Structural Closure and the Cosmological Misnomer: Admissibility, Expansion, and the Geometry of Closed Systems

First page of Structural Closure and the Cosmological Misnomer

Research Paper

Chast K. Wolfe · v3 · June 13, 2026

Manuscript Record

Work code: CRI-SCC
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 Not peer reviewed unless otherwise stated.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/scc/. DOI: 10.5281/zenodo.20694803.
Canonical page: closureresearchinitiative.org/scc/
Files: PDF · LaTeX source
Rights: All rights reserved
Citation record: Use the canonical page and BibTeX block below for the current version.

Distinguishes FLRW open/flat/closed curvature terminology from structural closure as an admissibility condition. SCC v3 aligns the S³ claim with the frame-complete manifold-stage theorem and separates local expansion kinematics from curvature-sensitive FLRW distance measures.

Method: The paper separates FLRW model classification from structural admissibility, then imports the frame-complete CFSG theorem at the faithful manifold stage and analyzes expansion intrinsically.
Main result: FLRW curvature labels do not decide structural closure. Under the stated frame-complete compact simply connected manifold-stage hypotheses, the admissible realized geometry is the S³ case; local expansion kinematics remain compatible with intrinsic metric scaling.
Scope: The paper does not reject FLRW parameter estimation or claim that all distance observables are topology-independent. Angular-diameter and luminosity distances remain curvature-sensitive within FLRW distance theory.

Scope: binding statements are the definitions, hypotheses, and theorems in the paper. Related internal sources: CFSG for the frame-complete S³ rigidity theorem, Overview for the geometric recovery diagram, Notation for terms, and Sources and Citation for the FLRW and distance-measure background.

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Version History

Version	Date	Status	File	Details
v3	June 13, 2026	Current version	PDF·Source·DOI	Frame-complete and distance-measure precision release Aligns the manifold-stage geometry claim with CFSG v3, states the frame-complete closed-realization criterion, records the simple-connectivity and gauge-reduced transport roles, and corrects the expansion discussion so angular-diameter and luminosity distances remain curvature-sensitive within FLRW.
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	Initial preprint Initial preprint; superseded archival release.

BibTeX Citation

@misc{wolfe2026structural, author = {Chast K. Wolfe}, title = {Structural Closure and the Cosmological Misnomer: Admissibility, Expansion, and the Geometry of Closed Systems}, year = {2026}, version = {3}, howpublished = {Closure Research Initiative preprint}, doi = {10.5281/zenodo.20694803}, note = {Version 3; current version at https://closureresearchinitiative.org/scc/}, url = {https://closureresearchinitiative.org/scc/}, license = {All Rights Reserved. See https://closureresearchinitiative.org/license/} }