Reading Guide

Logical dependencies and reading sequences

The monograph and six supporting papers develop a single argument, though each approaches it from a distinct angle and at a different level of formal specificity. Some introduce the foundational mathematical architecture; others apply it to particular problems or demonstrate its recurrence across domains otherwise thought unrelated. The present guide proposes a sequence of reading that respects the logical dependencies among the works.

1. Overview
   A non-technical exposition of the program’s central question, its logical structure, and the principal results. Provides a preliminary map of the conceptual terrain before the formal engagement.
2. Closed Comparison Worlds
   The formal foundation. Develops the theory of binary comparison predicates, rectangular completeness, profile-maximality, and the obstruction to subsystem attribution in a finitary setting. This paper establishes the core architecture from which all subsequent work proceeds.
3. Closed Systems from Comparison Completeness
   The primary monograph. Constructs the theory from comparison data through quotient semantics and transport obstruction, then develops the faithful smooth-realization interface by which the obstruction is read as curvature. Chapter 13 decomposes that interface into a torsion condition (T) and an intrinsic detectability axiom (D) and discharges it on a canonical realization; the principal geometric claims are stated in the ghost-free regime (T)+(D).
4. Rectangular Completeness Encompasses Standard Physical Closure
   Shows that closure as rectangular completeness equals the full-product component of classical closure and captures the product-state sector of quantum mechanics, while strictly generalizing standard closure to relational comparison data.
5. Foundational Closure and Primitive Structural Input
   Applies the closure framework as a diagnostic for foundational problems across physical theory. The four axes—externalization, artificial factorization, premature globalization, reification of repair—are shown to be logically independent and to recur across classical mechanics, quantum mechanics, quantum field theory, general relativity, and statistical mechanics.
6. Structural Closure and the Cosmological Misnomer
   Establishes that structural closure (closure under intrinsic comparison) and cosmological closure (open vs. closed FLRW) operate at different logical levels and cannot be identified.
7. Closure Forces Spherical Geometry
   Proves that at the manifold stage, a genuinely frame-complete closed three-dimensional realization is diffeomorphic to S³: isometry-induced frame transport gives frame-bundle transitivity, constant curvature, and—with simple connectivity—the 3-sphere.
8. Route Invariants and the Geometry of Gauge Transport
   Applies the factorization criterion to gauge transport and holonomy, showing that the obstruction to endpoint-determinedness in gauge theories is an instance of the same structural pattern identified across the program.

Foundations sequence. CCW for the finitary foundations, then CSM for the full construction. The remaining papers—RC, FE, SCC, CFSG, RIE—may be read in any order thereafter, as each addresses a specific aspect of the program without cross-dependencies.

Structural physics sequence. Overview, then FE and RC, which treat standard physical frameworks as recovery targets: their successful structures are classified as recovered where the papers derive them, while unrecovered inputs remain visible as interface conditions. CSM supplies the technical development of the geometry.

S³ theorem. Read Overview for the statement, Notation for the terms “faithful smooth realization,” “ghost-free regime (T)+(D),” and “transport obstruction,” then CFSG for the focused theorem. Use CSM Parts III–V for the quotient/transport/curvature background — including Chapter 13, §§13.14–13.16 — rather than treating them as a substitute for the focused CFSG proof.

Read Predictions for the charge-sector exclusion, then CSM Chapter 18 for the theorem chain behind it. The prediction is deliberately narrow: no free/asymptotic particle with true vacuum electromagnetic charge outside the denominator-3 lattice.

Reading sequences through the closure program are given above. The technical claims are carried by the linked papers and monograph; the external physics language used for comparison is anchored by the standard background sources below and collected on Sources.