{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1159",
  "content_hash": null,
  "slug": "support-three-zero-divisor-f2-group-ring-attempt-resolution-route",
  "type": "attempt",
  "title": "Resolve the stated acceptance condition",
  "summary": "For a positive answer, give a finite or recursive presentation of a torsion-free group \\(G\\), explicit finite supports and coefficients for nonzero \\(\\alpha,\\beta\\in\\mathbb F_2[G]\\), and verify \\(\\alpha\\beta=0\\) in the group algebra.",
  "relevance": "For A support-three zero divisor over a torsion-free group, record support-three-zero-divisor-f2-group-ring-attempt-resolution-route (“Resolve the stated acceptance condition”) documents a concrete method, search boundary, or failed route. The record states: For a positive answer, give a finite or recursive presentation of a torsion-free group \\(G\\), explicit finite supports and coefficients for nonzero \\(\\alpha,\\beta\\in\\mathbb F_2[G]\\), and verify \\(\\alpha\\beta=0\\) in the group algebra.",
  "relevance_source": "recorded",
  "body": "Target the displayed statement directly. For a positive answer, give a finite or recursive presentation of a torsion-free group \\(G\\), explicit finite supports and coefficients for nonzero \\(\\alpha,\\beta\\in\\mathbb F_2[G]\\), and verify \\(\\alpha\\beta=0\\) in the group algebra. Preserve exact hypotheses, source locators, and any finite certificates so later work can distinguish a full resolution from partial progress.",
  "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/62548/zero-divisor-conjecture-for-finite-fields",
      "locator": "Editorial research route recorded 2026-07-31"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/62548/zero-divisor-conjecture-for-finite-fields",
    "locator": "Editorial research route recorded 2026-07-31"
  },
  "relations": [
    {
      "slug": "R1160",
      "title": "Current status and unresolved remainder",
      "object_type": "claim",
      "relation": "addresses",
      "direction": "outgoing"
    },
    {
      "slug": "support-three-zero-divisor-f2-group-ring",
      "title": "support three zero divisor f2 group ring",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}