CHC Framework Series v2.0

Abstract

CHC Framework Series v2.0 is a coordinated collection of 72 theoretical and verification papers examining whether compact phase structure can yield testable physical relations rather than merely redescribe familiar equations. The series spans scalar-tensor gravity, cosmology, quantum measurement, detector memory, bound systems, strong-field problems, gauge models, and a finite compact-holonomy benchmark. Why read this release The central problem is predictive closure. A framework has physical content only when its observables descend from a declared action and a finite set of microscopic couplings, its probabilities are complete, its response is dynamically admissible, and at least one measured direction remains unavailable to calibration or nuisance retuning. Version 2.0 formulates those requirements as explicit theorems, no-go results, and rejection tests. The release is useful as a worked study of where a broad physical framework gains or loses predictive content. It shows which conclusions follow exactly, which require additional couplings, which are indistinguishable from standard descriptions, and which public-data comparisons reject or fail to identify the proposed relation. Principal results The root constrained action is reduced exactly, on each regular connected branch, to general relativity plus one canonical scalar. The compact branch is locally equivalent but globally circle-valued, with an invariant circumference, conserved winding sectors, a sharp winding-energy bound, and an obstruction to a regular phase-only disk core. The inverse variational problem is treated at scalar, joint-field, and global levels. Helmholtz symmetry determines local action integrability, while a Čech condition determines whether chartwise Lagrangians glue to a global compact-phase action. Positive detector sinks are embedded in completely positive trace-preserving instruments. The removed no-event norm is assigned to resolved jump outcomes, and unitary system-environment dilation yields normalized multi-time probabilities without assuming CP-divisible reduced dynamics. Passive memory is characterized through positive-pole Hankel rank and general rational state-space realizations satisfying a KYP storage inequality. Controllability and observability identify the minimal memory order, including models with damped oscillatory poles. A functional-nuisance theorem proves that an unrestricted constitutive family is locally non-predictive when its response spans the observable space. A finite single-spurion family has bounded rank, and the compatibility-manifold construction identifies the transverse combinations that remain testable after theory parameters and experimental nuisances are profiled out. CHC-MHB supplies one complete finite realization. A controlled compact phase threads a symmetric three-mode loop. Tree phases are removable, while the loop holonomy survives. The three measured frequencies obey the parameter-free relation 𝓘 = 3√6 ∏ⱼ(Ωⱼ − Ω̄) / [∑ⱼ(Ωⱼ − Ω̄)²]³ᐟ² = cos θ The same Hamiltonian determines phase loading, retarded response, loss, and resolved events. An open chain provides the phase-null control. A 1001-phase numerical calculation checks the spectrum, invariant, gradients, unitarity, probability completeness, and passivity. A 39-point comparison with a published superconducting-circuit figure gives an invariant RMSE of 0.02464. Because the source does not provide raw tomography covariance, this result is figure-level agreement with the finite emulator relation rather than a likelihood test of the wider CHC framework. A twelve-phase raw-data protocol states a prospective rejection rule. Suggested reading path Readers seeking the shortest route should begin with Paper 01 (CHC), which establishes the root scalar-tensor content; Paper 46 (CHC-MCL), which states the common microscopic-closure and predictive-rank criterion; and Paper 47 (CHC-MHB), which realizes that criterion in a finite model. The paper-by-paper guide then identifies the relevant sector paper, what changed from v1.0, and the strongest conclusion that the paper supports. Important corrections from v1.0 Version 2.0 separates fitted parameters from predictions and retains negative results. The CCL path factor is inferred rather than fixed to π. Planck-unit rescalings are shown to leave dimensionless observables unchanged. The PFW family is proved rank deficient. Finite compact-mode sums are not treated as ultraviolet completion. Area and symmetry matching are insufficient for duality or microscopic entropy. The minimal faithful complex representation dimension of (Z_p)^r is corrected to r, and representation theory alone does not determine charged-lepton masses. The Catalog-2 fast-radio-burst holdout is retained as a rejection of the declared transfer model. Scope of the conclusions The release does not establish CHC as a replacement for general relativity, quantum field theory, standard cosmology, detector physics, or open-system methods. Its strongest conclusions concern the exact content of a declared action, topology, response class, inference map, or finite benchmark. Several sectors still require a microscopic coupling fixed before the relevant data are examined, a complete likelihood with nuisance propagation, and a successful held-out comparison with the appropriate standard models. The archive includes all 72 PDFs and TeX sources, executable validation scripts, structured numerical outputs, the digitized compact-holonomy comparison with source provenance, a paper-by-paper v1.0-to-v2.0 guide, the remaining scientific limitations, and SHA-256 checksums. The 72 manuscripts contain 477 theorem-like statements and 477 proof environments and compile to 818 pages without unresolved references or citations. Version-specific DOI: https://doi.org/10.5281/zenodo.22542860 Concept DOI for all versions: https://doi.org/10.5281/zenodo.20282161 Series index: https://phaseorigin.com/research/chc/