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.

A boundary-only obstruction to four-dimensional disk embedding.