# Claim Ladder

## 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.

## Claim levels used in this engine

### Method universality (primary claim)

For every host reduction that fits the finite positivity template:

- RU either returns an audited contraction certificate with explicit rates, or
- RU returns an audited obstruction witness (OG1–OG4)

This is the main claim of the engine.

### In-class universality (conditional claim)

Within a fixed host instance:

- if Doeblin and recurrence are certified on the active face,
- then projective contraction holds with explicit exponential rate

This is always carried by a robust certificate object.

### Global universality across regions (conditional claim)

For a parameter region:

- the engine provides a chamberwise global report object
- it classifies chambers where contraction is certified
- it records explicit boundary obstruction chambers

The global report is an audited artifact and does not pretend to provide a single uniform rate across a region containing obstruction boundaries.

## What is not claimed

- No experimental validation of string theory is asserted.
- No claim that every string construction fits the RU template.
- No claim that the engine resolves the full infinite-dimensional bootstrap without truncation control.

## What is claimed

- When a reduction is specified, universality statements become certificates.
- When universality fails, the failure is reported as a finite obstruction witness.
