A Factorization Criterion for Route Invariants with Fixed Endpoint Data

First page of A Factorization Criterion for Route Invariants

Research Paper

Chast K. Wolfe · v3 · June 13, 2026

Manuscript Record

Work code: CRI-RIE
Work type: Research paper
Status: Public preprint; versioned research manuscript. Not peer reviewed unless otherwise stated.
Author identifier: Chast K. Wolfe, ORCID 0009-0008-8846-2539
Publisher: Closure Research Initiative
Version: v3, June 13, 2026
Citation target: Current version: closureresearchinitiative.org/rie/. DOI: 10.5281/zenodo.20694985.
Canonical page: closureresearchinitiative.org/rie/
Files: PDF · LaTeX source
Rights: All rights reserved
Citation record: Use the canonical page and BibTeX block below for the current version.

A factorization criterion for comparison data with fixed endpoints: a route invariant is determined by endpoint data if and only if it is constant on every endpoint fiber. Instances are recorded in quotient semantics, categories, gauge transport, holonomy, differential geometry, and general relativity.

Method: The paper abstracts route-dependence to a quotient problem. Routes with the same endpoints form endpoint fibers, and a proposed invariant is tested by whether it is constant on those fibers.
Main result: A route invariant is endpoint-determined exactly when it factors through the endpoint quotient, equivalently when it is constant on every endpoint fiber. The criterion is then matched to quotient semantics, categorical factorization, gauge transport, holonomy, curvature, and general-relativistic examples.
Scope: The result is a structural factorization theorem. The physical examples are comparison instances of the same formal obstruction, not new dynamical laws for the external theories cited.

Scope: binding statements are the definitions, hypotheses, and theorems in the paper. Related internal sources: Overview for the recurrence of endpoint-determinedness, Notation for transport-obstruction vocabulary, and Reading Guide for linked background sources on connections, holonomy, gauge theory, and general relativity.

Download

PDF LaTeX Source (ZIP) Citation DOI

Version History

Version	Date	Status	File	Details
v3	June 13, 2026	Current version	PDF·Source·DOI	Reversible-transport clarification The release clarifies the reversible-transport scope of the loop test, adds the current monograph as an internal reference, removes journal-submission declarations from the manuscript body, and uses compact numeric citations.
v2	June 10, 2026	Superseded version	PDF·Source	CRI metadata release Affiliation, correspondence, and manuscript format updated to the common Closure Research Initiative article style. Mathematical content unchanged from v1.
v1	June 5, 2026	Superseded version	PDF·Source·DOI	Initial preprint Initial preprint; superseded archival release.

BibTeX Citation

@misc{wolfe2026route, author = {Chast K. Wolfe}, title = {A Factorization Criterion for Route Invariants with Fixed Endpoint Data}, year = {2026}, version = {3}, howpublished = {Closure Research Initiative preprint}, doi = {10.5281/zenodo.20694985}, note = {Version 3; current version at https://closureresearchinitiative.org/rie/}, url = {https://closureresearchinitiative.org/rie/}, license = {All Rights Reserved. See https://closureresearchinitiative.org/license/} }