benchmarks: audit perfect-cuboid finite scope

benchmarks/datasets/conjecture-probes-v1/members/perfect-cuboid-scope-audit.toml

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+schema_version = "2"
+task_id = "perfect-cuboid-scope-audit"
+task_name = "jacobian/perfect-cuboid-scope-audit"
+evaluation_kind = "conjecture-probe"
+domain = "mathematical-sciences"
+primary_domain = "number-theory"
+field = "diophantine-equations"
+provenance_class = "authored-conjecture-probe"
+provenance_ref = "authored:unresolved-conjecture/C-012#perfect-cuboid-scope-audit"
+assurance_ceiling = "CHECKED"
+required_provider = "core"
+environment_profile = "core-python-minimal-verifier"
+verifier_contract_version = "1"
+evaluation_owner = "jacobian/conjecture-probes-v1"

benchmarks/datasets/conjecture-probes-v1/perfect-cuboid-scope-audit/README.md

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+# Perfect-cuboid finite scope audit
+
+This authored conjecture probe derives from retained spreadsheet row `C-012`.
+It asks an agent to distinguish Euler bricks, near-perfect cuboids, and perfect
+cuboids over twelve frozen triples using exact integer-square evidence.
+
+- **Family:** Assurance.
+- **Primary objective:** semantic scope handling for finite conjecture evidence.
+- **Portfolio contribution:** distinguishes three commonly conflated cuboid
+  predicates rather than rewarding a bounded search as an open-problem result.
+- **Shortcut audit:** a class label is insufficient; all four radicands and
+  their exact square roots must be supplied for every case, and case order is
+  not fixed.
+- **Difficulty:** Medium–Hard, provisional. The arithmetic is elementary, but
+  complete classification, exact evidence, and assurance calibration must all
+  agree; empirical calibration is pending.
+- **Quality score:** 86/100.
+
+The verifier independently recomputes every radicand and square predicate. It
+certifies only the frozen finite case set and never the existence or
+nonexistence of a perfect cuboid in general.
+
+## Sources
+
+The spreadsheet row is a curation lead, not an executable source. Definitions
+and current open status were checked against MathWorld's *Perfect Cuboid* and
+*Euler Brick* entries. The finite cases are authored fixtures; source examples
+do not serve as the verifier oracle.

benchmarks/datasets/conjecture-probes-v1/perfect-cuboid-scope-audit/environment/Dockerfile

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+FROM python:3.12-slim@sha256:57cd7c3a7a273101a6485ba99423ee568157882804b1124b4dd04266317710de
+COPY input.json submission_schema.json /app/
+WORKDIR /app

benchmarks/datasets/conjecture-probes-v1/perfect-cuboid-scope-audit/environment/input.json

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+{
+  "task_id": "jacobian/perfect-cuboid-scope-audit",
+  "conjecture_id": "C-012",
+  "scope_identity": "perfect-cuboid-scope-audit:case-set-v1",
+  "cases": [
+    {"id": "PC01", "edges": [44, 117, 240]},
+    {"id": "PC02", "edges": [85, 132, 720]},
+    {"id": "PC03", "edges": [140, 480, 693]},
+    {"id": "PC04", "edges": [160, 231, 792]},
+    {"id": "PC05", "edges": [240, 252, 275]},
+    {"id": "PC06", "edges": [104, 153, 672]},
+    {"id": "PC07", "edges": [3, 4, 12]},
+    {"id": "PC08", "edges": [6, 8, 24]},
+    {"id": "PC09", "edges": [1, 2, 2]},
+    {"id": "PC10", "edges": [7, 24, 25]},
+    {"id": "PC11", "edges": [9, 40, 41]},
+    {"id": "PC12", "edges": [20, 21, 29]}
+  ]
+}

benchmarks/datasets/conjecture-probes-v1/perfect-cuboid-scope-audit/environment/submission_schema.json

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+{
+  "$defs": {
+    "case": {
+      "additionalProperties": false,
+      "properties": {
+        "class": {
+          "enum": [
+            "PERFECT_CUBOID",
+            "EULER_BRICK_ONLY",
+            "SPACE_AND_TWO_FACES",
+            "OTHER"
+          ]
+        },
+        "edges": {
+          "items": {
+            "minimum": 1,
+            "type": "integer"
+          },
+          "maxItems": 3,
+          "minItems": 3,
+          "type": "array"
+        },
+        "face_radicands": {
+          "items": {
+            "minimum": 1,
+            "type": "integer"
+          },
+          "maxItems": 3,
+          "minItems": 3,
+          "type": "array"
+        },
+        "face_roots": {
+          "items": {
+            "$ref": "#/$defs/root_or_null"
+          },
+          "maxItems": 3,
+          "minItems": 3,
+          "type": "array"
+        },
+        "id": {
+          "pattern": "^PC(?:0[1-9]|1[0-2])$",
+          "type": "string"
+        },
+        "space_radicand": {
+          "minimum": 1,
+          "type": "integer"
+        },
+        "space_root": {
+          "$ref": "#/$defs/root_or_null"
+        }
+      },
+      "required": [
+        "id",
+        "edges",
+        "face_radicands",
+        "face_roots",
+        "space_radicand",
+        "space_root",
+        "class"
+      ],
+      "type": "object"
+    },
+    "root_or_null": {
+      "anyOf": [
+        {
+          "minimum": 0,
+          "type": "integer"
+        },
+        {
+          "type": "null"
+        }
+      ]
+    }
+  },
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "additionalProperties": false,
+  "properties": {
+    "claimed_assurance": {
+      "enum": [
+        "UNVERIFIED",
+        "COMPUTED",
+        "CHECKED",
+        "VERIFIED"
+      ]
+    },
+    "completeness": {
+      "const": "COMPLETE"
+    },
+    "conclusion": {
+      "const": "PERFECT_CUBOID_FINITE_SCOPE_AUDIT"
+    },
+    "evidence": {
+      "items": {
+        "additionalProperties": false,
+        "properties": {
+          "path": {
+            "const": "evidence/answer.txt"
+          },
+          "sha256": {
+            "pattern": "^sha256:[0-9a-f]{64}$",
+            "type": "string"
+          }
+        },
+        "required": [
+          "path",
+          "sha256"
+        ],
+        "type": "object"
+      },
+      "maxItems": 1,
+      "minItems": 1,
+      "type": "array"
+    },
+    "limitations": {
+      "const": [
+        "TWELVE_FROZEN_INTEGER_CUBOIDS",
+        "NO_GLOBAL_PERFECT_CUBOID_CONCLUSION"
+      ]
+    },
+    "result": {
+      "additionalProperties": false,
+      "properties": {
+        "case_counts": {
+          "additionalProperties": false,
+          "properties": {
+            "EULER_BRICK_ONLY": {
+              "minimum": 0,
+              "type": "integer"
+            },
+            "OTHER": {
+              "minimum": 0,
+              "type": "integer"
+            },
+            "PERFECT_CUBOID": {
+              "minimum": 0,
+              "type": "integer"
+            },
+            "SPACE_AND_TWO_FACES": {
+              "minimum": 0,
+              "type": "integer"
+            }
+          },
+          "required": [
+            "PERFECT_CUBOID",
+            "EULER_BRICK_ONLY",
+            "SPACE_AND_TWO_FACES",
+            "OTHER"
+          ],
+          "type": "object"
+        },
+        "cases": {
+          "items": {
+            "$ref": "#/$defs/case"
+          },
+          "maxItems": 12,
+          "minItems": 12,
+          "type": "array"
+        },
+        "contains_perfect_cuboid": {
+          "type": "boolean"
+        },
+        "scope_identity": {
+          "const": "perfect-cuboid-scope-audit:case-set-v1"
+        }
+      },
+      "required": [
+        "cases",
+        "case_counts",
+        "contains_perfect_cuboid",
+        "scope_identity"
+      ],
+      "type": "object"
+    },
+    "scope": {
+      "const": "perfect-cuboid-scope-audit:case-set-v1",
+      "type": "string"
+    },
+    "task_id": {
+      "const": "jacobian/perfect-cuboid-scope-audit"
+    }
+  },
+  "required": [
+    "task_id",
+    "conclusion",
+    "result",
+    "claimed_assurance",
+    "scope",
+    "completeness",
+    "evidence",
+    "limitations"
+  ],
+  "type": "object"
+}

benchmarks/datasets/conjecture-probes-v1/perfect-cuboid-scope-audit/instruction.md

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+# Audit finite evidence around the perfect-cuboid conjecture
+
+For every frozen integer-edge cuboid in `/app/input.json`, compute the three
+face-diagonal radicands and the space-diagonal radicand. Report an integer
+square root when the radicand is a perfect square and `null` otherwise, then
+classify the cuboid as exactly one of:
+
+- `PERFECT_CUBOID`: all three face diagonals and the space diagonal are integers;
+- `EULER_BRICK_ONLY`: all three face diagonals are integers but the space diagonal is not;
+- `SPACE_AND_TWO_FACES`: the space diagonal and exactly two face diagonals are integers;
+- `OTHER`: every remaining case.
+
+Submit all twelve cases exactly once, but their order is irrelevant. Report the
+counts of all four classes and whether the frozen family contains a perfect
+cuboid. The verifier recomputes every square predicate from the frozen edges.
+The three `face_radicands` entries and their aligned `face_roots` entries may
+be reported in any common order; the verifier compares the three aligned
+radicand/root pairs as an unordered set.
+
+`evidence/answer.txt` must be a JSON object with exactly `schema_version`,
+`task_id`, `result`, and `limitations`. Use schema version `1`, the task ID and
+limitations from the submission contract, and the same `result` object as in
+`submission.json`. The file must be no larger than 2 MiB.
+
+This is a finite semantic-scope audit. An Euler brick is not a perfect cuboid,
+and finding no perfect cuboid in these twelve cases is not evidence of global
+nonexistence. Claim `CHECKED` only for the frozen case set.
+
+<!-- BEGIN PUBLIC CONTRACT SUBMISSION BLOCK -->
+## Submission
+
+The verifier checks all finite square predicates independently; no bounded outcome resolves the open perfect-cuboid problem.
+
+Write `/app/submission.json` to the exact schema in `environment/submission_schema.json`. The submission envelope requires `task_id`, `conclusion`, `result`, `claimed_assurance`, `scope`, `completeness`, `evidence`, and `limitations`.
+
+- **Conclusion:** exactly `PERFECT_CUBOID_FINITE_SCOPE_AUDIT`
+- **Assurance:** scoreable values are `UNVERIFIED`, `COMPUTED`, `CHECKED` (ceiling `CHECKED`); the submission schema accepts any of `UNVERIFIED`, `COMPUTED`, `CHECKED`, `VERIFIED` but only scoreable assurances receive credit.
+- **Scope:** the exact value declared in `submission_schema.json`
+- **Completeness:** `COMPLETE`.
+- **Evidence:** 1-1 item(s); allowed path(s): `evidence/answer.txt`; digest must match `^sha256:[0-9a-f]{64}$`.
+- **Evidence media types:** `application/json`.
+- **Required artifact filenames:** `evidence/answer.txt`.
+<!-- END PUBLIC CONTRACT SUBMISSION BLOCK -->