Preprints
Monograph, research papers, and downloads
I. The Monograph
Comprehensive Treatise
A mathematically closed physical theory must be written without external scaffolding. The monograph develops the closure principle as a classification program, establishing the admissible architecture as rigid across geometric, field-theoretic, scalar, and matter sectors. The theory proceeds from primitive comparison data through quotient semantics, transport obstruction, curvature at the faithful smooth-realization stage, and the emergence of smooth geometry within that bridge.
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DOI
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@book{wolfe2026closed,
author = {Chast K. Wolfe},
title = {Closed Systems from Comparison Completeness},
year = {2026},
version = {3},
note = {Version 3; see change note on the CSM landing page},
publisher = {Closure Research Initiative},
doi = {10.5281/zenodo.20589038},
url = {https://doi.org/10.5281/zenodo.20589038},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
This is the comprehensive treatise. Supporting papers develop specific results in greater technical detail.
II. Research Papers
Download all papers and LaTeX source (ZIP)
A finitary structural account of subsystem attribution in closed two-subsystem comparison worlds, using only binary comparison predicates with no topology, metric, dynamics, background geometry, or gauge structure assumed. Among locally distinguishable worlds, rectangular completeness is equivalent to profile-maximality.
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@misc{wolfe2026ccw,
author = {Chast K. Wolfe},
title = {Closed Comparison Worlds and the Obstruction to Subsystem Attribution},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/ccw.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
At the manifold stage, a genuinely closed realized three-dimensional system is forced to the S³ case. The closure constraint, expressed through the orthonormal frame bundle and the admissible comparison groupoid, gives the rigidity result within that smooth-realization setting.
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@misc{wolfe2026closure,
author = {Chast K. Wolfe},
title = {Closure Forces Spherical Geometry: Genuinely Closed Three-Dimensional Systems Are Diffeomorphic to S\textsuperscript{3}},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/cfsg.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
Argues that the cosmological and structural uses of "open" and "closed" operate at different logical levels and cannot be identified. Structural closure functions as a precondition for invariant physical content, whereas cosmological closure is a specific geometric condition.
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@misc{wolfe2026structural,
author = {Chast K. Wolfe},
title = {Structural Closure and the Cosmological Misnomer: Admissibility, Expansion, and the Geometry of Closed Systems},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/scc.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
Closure as rectangular completeness stands in a precise relation to standard notions of closed two-subsystem systems. For classical systems it equals the full-product component; for quantum systems it captures the product-state sector.
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@misc{wolfe2026rectangular,
author = {Chast K. Wolfe},
title = {Rectangular Completeness Encompasses Standard Physical Closure},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/rc.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
Four independent axes of primitive structural input—externalization, artificial factorization, premature globalization, reification of repair—are isolated and proved logically independent. Applied to foundational tensions across classical and quantum physics.
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@misc{wolfe2026foundational,
author = {Chast K. Wolfe},
title = {Foundational Closure and Primitive Structural Input: A Four-Axis Taxonomy},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/fe.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}
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.
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@misc{wolfe2026route,
author = {Chast K. Wolfe},
title = {A Factorization Criterion for Route Invariants with Fixed Endpoint Data},
year = {2026},
howpublished = {Closure Research Initiative preprint},
doi = {},
url = {https://closureresearchinitiative.org/rie.pdf},
license = {All Rights Reserved. See https://closureresearchinitiative.org/license.html},
}