{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R1162",
  "content_hash": null,
  "slug": "ternary-orthogonal-full-row-order-claim-status-20260731",
  "type": "claim",
  "title": "Current status and unresolved remainder",
  "summary": "UNKNOWN as of 2026-07-31. The MathOverflow page has zero answers. Its comments report exact verification through n=20 and exclusions for several arithmetic families, while a primary 2004 paper proves nonexistence for orders p^k, 2p^k, and 3p with p odd; the full congruence claim remains unproved in the checked sources. Prove that no such matrix exists when n is odd or congruent to 2 modulo 4, or give an explicit counterexample of one of those orders.",
  "relevance": "For ternary orthogonal full row order, pins the dated research frontier: UNKNOWN as of 2026-07-31. The MathOverflow page has zero answers. Its comments report exact verification through n=20 and exclusions for several arithmetic families, while a primary 2004 paper proves nonexistence for orders p^k, 2p^k, and 3p with p odd; the full congruence claim remains unproved in.",
  "relevance_source": "recorded",
  "body": "UNKNOWN as of 2026-07-31. The MathOverflow page has zero answers. Its comments report exact verification through n=20 and exclusions for several arithmetic families, while a primary 2004 paper proves nonexistence for orders p^k, 2p^k, and 3p with p odd; the full congruence claim remains unproved in the checked sources.\n\nA complete resolution must satisfy this condition: Prove that no such matrix exists when n is odd or congruent to 2 modulo 4, or give an explicit counterexample of one of those orders.",
  "status": "reported",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "claim",
    "citation": {
      "url": "https://mathoverflow.net/questions/446995/orthogonal-vectors-with-entries-from-1-0-1",
      "locator": "See dataset.references[0] for the exact external source and locator."
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://mathoverflow.net/questions/446995/orthogonal-vectors-with-entries-from-1-0-1",
    "locator": "See dataset.references[0] for the exact external source and locator."
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R1161",
      "title": "Resolve the stated acceptance condition",
      "object_type": "attempt",
      "relation": "addresses",
      "direction": "incoming"
    },
    {
      "slug": "ternary-orthogonal-full-row-order",
      "title": "ternary orthogonal full row order",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}