# Host Structures to RU Reduction Targets Map

## 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.

## RU fit

- **Fit level:** Medium

## RU instantiation hooks

- Identifies which string mechanisms produce the kind of finite positive data RU needs, and which do not.
- Use it to route readers from host context documents into the RU bridge dictionary and worked examples.

## Purpose

This map answers a single practical question:

- Which mechanisms actually do the work in each application thread?

When an RU instantiation is real, it is usually because the same few structural levers keep reappearing as reliable reduction targets.

## Reusable mechanisms (short definitions)

- **Extended objects (strings)**
  - Replace pointlike interactions with worldsheet geometry, softening short-distance behavior in perturbation theory.

- **Worldsheet conformal field theory (CFT)**
  - Two-dimensional QFT controlling string dynamics; supplies vertex operators, OPEs, and the basic scattering toolkit.

- **D-branes and open strings**
  - Loci where open strings end; low-energy degrees of freedom become gauge theories; branes also supply nonperturbative charges and microstates.

- **Dualities (T, S, U)**
  - Equivalences relating apparently different regimes; practical role is to move a problem to a tractable frame while preserving invariants.

- **Compactification as a constraint machine**
  - Turning global consistency (anomalies, quantization, tadpoles) and special-holonomy geometry into a filter that outputs only allowed lower-dimensional effective theories.

- **Indices, localization, and protected partition functions**
  - Turning supersymmetry into computable invariants (indices, refined BPS counts, supersymmetric partition functions) that remain stable under coupling changes and can be evaluated exactly in tractable limits.

- **Supersymmetry and BPS protection**
  - Protect certain degeneracies and observables from continuous deformations; enables exact state counts and nonrenormalization results.

- **Near-horizon / decoupling limits**
  - Isolate universal sectors (often AdS regions) where a clean dictionary exists.

- **Gauge/gravity dictionary (holography)**
  - A map from boundary operators to bulk fields and from QFT generating functionals to bulk actions with boundary data.

- **Real-time holography (ingoing prescription and quasinormal modes)**
  - Finite-temperature ingredient that selects retarded correlators, encodes dissipation at the horizon, and identifies relaxation rates with quasinormal modes.

- **Color–kinematics duality and the double copy**
  - A field-theory refinement of “squaring” relations that builds gravity amplitudes (and related observables) from gauge-theory building blocks.

- **Amplitude factorization and “squaring” relations**
  - Structural relations (e.g., closed ≈ “product” of open) that reorganize calculations and export to gauge/gravity amplitude technology.

## Mechanism-to-application matrix

Legend: ✓ = essential lever, △ = supporting lever

| Mechanism → / Application ↓ | UV softness & consistency | Strong coupling tools | Black-hole microstates | Holography (AdS/CFT) | Transport (η/s, etc.) | Amplitudes export | Phenomenology (compactification) | Math exports |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| Extended objects (strings) | ✓ | △ | △ | △ | △ | ✓ | △ | △ |
| Worldsheet CFT | ✓ | △ | △ | △ | △ | ✓ | △ | △ |
| D-branes and open strings | △ | △ | ✓ | ✓ | △ | △ | ✓ | △ |
| Dualities (T/S/U) | △ | ✓ | ✓ | ✓ | △ | △ | △ | △ |
| Compactification consistency filters | ✓ | △ | △ | △ | △ | △ | ✓ | ✓ |
| Indices / localization / protected partition functions | △ | ✓ | ✓ | △ | △ | △ | △ | ✓ |
| SUSY and BPS protection | △ | △ | ✓ | △ | △ | △ | △ | △ |
| Near-horizon / decoupling limits | △ | △ | △ | ✓ | ✓ | △ | △ | △ |
| Gauge/gravity dictionary | △ | ✓ | △ | ✓ | ✓ | △ | △ | △ |
| Real-time holography (ingoing/QNMs) | △ | ✓ | △ | ✓ | ✓ | △ | △ | △ |
| Color–kinematics / double copy | △ | △ | △ | △ | △ | ✓ | △ | △ |
| Amplitude squaring relations | △ | △ | △ | △ | △ | ✓ | △ | △ |
| Topological / geometric transfer ideas | △ | △ | △ | △ | △ | △ | △ | ✓ |

## How each mechanism exports beyond string theory

- **Duality as a calculator**
  - Core export: translate an intractable regime into a dual description where computation is controlled.
  - Typical downstream: new identities, bounds, scaling laws, and structural constraints in QFT.

- **Branes as “organizers” of degrees of freedom**
  - Core export: a geometric way to engine gauge sectors, charges, and protected states.
  - Typical downstream: a template for emergent gauge structure and for microstate counting in protected sectors.

- **Holography as a dictionary method**
  - Core export: compute QFT correlators and transport from a gravity problem, or compute gravity observables from field-theory data.
  - Typical downstream: hydrodynamic coefficients, phase diagrams, and information measures in controlled model classes.

- **Real-time holography as a dissipation engine**
  - Core export: compute retarded correlators and transport by imposing ingoing conditions at horizons; interpret relaxation via quasinormal modes.
  - Typical downstream: universal transport ratios in model classes, relaxation time estimates, and frequency-dependent response functions.

- **Amplitude technology as a structural export**
  - Core export: relations that reorganize perturbation theory and connect gauge and gravity amplitudes.
  - Typical downstream: faster multi-loop calculations, cleaner UV analyses, and classical gravity solutions via double-copy ideas.

- **Topological field theory exports**
  - Core export: new invariants and computational techniques in low-dimensional topology.
  - Typical downstream: knot and 3-manifold invariants, and bridges between geometry and quantum field theory.

## A practical reading strategy

To evaluate “universal host suitability for RU instantiation” quickly, pick a single mechanism and trace it through at least two rows of the matrix.
If the same mechanism yields reproducible computation in multiple domains, it is a genuine universal lever.