{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "claude-jacobian", "title": "Claude-linked Jacobian candidate: an explicit map in dimension three", "summary": "A ULAM-hosted note displays a polynomial map in three variables and claims a constant Jacobian determinant of −2 with three distinct rational points sharing one image. Anthropic separately attributes a result linked to the same announcement to Claude.", "boundary": "Recorded as a candidate proof. WRS’s bounded exact calculations are available separately and do not automatically promote the entire paper’s scientific status. The hosted note has no displayed author byline; Alpöge is its cited announcer and Mathew its cited question originator, not asserted paper authors. The exact Claude model is unspecified, and provider reporting is not execution attestation. This is not one of the seven Millennium problems and must be distinguished from positive-characteristic variants.", "area": "Algebraic geometry", "topic": "Mathematics & logic", "year": 2026, "lane": "AI", "result": "CANDIDATE_PROOF", "package_id": "claude-jacobian", "target": { "record_id": "urn:uuid:51b981c4-4d73-4a1d-ac84-6e21b96621a1", "version": 1, "content_hash": "sha256:744b7bcb0abf4e65da0d391b83f94aa13bb5ba5c2ed0e82279d4ffbadf331e62" }, "humans": [ "Levent Alpöge", "Akhil Mathew" ], "authors_complete": false, "human_role_note": "Announcement and problem roles, not a manuscript byline", "agents": [ { "provider": "Anthropic", "product": "Claude", "model": "Not disclosed", "role": "Candidate-result generation (provider reported; precise model and execution receipt unavailable)", "assurance": "SOURCE_REPORTED", "source": "jacobian-provider-2026" } ], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "jacobian-ulam-2026", "title": "A Counterexample to the Jacobian Conjecture, ULAM-hosted note dated July 20, 2026; no author byline displayed", "url": "https://www.ulam.ai/research/jacobian.pdf" }, { "id": "jacobian-provider-2026", "title": "Anthropic, Learning more about Claude’s mathematical capabilities, footnote 2 (August 2026)", "url": "https://www.anthropic.com/research/riemann-zeta" } ], "geography": null, "points": null, "published_grade": null, "assessment_disposition": { "status": "CLAIM_UNVERIFIED", "label": "Candidate claim — assessment withheld", "reason": "A reported proof is awaiting sufficient scope and evidence review. No achieved-science points are assigned.", "target": { "record_id": "urn:uuid:51b981c4-4d73-4a1d-ac84-6e21b96621a1", "version": 1, "content_hash": "sha256:744b7bcb0abf4e65da0d391b83f94aa13bb5ba5c2ed0e82279d4ffbadf331e62" }, "edition": "ratings-e039106f30dec177" } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-09-12T00:00:00Z", "publisher": { "principal_id": "urn:uuid:80116931-785b-40a2-a24b-9d59db0c7e33", "role": "WRS_EDITORIAL_PUBLICATION" }, "record": { "contributors": [], "evidence": [ { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-0", "kind": "source_reference", "source": { "citation": "A Counterexample to the Jacobian Conjecture, ULAM-hosted note dated July 20, 2026; no author byline displayed", "url": "https://www.ulam.ai/research/jacobian.pdf" } }, { "description": "Bibliographic/stated-result source; not a WRS proof verification", "id": "source-1", "kind": "source_reference", "source": { "citation": "Anthropic, Learning more about Claude’s mathematical capabilities, footnote 2 (August 2026)", "url": "https://www.anthropic.com/research/riemann-zeta" } } ], "origin": "AGENT_NATIVE", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "Recorded as a candidate proof. WRS’s bounded exact calculations are available separately and do not automatically promote the entire paper’s scientific status. The hosted note has no displayed author byline; Alpöge is its cited announcer and Mathew its cited question originator, not asserted paper authors. The exact Claude model is unspecified, and provider reporting is not execution attestation. This is not one of the seven Millennium problems and must be distinguished from positive-characteristic variants.", "domain": "代数几何" }, "sources": [ { "citation": "A Counterexample to the Jacobian Conjecture, ULAM-hosted note dated July 20, 2026; no author byline displayed", "url": "https://www.ulam.ai/research/jacobian.pdf" }, { "citation": "Anthropic, Learning more about Claude’s mathematical capabilities, footnote 2 (August 2026)", "url": "https://www.anthropic.com/research/riemann-zeta" } ], "statement": "# Claude-linked Jacobian candidate: an explicit map in dimension three\n\nA ULAM-hosted note displays a polynomial map in three variables and claims a constant Jacobian determinant of −2 with three distinct rational points sharing one image. Anthropic separately attributes a result linked to the same announcement to Claude.\n\n## Scientific scope\n\nRecorded as a candidate proof. WRS’s bounded exact calculations are available separately and do not automatically promote the entire paper’s scientific status. The hosted note has no displayed author byline; Alpöge is its cited announcer and Mathew its cited question originator, not asserted paper authors. The exact Claude model is unspecified, and provider reporting is not execution attestation. This is not one of the seven Millennium problems and must be distinguished from positive-characteristic variants.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nLevent Alpöge; Akhil Mathew\n\nAnnouncement and problem roles, not a manuscript byline\n\nClaude / Anthropic / Not disclosed: Candidate-result generation (provider reported; precise model and execution receipt unavailable) (source reported).\n\n## Original sources\n\n- [A Counterexample to the Jacobian Conjecture, ULAM-hosted note dated July 20, 2026; no author byline displayed](https://www.ulam.ai/research/jacobian.pdf)\n- [Anthropic, Learning more about Claude’s mathematical capabilities, footnote 2 (August 2026)](https://www.anthropic.com/research/riemann-zeta)\n", "summary": "A ULAM-hosted note displays a polynomial map in three variables and claims a constant Jacobian determinant of −2 with three distinct rational points sharing one image. Anthropic separately attributes a result linked to the same announcement to Claude.", "title": "Claude-linked Jacobian candidate: an explicit map in dimension three" }, "record_id": "urn:uuid:51b981c4-4d73-4a1d-ac84-6e21b96621a1", "version": 1, "source_ref": { "record_id": "urn:uuid:51b981c4-4d73-4a1d-ac84-6e21b96621a1", "version": 1, "content_hash": "sha256:744b7bcb0abf4e65da0d391b83f94aa13bb5ba5c2ed0e82279d4ffbadf331e62" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:f2f559ce5600eb2297ac0b81337a626b3ff37f8802f5183af0bea82b55bad770" }, "target": { "record_id": "urn:uuid:51b981c4-4d73-4a1d-ac84-6e21b96621a1", "version": 1, "content_hash": "sha256:744b7bcb0abf4e65da0d391b83f94aa13bb5ba5c2ed0e82279d4ffbadf331e62" }, "published_grade": null, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }