# example Obstruction Artifact E: OG3 No-Doeblin from Real Ising 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 + matrices N_sigma, N_psi | `sources/host_data/ising_fusion_data.json` |
| Host model + OG3 witness | Reduction + bipartite support invariant | `sources/ru_bridge/og3_ising_fusion_no_doeblin_model.json` |
| RU robust certificate (obstruction) | Tight core + OG3 classification | `sources/ru/robust_certificate_og3_ising_fusion.json` |
| Bridge wrapper | Reduction record + claim classification | `sources/ru_bridge/bridge_certificate_og3_ising_fusion.json` |

## The OG3 witness (conceptual and checkable)

In Ising fusion:

- multiplying by σ toggles between the subspaces span{σ} and span{1,ψ}
- multiplying by ψ permutes {1,ψ} and fixes σ

Therefore, for any word w:

- each basis input is mapped into either span{σ} or span{1,ψ}, never both simultaneously
- hence no product matrix can have strictly positive entries in all rows for all columns

So δ(w)=0 for every word on the full cone, and no Doeblin block exists.

That is OG3, as a real host obstruction.

