# Host-Structure Evidence Map for RU Instantiation

## 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:** High

## RU instantiation hooks

- Turns string-theory host arenas into explicit candidate RU reductions by specifying what finite state set, templates, costs, and constraints must be extracted.
- Feeds directly into bridge certificates under `sources/ru_bridge/` and RU robust certificates under `sources/ru/`.

## Purpose

This map makes a different claim checkable: many string-theory constructions contain finite, positive, constrained propagation structures that can be reduced into RU certificates.

- Every application thread is tied to a specific, readable anchor in the supplied notes (PDF page numbers).
- Every external anchor is a standard primary paper or major review where the same idea is used operationally.

## What counts as a host structure candidate

An item counts as a “real application” here if it does at least one of the following.

- Produces repeatable computations that can be checked by others.
- Moves a hard question into a regime where it becomes tractable (duality as a calculator).
- Exports a durable method that is actively used outside string theory.
- Creates a computable invariant or correspondence that became part of mathematics.

## Claim-strength tags used below

- **Direct computation:** a calculational recipe with reproducible output.
- **Transfer principle:** an equivalence or map that moves problems between descriptions.
- **Structural constraint:** consistency conditions that eliminate possibilities or force structure.
- **Exported tool:** a method now used as part of mainstream technique elsewhere.

## Evidence table

PDF pages are 1-based as displayed by a typical PDF viewer.

| Application thread | Wray anchor (paraphrase or short excerpt) | Wray PDF page | What is actually being used | Claim-strength tag | External anchors (primary / standard) | Scope notes (limits stated up front) |
|---|---:|---:|---|---|---|---|
| UV softness and “finite extent cuts off divergences” | Strings replace point particles; short-distance behavior is softened and integrals become finite in perturbation theory; supersymmetry helps cancellations | 8–9 | Extended objects + consistency on the worldsheet | Structural constraint | Green–Schwarz (1984); Polchinski (1995) | This is the perturbative story; full nonperturbative definition is not “just the cutoff” |
| Unification viewpoint (one master entity with many excitations) | One underlying object (the string) has many excitation modes that appear as different particles; force unification is described as built in | 9 | Spectrum organization + symmetry constraints | Structural constraint | Standard textbook line (e.g., Polchinski volumes) | This is a conceptual unifier, not a direct experimental prediction |
| Strongly coupled QFT via dualities | Notes explicitly claim dualities taught us much about strongly coupled quantum field theories | 9 | Dualities transporting questions across coupling regimes | Transfer principle | Maldacena (hep-th/9711200) | Most sharp in large N / special symmetry limits |
| D-branes as dynamical objects carrying gauge theories | D-branes appear as loci where open strings end; their worldvolume degrees of freedom produce gauge theories | 10–11 (overview), later chapters | Open strings on branes → gauge sectors | Exported tool | Polchinski (hep-th/9510017) | Requires stringy setting, but the gauge-theory emergence idea exports widely |
| Black-hole entropy becomes a field-theory computation | At weak coupling the same brane system has a worldvolume gauge theory description; the black-hole entropy becomes a field-theory question; agreement holds in supersymmetric settings | 255 | BPS/protected degeneracy counting via branes | Direct computation | Strominger–Vafa (hep-th/9601029); Skenderis (hep-th/9901050) | Cleanest for BPS or near-BPS sectors; dynamical evaporation is more subtle |
| Holographic principle (gravity ↔ nongravitational QFT) | Conjecture: any gravity theory in (d+1) dims should have a description by a d-dim QFT without gravity | 255 | Dimensional “re-encoding” principle | Transfer principle | Maldacena (hep-th/9711200) | General claim is conjectural; best-controlled realization is AdS/CFT |
| Near-horizon limit and emergent AdS geometry from branes | In the low-energy/near-horizon limit, the D3-brane solution becomes a spacetime of the form AdS₅×S⁵ | 258 | Decoupling limit creating a universal sector | Transfer principle | Maldacena (hep-th/9711200); Witten (hep-th/9802150) | Requires large N / strong ’t Hooft coupling for the gravity side to be classical |
| AdS/CFT “dictionary” (operators ↔ bulk fields) | Gauge-invariant operators on the boundary correspond to bulk fields; correlators can be computed from the bulk action with specified boundary data | 259 | Practical map to compute correlators and responses | Direct computation | GKP (hep-th/9802109); Witten (hep-th/9802150) | Controlled in AdS/CFT; extensions beyond AdS are active research |
| Finite-temperature holography and transport | Once the dictionary is accepted, black-hole horizons encode thermal QFT response and transport | 259 (mechanism), plus standard literature | Horizon data → viscosities, diffusion, conductivities | Exported tool | Kovtun–Son–Starinets (hep-th/0405231) | Method is robust inside its model class; “universality” is model-limited |
| Amplitudes technology exporting gauge–gravity relations | String-based amplitude relations organize and simplify gauge and gravity computations | 10 (scattering chapter entry), plus standard literature | Closed amplitudes built from open amplitudes; double-copy structures | Exported tool | KLT (1986); BCJ (arXiv:0805.3993) | Now used far beyond strings, including classical gravity computations |
| Compactification and 4D effective physics | Extra dimensions must be small; even small extra dimensions affect interactions | 10 | Effective field theory from compactification | Transfer principle | Candelas et al. (1985) | Landscape and model dependence limit predictive sharpness |
| Mathematics outputs | Notes explicitly mention contributions to 4-manifolds and knot theory | 9 | Topological QFT and invariants | Exported tool | Witten (1989) | Many results are now fully mathematical and independent of the original physics motivation |

## How to use this map

- Use it as a filter: any “application” claim not traceable to a row above should be either removed or downgraded in strength.
- Use it as a routing tool: pick a row and follow the “what is actually being used” column to build a concrete narrative of host suitability for RU instantiation.