BKT 77A The Proton as a Stable Closure Class and Collision Spectroscopy as a Cascade of Energy-Driven Quasi-Closures

BKT-77A The Proton as a Stable Closure Class and Collision Spectroscopy as a Cascade of Energetically Forced Quasi-Closures This article presents a formal relational reinterpretation of proton structure, hadronic resonances, fragmentation, and hadronization, while preserving consistency with quantum chromodynamics, scattering theory, amplitude analysis, and S-matrix unitarity. Its point of departure is a distinction between two fundamentally different questions: which amplitude structures provide an adequate description of experimental data, and which physical status may be assigned to the reconstructed intermediate states. The proton is described as a stable relational closure class whose identity is determined by the preservation of invariants, dynamical coherence, and persistence within an admissible viability domain rather than by the invariance of every internal descriptor. A high-energy collision is treated as an active transformation of the system. Such a transformation may disrupt the original proton closure class, open additional interaction channels, and generate transient configurations that need not have existed before the collision as autonomous constituents of the proton. The central epistemic result of the study is that a common amplitude pole accompanied by a reproducible residue pattern confirms the existence of a specific dynamical structure, but does not by itself determine its pre-collision ontological status. On this basis, the article distinguishes between a stable closure class, an amplitude pole class, a relational quasi-closure, and a threshold- or interference-generated structure. The formal framework includes a structural-tolerance tensor, the geometry of symmetric positive-definite matrices, an affine-invariant distance metric, memory-dependent dynamics, the effective Feshbach Hamiltonian, exit-time models, a cascade description of hadronization, and statistical tests of identifiability. The three-level R0–R1–R2 architecture separates an interpretation equivalent to the Standard Model description, a predictive compression of Standard Model parameters, and a potential response irreducible to the complete QCD, hadronization, and detector model. The numerical module includes proton-stability anchors, the radius–spectrum relation, the N∗N^ state ladder, multichannel all-charm structures, threshold controls, benchmarks of SPD geometry, GKSL models, pole-flow analysis, and diagnostics designed to distinguish the R1 and R2 regimes. BKT-77A establishes a coherent programme for the classification, computation, and falsification of the relational quasi-closure hypothesis. At its present stage, the result has a formal and methodological status. The article does not claim the discovery of a new particle, field, or interaction, nor does it present empirical confirmation of an independent USC dynamics beyond the complete QCD description. Its principal contribution is the transformation of the concept of post-collision reorganisation into a precise framework of definitions, competing models, metrics, estimators, and decision gates.