BKT–37Y10 Derived Lepton Channels of the Proton.

Abstract

BKT–37Y10 — Derived Lepton Channels of the ProtonEmbedded Closure, Tolerance Bands, and Identifiability of the Relational Mechanismep Data, LUXqed/LUXlep, QCD–QED Evolution, Observation Geometry, and Numerical Validation This article develops the LOM–GTSFC–USC–GTCW research programme, whose central problem is the mechanism of formation and stabilisation of physical structures, rather than merely the classification of their masses, lifetimes, and interaction products. It forms a further contribution to the BKT–37 series, connecting the integrated proton-model synthesis of BKT–37Y06–SYN, the operator formalism of BKT–37Y07, the persistent relational–informational node description of BKT–37Y08, and the analysis of orthogonal residuals, eliminated sectors, and cross-channel identifiability in BKT–37Y09. The present work examines derived lepton channels: processes in which the electromagnetic response of the proton participates in producing measurable lepton–lepton scattering. The central thesis is the coexistence of local proton persistence with openness of its interaction channels. Closure does not mean isolation: the proton can preserve its state identity, respond to perturbations, and participate in atomic and nuclear structures. The embedded-closure description distinguishes the local proton state, its couplings to the environment, and the stability conditions of the complete system. Here, information denotes the physical organisation of relations, correlations, and admissible couplings, not computational code or an additional substance. The quasi-sphere is a compatibility boundary in the space of configurations satisfying conservation laws and other hard constraints, rather than a material proton shell. The empirical reference is the CMS–PAS–SMP–26–008 result discussed in the article, concerning lepton–lepton scattering in proton collisions at 13 and 13.6 TeV. The cited values include a reported integrated luminosity of 446 fb⁻¹, an observation significance of 5.4σ against the background-only hypothesis, and cross-section compatibility with the Standard Model prediction at p = 0.59. The article distinguishes the meanings of these tests: observing a process predicted by the Standard Model is neither an observation of an additional interaction nor evidence for a persistent leptonic constituent of the bound proton state. The physical analysis proceeds from electron–proton scattering data and electromagnetic form factors, through the LUXqed and LUXlep constructions, to coupled QCD–QED DGLAP evolution, the hard process, and the measurement response. The lepton parton-distribution representation is compared with the structure-function formalism, while boundary conditions, scale evolution, elastic and dissociative production, soft QCD interactions, selection, and detector effects are kept distinct. This chain separates the structure of the state from a scale-dependent representation of the process and from the final observation distribution. The methodological core is the author’s organisation of the BKT diagnostic framework: closure and non-closure estimators, logarithmic aggregation of local defects, profiled Fisher information, rank and conditioning analysis, and out-of-sample prediction tests. Identifiability is considered for full probability distributions, rather than changes in mean values alone. The analysis distinguishes absent linear response, higher-order response, variance changes, amplitude cancellation, and exact constraints. A remove-and-recover procedure for a known signal tests whether the method recognises an omitted standard process without interpreting it as new physics. Classical mathematical foundations remain explicitly distinguished from their application within the relational programme. The numerical component comprises explicitly specified control models and comparisons based on published inputs. For four cross sections digitised from a plot, the results are D² = 4.81813 in the directional diagonal scenario and D² = 5.20669 in a covariance model decomposed into uncertainty sources. The second scenario gives C = 0.074026, K_cov = 1.301671, and K_log = 0.673434. These quantities diagnose specified comparisons; they are neither probabilities of proton stability nor a reproduction of the official CMS test. At a scale of 100 GeV, using the literature photon momentum fraction of 4.3 × 10⁻³, a frozen-logarithm benchmark yields a combined momentum fraction of 1.536 × 10⁻⁴ for the three lepton pairs. This remains an approximation, distinct from a complete LUXlep calculation. The operator analysis specifies further admissibility conditions for the relational description: the appropriate baryon number, a three-quark operator with a Wilson junction, and the distinction between nucleon distribution amplitudes and parton distribution functions. It also separates curve torsion in the funnel–chiral–torsional LCT model from spacetime-connection torsion. Eliminating a specified auxiliary axial field yields a conditional current–current interaction, but does not derive LCT microdynamics. The calculated coefficient magnitude in the minimal Einstein–Cartan model, 3.16230 × 10⁻³⁸ GeV⁻², shows that a contact interaction at an independently assigned TeV scale would be an additional hypothesis, not a consequence of gravitational torsion alone. The work formulates a testing programme based on transfer across energies, lepton flavours, event categories, and environments without refitting the parameters of the mechanism under investigation. It discusses the role of PPS/AFP forward-proton tagging and complementary electron–proton, electron–nucleus, and beam–gas measurements. A decisive assessment depends on explicit operator maps, control of standard dynamics and uncertainties, calibrated distinguishability, and independent replication. The publication makes a theoretical and methodological contribution: it connects a relational description of persistence with operational conditions for testing and falsifying it. It does not present an empirically determined USC amplitude or an established predictive advantage of additional dynamics. Instead, it specifies which results could give the hypothesis distinct physical content through new, testable relations between observables within standard dynamics, or through a response distinguishable from the complete Standard Model.