{
  "date": "2026-09-08",
  "mode": "addition-only",
  "recognition": "Exact on recorded finite task probes; not a universal proof",
  "operations": [
    {
      "name": "op_001",
      "params": [
        "a",
        "b"
      ],
      "body": {
        "kind": "repeat",
        "value": null,
        "children": [
          {
            "kind": "read",
            "value": "b",
            "children": []
          },
          {
            "kind": "literal",
            "value": 0,
            "children": []
          },
          {
            "kind": "add",
            "value": null,
            "children": [
              {
                "kind": "read",
                "value": "state",
                "children": []
              },
              {
                "kind": "read",
                "value": "a",
                "children": []
              }
            ]
          }
        ]
      },
      "identity": "multiply",
      "task": "multiply",
      "training_cases": 25,
      "validation_cases": 21
    },
    {
      "name": "op_002",
      "params": [
        "n"
      ],
      "body": {
        "kind": "repeat",
        "value": null,
        "children": [
          {
            "kind": "read",
            "value": "n",
            "children": []
          },
          {
            "kind": "read",
            "value": "n",
            "children": []
          },
          {
            "kind": "read",
            "value": "i",
            "children": []
          }
        ]
      },
      "identity": "predecessor",
      "task": "predecessor",
      "training_cases": 6,
      "validation_cases": 6
    },
    {
      "name": "op_003",
      "params": [
        "n"
      ],
      "body": {
        "kind": "repeat",
        "value": null,
        "children": [
          {
            "kind": "read",
            "value": "n",
            "children": []
          },
          {
            "kind": "literal",
            "value": 1,
            "children": []
          },
          {
            "kind": "literal",
            "value": 0,
            "children": []
          }
        ]
      },
      "identity": "is_zero",
      "task": "is_zero",
      "training_cases": 6,
      "validation_cases": 6
    },
    {
      "name": "op_004",
      "params": [
        "a",
        "b"
      ],
      "body": {
        "kind": "repeat",
        "value": null,
        "children": [
          {
            "kind": "read",
            "value": "b",
            "children": []
          },
          {
            "kind": "read",
            "value": "a",
            "children": []
          },
          {
            "kind": "call",
            "value": "op_002",
            "children": [
              {
                "kind": "read",
                "value": "state",
                "children": []
              }
            ]
          }
        ]
      },
      "identity": "subtract",
      "task": "subtract",
      "training_cases": 25,
      "validation_cases": 10
    },
    {
      "name": "op_005",
      "params": [
        "a",
        "b"
      ],
      "body": {
        "kind": "call",
        "value": "op_003",
        "children": [
          {
            "kind": "call",
            "value": "op_004",
            "children": [
              {
                "kind": "repeat",
                "value": null,
                "children": [
                  {
                    "kind": "literal",
                    "value": 0,
                    "children": []
                  },
                  {
                    "kind": "read",
                    "value": "a",
                    "children": []
                  },
                  {
                    "kind": "read",
                    "value": "a",
                    "children": []
                  }
                ]
              },
              {
                "kind": "read",
                "value": "b",
                "children": []
              }
            ]
          }
        ]
      },
      "identity": "less_equal",
      "task": "less_equal",
      "training_cases": 25,
      "validation_cases": 10
    },
    {
      "name": "op_006",
      "params": [
        "n",
        "a",
        "b"
      ],
      "body": {
        "kind": "call",
        "value": "op_005",
        "children": [
          {
            "kind": "call",
            "value": "op_001",
            "children": [
              {
                "kind": "read",
                "value": "b",
                "children": []
              },
              {
                "kind": "read",
                "value": "a",
                "children": []
              }
            ]
          },
          {
            "kind": "read",
            "value": "n",
            "children": []
          }
        ]
      },
      "identity": "fits_groups",
      "task": "fits_groups",
      "training_cases": 80,
      "validation_cases": 12
    }
  ],
  "provenance": {
    "source_run": "7e539cda2e21425ebce4d1c2356c3379",
    "sha256": "a0046defe6daebe0a915e618949c0b4220c2fa956ad5ae3ec9310e17c8be238e",
    "source_options": {
      "seed": 0,
      "population": 400,
      "generations": 400,
      "attempts": 3,
      "max_steps": 200000,
      "training_steps": 30000,
      "recombine": true,
      "problems": [
        "multiply",
        "predecessor",
        "is_zero",
        "subtract",
        "less_equal",
        "fits_groups",
        "quotient",
        "remainder",
        "divmod"
      ]
    },
    "description": "Six genuinely evolved helpers. Trials start from this frozen learned library; no quotient, remainder, or diagnostic solution is supplied."
  },
  "sources": [
    {
      "artifact": "benchmarks/division/learned_helpers.yaml",
      "sha256": "a0046defe6daebe0a915e618949c0b4220c2fa956ad5ae3ec9310e17c8be238e"
    },
    {
      "artifact": "benchmarks/division/provenance.json",
      "sha256": "e20a67e50b4ebc8321154210ec82f3513b15cd0503e7aef7f0031df3479b86ee"
    },
    {
      "artifact": "genetic_gp/tools/addition.py",
      "sha256": "986dbc45bee80763ffcde96f4f66a813c95d29f66f0737322889791426af0e4d"
    }
  ]
}
