# Multiplicative sequence correlation benchmark

Family 007: Ordinary two-point correlations and the corrected Elliott conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Analytic-number-theory researchers can compare Liouville affine-form correlations and corrected Elliott conditions.

## Applicability and commercial boundary

Nonpretentiousness is a uniform analytic condition, and asymptotic correlations are not cryptographic unpredictability or finite pseudo-randomness certification.

## Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

## Next verification action

Extract effective constants and one exact finite correlation fixture.

## Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[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).