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Group-algebra zero-divisor counterexample fixture
Family 196: A counterexample to Kaplansky’s zero-divisor conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Symbolic algebra and formalization teams can use explicit nonzero products equaling zero to test group-ring representations.
Applicability and commercial boundary
The characteristic-two torsion-free-group example does not refute results over every field or supply an efficient generic zero-divisor decision algorithm.
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
Read the finite presentation and exact zero-divisor elements before implementing a verifier.
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.