What question did this study set out to answer?

To present a comprehensive framework for machine-checked mathematics through a universal fiber architecture.

April 7, 20260 citationsOpen Access

Certification, Realization, and Obstruction: A Universal Fiber Architecture

Key Points

To present a comprehensive framework for machine-checked mathematics through a universal fiber architecture.
Introduced a collapse/refinement/fiber architecture.
Validated internal structures in dependent type theory.
Tested framework across twelve external mathematical families.
Established a connection between certification and various mathematical domains.
Demonstrated applicability in algebra, arithmetic, topology, and logic.
Outlined remaining open questions in the implementation of the framework.

Abstract

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

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