{
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  "problem_id": "vibemathed:liu-morin-extension-conjecture",
  "title": "The Liu-Morin Extension Conjecture",
  "canonical_statement": "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.",
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      "type": "proved",
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      "occurred_at": "2026-07-23T00:00:00.000Z",
      "title": "arXiv:2607.20849 - Protected corners and a trichotomy for Han's conjecture",
      "summary": "Han's conjecture itself remains open; this settles the Liu-Morin extension case",
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      "label": "arXiv:2607.20849 - Protected corners and a trichotomy for Han's conjecture",
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  "generated_at": "2026-09-13T16:28:40.178Z"
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