# Host Extraction Playbook

## 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.

## Step A: Choose the finite sector

Pick a finite label set appropriate for the regime you want to certify.

Examples in this engine:

- Fibonacci fusion labels {1, tau}
- Ising fusion labels {1, psi, sigma}
- Toric code fusion labels {1, e, m, eps}

## Step B: Extract nonnegative templates

Construct nonnegative matrices that act on coefficient vectors on the cone.

Common sources:

- fusion matrices N_i
- channel composition matrices in a fixed basis
- transfer-matrix blocks after truncation to a finite sector

## Step C: Encode constraints as a finite graph

Constraints can encode:

- allowed channel schedules
- boundary selection rules
- defect insertion patterns
- prohibited subsequences

Encode these as a finite directed graph whose edges carry templates.

## Step D: Choose a cost model if studying an extremal regime

If the aim is a minimal-growth or extremal regime:

- assign costs to edges
- RU canonical normalization defines tight edges and the active core

If the aim is mixing universality:

- set costs to 0 and study forced contraction vs obstruction

## Step E: Run RU extraction and validation

Use the built-in extractor to generate audited objects from shipped host data.

Examples:

- `python tools/ru_bridge_extractor.py --example fibonacci_contraction --validate`
- `python tools/ru_bridge_extractor.py --example ising_og3 --alpha 0.15 --validate`

For a full self-check:

- `python tools/ci_selfcheck.py`

## Step F: Interpret outputs

Outputs are one of two types:

- contraction certificate:
  - explicit Doeblin witness word
  - recurrence predicate RC1
  - explicit contraction rate pack and robustness tolerances

- obstruction certificate:
  - OG1 periodic core
  - OG2 active-face inconsistency
  - OG3 no Doeblin exists
  - OG4 avoidable Doeblin

Use the bridge wrapper to see the reduction choices and pointers to the robust certificate instance.
