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Overgroup equation solvability contract
Family 256: Nonsingular systems of equations over arbitrary groups. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Prevent group equation solvers from reporting a solution in the original group when the theorem guarantees a solution only in an overgroup.
Applicability and commercial boundary
Full row rank of the rational exponent-sum matrix is required; an embedding in a quotient does not give a cheap witness inside the coefficient 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
Extract one explicit equation and construct the ambient extension 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.