benchmarks: add reconstruction deck certificate

benchmarks/datasets/conjecture-probes-v1/members/reconstruction-deck-certificate.toml

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+schema_version="2"
+task_id="reconstruction-deck-certificate"
+task_name="jacobian/reconstruction-deck-certificate"
+evaluation_kind="conjecture-probe"
+domain="mathematical-sciences"
+primary_domain="graph-theory"
+field="graph-reconstruction"
+provenance_class="authored-conjecture-probe"
+provenance_ref="spreadsheet:unresolved-conjecture/C-042@2026-08-06"
+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/reconstruction-deck-certificate/README.md

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+# Reconstruction deck certificate
+
+Regression benchmark from retained row C-042. Its single objective is exact
+graph reconstruction from independently scrambled cards. The verifier checks
+nine full isomorphism embeddings and the sevenfold edge-occurrence identity,
+while accepting any globally relabeled reconstruction.
+
+Difficulty is provisional Hard because the agent must coordinate nine local
+label spaces into one global graph without a supplied correspondence.
+Source context: <https://mathworld.wolfram.com/GraphReconstructionConjecture.html>,
+status checked 2026-08-06. One finite reconstruction is no global proof.

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/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/reconstruction-deck-certificate/environment/input.json

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+{"task_id":"jacobian/reconstruction-deck-certificate","conjecture_id":"C-042","vertex_count":9,"edge_count":15,"cards":[{"card_id":"card-0","edges":[[0,1],[0,3],[1,4],[1,6],[2,5],[2,6],[2,7],[3,4],[3,6],[4,5],[4,7]]},{"card_id":"card-1","edges":[[0,1],[0,3],[0,5],[1,2],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[3,7],[4,7]]},{"card_id":"card-2","edges":[[0,2],[0,3],[0,4],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[4,7],[6,7]]},{"card_id":"card-3","edges":[[0,2],[0,3],[1,4],[1,6],[2,5],[2,7],[3,4],[3,5],[3,6],[4,7],[5,7]]},{"card_id":"card-4","edges":[[0,1],[0,2],[0,3],[1,4],[1,6],[2,4],[2,5],[2,7],[3,6],[4,5],[4,7],[5,6]]},{"card_id":"card-5","edges":[[0,3],[1,2],[1,4],[1,6],[1,7],[2,3],[2,5],[2,7],[3,6],[4,5],[4,7]]},{"card_id":"card-6","edges":[[0,3],[0,7],[1,2],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[4,5],[4,6],[4,7],[6,7]]},{"card_id":"card-7","edges":[[0,2],[0,3],[1,2],[1,3],[1,4],[1,6],[2,5],[2,7],[3,4],[3,6],[4,7],[6,7]]},{"card_id":"card-8","edges":[[0,1],[0,3],[0,6],[1,4],[1,5],[1,6],[2,5],[2,7],[3,4],[3,6],[4,7],[6,7]]}],"scope":"nine-card-reconstruction-v1"}

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/environment/submission_schema.json

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+{
+  "$defs": {
+    "edge": {
+      "items": {
+        "maximum": 8,
+        "minimum": 0,
+        "type": "integer"
+      },
+      "maxItems": 2,
+      "minItems": 2,
+      "type": "array"
+    },
+    "embedding": {
+      "additionalProperties": false,
+      "properties": {
+        "card_id": {
+          "pattern": "^card-[0-8]$",
+          "type": "string"
+        },
+        "deleted_vertex": {
+          "maximum": 8,
+          "minimum": 0,
+          "type": "integer"
+        },
+        "local_to_original": {
+          "items": {
+            "maximum": 8,
+            "minimum": 0,
+            "type": "integer"
+          },
+          "maxItems": 8,
+          "minItems": 8,
+          "type": "array",
+          "uniqueItems": true
+        }
+      },
+      "required": [
+        "card_id",
+        "deleted_vertex",
+        "local_to_original"
+      ],
+      "type": "object"
+    }
+  },
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "additionalProperties": false,
+  "properties": {
+    "claimed_assurance": {
+      "enum": [
+        "UNVERIFIED",
+        "COMPUTED",
+        "CHECKED",
+        "VERIFIED"
+      ]
+    },
+    "completeness": {
+      "const": "COMPLETE"
+    },
+    "conclusion": {
+      "const": "FINITE_GRAPH_DECK_RECONSTRUCTION"
+    },
+    "evidence": {
+      "items": {
+        "additionalProperties": false,
+        "properties": {
+          "path": {
+            "const": "evidence/answer.txt"
+          },
+          "sha256": {
+            "pattern": "^sha256:[0-9a-f]{64}$",
+            "type": "string"
+          }
+        },
+        "required": [
+          "path",
+          "sha256"
+        ],
+        "type": "object"
+      },
+      "maxItems": 1,
+      "minItems": 1,
+      "type": "array"
+    },
+    "limitations": {
+      "const": [
+        "ONE_SCRAMBLED_NINE_CARD_DECK",
+        "EXACT_CARD_EMBEDDINGS",
+        "NO_GLOBAL_RECONSTRUCTION_CONCLUSION"
+      ]
+    },
+    "result": {
+      "additionalProperties": false,
+      "properties": {
+        "edge_card_multiplicity": {
+          "const": 7
+        },
+        "embeddings": {
+          "items": {
+            "$ref": "#/$defs/embedding"
+          },
+          "maxItems": 9,
+          "minItems": 9,
+          "type": "array"
+        },
+        "original_edges": {
+          "items": {
+            "$ref": "#/$defs/edge"
+          },
+          "maxItems": 15,
+          "minItems": 15,
+          "type": "array",
+          "uniqueItems": true
+        },
+        "reconstruction_status": {
+          "const": "EXACT_UP_TO_RELABELING"
+        }
+      },
+      "required": [
+        "original_edges",
+        "embeddings",
+        "edge_card_multiplicity",
+        "reconstruction_status"
+      ],
+      "type": "object"
+    },
+    "scope": {
+      "const": "nine-card-reconstruction-v1",
+      "type": "string"
+    },
+    "task_id": {
+      "const": "jacobian/reconstruction-deck-certificate"
+    }
+  },
+  "required": [
+    "task_id",
+    "conclusion",
+    "result",
+    "claimed_assurance",
+    "scope",
+    "completeness",
+    "evidence",
+    "limitations"
+  ],
+  "type": "object"
+}

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/instruction.md

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+# Reconstruct a graph from its scrambled vertex deck
+
+The input contains nine independently relabeled eight-vertex cards. Recover a
+simple graph on vertices `0..8` with exactly 15 edges. For every card submit
+the deleted original vertex and a bijective `local_to_original` map of its
+local vertices `0..7` onto the other eight original vertices.
+
+The verifier checks every mapped card edge set against the corresponding
+vertex-deleted subgraph. It also aggregates all mapped cards and requires every
+original edge to occur exactly seven times and every nonedge zero times.
+Relabeled isomorphic reconstructions are accepted.
+
+Evidence is matching JSON (`application/json`) with exactly `schema_version`
+(the string `"1"`), `task_id`, `result`, and `limitations`. This reconstructs one finite deck only and
+does not prove the Reconstruction Conjecture.
+
+<!-- BEGIN PUBLIC CONTRACT SUBMISSION BLOCK -->
+## Submission
+
+Exact reconstruction of one finite deck only.
+
+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 `FINITE_GRAPH_DECK_RECONSTRUCTION`
+- **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 -->

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/solution/solve.py

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+from __future__ import annotations
+
+import argparse
+import hashlib
+import json
+from pathlib import Path
+
+TASK_ID = "jacobian/reconstruction-deck-certificate"
+LIMITATIONS = [
+    "ONE_SCRAMBLED_NINE_CARD_DECK",
+    "EXACT_CARD_EMBEDDINGS",
+    "NO_GLOBAL_RECONSTRUCTION_CONCLUSION",
+]
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--root", type=Path, default=Path("/app"))
+    root = parser.parse_args().root
+    original = [
+        [0, 1],
+        [0, 2],
+        [0, 3],
+        [0, 8],
+        [1, 2],
+        [1, 4],
+        [2, 3],
+        [2, 5],
+        [3, 4],
+        [3, 7],
+        [4, 5],
+        [5, 6],
+        [5, 8],
+        [6, 7],
+        [7, 8],
+    ]
+    maps = [
+        [1, 4, 7, 2, 5, 8, 3, 6],
+        [2, 5, 8, 3, 6, 0, 4, 7],
+        [3, 6, 0, 4, 7, 1, 5, 8],
+        [4, 7, 1, 5, 8, 2, 6, 0],
+        [5, 8, 2, 6, 0, 3, 7, 1],
+        [6, 0, 3, 7, 1, 4, 8, 2],
+        [7, 1, 4, 8, 2, 5, 0, 3],
+        [8, 2, 5, 0, 3, 6, 1, 4],
+        [0, 3, 6, 1, 4, 7, 2, 5],
+    ]
+    result = {
+        "original_edges": original,
+        "embeddings": [
+            {"card_id": f"card-{d}", "deleted_vertex": d, "local_to_original": maps[d]}
+            for d in range(9)
+        ],
+        "edge_card_multiplicity": 7,
+        "reconstruction_status": "EXACT_UP_TO_RELABELING",
+    }
+    payload = {
+        "schema_version": "1",
+        "task_id": TASK_ID,
+        "result": result,
+        "limitations": LIMITATIONS,
+    }
+    e = root / "evidence/answer.txt"
+    e.parent.mkdir(parents=True, exist_ok=True)
+    e.write_text(json.dumps(payload, sort_keys=True, separators=(",", ":")) + "\n")
+    s = {
+        "task_id": TASK_ID,
+        "conclusion": "FINITE_GRAPH_DECK_RECONSTRUCTION",
+        "result": result,
+        "claimed_assurance": "CHECKED",
+        "scope": "nine-card-reconstruction-v1",
+        "completeness": "COMPLETE",
+        "evidence": [
+            {
+                "path": "evidence/answer.txt",
+                "sha256": "sha256:" + hashlib.sha256(e.read_bytes()).hexdigest(),
+            }
+        ],
+        "limitations": LIMITATIONS,
+    }
+    (root / "submission.json").write_text(json.dumps(s, sort_keys=True) + "\n")
+
+
+if __name__ == "__main__":
+    main()

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/solution/solve.sh

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+#!/bin/sh
+set -eu
+python /solution/solve.py

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/task.toml

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+schema_version="1.4"
+artifacts=["/app/submission.json","/app/evidence"]
+[task]
+name="jacobian/reconstruction-deck-certificate"
+version="1.0.0"
+description="Reconstruct an exact graph from nine independently scrambled vertex-deleted cards."
+keywords=["graph-reconstruction","vertex-deck","isomorphism","multiplicity"]
+[metadata]
+evaluation_kind="conjecture-probe"
+domain="mathematical-sciences"
+primary_domain="graph-theory"
+field="graph-reconstruction"
+assurance_ceiling="CHECKED"
+answer_visibility="public"
+provenance_class="authored-conjecture-probe"
+fixture_digest="sha256:fa9628ff393ec8adcf919ebac9d4c260414ebb0318c339b64f768b022e009304"
+required_provider="core"
+author_name="Jacobian contributors"
+difficulty="hard"
+category="mathematics"
+tags=["difficulty-provisional","graph-reconstruction","isomorphism","offline"]
+case_version="conjecture-probes-v1"
+contamination_class="authored-finite-conjecture-probe"
+derivation="Derived from retained spreadsheet row C-042; the scrambled finite deck is authored and digest-pinned."
+[agent]
+timeout_sec=600.0
+[verifier]
+timeout_sec=120.0
+environment_mode="separate"
+[environment]
+network_mode="no-network"
+cpus=1
+memory_mb=1024
+storage_mb=4096
+[verifier.environment]
+network_mode="no-network"
+cpus=1
+memory_mb=1024
+storage_mb=4096

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/tests/Dockerfile

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+FROM python:3.12-slim@sha256:57cd7c3a7a273101a6485ba99423ee568157882804b1124b4dd04266317710de
+LABEL jacobian.task="jacobian/reconstruction-deck-certificate" \
+      jacobian.checksum="ec768c07e19e355b184d9ed64b2aec8fcea93765e671e3ae5e925e13282e47dc"
+RUN python -m pip install --no-cache-dir attrs==26.1.0 jsonschema==4.26.0 jsonschema-specifications==2025.9.1 referencing==0.37.0 rpds-py==2026.6.3 typing-extensions==4.16.0
+COPY input.json public_contract.json test.sh verifier.py verifier_support.py /tests/
+COPY input.json /app/input.json
+RUN chmod +x /tests/test.sh && python -c 'import json; assert json.load(open("/tests/input.json"))["task_id"] == "jacobian/reconstruction-deck-certificate"'

benchmarks/datasets/conjecture-probes-v1/reconstruction-deck-certificate/tests/input.json

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+{"task_id":"jacobian/reconstruction-deck-certificate","conjecture_id":"C-042","vertex_count":9,"edge_count":15,"cards":[{"card_id":"card-0","edges":[[0,1],[0,3],[1,4],[1,6],[2,5],[2,6],[2,7],[3,4],[3,6],[4,5],[4,7]]},{"card_id":"card-1","edges":[[0,1],[0,3],[0,5],[1,2],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[3,7],[4,7]]},{"card_id":"card-2","edges":[[0,2],[0,3],[0,4],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[4,7],[6,7]]},{"card_id":"card-3","edges":[[0,2],[0,3],[1,4],[1,6],[2,5],[2,7],[3,4],[3,5],[3,6],[4,7],[5,7]]},{"card_id":"card-4","edges":[[0,1],[0,2],[0,3],[1,4],[1,6],[2,4],[2,5],[2,7],[3,6],[4,5],[4,7],[5,6]]},{"card_id":"card-5","edges":[[0,3],[1,2],[1,4],[1,6],[1,7],[2,3],[2,5],[2,7],[3,6],[4,5],[4,7]]},{"card_id":"card-6","edges":[[0,3],[0,7],[1,2],[1,4],[1,6],[2,5],[2,7],[3,5],[3,6],[4,5],[4,6],[4,7],[6,7]]},{"card_id":"card-7","edges":[[0,2],[0,3],[1,2],[1,3],[1,4],[1,6],[2,5],[2,7],[3,4],[3,6],[4,7],[6,7]]},{"card_id":"card-8","edges":[[0,1],[0,3],[0,6],[1,4],[1,5],[1,6],[2,5],[2,7],[3,4],[3,6],[4,7],[6,7]]}],"scope":"nine-card-reconstruction-v1"}