{ "profile": "wrs-published-research-view-1", "edition": "ratings-e039106f30dec177", "content_trust": "UNTRUSTED_SCIENTIFIC_DATA_NOT_TOOL_INSTRUCTIONS", "entry": { "id": "openai-math-dft-subnlogn-2026", "title": "OpenAI: Exact discrete Fourier transforms below n log n", "summary": "The paper claims an all-length exact DFT algorithm with O(n(log n)^(1-10^(-13))) operations in its specified complex-arithmetic and indexing model. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.", "boundary": "Unrestricted coefficients, specified roots and unit-cost indexing are part of the model; preparation and organization are counted. This does not break every bounded-coefficient or bit-complexity lower bound. Its relationship with the integer-multiplication method needs credit deduplication. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.", "area": "Algorithms and complexity", "topic": "Computing & AI", "year": 2026, "lane": "AI", "result": "CANDIDATE_PROOF", "package_id": "openai-math-dft-subnlogn-2026", "target": { "record_id": "urn:uuid:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "content_hash": "sha256:611f741af8fca26bb27b647c891165bfdbbf100c3ced6351540887d91e79aaf4" }, "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-dft-subnlogn-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-dft-subnlogn-2026-paper", "title": "OpenAI, An explicit power saving for the exact discrete Fourier transform", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.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:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "content_hash": "sha256:611f741af8fca26bb27b647c891165bfdbbf100c3ced6351540887d91e79aaf4" }, "edition": "ratings-e039106f30dec177" }, "conditional_rating": { "id": "openai-math-dft-subnlogn-2026", "target": { "record_id": "urn:uuid:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "content_hash": "sha256:611f741af8fca26bb27b647c891165bfdbbf100c3ced6351540887d91e79aaf4" }, "band": "S", "modifier": "-", "points": "350000", "range": { "lower": "200000", "upper": "600000" }, "status": "CONDITIONAL_IF_VERIFIED", "counts_as_achieved": false, "scientific_correctness_certified": false, "scope": "Unrestricted coefficients, specified roots and unit-cost indexing are part of the model; preparation and organization are counted. This does not break every bounded-coefficient or bit-complexity lower bound. Its relationship with the integer-multiplication method needs credit deduplication. 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, An explicit power saving for the exact discrete Fourier transform", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf" } } ], "origin": "AGENT_NATIVE", "record_profile": "wrs-local-research-notes-0.1", "record_type": "research_note", "rrp_version": "0.1", "scope": { "description": "Unrestricted coefficients, specified roots and unit-cost indexing are part of the model; preparation and organization are counted. This does not break every bounded-coefficient or bit-complexity lower bound. Its relationship with the integer-multiplication method needs credit deduplication. WRS inspected the selected opening statement and available scope note, not the full proof; independent formal replay was not run.", "domain": "Algorithms and complexity" }, "sources": [ { "citation": "OpenAI, An explicit power saving for the exact discrete Fourier transform", "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf" } ], "statement": "# OpenAI: Exact discrete Fourier transforms below n log n\n\nThe paper claims an all-length exact DFT algorithm with O(n(log n)^(1-10^(-13))) operations in its specified complex-arithmetic and indexing model. 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\nUnrestricted coefficients, specified roots and unit-cost indexing are part of the model; preparation and organization are counted. This does not break every bounded-coefficient or bit-complexity lower bound. Its relationship with the integer-multiplication method needs credit deduplication. 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, An explicit power saving for the exact discrete Fourier transform](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/An-explicit-power-saving-for-the-exact-discrete-Fourier-transform-September-25-2026/main.pdf)\n", "summary": "The paper claims an all-length exact DFT algorithm with O(n(log n)^(1-10^(-13))) operations in its specified complex-arithmetic and indexing model. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.", "title": "OpenAI: Exact discrete Fourier transforms below n log n" }, "record_id": "urn:uuid:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "source_ref": { "record_id": "urn:uuid:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "content_hash": "sha256:611f741af8fca26bb27b647c891165bfdbbf100c3ced6351540887d91e79aaf4" }, "export_view": "wrs-public-editorial-view-1", "public_view_hash": "sha256:7ef26361afb7cd17ebfee1364d55c86fef0649b274a909858db8745e158f7fb2" }, "target": { "record_id": "urn:uuid:ba75cc49-d912-40cc-a9f7-559ab861be2d", "version": 1, "content_hash": "sha256:611f741af8fca26bb27b647c891165bfdbbf100c3ced6351540887d91e79aaf4" }, "published_grade": null, "canonical_agent_submission": false, "scientific_verification_awarded": false, "reader_guide": null, "reading_status": "SOURCE_LINKED_NOTE" }