# Multiplicity monotonicity formal adapter

Family 194: Lech’s multiplicity conjecture. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Algebra software researchers can record when a flat local map must preserve the stated multiplicity ordering.

## Applicability and commercial boundary

Flatness, local Noetherian hypotheses and exact multiplicity computation may be expensive. The inequality is not a general numeric monotonicity rule.

## 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

Choose one explicit flat map and compute both multiplicities independently.

## 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).

[Lech's multiplicity conjecture](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Lechs-multiplicity-conjecture-September-23-2026/paper.pdf).