# example Obstruction Artifact J: OG3 No-Doeblin from Real Toric Code Fusion Data

## Overview

RU is a certificate engine for universality and obstructions in constrained nonnegative propagation. Host structures supply finite inputs. Outputs are audited certificates or finite obstruction witnesses.

## What is shipped

| Artifact | Role | Path |
|---|---|---|
| Real host fusion data | Fusion rules + permutation fusion matrices | `sources/host_data/toric_code_fusion_data.json` |
| Host model + OG3 witness | Permutation-only templates imply no mixing block | `sources/ru_bridge/og3_toric_code_fusion_no_doeblin_model.json` |
| RU robust certificate (obstruction) | Records OG3 classification | `sources/ru/robust_certificate_og3_toric_code_fusion.json` |
| Bridge wrapper | Reduction record + claim classification | `sources/ru_bridge/bridge_certificate_og3_toric_code_fusion.json` |

## OG3 witness (finite)

- Each fusion matrix is a permutation matrix.
- Products of permutation matrices are permutation matrices.
- Therefore every product has zeros.
- Hence no word yields a strictly positive product matrix on the full cone.
- So delta(w)=0 for every word w.

That is OG3, anchored to a standard real host dataset.
