# Real Host Data Upgrade: Fibonacci and Ising Fusion Systems (RCFT/MTC Sectors)

## 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.

## Shipped real host datasets

| Host dataset | What it is | File |
|---|---|---|
| Fibonacci fusion | Two-label fusion ring with τ×τ = 1+τ | `sources/host_data/fibonacci_fusion_data.json` |
| Ising fusion | Three-label fusion ring with σ×σ = 1+ψ | `sources/host_data/ising_fusion_data.json` |
| Toric code fusion | Four-label abelian fusion ring (Z2×Z2) | `sources/host_data/toric_code_fusion_data.json` |

##  audited artifacts built from real host data

| Artifact | Outcome type | File |
|---|---|---|
| Real Fibonacci → contraction certificate | Certified contraction + explicit rate | `docs/Fibonacci_Contraction_Certificate.md` |
| Real Ising → OG3 obstruction | Certified “no Doeblin exists” witness | `docs/OG3_Ising_NoDoeblin.md` |
| Real Ising + projection constraint → OG2 boundary | Certified active-face inconsistency witness | `docs/OG2_Ising_Projection_Inconsistency.md` |
| Real Toric code → OG3 obstruction | Certified permutation-only no-Doeblin witness | `docs/OG3_ToricCode_NoDoeblin.md` |
| Real Fibonacci → OG4 boundary (idle channel) | Certified avoidable-Doeblin witness | `docs/OG4_Fibonacci_AvoidableDoeblin.md` |
| Real Fibonacci → OG1 periodic core (strict 2-cycle) | Certified periodic-core witness | `docs/OG1_Fibonacci_PeriodicCore.md` |

## Why this matters

A “” posture requires two things to be true at once:

- the engine certifies universality with explicit rates when hypotheses hold
- the engine returns finite obstruction witnesses when hypotheses fail

Real host data lets you demonstrate both outcomes without any appeal to toy matrices.

## How to use these datasets in the bridge

- Extract fusion matrices N_i from the host fusion coefficients.
- Choose a constraint graph (allowed channel scheduling) and a cost model.
- Feed (graph, templates, costs) into the RU certificate schema.
- Emit either:
  - `sources/ru/robust_certificate_*.json` (contraction), or
  - `sources/ru/robust_certificate_*.json` tagged as obstruction (OG1–OG4), plus the host witness file under `sources/ru_bridge/`.

The reduction choices are recorded in the bridge certificate wrapper objects under `sources/ru_bridge/bridge_certificate_*.json`.
