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The binary corrected Elliott conjecture for ordinary averages

For multiplicative $f_1,f_2:\mathbb{N}\to\{|z|\le1\}$ , at least one satisfying $\inf_{|t|\le N}D(f_j,\chi n^{it};N)\to\infty$ for every fixed Dirichlet character, and fixed distinct $h_1,h_2\ge0$ : $\frac1N\sum_{n\le N}f_1(n+h_1)f_2(n+h_2)\to0$ . Also for fixed nonproportional affine forms and in fixed residue classes. Functions may be complex and need not be completely multiplicative. Qualitative only, no rate; the $k$ -point Elliott conjecture for $k\ge3$ is not addressed.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The binary corrected Elliott conjecture for ordinary averages · Binary corrected Elliott conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The binary corrected Elliott conjecture for ordinary averages

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.2 and Corollary 1.3 were read against the binary corrected Elliott conjecture with ordinary averages. The challenges are not in the formalization catalogue (lean/formalization.yaml); lean/ComparatorChallenges/OrdinaryTwoPointCorrelations.json and OrdinaryElliott.json exist with solution modules OAI.NumberTheory.TwoPointCorrelations.FinalMain and OAI.NumberTheory.OrdinaryCorrelations.Elliott.Main present at the pinned commit, permitted axioms propext, Quot.sound and Classical.choice. The statements OAI.OrdinaryCorrelations.binary_corrected_elliott and OAI.OrdinaryTwoPointCorrelations.binary_corrected_elliott and affine_corrected_elliott were read: multiplicative one-bounded f1, f2, one of them with inf over |t| <= N of the distance to chi(n) n^{it} tending to infinity for every Dirichlet character, imply the shifted (and affine) correlation averages tend to 0. That is the headline. Not rebuilt here. The paper makes no rate claim for general functions.

Source ↗

The two-point Chowla conjecture (ordinary averages)

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lean proof: OAI/NumberTheory/TwoPointCorrelations/FinalMain.lean

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Lean proof: OAI/NumberTheory/OrdinaryCorrelations/Elliott/Main.lean

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Abridged summary of the model's reasoning (release reasoning_traces)

witness · pending

other link supplied by the VibeMathed registry.

Source ↗

Matomaki, Radziwill, Tao, An averaged form of Chowla's conjecture (corrected Elliott condition, arXiv:1503.05121)

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Lean proof: OAI/NumberTheory/TwoPointCorrelations/FinalMain.lean

lean artifact · pending

Artifact ↗

Lean proof: OAI/NumberTheory/OrdinaryCorrelations/Elliott/Main.lean

lean artifact · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Matomaki, Radziwill, Tao, An averaged form of Chowla's conjecture (corrected Elliott condition, arXiv:1503.05121) evidence for this event

Abridged summary of the model's reasoning (release reasoning_traces) evidence for this event

This event attributed to Unreleased internal OpenAI model

The binary corrected Elliott conjecture for ordinary averages parent of this event

The two-point Chowla conjecture (ordinary averages) evidence for this event

VibeMathed record: The binary corrected Elliott conjecture for ordinary averages evidence for this event

Lean proof: OAI/NumberTheory/OrdinaryCorrelations/Elliott/Main.lean evidence for this event

Lean proof: OAI/NumberTheory/TwoPointCorrelations/FinalMain.lean evidence for this event

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