{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1328",
  "content_hash": null,
  "slug": "kaplansky-sixth-semisimple-hopf-next-route-20260801",
  "type": "attempt",
  "title": "Complete the stated acceptance conditions",
  "summary": "Prove that \\(\\dim_k V\\mid\\dim_k H\\) for every triple \\((k,H,V)\\) satisfying the displayed hypotheses. Alternatively, give explicit Hopf structure maps for a finite-dimensional semisimple counterexample, identify a simple module \\(V\\), prove simplicity, and verify the failed divisibility.",
  "relevance": "For Kaplansky's sixth conjecture for semisimple Hopf algebras, record kaplansky-sixth-semisimple-hopf-next-route-20260801 (“Complete the stated acceptance conditions”) documents a concrete method, search boundary, or failed route. The record states: Prove that \\(\\dim_k V\\mid\\dim_k H\\) for every triple \\((k,H,V)\\) satisfying the displayed hypotheses.",
  "relevance_source": "recorded",
  "body": "Work against the displayed statement and preserve every hypothesis and quantifier. Prove that \\(\\dim_k V\\mid\\dim_k H\\) for every triple \\((k,H,V)\\) satisfying the displayed hypotheses. Alternatively, give explicit Hopf structure maps for a finite-dimensional semisimple counterexample, identify a simple module \\(V\\), prove simplicity, and verify the failed divisibility. Any computation must retain a replayable witness and a matching exclusion or completeness certificate.",
  "status": "open_strategy",
  "evidence_grade": "self_reported",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://mathoverflow.net/questions/108404/kaplanskys-6th-conjecture-dimirrep-dimalgebra-for-semi-simple-hopf-alg",
      "locator": "Editorial research route recorded 2026-08-01."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/108404/kaplanskys-6th-conjecture-dimirrep-dimalgebra-for-semi-simple-hopf-alg",
    "locator": "Editorial research route recorded 2026-08-01."
  },
  "relations": [
    {
      "slug": "R1329",
      "title": "Current checked status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "kaplansky-sixth-semisimple-hopf",
      "title": "kaplansky sixth semisimple hopf",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}