Homotopy-to-homeomorphism inference fixture

Family 320: Nonhomeomorphic closed aspherical four-manifolds. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Track closed aspherical four-manifolds with the same hyperbolic group and homotopy type but different homeomorphism types.

Applicability and commercial boundary

Group and homotopy invariants do not always recover topology; this does not imply every finite reconstruction problem is ambiguous.

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

Extract explicit manifold invariants and the obstruction.

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.

Nonhomeomorphic closed aspherical four-manifolds with the same homotopy type.