Logical Status
Claim Register
This page records the public claims by logical role. The entries below do not replace the proofs; they identify the controlling source, the status of the assertion, and the hypotheses or limits under which the assertion is made.
The primitive object is a comparison world (U,C): states together with comparison predicates. Intrinsicality says that comparison predicates are relations among states, invariant under the automorphisms of the comparison world they help constitute.
Control: CSM, Definition 0.1.1 and Chapter 2; finitary two-subsystem use in CCW.
A comparison world is closed at this stage when no admissible profile-pair omission remains invisible to its own comparison structure: admissible combinations are realized or internally excluded.
Control: CSM Lemma 2.6.2 and Corollary 2.6.3; comparison with standard product closure in RC.
Under local distinguishability, intrinsicality, and the conservative-completion/self-containment hypotheses stated in the monograph, the full admissible profile rectangle is forced. The finite-to-global boundary is handled by the refinement-tower and finite-witness results.
Control: CSM Theorem 2.6.4; two-subsystem record in CCW; standard-closure comparison in RC.
Once the relevant group action and quotient are fixed, coherent reports factor through the orbit quotient. Twin representatives can differ in whether the change is assigned to subsystem A or subsystem B while giving the same quotient-level report.
Control: CCW; motivating figure and plain-language account on Overview.
A route invariant with fixed endpoint data is determined by endpoint data exactly when it is constant on each endpoint fiber. Endpoint agreement alone does not imply equality of transported route data.
Control: RIE. This is a route-invariant criterion, not an empirical claim.
The smooth geometric branch reads the stabilized degree-2 transport carrier as curvature only through the explicit interface (T)+(D). Condition (T) controls torsion in the stabilized quadratic carrier; axiom (D) supplies uniform defect detectability on the tower; together they select the Lie branch and support the canonical Malcev realization.
Control: CSM Chapter 13 and Appendix A. Torsion and profinite ghost models mark the failure modes.
The second-jet layer is the first stable obstruction layer in the transport filtration. First-order data records transport/connection data; the quadratic square-defect carrier F2/F3 is where closed-loop tensorial obstruction first appears. Higher jets refine later obstruction layers.
Control: CSM Chapter 13 and Appendix A. Background differential geometry is cited in References [1]-[3].
At the faithful smooth-realization stage, a compact connected simply connected orientable Riemannian three-manifold satisfying the stated closed-system frame-completeness hypotheses has isometry-induced frame transport, hence transitivity on the orthonormal frame bundle, constant sectional curvature, and the simply connected compact space-form case S3.
Control: CFSG; compactification intuition on Foundations.
General relativity, quantum field theory, and standard cosmological machinery are treated as successful structures to be classified: recovered from the closed comparison architecture, retained as explicit interface conditions, or left outside the closed-system claim. The site does not assert that compact S3 by itself removes local ultraviolet divergences or proves a cosmological bounce.
Control: Overview, SCC, Sources and Citation.
The flat transverse-distance law DM=DC and the closed law DM=Rc sin(DC/Rc) are compared to show local agreement for large curvature radius and global closure in the S3 case. This is a structural comparison, not a fitted cosmological parameter result.
Control: SCC and the FLRW distance-measure references on Sources and Citation.
If the closed electromagnetic phase sector constructed in CSM Chapter 18 is physically realized, and the primitive charge unit is normalized by the observed electron charge magnitude, then every free or asymptotic particle with true vacuum electromagnetic charge lies in the denominator-3 lattice.
Control: Predictions and CSM Chapter 18.
The four-axis taxonomy classifies primitive structural input by externalization, artificial factorization, premature globalization, and reification of repair. It is a diagnostic framework for comparing theory architectures; it is not an empirical discriminator by itself.
Control: FE.
The monograph separates forced intrinsic content from compatibility-level or realization-level statements: unique scalar channel up to normalization, quartic leading behavior under the stated structural hypotheses, absence of intrinsic absolute normalization, and later conditional Hilbert-branch/operator realization.
Control: CSM Chapters 19-23.
Version records, superseded files, and correction procedure are maintained separately on Corrections and Version Record. Current citation targets are collected on Sources and Citation and on the individual work pages.
References [1]-[3] support the standard differential-geometric background behind the smooth reading of curvature, holonomy, and second-order data. They are not sources for the closure program’s own theorem claims, which are controlled by the monograph and public preprints listed above.
References
[1] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. I (Interscience, 1963), for connections, curvature, and frame-bundle background.
[2] M. Nakahara, Geometry, Topology and Physics, 2nd ed. (Institute of Physics, 2003), Chs. 10–11, for connections, holonomy, and gauge-field geometry.
[3] R. M. Wald, General Relativity (University of Chicago Press, 1984), for curvature, parallel transport, normal-coordinate methods, and the standard second-order metric reading.