# Singularity-family topological triviality contract

Family 064: Topological triviality of <i>μ</i>-constant surface singularities. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Record topological right triviality of the specified one-parameter isolated hypersurface family with constant Milnor number.

## Applicability and commercial boundary

This is a family of germs in complex three-space; topological homeomorphisms need not be differentiable or cheaply computable.

## 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 family assumptions and construction of homeomorphisms.

## 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).

[Topological triviality of mu-constant families of surface singularities](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Topological-triviality-of-mu-constant-families-of-surface-singularities-September-24-2026/main.pdf).