# example Obstruction Artifact C: OG2 Active-Face Inconsistency 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 + finite witness | Projection-like templates + explicit contradiction argument | `sources/ru_bridge/og2_active_face_inconsistency_model.json` |
| RU robust certificate (obstruction) | Records tight core + OG2 obstruction note | `sources/ru/robust_certificate_og2_active_face_inconsistency.json` |
| Bridge wrapper | Reduction record + obstruction classification | `sources/ru_bridge/bridge_certificate_og2_active_face_inconsistency.json` |

## The contradiction (finite, checkable)

- Edge e10 forces coord2 to appear at s0 whenever coord1 is present at s1 (support-forcing step).
- Edge e00 is a tight self-loop on s0 that kills coord2 (support-killing step).
- Any candidate “active support” at s0 must both include coord2 (forced by e10) and exclude coord2 (preserved by e00 without collapsing to zero).

No consistent active face exists. That is OG2.

## Why this pushes toward 

This closes the remaining gap in the obstruction atlas as an audited object:

- you now have contraction certificates (positive universality)
- OG4 avoidable Doeblin boundary
- OG1 periodic tight-core boundary
- OG2 active-face inconsistency boundary

These are the “referee-hard” completeness ingredients: the universality engine classifies both success and failure with finite artifacts.
