# Host-Structure Taxonomy for RU Reductions

## 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

- Classifies host arenas by how likely they are to yield finite, positive, constrained propagation after sector selection and truncation.
- Use this taxonomy to decide where a bridge certificate is plausible before attempting a reduction.

## Purpose

“Application” means different things to different audiences. This taxonomy separates major types of host-structure patterns so the discussion does not collapse into hype on one side or dismissal on the other.

The organizing idea is:

- An RU reduction is most credible where string-theory host data exports **methods** and **transfer principles** that generate reproducible calculations in regimes that were otherwise inaccessible.

## Scope flags (honest regime labels)

These flags are used throughout the engine.

| Flag | Meaning | Why it matters |
|---|---|---|
| **BPS / protected** | Result is stable under continuous deformations due to supersymmetry or index protection | This is where exact microstate counting and nonrenormalization work |
| **Large N** | A limit where gauge theories simplify and gravity duals become classical | Many clean holographic computations live here |
| **AdS asymptotics** | Bulk spacetime has anti–de Sitter boundary conditions | Most precise holographic dictionary is formulated here |
| **Model-dependent** | The method is controlled, but the mapping to a specific real system is interpretive | Common in AdS/CMT and QCD-like modeling |
| **Conjectural extension** | A framework exists but is not fully proven or universally controlled | Honest placement avoids overclaim |

## Maturity rubric

A method can be genuinely reducible into RU certificates even if regime-limited. Maturity is about **control** rather than breadth.

- **Established**
  - Reproducible computations and a stable dictionary inside a stated regime.
  - Broad consensus on how the method is used and what it does not claim.
- **Active**
  - Widely used with a growing frontier; key boundary cases are still being mapped.
- **Exploratory**
  - Promising frameworks; results depend strongly on special structure or assumptions.
- **Speculative**
  - Conceptual proposals without stable computational traction.

## Taxonomy of host suitability for RU instantiation

| Category | What it targets | Typical outputs | Typical scope flags | Maturity (typical) | Canonical entry points |
|---|---|---|---|---|---|
| Quantum gravity consistency (UV completion) | A consistent quantum framework including gravity | Consistency constraints; anomaly cancellation; UV-soft perturbation theory | Conjectural extension; sometimes BPS/protected | Active | Green–Schwarz (1984); Polchinski (1995) |
| Black holes (microstates and entropy) | Microscopic account of black-hole thermodynamics | Exact entropy counts in protected sectors; microstate constructions | BPS/protected | Established for key entropy matches; Active for dynamics | Strominger–Vafa (hep-th/9601029); Skenderis (hep-th/9901050) |
| Holography (AdS/CFT and dictionary methods) | Gravity/QFT equivalence as a computational engine | Correlators, thermodynamics, phase structure; geometric formulas for information measures | AdS asymptotics; Large N | Established in AdS/CFT; Active beyond AdS | Maldacena (hep-th/9711200); Witten (hep-th/9802150); GKP (hep-th/9802109) |
| Strong-coupling tools in QFT | Nonperturbative QFT control | Dual descriptions; protected observables; new structural identities | Large N; BPS/protected | Active | Maldacena (hep-th/9711200) |
| Transport and hydrodynamics (export from holography) | Real-time response of strongly coupled systems | Viscosity, diffusion, conductivity from horizon data and Green’s functions | Large N; Model-dependent | Established as a method | Kovtun–Son–Starinets (hep-th/0405231) |
| Condensed matter modeling (AdS/CMT) | Controlled laboratories for strongly coupled phases | Superconducting instabilities; scaling behavior; conductivity curves | Model-dependent | Active | Hartnoll–Herzog–Horowitz (0810.1563); Horowitz (1002.1722) |
| Scattering amplitudes and gauge–gravity relations | Simplify gauge and gravity computations | KLT relations; color–kinematics duality; double copy; loop organization | Broad export; not limited to AdS | Established as a method; Active in new domains | KLT (1986); BCJ (0805.3993) |
| Compactification and phenomenology | Derive 4D effective theories from higher-dimensional consistency | Gauge groups, spectra, moduli, effective actions | Model-dependent; Conjectural extension | Exploratory to Active | Candelas et al. (1985) |
| Mathematics exports | New invariants and correspondences | Knot and 3-manifold invariants; topology/geometry bridges | Many now fully mathematical | Established for major branches | Witten (1989) |

## Exported tools versus internal engines

A practical way to judge “host suitability for RU instantiation” is to separate tools exported to other communities from mechanisms mainly used internally.

**Exported tools (widely used outside string theory)**
- Holographic dictionary methods for correlators and response in AdS/CFT regimes.
- Horizon-based transport computations (η/s and related response functions) inside holographic model classes.
- Amplitude relations and the double copy for gauge theory, gravity, and classical solution building.
- Topological field theory techniques that became standard in low-dimensional topology.

**Internal engines (often powering exports)**
- Worldsheet CFT and vertex-operator technology.
- D-branes and open strings generating gauge sectors and protected state counts.
- Dualities (T, S, U) transporting problems across regimes.
- Supersymmetry and BPS protection stabilizing exact quantities.
- Near-horizon limits isolating universal sectors.

## “Universal host suitability for RU instantiation” without overclaim

Universal host suitability for RU instantiation is best read as a pattern rather than a promise of universal empirical prediction:

- A small set of mechanisms repeatedly yields calculational control in very different problems.
- The same ideas survive translation into other languages (QFT, geometry, topology, quantum information).

The strongest cross-domain levers are:
- **Duality** (problem transport)
- **Emergence** (geometry/gravity from nongravitational degrees of freedom)
- **Protection** (stable quantities under deformation)
- **Consistency constraints** (anomalies and symmetry forcing structure)
- **Geometry–algebra transfer** (turning geometric questions into algebraic computations and back)