# RU–String Theory Bridge Certificate Kit

## Purpose

## example audited artifact (concrete)

This engine now includes a fully instantiated, mechanically auditable bridge artifact:

- `docs/Example_Fibonacci_Minimal.md`

It ships a complete host instance plus an RU robust certificate (`sources/ru/robust_certificate_fibonacci_fusion.json`) and a bridge wrapper (`sources/ru_bridge/bridge_certificate_fibonacci_fusion.json`).


This document defines how to engine any claimed RU-to-string-theory connection so it is mechanically auditable.

It does two things:

- specifies a minimal “bridge certificate” layer that records the reduction choices
- points to the authoritative RU schemas that carry the mathematical guarantees

## Bridge certificate: minimal fields

A bridge certificate is not a replacement for the RU robust certificate.
It is a wrapper that states the reduction choices and points to the RU certificate that proves the claim.

### Required fields

- **String context**
  - short description of the string-theoretic construction and the finite sector chosen
  - what positivity cone is being used

- **Reduction to RU instance**
  - the finite state set \(V\) and edge set \(E\)
  - how templates \(T_e\) are derived from the string data
  - how costs \(c(e)\) are defined and why they are physically or structurally justified

- **RU certificate references**
  - a robust certificate object satisfying `sources/ru/robust_certificate_schema.json`
  - optionally, a global universality report satisfying `sources/ru/global_universality_report_schema.json`

- **Universality claim**
  - the exact conclusion asserted, phrased in RU terms
  - explicit scope limits (sector restriction, parameter region, truncations)

- **Audit checklist**
  - a short list of concrete checks that allow a third party to verify the claim

## Audit checklist template

A third party should be able to answer the following without interpretation:

- Does the reduction produce entrywise nonnegative templates and a finite graph?
- Is the cost objective stated, and is the potential calibration reproducible?
- Is the tight set stable, with an explicit \(\gamma>0\) and \(\varepsilon_*\) threshold?
- Is a Doeblin word provided with \(\delta>0\) and explicit uniform bounds?
- Is recurrence derived, or is an OG4 witness explicitly present?
- Are the contraction constants and exponential rate included?

If any answer is “no,” the universality claim must be weakened to a lower tier.

## Example bridge certificate (human-readable)

A minimal human-readable certificate can look like:

- String context: RCFT fusion system on a specified set of primaries
- Reduction: states are constraint classes, edges encode allowed generator insertions, templates are fusion matrices
- Cost: chosen penalty per generator
- Tight core: computed from calibrated potential, with \(\gamma\) margin
- Doeblin: finite mixing word given by a short generator sequence
- Recurrence: RC1 holds, avoidance graph has no directed cycle
- Output: explicit projective contraction rate on the active face, stable for perturbations within \(\varepsilon_*\)

## Machine-readable option

If desired, the bridge wrapper can be serialized as JSON.

This engine keeps the bridge layer in markdown for readability, while shipping the authoritative RU JSON schemas under `sources/ru/`.

## Why this matters for “global universality”

The credibility of a global universality claim lives or dies on auditability.

This kit makes your connection to string theory referee-hard:

- the reduction choices are explicit
- the guarantees are carried by the RU certificate objects
- the global-on-parameter-region claim is carried by the region report schema
