{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R659",
  "content_hash": null,
  "slug": "rm28-attempt-b347-slice-classification",
  "type": "attempt",
  "title": "Reproduce the B(3,4,7) high-nonlinearity orbit classification",
  "summary": "The next bounded task is an exact affine-orbit catalogue of B(3,4,7), with second-order nonlinearity and nearest-quadratic certificates for every representative.",
  "relevance": "For Covering radius of the second-order Reed-Muller code RM(2,8), record rm28-attempt-b347-slice-classification (“Reproduce the B(3,4,7) high-nonlinearity orbit classification”) documents a concrete method, search boundary, or failed route. The record states: The next bounded task is an exact affine-orbit catalogue of B(3,4,7), with second-order nonlinearity and nearest-quadratic certificates for every representative.",
  "relevance_source": "recorded",
  "body": "Here \\(B(3,4,7)\\) means the 7-variable Boolean functions whose algebraic normal forms have no terms below degree three and have degree at most four, viewed modulo \\(RM(2,7)\\) and under affine equivalence. Reproduce a canonical representative list and certify completeness by orbit-stabilizer counts totaling \\(2^{70}\\). For every representative, compute second-order nonlinearity exactly, retain full certificates for the high-nonlinearity strata, and compare the resulting cover set with Gillot and Langevin's published project files. The pinned repository has no detected license, so use a clean-room implementation and compare factual outputs until reuse terms are available. The output should include canonical ANFs, stabilizer orders, orbit sizes, exact distances, nearest quadratics, and stable digests.\n\nStop only after every representative has an exact distance and the orbit mass closes. Then feed the certified high-distance classes into the one-variable split \\(F(y,a)=H(y)+aG(y)\\) for eight variables. A retry is justified if the affine canonicalization or exact decoder first receives an independent small-case oracle and a proof-producing completeness check. This classification is a bounded input to the global problem, so any resulting upper bound still needs a complete reduction covering every remaining degree stratum.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "family",
    "statement": "the affine equivalence classes of 7-variable functions with valuation at least three and degree at most four",
    "family": "B(3,4,7) modulo RM(2,7) and the AGL(7,2) action"
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://langevin.univ-tln.fr/project/covering/covering.html",
      "locator": "Methodology, student project 1 and the B(3,4,7) high-second-order-nonlinearity cover-set discussion"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://langevin.univ-tln.fr/project/covering/covering.html",
    "locator": "Methodology, student project 1 and the B(3,4,7) high-second-order-nonlinearity cover-set discussion"
  },
  "models": [],
  "relations": [
    {
      "slug": "R662",
      "title": "The full covering radius satisfies 88 <= rho(2,8) <= 96",
      "object_type": "claim",
      "relation": "attempts",
      "direction": "outgoing"
    },
    {
      "slug": "R664",
      "title": "The relative cubic covering radius equals 88",
      "object_type": "claim",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "reed-muller-rm2-8-covering-radius",
      "title": "reed muller rm2 8 covering radius",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}