this settles the Liu-Morin extension case
What the AI did
The disclosure states that the author used the model for deep research, formulation of theorems, and drafts of their proofs, reviewing and editing the output as needed.
Verification
Single-author arXiv preprint; not yet peer-reviewed.
Source
arXiv:2607.20849 - Protected corners and a trichotomy for Han's conjecture