# Schrödinger initial-data convergence reference

Family 080: The exact Sobolev endpoint for Schrödinger convergence. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Dispersive solver researchers can document the exact Sobolev endpoint for almost-everywhere return to initial data.

## Applicability and commercial boundary

An endpoint convergence statement does not give a finite-time error rate or apply to arbitrary nonlinear Schrödinger models.

## Initial business decision

Research or conditional engineering only until an effective implementation and a recurring buyer problem are identified. No commercial demand or profitability is established. Where a direct product bridge is weak, the legitimate use is a research reference or evidence adapter, rather than a new standalone company.

## Next verification action

Inspect quantitative estimates and choose a finite reference datum.

## Evidence scope

The catalog statement was individually reviewed. The manuscript proof and selected formal statement have not yet been compared in depth for this family. No independent proof verification was run. Pinned source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

[Endpoint convergence for the planar Schrodinger equation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026/paper.pdf).