# 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](source.json).

[Positivity of Serre's Intersection Multiplicity](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Positivity-of-Serres-Intersection-Multiplicity-September-23-2026/paper.pdf).