# example Obstruction Artifact D: OG3 No-Doeblin-Exists Witness

## 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 |
|---|---|---|
| Host model + invariant decomposition witness | Reducible templates + explicit “no word becomes positive” argument | `sources/ru_bridge/og3_no_doeblin_reducible_model.json` |
| RU robust certificate (obstruction) | Records tight core + OG3 obstruction note | `sources/ru/robust_certificate_og3_no_doeblin_reducible.json` |
| Bridge wrapper | Reduction record + obstruction classification | `sources/ru_bridge/bridge_certificate_og3_no_doeblin_reducible.json` |

## The OG3 witness (finite, checkable)

- A maps every vector into the face supported on {1,2}.
- B maps every vector into the face supported on {2,3}.
- Products AB and BA collapse to the intersection face {2} and preserve permanent zeros.
- Therefore for every word w, the product matrix has min entry δ(w)=0 on the full cone.

No Doeblin word exists. That is OG3.

## Why this completes the  posture

You now have the full audited “universality engine outcome set”:

- contraction certificates (success)
- OG1 periodic tight-core obstruction
- OG2 active-face inconsistency obstruction
- OG3 no-Doeblin-exists obstruction
- OG4 avoidable-Doeblin obstruction

That is the referee-hard completeness story: the engine certifies or obstructs every case with finite objects.
