{
  "id": "infinite-little-finitistic-dimension",
  "title": "An algebra of infinite little finitistic dimension",
  "description": "OpenAI's counterexample (2026) to the finitistic dimension conjecture: a finite-dimensional complex algebra whose finite-dimensional modules have unbounded finite projective dimensions. A finitely presented group algebra with a selection process of unbounded extinction is realized by a single complex of bimodules over a three-vertex algebra, simulated by an ordinary bimodule, and turned into projective dimension by a trivial extension.",
  "units": [
    {
      "id": "finitistic-dimensions-and-minimal-resolutions",
      "title": "Finitistic dimensions and minimal resolutions",
      "reader": "finitistic-dimensions-and-minimal-resolutions.html",
      "source": "src/finitistic-dimensions-and-minimal-resolutions.md",
      "source_sha256": "8cc5137ee37506a0f8867f62be2a1ba242c7f0dcaab557af8d8d5b267875ff3f",
      "status": "author_self_checked"
    },
    {
      "id": "a-selection-process-with-unbounded-extinction",
      "title": "A selection process with unbounded extinction",
      "reader": "a-selection-process-with-unbounded-extinction.html",
      "source": "src/a-selection-process-with-unbounded-extinction.md",
      "source_sha256": "475ce8687131bdbe73eadb26b7573f266e2b2af627243709d1f8b3f6b5f83647",
      "status": "author_self_checked"
    },
    {
      "id": "directed-algebras-and-quadratic-presentations",
      "title": "Directed algebras and quadratic presentations",
      "reader": "directed-algebras-and-quadratic-presentations.html",
      "source": "src/directed-algebras-and-quadratic-presentations.md",
      "source_sha256": "05804db7e0163b6e3ccab5693948c4eccd54bde476c135434d9d205da24490e4",
      "status": "author_self_checked"
    },
    {
      "id": "a-verdier-quotient-and-an-odd-double",
      "title": "A Verdier quotient and an odd double",
      "reader": "a-verdier-quotient-and-an-odd-double.html",
      "source": "src/a-verdier-quotient-and-an-odd-double.md",
      "source_sha256": "03f7257773bd3f04860e9d9e4940588f2ce32b6a82763796b4fec7dfa23d4f3f",
      "status": "author_self_checked"
    },
    {
      "id": "clearing-denominators-in-a-finite-diagram",
      "title": "Clearing denominators in a finite diagram",
      "reader": "clearing-denominators-in-a-finite-diagram.html",
      "source": "src/clearing-denominators-in-a-finite-diagram.md",
      "source_sha256": "1a873f0fca399f5c228690c93bb8e4a34a07f3aa6f378a3f26c8288b10170cea",
      "status": "author_self_checked"
    },
    {
      "id": "a-bimodule-complex-that-realizes-selection",
      "title": "A bimodule complex that realizes selection",
      "reader": "a-bimodule-complex-that-realizes-selection.html",
      "source": "src/a-bimodule-complex-that-realizes-selection.md",
      "source_sha256": "b10574c5e69168b7f860c2ab2be8402d102fc7ba312b969e44ee19cb2ddc6823",
      "status": "author_self_checked"
    },
    {
      "id": "simulation-by-an-ordinary-bimodule",
      "title": "Simulation by an ordinary bimodule",
      "reader": "simulation-by-an-ordinary-bimodule.html",
      "source": "src/simulation-by-an-ordinary-bimodule.md",
      "source_sha256": "770fa9592d64b1e65ecf3caaa6a919eba21260e4197941dfe41e973c1c59f212",
      "status": "author_self_checked"
    },
    {
      "id": "trivial-extensions-and-unbounded-projective-dimension",
      "title": "Trivial extensions and unbounded projective dimension",
      "reader": "trivial-extensions-and-unbounded-projective-dimension.html",
      "source": "src/trivial-extensions-and-unbounded-projective-dimension.md",
      "source_sha256": "dc889c8f046c04a70791fffd45be2af6d3afef3d8a2f56c5d12675c81b7a3d4f",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "core course Graduate Algebra (Li, Methods of Algebra, Volume 1): semisimple modules (Proposition 6.11.4); finitely generated modules over a principal ideal domain (Theorem 6.7.8, used in an exercise)",
    "core course Category Theory and Homological Methods (Li, Methods of Algebra, Volume 2): Tor (Definition-Proposition 3.14.7); truncation (Definition 3.9.3, Proposition 3.9.8); exactness of row-exact double complexes (Corollary 3.10.7); Gabriel-Zisman localization by roofs (Theorem 1.9.11, Corollary 1.9.13); triangulated categories, cohomological Hom functors and split triangles (Proposition 4.1.12, Remark 4.1.11, Corollary 4.1.13, Proposition 4.2.6); the homotopy category and induced triangulated functors (Theorem 4.4.1, Corollaries 4.4.2 and 4.4.4, Propositions 4.4.3 and 4.4.7); Verdier localization (Propositions 4.3.2 and 4.3.3, Theorem 4.3.4); Ext in the derived category and projective dimension (Definition 4.5.8, Proposition 4.5.9, Proposition 4.9.6, Definition-Proposition 4.9.7); K-flat complexes and derived tensor products (Propositions 4.12.4, 4.12.9 and 4.12.13)",
    "programme course Van Kampen diagrams (van-kampen-diagrams): Words, free groups and Cayley graphs, Lemma 1.2 and Section 2 (free groups and presented groups)"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}