# Normalized-volume singularity reference

Family 037: The ordinary-double-point volume gap. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Compare claimed upper volume bounds with equality at an ordinary double point for a singular klt complex germ.

## Applicability and commercial boundary

The zero-boundary and dimension-at-least-two hypotheses matter; calculating the infimum defining normalized volume may remain difficult.

## 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 the equality certificate and computable volume input before implementing a diagnostic.

## 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 ordinary-double-point gap in every dimension](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/The-ordinary-double-point-gap-in-every-dimension-September-24-2026/paper.pdf).