# One-Page Abstract

This engine presents a certification engine for universality phenomena in constrained positive propagation systems.

The engine is the RU gap-free global-universality pipeline: given finite data (a constraint graph, nonnegative template operators, and a cost model), it performs canonical normalization to extract a tight core, then either certifies projective universality with explicit quantitative rates or returns a finite obstruction witness explaining why universality is not forced.

The engine is not organized around “string theory usefulness.” Instead, string-theory-adjacent structures appear only as sources of concrete host inputs (finite worldsheet/CFT sectors, boundary constraints, fusion/channel systems) where the RU hypotheses can be instantiated and audited. Strong statements are carried by auditable JSON objects: robust certificates record margins (tight gap, Doeblin margin), recurrence information, explicit contraction-rate packs, and robustness tolerances; obstruction certificates record explicit finite witnesses for periodic cores (OG1), active-face inconsistencies (OG2), absence of mixing blocks (OG3), or avoidable mixing (OG4).

Three standard fusion hosts (Fibonacci, Ising, and toric code) are included as real datasets. From Fibonacci fusion data, the engine produces a concrete contraction certificate using a length-2 Doeblin witness (N_tau^2 strictly positive). From Ising fusion data, the engine produces a real-host OG3 obstruction via an invariant support dichotomy that prevents any Doeblin block on the full cone. Additional real-host boundaries (OG1 and OG4 from Fibonacci) and a real-host-derived OG2 example (Ising plus a projection constraint) demonstrate that the engine classifies both success and failure with finite, checkable artifacts.

The engine includes reproducibility tools to regenerate and schema-validate the audited suite and to build a chamberwise global report across a one-parameter family. The intended outcome is a reusable, referee-hard technology: universality claims become certificates, and failures become explicit obstruction witnesses.
