Topology-versus-multiplicity counterexample

Family 059: Counterexamples to Zariski’s multiplicity conjecture. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Help singularity tools avoid assuming ambient topological equivalence determines multiplicity.

Applicability and commercial boundary

The specified germs with multiplicities four and five concern exact local complex singularities, not ordinary regression complexity.

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 equations and the topological equivalence witness.

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.

Ambiently homeomorphic isolated hypersurfaces of multiplicities two and three.