Closed Comparison Worlds and the Obstruction to Subsystem Attribution

Research Paper

Chast K. Wolfe · v3 · June 12, 2026

Manuscript Record

Work code: CRI-CCW
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 Not peer reviewed unless otherwise stated.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 12, 2026
Citation target: Current version: closureresearchinitiative.org/ccw/. DOI: 10.5281/zenodo.20694701.
Canonical page: closureresearchinitiative.org/ccw/
Files: PDF · LaTeX source · figure PNG
Rights: All rights reserved
Citation record: Use the canonical page and BibTeX block below for the current version.

A finitary structural account of subsystem attribution in closed two-subsystem comparison worlds, using only binary comparison predicates as primitive data: no topology, metric, dynamics, background geometry, or gauge structure. Among locally distinguishable worlds, rectangular completeness is equivalent to profile-maximality.

Method: The paper works entirely in finite comparison worlds. It defines subsystem profiles from binary comparison predicates, studies admissible extensions by profile data, and then passes to quotient reports under the relevant symmetry action.
Main results: For locally distinguishable two-subsystem comparison worlds, rectangular completeness is equivalent to profile-maximality. The quotient analysis then shows that twin representatives can agree on all admissible reports while assigning the relative change to different subsystems.
Scope: The result is a finitary theorem about comparison structure and subsystem attribution. It does not assume a background metric, gauge field, topology, or dynamics, and it does not assert that arbitrary physical subsystems are closed in the closure-theoretic sense.

Motivation: the figure abstracts a frame-attribution thought experiment. If a field-like subsystem and a reference subsystem are described only by their mutual comparison data, then “the field changes relative to the reference” and “the reference assignment changes relative to the field” need not be distinct invariant claims. The paper replaces that intuition by the finitary orbit statement shown here.

Relational indistinguishability of orbit-projection-equivalent descriptions. The top half is an A-fixed, hence B-supported, description; the bottom half is a B-fixed, hence A-supported, twin description. Both project to the same physical quotient history, so no coherent report distinguishes the two support readings. The edge labels x and y denote comparison-relation values; the heading x = y denotes equality of report values, not equality of states or edge values.

Scope: binding statements are the definitions, hypotheses, and theorems in the paper. Related internal sources: Notation for terms, Worked Example for the explicit finite case, and Logical Status for the closure/rectangular-completeness criterion. Cite the current-version BibTeX block below.

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Version History

Version	Date	Status	File	Details
v3	June 12, 2026	Current version	PDF·Source·DOI	Admissibility and references Closed-world admissibility terminology is stated as a criterion with requirements, external reference metadata is expanded with DOI and publisher links, and the current PDF/source bundle is rebuilt from the v3 source. The mathematical results are unchanged from v2.
v2	June 10, 2026	Superseded version	PDF·Source	Institutional 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{wolfe2026ccw, author = {Chast K. Wolfe}, title = {Closed Comparison Worlds and the Obstruction to Subsystem Attribution}, year = {2026}, version = {3}, howpublished = {Closure Research Initiative preprint}, doi = {10.5281/zenodo.20694701}, note = {Version 3; current version at https://closureresearchinitiative.org/ccw/}, url = {https://closureresearchinitiative.org/ccw/}, license = {All Rights Reserved. See https://closureresearchinitiative.org/license/} }