# Literature Positioning

## Purpose

This document explains how the engine fits within standard universality and positivity traditions while remaining explicit about what is new.

RU is the engine. The novelty is the audited certificate technology and complete obstruction taxonomy.

## Standard background threads

- Perron–Frobenius theory and positive operators motivate why nonnegative propagation tends to develop dominant directions.
- Hilbert projective metric and Birkhoff contraction provide a quantitative framework for contraction of positive maps.
- Transfer-matrix methods and products of positive matrices appear in statistical physics and dynamical systems.
- In CFT and related sectors, fusion matrices provide canonical nonnegative host templates.

## What is new here

### Certificate-first universality

Instead of asserting that a system mixes, the engine requires:

- a Doeblin witness word with explicit margin δ
- a recurrence predicate ensuring mixing blocks are unavoidable
- explicit contraction rates derived from certificate constants
- robustness tolerances ε* for perturbations

### Obstruction completeness as finite objects

The engine does not treat failure as vague.

Failure is classified as audited finite witnesses:

- OG1 periodic-core
- OG2 active-face inconsistency
- OG3 no mixing block exists
- OG4 mixing exists but is avoidable

### Global chamber reporting

The global layer is packaged as an audited report object:

- region description
- chamber classification
- explicit obstruction boundaries
- explicit index of supporting certificates

## References in this engine

See `docs/References.md` for DOI entries used to anchor the real-host datasets.
