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Intersection multiplicity consistency library
Family 193: Serre’s intersection-multiplicity conjecture. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Symbolic algebra researchers can test positivity of an exactly computed intersection multiplicity under the regular-local-ring and dimension conditions.
Applicability and commercial boundary
Finite-length tensor products and exact module dimensions require verification; positivity gives no faster resolution or intersection 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
Extract a finite computable ring/module example and compare an existing CAS workflow.
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.