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yuelgrace1810-opsGrace Lee Rui Yuemorlutocursoragent
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benchmarks: construct an order-12 Hadamard certificate (#593)
* benchmarks: add order-12 Hadamard construction * fix(benchmarks): address hadamard-order12 verifier review comments - Change evidence media type from text/plain to application/json with payload_shape in instruction.md and public_contract.json - Decouple mathematics, evidence, scope, and assurance from contract; use require_input_binding=False and independent computation - Emit canonical reward dimensions (correctness, evidence_validity, scope_accuracy, assurance_calibration) in both main path and exception handler - Bound evidence memory to 2 MiB via max_bytes in evidence_list_is_bound and read_evidence_json - Accept all scoreable assurances (UNVERIFIED, COMPUTED, CHECKED) - Drop whitespace-churn commits during rebase onto origin/main * fix(benchmarks): address second-round review comments * fix(benchmarks): repair hadamard-order12-construction CI contract and lint Co-authored-by: morluto <morluto@users.noreply.github.com> --------- Co-authored-by: Grace Lee Rui Yue <graceleeruiyue@mac.lan> Co-authored-by: morluto <76467478+morluto@users.noreply.github.com> Co-authored-by: Cursor Agent <cursoragent@cursor.com> Co-authored-by: morluto <morluto@users.noreply.github.com>
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‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/README.md‎

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# Normalized order-12 Hadamard construction
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This authored finite conjecture probe derives from retained spreadsheet row
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`C-007`. It requires a complete non-Sylvester order-12 construction and exact
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orthogonality and determinant evidence.
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- **Family:** Regression.
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- **Primary objective:** exact combinatorial matrix construction.
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- **Portfolio contribution:** adds a non-power-of-two Hadamard construction,
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distinct from graph enumeration and semantic-scope audits.
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- **Shortcut audit:** knowing that order 12 exists or submitting a matrix label
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is insufficient; all 144 entries, all 144 Gram entries, normalization, and
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the exact determinant are independently replayed. Equivalent normalized
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constructions are accepted.
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- **Difficulty:** Hard, provisional. A valid non-Sylvester construction must be
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found and coordinated with exact determinant evidence; baseline calibration
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remains pending.
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- **Quality score:** 87/100.
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The verifier certifies only the submitted finite matrix. It does not establish
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the general Hadamard conjecture.
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## Sources
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The spreadsheet row is a curation lead. The finite task was authored after
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checking the Hadamard-matrix definition and open general status in MathWorld
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and the classical Paley construction literature. No source matrix is used as
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the verifier oracle.

‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/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/hadamard-order12-construction/environment/input.json‎

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{
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"task_id": "jacobian/hadamard-order12-construction",
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"conjecture_id": "C-007",
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"order": 12,
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"entry_domain": [-1, 1],
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"normalization": "FIRST_ROW_AND_COLUMN_POSITIVE",
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"scope_identity": "hadamard-order12-construction:normalized-v1"
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}

‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/environment/submission_schema.json‎

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{
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"$defs": {
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"entry_row": {
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"items": {
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"enum": [
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-1,
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1
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]
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},
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"maxItems": 12,
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"minItems": 12,
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"type": "array"
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},
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"integer_row": {
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"items": {
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"type": "integer"
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},
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"maxItems": 12,
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"minItems": 12,
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"type": "array"
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}
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},
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"$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": "HADAMARD_ORDER12_CONSTRUCTION"
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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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"ORDER_12_ONLY",
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"NO_GENERAL_HADAMARD_CONJECTURE_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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"determinant": {
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"type": "integer"
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},
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"determinant_abs": {
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"const": 2985984
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},
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"gram": {
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"items": {
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"$ref": "#/$defs/integer_row"
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},
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"maxItems": 12,
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"minItems": 12,
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"type": "array"
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},
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"matrix": {
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"items": {
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"$ref": "#/$defs/entry_row"
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},
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"maxItems": 12,
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"minItems": 12,
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"type": "array"
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},
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"scope_identity": {
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"const": "hadamard-order12-construction:normalized-v1"
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}
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},
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"required": [
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"matrix",
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"gram",
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"determinant",
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"determinant_abs",
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"scope_identity"
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],
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"type": "object"
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},
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"scope": {
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"const": "hadamard-order12-construction:normalized-v1",
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"type": "string"
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},
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"task_id": {
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"const": "jacobian/hadamard-order12-construction"
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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/hadamard-order12-construction/instruction.md‎

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# Construct and certify a normalized Hadamard matrix of order 12
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Construct a `12 × 12` matrix with entries in `{−1, 1}` whose first row and
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first column are all `1`. Supply the complete matrix, its complete integer Gram
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matrix `H H^T`, and the exact signed determinant.
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The verifier independently recomputes matrix dimensions, entries,
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normalization, every Gram entry, and the determinant using exact integer
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arithmetic. Any normalized order-12 Hadamard matrix is accepted; the matrix is
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not required to match a particular Paley presentation.
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This finite construction is evidence for one admissible order only. It does
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not prove the Hadamard matrix conjecture for every positive multiple of four.
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Claim `CHECKED` only for this order-12 certificate.
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<!-- BEGIN PUBLIC CONTRACT SUBMISSION BLOCK -->
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## Submission
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The verifier checks one complete normalized order-12 matrix; this finite construction does not prove the general conjecture.
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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 `HADAMARD_ORDER12_CONSTRUCTION`
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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:** `application/json`.
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- **Required artifact filenames:** `evidence/answer.txt`.
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<!-- END PUBLIC CONTRACT SUBMISSION BLOCK -->

‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/solution/solve.py‎

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"""Produce a Paley order-12 Oracle certificate."""
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from __future__ import annotations
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import hashlib
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import json
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import sys
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from pathlib import Path
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TASK_ID = "jacobian/hadamard-order12-construction"
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SCOPE = "hadamard-order12-construction:normalized-v1"
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LIMITATIONS = ["ORDER_12_ONLY", "NO_GENERAL_HADAMARD_CONJECTURE_CONCLUSION"]
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def determinant(matrix: list[list[int]]) -> int:
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work = [row[:] for row in matrix]
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sign = 1
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previous = 1
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for pivot_index in range(len(work) - 1):
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pivot_row = next(
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row for row in range(pivot_index, len(work)) if work[row][pivot_index]
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)
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if pivot_row != pivot_index:
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work[pivot_index], work[pivot_row] = work[pivot_row], work[pivot_index]
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sign = -sign
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pivot = work[pivot_index][pivot_index]
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for row in range(pivot_index + 1, len(work)):
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for column in range(pivot_index + 1, len(work)):
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work[row][column] = (
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work[row][column] * pivot
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- work[row][pivot_index] * work[pivot_index][column]
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) // previous
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work[row][pivot_index] = 0
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previous = pivot
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return sign * work[-1][-1]
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def main() -> None:
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root = (
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Path(sys.argv[2])
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if len(sys.argv) == 3 and sys.argv[1] == "--root"
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else Path("/app")
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)
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modulus = 11
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residues = {value * value % modulus for value in range(1, modulus)}
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matrix = [[1] * 12]
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for row in range(modulus):
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matrix.append(
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[1]
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+ [
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-1
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if row == column
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else (1 if (row - column) % modulus in residues else -1)
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for column in range(modulus)
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]
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)
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gram = [
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[sum(matrix[i][k] * matrix[j][k] for k in range(12)) for j in range(12)]
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for i in range(12)
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]
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det = determinant(matrix)
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result = {
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"matrix": matrix,
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"gram": gram,
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"determinant": det,
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"determinant_abs": abs(det),
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"scope_identity": SCOPE,
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}
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evidence = {
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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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evidence_path = root / "evidence/answer.txt"
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evidence_path.parent.mkdir(parents=True, exist_ok=True)
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evidence_path.write_text(
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json.dumps(evidence, sort_keys=True, separators=(",", ":")) + "\n"
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)
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digest = "sha256:" + hashlib.sha256(evidence_path.read_bytes()).hexdigest()
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submission = {
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"task_id": TASK_ID,
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"conclusion": "HADAMARD_ORDER12_CONSTRUCTION",
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"result": result,
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"claimed_assurance": "CHECKED",
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"scope": SCOPE,
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"completeness": "COMPLETE",
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"evidence": [{"path": "evidence/answer.txt", "sha256": digest}],
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"limitations": LIMITATIONS,
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}
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(root / "submission.json").write_text(
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json.dumps(submission, sort_keys=True, separators=(",", ":")) + "\n"
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)
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if __name__ == "__main__":
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main()

‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/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/hadamard-order12-construction/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/hadamard-order12-construction"
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version = "1.0.0"
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description = "Construct and exactly certify a normalized Hadamard matrix of order 12."
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keywords = ["combinatorics", "hadamard-matrix", "exact-linear-algebra", "construction", "conjecture-probe"]
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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 = "combinatorics"
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field = "design-theory"
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assurance_ceiling = "CHECKED"
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answer_visibility = "hidden-at-runtime"
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provenance_class = "authored-conjecture-probe"
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fixture_digest = "sha256:e6342e43bac8fb5814706966e2d84877864467d347ac1ccdf8bdabcbf50d0e61"
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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", "combinatorics", "matrix-construction", "exact-arithmetic", "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 = "Authored order-12 construction probe derived from retained conjecture row C-007."
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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/hadamard-order12-construction/tests/Dockerfile‎

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FROM python:3.12-slim@sha256:57cd7c3a7a273101a6485ba99423ee568157882804b1124b4dd04266317710de
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LABEL jacobian.task="jacobian/hadamard-order12-construction" \
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jacobian.checksum="4af579f4cb9122c49f115002ced5ff677c092a62ffd2635c3c949327f2e64e12"
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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/hadamard-order12-construction"'

‎benchmarks/datasets/conjecture-probes-v1/hadamard-order12-construction/tests/input.json‎

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{
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"task_id": "jacobian/hadamard-order12-construction",
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"conjecture_id": "C-007",
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"order": 12,
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"entry_domain": [-1, 1],
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"normalization": "FIRST_ROW_AND_COLUMN_POSITIVE",
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"scope_identity": "hadamard-order12-construction:normalized-v1"
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}

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