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Algebraic inverse and cellular-automaton scope audit
Family 197: A torsion-free group algebra that is not directly finite. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Researchers can distinguish left/right inverses, surjectivity and determinant conjectures across the specified group and coefficient regimes.
Applicability and commercial boundary
The infinite group/configuration counterexamples do not show ordinary finite matrices have one-sided inverses without two-sided inverses. Integral and rational group-ring determinant claims have different inputs.
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 each manuscript separately and extract finite descriptions with exact test semantics.
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.