# Glossary: String-Theory Host Terms to RU Objects

## Purpose

This glossary keeps the bridge honest by mapping host language to RU inputs.

RU is the engine. Host terms only matter insofar as they specify finite input data.

## Mappings

### Worldsheet CFT sector
- RU input: finite label set, nonnegative fusion or channel templates, constraint graph encoding allowed compositions

### Fusion rules and fusion coefficients
- RU input: nonnegative matrices N_i acting on the cone of coefficient vectors
- RU templates: the selected N_i on edges of a constraint graph

### Boundary conditions and selection rules
- RU input: constraints on allowed sequences of templates, encoded as a finite graph or subshift
- RU input (optional): projection templates that restrict to an allowed sector

### Channel dominance, extremal regimes
- RU input: cost model for edges, canonical normalization, tight-core extraction

### Universality heuristics
- RU output: either a contraction certificate with explicit rate, or a finite obstruction witness explaining why universality is not forced

## Diagnostic meanings of obstructions

### OG1 periodic core
- Meaning: the tight SCC is periodic; strongest aperiodic universality is obstructed

### OG2 active-face inconsistency
- Meaning: constraints force contradictory support requirements; no consistent active face exists

### OG3 no Doeblin exists
- Meaning: propagation is reducible in a way that prevents any finite mixing block on the active cone

### OG4 avoidable Doeblin
- Meaning: a mixing block exists but can be avoided forever by legal tight paths
