What is recorded here?
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.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
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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People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed The recorded author list is incomplete.
OpenAI 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 attribution; provider attestation is unavailable.
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English catalogue narrative
OpenAI: Claimed ordinary two-point Chowla cancellation
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.
Scientific scope
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.
Reading status
This 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.
People and systems
OpenAI (organizational manuscript byline); individual human roles not fully disclosed
OpenAI 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).