# Tensor-network representation feasibility audit

Family 265: Area laws and tensor networks for two-dimensional gapped systems. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Quantum simulation teams can distinguish a claimed polynomial PEPS representation from an executable preparation, contraction or ground-state search algorithm.

## Applicability and commercial boundary

The PEPS statement is explicitly existential, assumes unique uniformly gapped square-grid ground states and gives a global vector approximation. Polynomial bond dimension alone does not imply cheap contraction or efficient construction.

## Initial business decision

Conditional evidence workflow. Buyer budget, commercial novelty and profitability are unvalidated.

## Next verification action

Extract polynomial exponents and constants if available, then compare practical bond and contraction budgets on an existing tensor library.

## Evidence scope

The catalog statement was individually reviewed. Main-paper abstract passages and available family scope notes were also inspected; paper-level theorem and algorithm details still require deeper review. No independent Lean check was run. Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json).

## Main source

[A two-dimensional area law from a global spectral gap](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-two-dimensional-area-law-from-a-global-spectral-gap-September-24-2026/paper.pdf).