# Cubic-fourfold rationality scope audit

Family 054: Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Separate irrationality claims for very general large-discriminant cubic fourfolds from categorical or Hodge association with a K3 surface.

## Applicability and commercial boundary

The threshold is ineffective and very-general assumptions exclude a universal finite rationality classifier.

## Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

## Next verification action

Inspect whether any explicit discriminant threshold or computable instance survives the proof.

## Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Irrational cubic fourfolds with geometric K3 categories](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf).