Special-manifold group implication ledger

Family 057: Fundamental groups of special complex varieties and root orbifolds. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Track virtual abelianity for special compact Kähler fundamental groups and separate restrictions on linear representations in the quasi-projective case.

Applicability and commercial boundary

A virtually nilpotent image of class at most two is not the same as a virtually abelian source group.

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

Map the geometric and representation hypotheses separately.

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.

The abelianity conjecture for special compact Kähler manifolds.