{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "openai-math-kakeya-maximal-3d-2026", "title": "OpenAI: The three-dimensional Kakeya maximal conjecture", "summary": "For every positive epsilon the paper claims an L3(R3) to L3(S2) Kakeya maximal bound C_epsilon delta^(-epsilon), uniform over tube scale. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.", "boundary": "This is the maximal estimate, distinct from the prior three-dimensional set-dimension theorem and from the separate four-dimensional companion. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.", "area": "Harmonic analysis", "topic": "Mathematics", "year": 2026, "lane": "AI", "result": "CANDIDATE_PROOF", "package_id": "openai-math-kakeya-maximal-3d-2026", "target": { "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "content_hash": "sha256:d6185f66d122989b3be7fc2204ffb198cb1fe687e531c73245a0ba70448706c4" }, "humans": [], "authors_complete": false, "human_role_note": "OpenAI organizational byline; individual human preparation and verification roles incompletely disclosed", "agents": [ { "product": "OpenAI research model", "model": "Unreleased internal frontier model; exact identifier not disclosed", "provider": "OpenAI", "role": "Source-reported mathematical argument generation", "assurance": "SOURCE_REPORTED", "source": "openai-math-kakeya-maximal-3d-2026-paper" } ], "related": [], "subresults": [], "scientific_assessment": { "source_review": "SOURCE_CURATED", "scientific_review": "NOT_REVIEWED_BY_WRS", "formal_replay": "NOT_RUN", "provider_attestation": "NONE" }, "sources": [ { "id": "openai-math-kakeya-maximal-3d-2026-paper", "title": "OpenAI, The Kakeya maximal conjecture in three dimensions", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf", "kind": "ORIGINAL_MANUSCRIPT" } ], "geography": null, "points": null, "published_grade": null, "assessment_disposition": { "status": "CLAIM_UNVERIFIED", "label": "Reported result ยท unverified", "reason": "Provisional grade and reference score included in rankings; scientific correctness has not been independently established.", "target": { "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "content_hash": "sha256:d6185f66d122989b3be7fc2204ffb198cb1fe687e531c73245a0ba70448706c4" }, "edition": "ratings-e039106f30dec177" }, "conditional_rating": { "id": "openai-math-kakeya-maximal-3d-2026", "target": { "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "content_hash": "sha256:d6185f66d122989b3be7fc2204ffb198cb1fe687e531c73245a0ba70448706c4" }, "band": "S", "modifier": null, "points": "500000", "range": { "lower": "300000", "upper": "750000" }, "status": "CONDITIONAL_IF_VERIFIED", "counts_as_achieved": false, "scientific_correctness_certified": false, "scope": "This is the maximal estimate, distinct from the prior three-dimensional set-dimension theorem and from the separate four-dimensional companion. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run." } }, "version": { "kind": "PUBLIC_RECORD_VIEW", "previous": null, "published_at": "2026-10-12T00:00:00Z", "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": "OpenAI, The Kakeya maximal conjecture in three dimensions", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf" } } ], "origin": "AGENT_NATIVE", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "This is the maximal estimate, distinct from the prior three-dimensional set-dimension theorem and from the separate four-dimensional companion. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.", "domain": "Harmonic analysis" }, "sources": [ { "citation": "OpenAI, The Kakeya maximal conjecture in three dimensions", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf" } ], "statement": "# OpenAI: The three-dimensional Kakeya maximal conjecture\n\nFor every positive epsilon the paper claims an L3(R3) to L3(S2) Kakeya maximal bound C_epsilon delta^(-epsilon), uniform over tube scale. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.\n\n## Scientific scope\n\nThis is the maximal estimate, distinct from the prior three-dimensional set-dimension theorem and from the separate four-dimensional companion. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.\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\n\n\nOpenAI organizational byline; individual human preparation and verification roles incompletely disclosed\n\nOpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation (source reported).\n\n## Original sources\n\n- [OpenAI, The Kakeya maximal conjecture in three dimensions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Kakeya-maximal-conjecture-in-three-dimensions-September-23-2026/paper.pdf)\n", "summary": "For every positive epsilon the paper claims an L3(R3) to L3(S2) Kakeya maximal bound C_epsilon delta^(-epsilon), uniform over tube scale. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.", "title": "OpenAI: The three-dimensional Kakeya maximal conjecture" }, "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "source_ref": { "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "content_hash": "sha256:d6185f66d122989b3be7fc2204ffb198cb1fe687e531c73245a0ba70448706c4" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:b50b76823fb0ecf4cfb8f3fc464603e91d41ef0d4f2afec79cc262037308fac8" }, "target": { "record_id": "urn:uuid:56bd512f-3fc1-41f6-aeb3-dcbf3b682d82", "version": 1, "content_hash": "sha256:d6185f66d122989b3be7fc2204ffb198cb1fe687e531c73245a0ba70448706c4" }, "published_grade": null, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }