{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R24",
  "content_hash": null,
  "slug": "asq-attempt-low-expansion-morphism-search",
  "type": "attempt",
  "title": "Search for a low-expansion morphism and certify it",
  "summary": "Synthesize a primitive morphism with at most two expanding eigendirections and a finite integer weighting, then apply the finite template-ancestor test under its valid spectral hypothesis.",
  "relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-attempt-low-expansion-morphism-search (“Search for a low-expansion morphism and certify it”) documents a concrete method, search boundary, or failed route. The record states: Synthesize a primitive morphism with at most two expanding eigendirections and a finite integer weighting, then apply the finite template-ancestor test under its valid spectral hypothesis.",
  "relevance_source": "recorded",
  "body": "Search primitive prolongable morphisms on four to six letters together with distinct normalized integer weights. The first bounded batch uses uniform image lengths 2 through 6 and weights between 0 and 20, with letter-permutation, translation, gcd, and reflection symmetries removed. A SAT or constraint model should reject additive squares in iterated prefixes and require no incidence eigenvalue of absolute value 1. Retain candidates whose expanding eigenspace has dimension at most 2 and on which Phi(letter)=(1,weight(letter)) is injective. For each survivor, use exact algebraic arithmetic to verify the spectral condition, enumerate the finite forbidden-template ancestor set, and check the theorem's finite factor bound. Save the symmetry quotient, candidate morphism, weight map, linear-algebra certificate, template set, and checker output. A passing certificate would answer the canonical problem.",
  "status": "next_experiment",
  "evidence_grade": "self_reported",
  "scope": {
    "kind": "bounded",
    "statement": "the first morphism-synthesis batch on 4 to 6 letters, uniform lengths 2 to 6, and normalized weights 0 to 20",
    "bounds": {
      "morphism_alphabet_size": {
        "min": 4,
        "max": 6
      },
      "uniform_image_length": {
        "min": 2,
        "max": 6
      },
      "integer_weight": {
        "min": 0,
        "max": 20
      },
      "prefix_screen_length": {
        "min": 100000,
        "max": 100000
      }
    },
    "exhaustive": false
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "source_only",
    "kind": "attempt",
    "citation": {
      "url": "https://arxiv.org/abs/1511.05875",
      "locator": "Rao and Rosenfeld, arXiv:1511.05875v2, Applications section, proposition on finite parents and theorem deciding k-th-power-modulo-Phi freeness"
    },
    "missing": [
      "source",
      "command",
      "runtime",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://arxiv.org/abs/1511.05875",
    "locator": "Rao and Rosenfeld, arXiv:1511.05875v2, Applications section, proposition on finite parents and theorem deciding k-th-power-modulo-Phi freeness"
  },
  "models": [],
  "relations": [
    {
      "slug": "R25",
      "title": "The smallest height-361 projection survivor fails at 250952",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R28",
      "title": "The exact finite maximum for {0,1,2,4} is 62",
      "object_type": "claim",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "R23",
      "title": "The direct h6 template criterion fails by dimension",
      "object_type": "attempt",
      "relation": "informs",
      "direction": "incoming"
    },
    {
      "slug": "additive-square-finite-alphabet",
      "title": "additive square finite alphabet",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}