BKT–37Y08 The Proton as a Persistent Self-Maintaining Relational-Informational Node

BKT–37Y08 — The Proton as a Persistent Self-Maintaining Relational-Informational Node. Global QCD Closure, Relational Ontology, BRST Cohomology, Operator Weaves, and the Geometry of Stability This publication presents an integrated theoretical and phenomenological model of the proton as a single persistent, dynamic, and gauge-invariant state of quantum chromodynamics. Its starting point is the contemporary physical description of the proton: it is not a static system of three immobile quarks, but a nonperturbative bound state realized through quark and gluon fields, the partonic sea, gluon self-interactions, orbital angular momentum, multiparton correlations, Wilson lines, and a scale-dependent hierarchy of operators. Its persistence does not result from the invariance of its individual constituents, but from the preservation of one physical state class despite continuous fluctuations, internal energy-momentum transfers, and scale-dependent changes in representation. The minimal central thesis of the article is that the proton can be described as one global, gauge-invariant relational closure of QCD, realized through an interdependent network of renormalized quark-gluon correlators, Wilson transporters, sum rules, operator matrix elements, and transport maps between observable channels. In this framework, the term “self-maintaining” denotes dynamical self-consistency and spectral stability rather than autonomous energy production. The total energy-momentum tensor remains conserved, while the partial quark and gluon sectors can exchange energy and momentum through mutually compensating currents. The construction therefore explicitly excludes any interpretation of the proton as a perpetual-motion system. The term “information” does not denote an additional substance, field, or hidden energy carrier. It refers to an ordered structure of physical distinctions and dependencies: a state on the algebra of observables, connected correlators, reduced density matrices, mutual information, Wilson transport, sum rules, and relations among observables. In this sense, an “informational weave” is a mathematical-physical organization of relations already present in QCD. It does not, by itself, constitute evidence for dynamics beyond the Standard Model. The article distinguishes four levels of description. The first is the full QCD-QED-EW null model, including reaction dynamics, experimental reconstruction, and systematic uncertainties. The second, denoted as the relational hypothesis, interprets PDFs, GPDs, gravitational form factors, electromagnetic form factors, generalized polarizabilities, spin distributions, and multiparton observables as distinct but compatible projections of one proton state. The third level is a standard effective-field-theory extension through local higher-dimensional operators. The fourth is the strong hypothesis of the Universal Structural Code, according to which one low-dimensional, frozen parameter set should predict the responses of multiple channels without refitting. The implications among these levels are one-directional: HUSC⇒HEFT⇒HR, while: HR⇒HEFT,HEFT⇒HUSC. Consequently, the compatibility of a relational description with QCD does not establish the existence of an additional operator, and the existence of an admissible EFT operator does not establish a universal structural code. The formal framework includes the spectral definition of the proton state, the algebra of physical observables, local BRST/BV cohomology, operator reduction modulo BRST-exact terms, equations of motion, total derivatives, and field redefinitions, as well as an analysis of operators of canonical dimension eight. Three candidate classes are considered: a scalar-gluonic class, a class associated with the squared topological-density fluctuation, and a tensor-mechanical class constructed from the traceless part of the energy-momentum tensor. Their actual independence relative to the complete null model is not assumed. It is reduced to the computable problem of determining the rank increment of the projection matrix in a complete, reduced, and renormalized operator basis of full QCD. A central component of the work is the identifiability framework. A nonzero cohomology class alone does not establish new physics. Distinct dynamics can be identified only when the response generated by a candidate operator contains a nonzero component outside the tangent space of the complete null model. For this purpose, the study defines an operator-response matrix, a projector onto nuisance and standard-model directions, an orthogonal residual, and a profiled Fisher-information matrix. This construction distinguishes a genuinely new physical component from changes in PDFs, GPDs, reaction parameters, normalization, detector systematics, or an ordinary refit of the QCD model. The empirical foundation of the article is a synthesis of results concerning high-Bjorken-x parton distributions, generalized parton distributions, Mellin moments, the energy-momentum tensor, gluonic gravitational form factors, transversity and tensor charge, generalized electromagnetic polarizabilities, partonic entanglement, gluon saturation, and the response of the quark-gluon medium. These results support a description of the proton as one state revealed through multiple operator-distinct but physically interdependent channels. They do not, however, establish an additional USC dynamics, because each result has a standard operator interpretation within QCD and its own identifiability limitations. Particular methodological importance is assigned to the controlled null result obtained in the preceding BKT–37Y07 test: p_boot = 0.799Delta_OOS = -0.0106 +/- 0.059sim = 0.43-0.86 sim >= 0.90 and the preregistered bootstrap threshold was substantially more restrictive. The result therefore does not confirm the tested strong realization of USC. At the same time, it does not falsify the QCD-compatible relational interpretation of the proton. Its methodological significance lies in demonstrating that the research program can return a negative result and does not equate interpretative compatibility with the discovery of new physics. Appendices A–N form an integral part of the argument. They develop the conditional gluing theorem for channel sections, the epistemic classification, the preregistered PASS/FAIL/INCONCLUSIVE gates, the complete BRST/BV algorithm, the dimension-eight operator benchmark, dimensional corrections, the lattice-QCD protocol, interpretation cards for the principal equations, reproducible numerical calculations, the hierarchy of hypotheses, and the precise status of the funnel-chiral-torsional geometric ansatz. Their joint result is not a positive detection of USC. Instead, they transform the strong USC hypothesis into a finite, staged, and falsifiable computational-experimental program. The decisive chain is: nontrivial physical operator class→nonredundancy relative to the null model→K⊥=0→rankIeff≥1→stable direction→positive out-of-sample prediction→transfer without refitting→independent replication. Within the wider research architecture, the article constitutes a physical anchor for the LOM-GTSFC-USC-GTCW program: the Law of One Mechanism, the Global Theory of Shared Couplings of Fundamental Structures, the Universal Structural Code, and the Global Theory of the Cyclicity of Universes. In this program, the proton serves as the most tightly controlled example of stability realized through relation, coupling, transport, constraint, closure, and preservation of physical identity. Any extension of this scheme to nuclei, atoms, complex matter, or cosmology requires an independently derived and empirically validated map between the respective scales. The principal result of the publication is therefore not a declaration of newly discovered physics. It is the establishment of a coherent language and a rigorous decision protocol. The minimal description of the proton as a relational-informational node remains compatible with QCD. The strong USC hypothesis remains open and can acquire distinct physical content only after demonstrating a nonredundant operator class, a nonzero profiled response, a positive out-of-sample prediction, transfer without refitting, and independent replication.