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yuelgrace1810-opsGrace Lee Rui Yuemorlutocursoragent
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benchmarks: add Hodge blow-up divisor certificate (#601)
* benchmarks: add Hodge blow-up divisor certificate * benchmarks: use registered Hodge primary domain * fix(benchmarks): address hodge-divisor verifier review comments - Document required evidence schema_version (string "1") in instruction.md and public_contract.json with payload_shape - Change evidence media type from text/plain to application/json - Document primitive-coefficient requirement (GCD must be 1) in instruction.md - Decouple mathematics, evidence, scope, and assurance from contract - Detect VERIFIED claims from raw submission before schema validation for false_certification detection - Accept all scoreable assurances (UNVERIFIED, COMPUTED, CHECKED) - Drop whitespace-churn commits during rebase onto origin/main * fix(benchmarks): bound raw submission, remove evidence cap, refresh checksum - Bound _raw_submission() with is_regular_bounded_file - Remove undocumented evidence size limit per benchmark policy - Refresh Dockerfile checksum label * fix(benchmarks): repair hodge-blowup-divisor-certificate CI contract and lint Co-authored-by: morluto <morluto@users.noreply.github.com> * fix(benchmarks): bound raw parser, accept integral coefficients, refresh checksum - Add is_regular_bounded_file check before reading /app/submission.json - Accept schema-valid integral coefficient numbers (12.0 as 12) - Refresh Dockerfile checksum label * fix(benchmarks): parse diagnostics independently, accept integral-only coefficients, refresh checksum --------- 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/hodge-blowup-divisor-certificate/README.md‎

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# Hodge blow-up divisor certificate
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Assurance benchmark from retained row C-039. Its single objective is exact
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algebraic-cycle certification: polynomial incidence and simple multiplicity at
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six points, followed by divisor-class, intersection, and adjunction replay.
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Alternative primitive cubics satisfying the same contract are accepted.
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Difficulty is provisional Hard because symbolic polynomial evaluation,
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derivatives, blow-up signs, canonical pairing, genus, and scope calibration
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must all align. Lefschetz (1,1) is trusted; no higher-codimension Hodge claim is
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made. Source: <https://www.claymath.org/millennium-problems/hodge-conjecture/>,
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status checked 2026-08-06.

‎benchmarks/datasets/conjecture-probes-v1/hodge-blowup-divisor-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/hodge-blowup-divisor-certificate/environment/input.json‎

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{"task_id":"jacobian/hodge-blowup-divisor-certificate","conjecture_id":"C-039","degree":3,"monomial_order":["x^3","x^2y","x^2z","xy^2","xyz","xz^2","y^3","y^2z","yz^2","z^3"],"blowup_points":[[0,0,1],[1,0,1],[0,1,1],[1,1,1],[2,0,1],[0,2,1]],"coefficient_bound":20,"scope":"six-point-p2-blowup-divisor-v1"}

‎benchmarks/datasets/conjecture-probes-v1/hodge-blowup-divisor-certificate/environment/submission_schema.json‎

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{
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"$defs": {
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"point_check": {
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"additionalProperties": false,
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"properties": {
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"gradient": {
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"items": {
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"type": "integer"
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},
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"maxItems": 3,
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"minItems": 3,
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"type": "array"
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},
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"multiplicity": {
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"const": 1
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},
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"point_index": {
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"maximum": 5,
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"minimum": 0,
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"type": "integer"
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},
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"value": {
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"const": 0
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}
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},
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"required": [
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"point_index",
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"value",
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"gradient",
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"multiplicity"
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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": "ALGEBRAIC_DIVISOR_CLASS_CERTIFICATE"
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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_CUBIC_DIVISOR_ON_ONE_BLOWUP",
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"LEFSCHETZ_1_1_TRUSTED",
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"NO_HIGHER_CODIMENSION_HODGE_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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"arithmetic_genus": {
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"const": 1
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},
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"canonical_intersection": {
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"const": -3
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},
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"coefficients": {
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"items": {
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"maximum": 20,
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"minimum": -20,
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"type": "integer"
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},
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"maxItems": 10,
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"minItems": 10,
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"type": "array"
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},
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"cycle_classification": {
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"const": "ALGEBRAIC_DIVISOR_HODGE_1_1"
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},
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"divisor_class": {
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"const": [
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3,
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-1,
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-1,
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-1,
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-1,
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-1,
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-1
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]
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},
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"point_checks": {
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"items": {
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"$ref": "#/$defs/point_check"
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},
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"maxItems": 6,
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"minItems": 6,
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"type": "array"
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},
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"self_intersection": {
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"const": 3
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}
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},
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"required": [
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"coefficients",
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"point_checks",
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"divisor_class",
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"self_intersection",
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"canonical_intersection",
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"arithmetic_genus",
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"cycle_classification"
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],
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"type": "object"
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},
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"scope": {
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"const": "six-point-p2-blowup-divisor-v1",
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"type": "string"
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},
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"task_id": {
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"const": "jacobian/hodge-blowup-divisor-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/hodge-blowup-divisor-certificate/instruction.md‎

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# Certify an algebraic divisor class on a six-point blow-up
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Submit a nonzero homogeneous cubic over `ZZ`, in the frozen ten-monomial
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order, that vanishes simply at all six frozen points. For each point report the
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polynomial value and three first partial derivatives. At least one derivative
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must be nonzero, certifying multiplicity exactly one.
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For the strict-transform divisor class `D=3H-E1-...-E6`, report its class
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vector, `D^2`, `D·K` for `K=-3H+E1+...+E6`, and the adjunction arithmetic
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genus. The verifier recomputes all evaluations and intersection arithmetic.
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The coefficients must be primitive (i.e., their GCD must be 1); scalar multiples
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are rejected. Evidence is matching JSON with exactly `schema_version`, `task_id`, `result`,
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and `limitations`. Lefschetz (1,1) is a declared trusted theorem.
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This one divisor certificate does not address higher-codimension Hodge classes
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or prove the Hodge Conjecture.
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<!-- BEGIN PUBLIC CONTRACT SUBMISSION BLOCK -->
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## Submission
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Exact divisor-class certificate under trusted Lefschetz (1,1); no general Hodge conclusion.
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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 `ALGEBRAIC_DIVISOR_CLASS_CERTIFICATE`
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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/hodge-blowup-divisor-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/hodge-blowup-divisor-certificate"
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LIMITATIONS = [
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"ONE_CUBIC_DIVISOR_ON_ONE_BLOWUP",
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"LEFSCHETZ_1_1_TRUSTED",
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"NO_HIGHER_CODIMENSION_HODGE_CONCLUSION",
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]
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EXP = [
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(3, 0, 0),
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(2, 1, 0),
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(2, 0, 1),
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(1, 2, 0),
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(1, 1, 1),
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(1, 0, 2),
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(0, 3, 0),
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(0, 2, 1),
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(0, 1, 2),
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(0, 0, 3),
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]
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POINTS = [(0, 0, 1), (1, 0, 1), (0, 1, 1), (1, 1, 1), (2, 0, 1), (0, 2, 1)]
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def ev(c, p):
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return sum(
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v * p[0] ** a * p[1] ** b * p[2] ** d
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for v, (a, b, d) in zip(c, EXP, strict=True)
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)
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def grad(c, p):
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out = []
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for axis in range(3):
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total = 0
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for v, e in zip(c, EXP, strict=True):
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if e[axis]:
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q = list(e)
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q[axis] -= 1
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total += v * e[axis] * p[0] ** q[0] * p[1] ** q[1] * p[2] ** q[2]
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out.append(total)
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return out
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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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c = [1, 0, -3, 0, 0, 2, 1, -3, 2, 0]
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result = {
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"coefficients": c,
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"point_checks": [
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{
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"point_index": i,
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"value": ev(c, p),
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"gradient": grad(c, p),
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"multiplicity": 1,
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}
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for i, p in enumerate(POINTS)
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],
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"divisor_class": [3, -1, -1, -1, -1, -1, -1],
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"self_intersection": 3,
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"canonical_intersection": -3,
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"arithmetic_genus": 1,
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"cycle_classification": "ALGEBRAIC_DIVISOR_HODGE_1_1",
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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": "ALGEBRAIC_DIVISOR_CLASS_CERTIFICATE",
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"result": result,
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"claimed_assurance": "CHECKED",
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"scope": "six-point-p2-blowup-divisor-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/hodge-blowup-divisor-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/hodge-blowup-divisor-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/hodge-blowup-divisor-certificate"
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version="1.0.0"
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description="Construct and replay a cubic divisor class on the blow-up of P2 at six rational points."
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keywords=["hodge","divisors","blowup","intersection-theory","adjunction"]
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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="geometry-topology"
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field="algebraic-cycles"
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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="sha256:7aed2472755c817517af313292b09ff011f0cd000b82c6077e8ead0e5b3a9105"
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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","algebraic-geometry","intersection-theory","scope-audit","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-039; the cubic and six-point blow-up fixture are authored."
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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/hodge-blowup-divisor-certificate/tests/Dockerfile‎

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FROM python:3.12-slim@sha256:57cd7c3a7a273101a6485ba99423ee568157882804b1124b4dd04266317710de
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LABEL jacobian.task="jacobian/hodge-blowup-divisor-certificate" \
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jacobian.checksum="4d810a82740d05f3014e3bf9f4b61324c65988a60e07cbd4d579b7708585df24"
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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/hodge-blowup-divisor-certificate"'

‎benchmarks/datasets/conjecture-probes-v1/hodge-blowup-divisor-certificate/tests/input.json‎

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{"task_id":"jacobian/hodge-blowup-divisor-certificate","conjecture_id":"C-039","degree":3,"monomial_order":["x^3","x^2y","x^2z","xy^2","xyz","xz^2","y^3","y^2z","yz^2","z^3"],"blowup_points":[[0,0,1],[1,0,1],[0,1,1],[1,1,1],[2,0,1],[0,2,1]],"coefficient_bound":20,"scope":"six-point-p2-blowup-divisor-v1"}

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