# Literature Anchoring for the RU Engine

## 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.

## Where the engine lives mathematically

- Positivity and Perron–Frobenius traditions
  - The setting of nonnegative operators and dominance of projective directions is classical.
  - See `docs/References.md` entries by Seneta and Lemmens–Nussbaum.

- Hilbert projective metric and quantitative contraction
  - The contraction mechanism for positive maps is anchored in Birkhoff and Bushell.
  - The engine’s rate packs are an auditable instantiation of this tradition.

- Random matrix products and Lyapunov exponents
  - Products of positive matrices and growth rates are foundational in Furstenberg–Kesten and Bougerol–Lacroix.
  - The RU obstruction taxonomy can be interpreted as a finite classification of when projective contraction is forced in constrained template products.

- Symbolic dynamics and cocycles
  - Encoding constraints as finite graphs is standard in symbolic dynamics and cocycle viewpoints.
  - Background references include Katok–Hasselblatt and Ruelle’s thermodynamic formalism.

## What the engine adds

- A certificate-first interface
  - A universality claim is either a robust certificate with explicit margins and rates, or an obstruction witness.

- A finite obstruction taxonomy
  - OG1–OG4 are carried as finite auditable witnesses, not narrative exceptions.

- A global chamber reporting layer
  - The global report object records region description, chamber classification, and explicit boundary obstructions.

All citations for these anchors are recorded in `docs/References.md`.
