# Fano invariant inequality reference

Family 063: The generalized Mukai conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Cross-check the Picard-number and pseudoindex inequality and its product-of-projective-spaces equality case.

## Applicability and commercial boundary

Computing the invariants and verifying smooth Fano hypotheses may dominate the task; the inequality is not a classifier by itself.

## 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

Compare explicit varieties and independently calculated invariants.

## 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).

[The generalized Mukai conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-Generalized-Mukai-Conjecture-September-24-2026/article.pdf).