# example Obstruction Artifact I: OG2 Active-Face Inconsistency from Real Ising Host Data (with Projection Constraint)

## 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 Ising host fusion data | Fusion rules + matrices | `sources/host_data/ising_fusion_data.json` |
| Host model + OG2 witness | Ising fusion + even-sector projection + explicit contradiction | `sources/ru_bridge/og2_ising_projection_inconsistency_model.json` |
| RU robust certificate (obstruction) | Tight SCC is aperiodic, but active face is inconsistent | `sources/ru/robust_certificate_og2_ising_projection_inconsistency.json` |
| Bridge wrapper | Reduction record + OG2 classification | `sources/ru_bridge/bridge_certificate_og2_ising_projection_inconsistency.json` |

## OG2 contradiction (finite)

- Return edge e10 uses P_even ∘ N_sigma and is nonzero only if sigma-support is present at s1_bulk.
- Tight self-loop e11 is P_even at s1_bulk, which kills sigma and therefore forces sigma-support to be absent for any invariant active face.
- Hence s1_bulk must both include sigma and exclude sigma. No consistent active-face support sets exist.

That is OG2, now anchored to real Ising fusion data plus a boundary/selection projection.

## Why this is a -type improvement

This artifact shows the RU engine can do more than certify contraction:

- it can act as a finite consistency auditor for worldsheet/boundary constraint choices
- it returns a concrete obstruction witness when the host constraints cannot be made consistent

That is exactly what makes the bridge useful in a string-theory-adjacent setting.
