{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R498",
  "content_hash": null,
  "slug": "mdsc-attempt-full-singer-lower-bound",
  "type": "attempt",
  "title": "Test full Singer invariance as a lower-bound route",
  "summary": "The route fails to approach the known lower bound: exhaustive enumeration caps every fully Singer-invariant mixed code at 255, compared with the published size 334.",
  "relevance": "For Exact mixed-dimension subspace-code number A_2(7,4), record mdsc-attempt-full-singer-lower-bound (“Test full Singer invariance as a lower-bound route”) documents a concrete method, search boundary, or failed route. The record states: The route fails to approach the known lower bound: exhaustive enumeration caps every fully Singer-invariant mixed code at 255, compared with the published size 334.",
  "relevance_source": "recorded",
  "body": "The experiment fixes the irreducible action given by multiplication by x modulo x⁷+x+1. It enumerates all subspace orbits, discards every orbit with an internal distance below 4, and builds the complete compatibility graph of the survivors. The graph calculation proves a maximum invariant code size of 255. Full order-127 invariance is therefore too restrictive for improving the lower bound.",
  "status": "failed",
  "evidence_grade": "computational",
  "scope": {
    "kind": "bounded",
    "statement": "all codes invariant under the fixed order-127 Singer action represented by x modulo x^7+x+1",
    "bounds": {
      "ambient_subspaces": {
        "min": 29212,
        "max": 29212
      },
      "group_order": {
        "min": 127,
        "max": 127
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "locator": "Exact Singer-orbit experiment in mdsc-artifact-exact-f2-seven-census, executed 2026-07-28 UTC"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": null,
    "locator": "Exact Singer-orbit experiment in mdsc-artifact-exact-f2-seven-census, executed 2026-07-28 UTC"
  },
  "relations": [
    {
      "slug": "R497",
      "title": "Exact F₂⁷ census, Appendix C replay, and Singer-orbit search",
      "object_type": "artifact",
      "relation": "uses",
      "direction": "outgoing"
    },
    {
      "slug": "mixed-dimension-subspace-code-f2-7-d4",
      "title": "mixed dimension subspace code f2 7 d4",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}