Homological conjecture dependency and counterexample graph

Family 199: Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Formalization teams can record which characteristic-two examples refute each named module/algebra implication.

Applicability and commercial boundary

Several distinct conjectures and associated algebras share a family; a single blanket counterexample or formal badge is inaccurate. Field-extension persistence is a specific theorem.

Initial business decision

Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.

Next verification action

Map assumptions, algebras and implications paper by paper.

Evidence scope

The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

An explicit counterexample to the Auslander-Reiten conjecture.