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Grace Lee Rui Yue
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benchmarks: add reconstruction deck certificate
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‎benchmarks/datasets/conjecture-probes-v1/members/reconstruction-deck-certificate.toml‎

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schema_version="2"
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task_id="reconstruction-deck-certificate"
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task_name="jacobian/reconstruction-deck-certificate"
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evaluation_kind="conjecture-probe"
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domain="mathematical-sciences"
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primary_domain="graph-theory"
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field="graph-reconstruction"
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provenance_class="authored-conjecture-probe"
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provenance_ref="spreadsheet:unresolved-conjecture/C-042@2026-08-06"
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assurance_ceiling="CHECKED"
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required_provider="core"
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environment_profile="core-python-minimal-verifier"
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verifier_contract_version="1"
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evaluation_owner="jacobian/conjecture-probes-v1"

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

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# Reconstruction deck certificate
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Regression benchmark from retained row C-042. Its single objective is exact
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graph reconstruction from independently scrambled cards. The verifier checks
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nine full isomorphism embeddings and the sevenfold edge-occurrence identity,
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while accepting any globally relabeled reconstruction.
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Difficulty is provisional Hard because the agent must coordinate nine local
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label spaces into one global graph without a supplied correspondence.
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Source context: <https://mathworld.wolfram.com/GraphReconstructionConjecture.html>,
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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
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COPY input.json submission_schema.json /app/
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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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{
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"$defs": {
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"edge": {
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"items": {
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"maximum": 8,
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"minimum": 0,
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"type": "integer"
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},
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"maxItems": 2,
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"minItems": 2,
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"type": "array"
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},
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"embedding": {
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"additionalProperties": false,
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"properties": {
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"card_id": {
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"pattern": "^card-[0-8]$",
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"type": "string"
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},
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"deleted_vertex": {
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"maximum": 8,
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"minimum": 0,
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"type": "integer"
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},
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"local_to_original": {
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"items": {
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"maximum": 8,
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"minimum": 0,
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"type": "integer"
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},
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"maxItems": 8,
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"minItems": 8,
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"type": "array",
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"uniqueItems": true
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}
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},
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"required": [
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"card_id",
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"deleted_vertex",
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"local_to_original"
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],
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"type": "object"
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}
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},
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"$schema": "https://json-schema.org/draft/2020-12/schema",
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"additionalProperties": false,
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"properties": {
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"claimed_assurance": {
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"enum": [
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"UNVERIFIED",
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"COMPUTED",
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"CHECKED",
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"VERIFIED"
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]
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},
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"completeness": {
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"const": "COMPLETE"
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},
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"conclusion": {
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"const": "FINITE_GRAPH_DECK_RECONSTRUCTION"
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},
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"evidence": {
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"items": {
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"additionalProperties": false,
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"properties": {
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"path": {
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"const": "evidence/answer.txt"
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},
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"sha256": {
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"pattern": "^sha256:[0-9a-f]{64}$",
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"type": "string"
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}
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},
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"required": [
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"path",
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"sha256"
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],
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"type": "object"
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},
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"maxItems": 1,
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"minItems": 1,
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"type": "array"
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},
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"limitations": {
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"const": [
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"ONE_SCRAMBLED_NINE_CARD_DECK",
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"EXACT_CARD_EMBEDDINGS",
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"NO_GLOBAL_RECONSTRUCTION_CONCLUSION"
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]
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},
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"result": {
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"additionalProperties": false,
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"properties": {
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"edge_card_multiplicity": {
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"const": 7
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},
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"embeddings": {
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"items": {
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"$ref": "#/$defs/embedding"
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},
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"maxItems": 9,
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"minItems": 9,
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"type": "array"
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},
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"original_edges": {
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"items": {
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"$ref": "#/$defs/edge"
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},
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"maxItems": 15,
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"minItems": 15,
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"type": "array",
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"uniqueItems": true
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},
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"reconstruction_status": {
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"const": "EXACT_UP_TO_RELABELING"
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}
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},
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"required": [
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"original_edges",
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"embeddings",
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"edge_card_multiplicity",
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"reconstruction_status"
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],
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"type": "object"
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},
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"scope": {
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"const": "nine-card-reconstruction-v1",
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"type": "string"
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},
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"task_id": {
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"const": "jacobian/reconstruction-deck-certificate"
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}
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},
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"required": [
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"task_id",
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"conclusion",
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"result",
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"claimed_assurance",
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"scope",
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"completeness",
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"evidence",
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"limitations"
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],
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"type": "object"
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}

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

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# Reconstruct a graph from its scrambled vertex deck
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The input contains nine independently relabeled eight-vertex cards. Recover a
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simple graph on vertices `0..8` with exactly 15 edges. For every card submit
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the deleted original vertex and a bijective `local_to_original` map of its
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local vertices `0..7` onto the other eight original vertices.
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The verifier checks every mapped card edge set against the corresponding
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vertex-deleted subgraph. It also aggregates all mapped cards and requires every
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original edge to occur exactly seven times and every nonedge zero times.
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Relabeled isomorphic reconstructions are accepted.
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Evidence is matching JSON with exactly `schema_version`, `task_id`, `result`,
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and `limitations`, at most 2 MiB. This reconstructs one finite deck only and
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does not prove the Reconstruction Conjecture.
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<!-- BEGIN PUBLIC CONTRACT SUBMISSION BLOCK -->
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## Submission
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Exact reconstruction of one finite deck only.
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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`.
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- **Conclusion:** exactly `FINITE_GRAPH_DECK_RECONSTRUCTION`
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- **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.
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- **Scope:** the exact value declared in `submission_schema.json`
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- **Completeness:** `COMPLETE`.
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- **Evidence:** 1-1 item(s); allowed path(s): `evidence/answer.txt`; digest must match `^sha256:[0-9a-f]{64}$`.
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- **Evidence media types:** `text/plain`.
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- **Required artifact filenames:** `evidence/answer.txt`.
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<!-- END PUBLIC CONTRACT SUBMISSION BLOCK -->

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

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

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

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

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

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

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

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FROM python:3.12-slim@sha256:57cd7c3a7a273101a6485ba99423ee568157882804b1124b4dd04266317710de
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LABEL jacobian.task="jacobian/reconstruction-deck-certificate" \
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jacobian.checksum="a6dd6b70690d8cb40cb925d65f830d589d97508d511b2fa95cec76631303df4e"
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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
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COPY input.json public_contract.json test.sh verifier.py verifier_support.py /tests/
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COPY input.json /app/input.json
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RUN chmod +x /tests/test.sh && python -c 'import json; assert json.load(open("/tests/input.json"))["task_id"] == "jacobian/reconstruction-deck-certificate"'

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