{
  "schemaVersion": "1.0",
  "title": "Executable research routes — bounded graph pilot",
  "claimCeiling": "A curated, hypothesis-aware route library with one executable operator. Not an autonomous general research system. Matches are conditional; finite witness checking does not establish novelty or general acceleration.",
  "methods": [
    {
      "id": "reformulation",
      "status": "executable",
      "implementation": "Graph endpoint choices become a Boolean formula; witness mapped back to raw graph."
    },
    {
      "id": "serial-search",
      "status": "bounded",
      "implementation": "Retains every assignment count and route outcome in downloadable run records; no automatic open-ended campaign."
    },
    {
      "id": "named-obstructions",
      "status": "executable",
      "implementation": "Missing hypotheses and no-transversal are explicit; budget exhaustion is inconclusive."
    },
    {
      "id": "prove-too-much",
      "status": "tested",
      "implementation": "Small-graph exhaustive controls, 50-vertex obstruction and known domination-without-transversal control."
    },
    {
      "id": "lemma-recombination",
      "status": "bounded",
      "implementation": "Typed conditions compose curated lemma cards; not extraction from arbitrary papers."
    },
    {
      "id": "distant-imports",
      "status": "bounded",
      "implementation": "Public external graph-to-SAT bridge with precise source locations; keyword retrieval over curated cards."
    },
    {
      "id": "scale-recursion",
      "status": "not-implemented",
      "implementation": "This pilot has no scale-recursive operator; no claim that all nine patterns are automated."
    },
    {
      "id": "bookkeeping",
      "status": "executable",
      "implementation": "Exact integer counts, input hashes, missing hypotheses and scoped result states."
    },
    {
      "id": "chaining",
      "status": "bounded",
      "implementation": "Checked witness outputs feed route conditions in the same input-bound run; imported assertions are not trusted as checks."
    }
  ],
  "rules": [
    {
      "id": "matching-count-bound",
      "title": "Certify the supplied matching is minimum",
      "requires": [
        {
          "field": "maximalMatching",
          "op": "eq",
          "value": true
        },
        {
          "field": "matchingSize",
          "op": "eq",
          "otherField": "matchingLowerBound"
        }
      ],
      "produces": [
        "minimumMatchingByCounting"
      ],
      "methods": [
        "bookkeeping",
        "chaining"
      ],
      "source": {
        "url": "https://evidencepress.org/releases/txgraffiti-order48-successor/",
        "location": "Exact result for specialists"
      },
      "basis": "A maximal matching edge-dominates all edges. Each edge covers at most 2 Delta - 1 edges; ceiling(m/(2 Delta - 1)) is a lower bound. Equality with a checked witness establishes minimality.",
      "limit": "Works when this elementary lower bound is attained. Otherwise minimality remains unknown, not false."
    },
    {
      "id": "graph-to-sat",
      "title": "Reformulate domination as endpoint-transversal SAT",
      "requires": [
        {
          "field": "finiteSimple",
          "op": "eq",
          "value": true
        },
        {
          "field": "maximalMatching",
          "op": "eq",
          "value": true
        }
      ],
      "produces": [
        "transversalEncoding"
      ],
      "methods": [
        "reformulation",
        "distant-imports"
      ],
      "source": {
        "url": "https://arxiv.org/html/2608.22498v1",
        "location": "Definition 2 and Proposition 6"
      },
      "basis": "One Boolean variable selects an endpoint of each matching edge. A clause for every unmatched vertex requires a neighbour to be selected. Vertices adjacent to both endpoints of one edge give tautologies. Matched vertices are automatically dominated.",
      "limit": "SAT is equivalent to a dominating transversal of this matching, not to an arbitrary dominating set. The implemented equivalence also handles non-cubic finite simple graphs."
    },
    {
      "id": "enumerate-transversals",
      "title": "Find and independently check an explicit transversal",
      "requires": [
        {
          "field": "transversalEncoding",
          "op": "eq",
          "value": true
        },
        {
          "field": "matchingSize",
          "op": "lte",
          "value": 20
        }
      ],
      "produces": [
        "boundedSearchAvailable"
      ],
      "action": "matching-transversal",
      "methods": [
        "serial-search",
        "bookkeeping",
        "prove-too-much"
      ],
      "source": {
        "url": "https://arxiv.org/html/2608.22498v1",
        "location": "Proposition 6; finite assignment enumeration supplied by this pilot"
      },
      "basis": "Enumerate all 2^|M| assignments, reconstruct each first satisfying selection, then check domination from the original edges without using the clauses.",
      "limit": "At most 20 matching edges and 1,048,576 assignments. An exhausted user budget is inconclusive. No-transversal excludes only this restricted route."
    },
    {
      "id": "checked-domination-bound",
      "title": "Chain the checked witness into an ordinary-domination upper bound",
      "requires": [
        {
          "field": "witnessVerified",
          "op": "eq",
          "value": true
        }
      ],
      "produces": [
        "ordinaryUpperBoundCertified"
      ],
      "methods": [
        "chaining"
      ],
      "source": {
        "url": "https://arxiv.org/html/2609.10783v1",
        "location": "Section 1: definition of domination; Section 4: witness upper bound"
      },
      "basis": "Every vertex is either in the selected set or adjacent to it, so gamma(G) is at most the witness size.",
      "limit": "An upper bound is not an exact minimum. No lower bound is inferred from failure of a restricted search."
    },
    {
      "id": "compare-matching",
      "title": "Decide that this graph is not an ordinary-domination counterexample",
      "requires": [
        {
          "field": "ordinaryUpperBoundCertified",
          "op": "eq",
          "value": true
        },
        {
          "field": "minimumMatchingByCounting",
          "op": "eq",
          "value": true
        },
        {
          "field": "dominationUpper",
          "op": "lte",
          "otherField": "matchingSize"
        }
      ],
      "produces": [
        "ordinaryCounterexampleRuledOut"
      ],
      "methods": [
        "lemma-recombination",
        "chaining"
      ],
      "source": {
        "url": "https://arxiv.org/html/2608.22498v1",
        "location": "Proposition 1 (dominating transversal reduction)"
      },
      "basis": "Combine a graph-checked dominating set of size at most |M| with a checked minimum maximal matching M. This proves gamma(G) <= gamma_e(G) for this exact graph.",
      "limit": "No universal statement about regular graphs; the two graph objects and parameter meanings must be identical."
    },
    {
      "id": "external-order48",
      "title": "Prior-art stop: the order-48 inequality is already covered",
      "requires": [
        {
          "field": "degree",
          "op": "eq",
          "value": 3
        },
        {
          "field": "order",
          "op": "lte",
          "value": 48
        }
      ],
      "produces": [
        "knownGeneralResultApplicable"
      ],
      "methods": [
        "named-obstructions",
        "lemma-recombination"
      ],
      "source": {
        "url": "https://arxiv.org/html/2608.22498v1",
        "location": "Proposition 7, importing Zhang–Peitl–Szeider 2024"
      },
      "basis": "The cited preprint states gamma <= gamma_e for cubic graphs of order at most 48, using a minimum unsatisfiable bounded-occurrence CNF classification.",
      "limit": "Imported preprint and classification, not reverified here. Use this as a duplicate-research warning; the direct finite witness removes the imported classification from the pilot's conclusion."
    },
    {
      "id": "independent-upper",
      "title": "Independent domination transfers only an upper bound",
      "requires": [
        {
          "field": "independentWitnessVerified",
          "op": "eq",
          "value": true
        }
      ],
      "produces": [
        "independentWitnessGivesOrdinaryUpper"
      ],
      "methods": [
        "prove-too-much",
        "named-obstructions"
      ],
      "source": {
        "url": "https://arxiv.org/html/2609.10783v1",
        "location": "Section 8: ordinary versus independent domination"
      },
      "basis": "Every independent dominating set is dominating: gamma <= i. A lower bound on i is NOT a lower bound on gamma.",
      "limit": "Knowing i=16 does not prove gamma>=16. This invalid transfer is deliberately absent from the rule library."
    }
  ]
}