# Graph refinement cost and capability evaluator

Family 133: The computational complexity of Weisfeiler–Leman refinement. First review, 8 October 2026.

## Problem and potential new use

Graph-ML and canonicalization teams can understand dimensional refinement's worst-case computational limits and failures.

## Applicability and commercial boundary

The sequential adjacency-matrix models and variable-dimensional complexity are specific. This does not establish a general lower bound for all graph neural networks or practical fixed-k tools.

## Initial business decision

Research infrastructure. Buyer demand and profitability remain hypotheses. This first pass does not establish a validated commercial market.

## Next verification action

Build bounded-treewidth witness fixtures and preserve the exact refinement model in benchmarks.

## Evidence scope

Catalog statement reviewed; inspect linked opportunity dossier for any deeper source review. This record alone does not establish full manuscript or proof verification.

Source revision `fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb`. See [source metadata](source.json) for the exact manuscripts and available scope notes.