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    "title": "OpenAI: Claimed ordinary two-point Chowla cancellation",
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        "title": "OpenAI, Ordinary two-point correlations of multiplicative functions",
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        "description": "The constants may depend on fixed affine forms and need not be effective. No uniformity for coefficients growing with X is asserted. The result concerns two-point correlations, not the full higher-order Chowla conjecture. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.",
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      "statement": "# OpenAI: Claimed ordinary two-point Chowla cancellation\n\nThe manuscript claims a correlation bound O(X/(log X)^c) for Liouville values on every fixed pair of nonproportional affine forms, with an absolute positive c. It also claims a binary Elliott cancellation result under uniform nonpretentiousness. Ordinary averages count all integers equally. 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\nThe constants may depend on fixed affine forms and need not be effective. No uniformity for coefficients growing with X is asserted. The result concerns two-point correlations, not the full higher-order Chowla conjecture. WRS has inspected the cited statement and source-reported formalization scope where available; it has not audited the full proof or replayed Lean.\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 manuscript byline); individual human roles not fully disclosed\n\nOpenAI research model / OpenAI / Unreleased internal frontier model; exact identifier not disclosed: Source-reported mathematical argument generation; human preparation/editing roles retained separately where disclosed (source reported).\n\n## Original sources\n\n- [OpenAI, Ordinary two-point correlations of multiplicative functions](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Ordinary-two-point-correlations-of-multiplicative-functions-September-24-2026/final.pdf)\n",
      "summary": "The manuscript claims a correlation bound O(X/(log X)^c) for Liouville values on every fixed pair of nonproportional affine forms, with an absolute positive c. It also claims a binary Elliott cancellation result under uniform nonpretentiousness. Ordinary averages count all integers equally. Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.",
      "title": "OpenAI: Claimed ordinary two-point Chowla cancellation"
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