# Density-functional representation limitation audit

Family 278: Failure of Kohn–Sham ensemble representation. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Electronic-structure researchers can flag universal claims that every interacting ground density has an ensemble representation by a local noninteracting potential.

## Applicability and commercial boundary

The counterexample has a specific three-electron two-nucleus structure and nonnumerically specified charge. It does not make ordinary Kohn–Sham calculations invalid or provide a better density solver.

## Initial business decision

Research infrastructure. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Inspect whether a concrete computable counterexample and observable diagnostic can be extracted.

## Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[A Coulomb ground-state density without Kohn-Sham ensemble representation](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Coulomb-Ground-State-Density-without-Kohn-Sham-Ensemble-Representation-September-25-2026/paper.pdf).