# example Audited Bridge Artifact: Fibonacci Fusion → RU Universality Certificate

## engine center (reminder)

- RU gap-free global-universality is the theorem engine.
- String theory supplies host structures where RU hypotheses can be instantiated and audited.

This file is the “ push” anchor: a fully specified host instance plus a robust RU certificate that can be audited mechanically.

## What is shipped (all concrete, no placeholders)

| Artifact | Role | Path |
|---|---|---|
| Host-structure model | Finite fusion propagation instance (templates + constraints) | `sources/ru_bridge/fibonacci_fusion_model.json` |
| RU robust certificate | The proof-carrying object: tight core, Doeblin witness, recurrence, rate pack, ε* | `sources/ru/robust_certificate_fibonacci_fusion.json` |
| Bridge wrapper | Records the reduction choices and points to RU proof carriers | `sources/ru_bridge/bridge_certificate_fibonacci_fusion.json` |
| RU schemas | Define the required fields and meaning of certificate objects | `sources/ru/robust_certificate_schema.json`, `sources/ru/global_universality_report_schema.json` |

## The reduction, in one line

Fusion matrix propagation (nonnegative) + finite constraint graph → RU constrained template products on a cone.

## The universality statement that is actually certified here

From the robust certificate:

- the tight core is the full constraint system (single aperiodic SCC, period 1)
- the Doeblin word is length 2: (A_tau, A_tau)
- the Doeblin margin is δ = 1 on the full cone for the product matrix A_tau^2
- the projective diameter bound is Δ = 2 log(2)
- the Birkhoff contraction coefficient is τ = tanh(Δ/4) = 1/3
- recurrence is combinatorial with gap bound B=0, so Doeblin blocks are unavoidable
- therefore normalized products contract projectively with an explicit exponential rate

This is the “RU universality engine” applied to a string-theory-adjacent host structure in a way that can be audited by reading the JSON.

## How a skeptic audits this in minutes

- Open the model file and confirm the template matrix and constraints.
- Multiply A_tau by itself to confirm the Doeblin product is strictly positive and that δ=1, U=2.
- Confirm τ = tanh((2 log(U/δ))/4) = tanh(log 2 /2) = 1/3.
- Check that the robust certificate fields match these computed quantities.
- Confirm the schema requirements by validating the certificate against `sources/ru/robust_certificate_schema.json`.

## Why this matters for the  posture

A lot of universality talk in physics stays qualitative.

This artifact forces the discussion into finite, verifiable objects:

- either you produce a robust certificate and a rate, or
- you produce a finite obstruction witness (OG atlas)

That is the core “” value: universality becomes a certified technology, not a narrative.
