# Class-VII surface classification evidence

Family 060: The Global Spherical Shell conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Track existence of a global spherical shell on a minimal class-VII surface with positive second Betti number.

## Applicability and commercial boundary

An embedded sphere collar with connected complement does not directly supply a constructive triangulation or surface-recognition algorithm.

## 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 effective construction and restricted explicit surfaces.

## 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).

[Global Spherical Shells on Minimal Surfaces of Class VII](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Spherical-Shells-on-Minimal-Surfaces-of-Class-VII-September-24-2026/paper.pdf).