BKT-37Y03-INT The Proton as a Dynamic Relational–Informational Node

This record contains the complete English mirror edition of BKT-37Y03-INT, “The Proton as a Dynamic Relational–Informational Node: The USC–GTCW Layer over QCD: Self-Sustaining Helicoidal–Funnel Modes, the Closure Operator, and the Wilson–Sheaf–Spectrum Program.” The work develops a theoretical and computational framework for describing proton identity and persistence at a level complementary to quantum chromodynamics (QCD). QCD and the Standard Model remain the physical reference for the proton mass, spectrum, amplitudes, quantum numbers, form factors, parton distributions, and scattering observables. The proposed Universal Structural Code (USC) layer does not replace these theories and does not introduce alternative catalog values. Instead, it asks whether the recognizable identity of a proton can be represented as a path-connected class of admissible QCD configurations rather than as one fixed instantaneous microstate. The central construction models the proton as a coupled family of active helicoidal–funnel relational modes. Each mode is characterized by an axis, a variable circular cross-section, phase winding, chirality, curvature, covariant twist, and combined color–geometric holonomy. Their common envelope defines a proton quasi-surface, while an operator-valued compatibility core compares and synchronizes complete modes. The formalism distinguishes nonlinear mode dynamics from its local cellular-sheaf linearization. It also separates the closure estimator, the spectral projector, the reduced-dynamics generator, and the transition quasi-potential, thereby avoiding the identification of topology or a spectral gap with a decay lifetime. A principal objective is to convert this ontology into a falsifiable program connected to physical QCD configurations. The proposed Wilson–sheaf–spectrum workflow proceeds from lattice-QCD ensembles and gradient flow to persistent-feature extraction, helicoidal-mode reconstruction, Wilson transport, sheaf and internal operators, spectral analysis, closure estimators, proton correlators, gravitational and generalized parton observables, and diffractive data. The work includes a lattice-QCD error budget, chiral and excited-state systematics, generalized-eigenvalue-problem control, spectral-subspace stability, Mori–Zwanzig reduction, and large-deviation methods for metastability. The article explicitly distinguishes established data, standard theory, model definitions, control mathematics, calibrations, open problems, and genuine predictions. The experimental proton-lifetime constraint is used only to derive a calibration target within a stated ansatz; it is not presented as a USC prediction. The existence of stable physical helicoidal modes, a common return map, a distinct metafield, and a USC transition barrier remains unproven. The framework acquires independent physical content only if it yields gauge-invariant, regulator-stable, low-dimensional, and out-of-sample predictions that cannot be absorbed into the complete QCD, Standard Model, and detector-response model. The deposited materials include the 283-page main article, the stand-alone technical and numerical annex, and the complete Overleaf-ready source package with bibliography, figures, numerical data, scripts, generated tables, environment information, checksums, and build instructions. The package is intended to support independent review, exact recompilation, numerical audit, and future lattice-QCD implementation.