Certification, Realization, and Obstruction: A Universal Fiber Architecture

This paper closes the editorial loop for a multi-manuscript program in machine-checked mathematics. The executive claim is that a single collapse / refinement / fiber architecture---certification at a bare carrier, strict comparison upstairs, obstruction organized as fiber and section data---is instantiated internally in dependent type theory, validated on twelve external mathematical families, and then discharged into algebra, arithmetic (embedding problems), topology (Quillen for Galois connections), and logic/computability (self-certification and halting anchors). We state the role of each companion paper, a cross-domain dictionary, route labels used in the program (C/A/B/D), and what remains open. The intended reader is an advanced mathematician who has not read the series; citations p