f0909172434.github.io

{
  "name": "get_workspace_state",
  "kind": "answer",
  "impl": "imperative",
  "description": "Read the current Finite Witness conjecture, search bound, latest result, and saved evidence without changing the workspace.",
  "inputSchema": {
    "type": "object",
    "properties": {},
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "load_demo_scenario",
  "kind": "act",
  "impl": "imperative",
  "description": "Load one curated graph conjecture into the visible workbench so the person and agent can inspect and test it together.",
  "inputSchema": {
    "type": "object",
    "properties": {
      "scenario": {
        "type": "string",
        "enum": [
          "triangle",
          "even-cycle",
          "perfect-matching",
          "diameter"
        ],
        "description": "The curated conjecture to load."
      }
    },
    "required": [
      "scenario"
    ],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "configure_conjecture",
  "kind": "act",
  "impl": "imperative",
  "description": "Configure a finite simple graph conjecture in the visible workbench. Omitted fields keep their current values. This changes the shared page but does not run a search.",
  "inputSchema": {
    "type": "object",
    "properties": {
      "name": {
        "type": "string",
        "minLength": 1,
        "maxLength": 72
      },
      "connected": {
        "type": "boolean"
      },
      "min_degree": {
        "type": [
          "integer",
          "null"
        ],
        "minimum": 1,
        "maximum": 3
      },
      "bipartite": {
        "type": "string",
        "enum": [
          "any",
          "yes",
          "no"
        ]
      },
      "triangle_free": {
        "type": "boolean"
      },
      "all_even_degrees": {
        "type": "boolean"
      },
      "even_order": {
        "type": "boolean"
      },
      "edge_surplus": {
        "type": [
          "integer",
          "null"
        ],
        "enum": [
          null,
          0,
          1
        ]
      },
      "max_diameter": {
        "type": [
          "integer",
          "null"
        ],
        "enum": [
          null,
          2,
          3
        ]
      },
      "conclusion": {
        "type": "string",
        "enum": [
          "contains_triangle",
          "is_cycle",
          "is_bipartite",
          "has_perfect_matching",
          "has_even_edge_count",
          "diameter_at_most_2"
        ]
      },
      "max_vertices": {
        "type": "integer",
        "minimum": 3,
        "maximum": 6
      }
    },
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "search_counterexample",
  "kind": "act",
  "impl": "imperative",
  "description": "Exhaustively search labeled finite simple graphs in increasing vertex order for the smallest counterexample to the visible conjecture. Updates the shared visualization and returns exact metrics and search counts.",
  "inputSchema": {
    "type": "object",
    "properties": {},
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "save_current_witness",
  "kind": "act",
  "impl": "imperative",
  "description": "Save the current counterexample and its exact conjecture, metrics, and search count to the browser-local evidence shelf. Requires a counterexample to be visible.",
  "inputSchema": {
    "type": "object",
    "properties": {
      "note": {
        "type": "string",
        "maxLength": 180,
        "description": "Optional short reason for saving this witness."
      }
    },
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "suggest_conjecture_repairs",
  "kind": "act",
  "impl": "imperative",
  "description": "Return up to three stronger assumptions that exclude the current counterexample, including machine-readable patches and the resulting next claim. Suggestions are hypotheses, not proofs.",
  "inputSchema": {
    "type": "object",
    "properties": {},
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "apply_conjecture_repair",
  "kind": "act",
  "impl": "imperative",
  "description": "Apply one suggested repair to the shared conjecture and optionally run the next exhaustive search. This creates a visible, verifiable human-agent repair loop.",
  "inputSchema": {
    "type": "object",
    "properties": {
      "repair_id": {
        "type": "string",
        "enum": [
          "min-degree-3",
          "non-bipartite",
          "diameter-2",
          "edge-surplus-1",
          "all-even"
        ]
      },
      "run_search": {
        "type": "boolean",
        "description": "When true, immediately test the repaired conjecture."
      }
    },
    "required": [
      "repair_id"
    ],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}

{
  "name": "get_counterexample_certificate",
  "kind": "answer",
  "impl": "imperative",
  "description": "Return a deterministic certificate for the visible counterexample, including the exact claim, edge mask, edge list, metrics, bounded enumeration order, and search counts.",
  "inputSchema": {
    "type": "object",
    "properties": {},
    "required": [],
    "additionalProperties": false
  },
  "page": "/finite-witness-webmcp/"
}