# Four-dimensional embedding obstruction fixture

Family 305: Four-dimensional disk embedding and Wall's conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Help topology workflows avoid applying disk embedding from algebraic dual-sphere data alone in the stated fundamental-group regime.

## Applicability and commercial boundary

The free-group counterexample and Poincaré-duality companion are not a generic failure of geometric meshing.

## 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

Read explicit manifolds, framing assumptions and obstruction witnesses.

## 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).

[A boundary-only obstruction to four-dimensional disk embedding](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-boundary-only-obstruction-to-four-dimensional-disk-embedding-September-24-2026/paper.pdf).