{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R783",
  "content_hash": null,
  "slug": "threshold-six-three-attempt-literature-audit",
  "type": "attempt",
  "title": "The six-variable classification is the next exactness check",
  "summary": "Primary sources give the degree bound, general symmetric-function circuits, and an exact classification of all affine classes on six variables.",
  "relevance": "For Multiplicative complexity of the six-bit threshold-at-least-three function, record threshold-six-three-attempt-literature-audit (“The six-variable classification is the next exactness check”) documents a concrete method, search boundary, or failed route. The record states: Primary sources give the degree bound, general symmetric-function circuits, and an exact classification of all affine classes on six variables.",
  "relevance_source": "recorded",
  "body": "Boyar and Peralta develop lower and upper bounds for threshold functions and prove the degree bound used here. Çalık, Sönmez Turan, and Peralta later classified all 150,357 affine-equivalence classes of six-variable Boolean functions by multiplicative complexity. Their published distribution has complexities 0 through 6, and the associated NIST repository provides one representative and an AND-optimal circuit for each class.\n\nThis audit did not complete the affine-class identification for truth table `fffefee8fee8e880`. A reproducible exactness certificate can proceed in either of two ways: map this truth table to its NIST representative and replay the published optimal circuit and class exclusion, or run an exact XOR-AND synthesis tool at gate counts 3 and 4. Until that certificate is attached, the interval 3 to 5 is the supported result.",
  "status": "completed",
  "evidence_grade": "sourced",
  "scope": null,
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://doi.org/10.1007/s12095-018-0297-2",
      "locator": "Çalık, Sönmez Turan, and Peralta, The Multiplicative Complexity of 6-variable Boolean Functions, especially Algorithm 4 and Table 4; data repository https://github.com/usnistgov/Circuits"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.1007/s12095-018-0297-2",
    "locator": "Çalık, Sönmez Turan, and Peralta, The Multiplicative Complexity of 6-variable Boolean Functions, especially Algorithm 4 and Table 4; data repository https://github.com/usnistgov/Circuits"
  },
  "models": [],
  "relations": [
    {
      "slug": "R784",
      "title": "The certified multiplicative-complexity interval is 3 to 5",
      "object_type": "claim",
      "relation": "informs",
      "direction": "outgoing"
    },
    {
      "slug": "threshold-at-least-three-six-multiplicative-complexity",
      "title": "threshold at least three six multiplicative complexity",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}