# L-function assumption and algorithm dependency audit

Family 003: The quasi-Riemann hypothesis. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algorithm researchers can review which deterministic finite-field procedures previously relied on a zero-free hypothesis and whether the stated 7/8 theorem suffices.

## Applicability and commercial boundary

A 7/8 zero-free half-plane is not the full Riemann hypothesis. The selected scope excludes later applications; the Landau–Siegel logarithmic gap has no explicit constant.

## 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

Trace an exact algorithm theorem and its constants before strengthening opportunity 016.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstracts and available selected formal scope notes were also inspected. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[The Quasi-Riemann Hypothesis: A Zero-Free Half-Plane $`\Re s\gt 7/8`$ ](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Quasi-Riemann-Hypothesis-September-30-2026/paper.pdf).