BKT–37Y11 Coupling of Proton Channels through Photon Exchange

Coupling of Proton Channels through Photon Exchange Closure, Tensor Equilibrium, and Multi-Operator Response Robert Kupski | BKT–37Y11 | Version 2.4 This publication extends the BKT–37 series on the proton as a persistent relational structure and presents a consistent account of closure, channel couplings, stress equilibrium, and response to external interactions within the LOM–GTSFC–USC–GTCW research program. Its starting point is the question of how the proton can exhibit a nonzero, differentiated electromagnetic response while preserving a specified state identity and stability conditions. Quantum chromodynamics (QCD) and quantum electrodynamics (QED) provide the physical baseline; the program’s hypotheses are examined in relation to their operators, conservation laws, and measurable consequences. Three fundamental concepts are defined: relational closure as compatibility of the relations, constraints, and balances specifying a class of structure; non-closure as a specified defect in that compatibility; and relational contact as a connection between channel descriptions through a shared physical quantity, amplitude, correlator, or matching rule. Closure implies neither isolation nor an impermeable shell, and contact does not mean material surfaces touching. Non-closure of a structure is also distinguished from non-closure of its description: an omitted relation can produce a numerical residual despite preserved physical equilibrium. The strong empirical hypothesis of the Law of One Mechanism (LOM; Polish PJM) in the sector examined here posits that the surface channel, which makes electromagnetic coupling accessible beyond the proton’s dominant region, and the deep channel, which has its own nested compatibility conditions, are interconnected realizations of a shared mechanism whose specified parameter set and operator maps impose quantitative relations among form factors, susceptibilities, transition amplitudes, and the Compton response, allowing calibration in some channels to predict independent channels without retuning, whereas significant disagreement between those predictions and data within the stated domain of applicability, after accounting for uncertainties and the complete baseline model, rejects the mechanism realization under test. One of the main constructive results is a model in which an unchanged zero-field energy spectrum and unchanged positive Hessian eigenvalues coexist with variable interchannel susceptibility relative to fixed sources. A necessary and sufficient criterion for exponential stability is also established for a specified class of finite-dimensional models. It shows that direct damping of every channel is not necessary: the coupling structure can transfer energy from an undamped sector to a damped one. Sector preservation, mechanical equilibrium, and dynamical stability remain distinct properties. An important methodological contribution is the analysis of an equilibrium error in the energy–momentum tensor (EMT). Replacing the derivative of radial stress with the derivative of isotropic pressure alone omits variation of the deviatoric contribution and can generate an apparent balance violation in an exactly equilibrated system. A counterexample, conditions for valid reconstruction, and a general criterion for reduction that preserves a specified observable are presented. The problem is not the use of scalars, but the loss of relations needed to reconstruct a physical quantity. The numerical analysis distinguishes the mechanical radius from the slope radius and demonstrates the dependence of reconstruction on the assumed form-factor shape. Recalculation using central quark–gluon dipole parameters from Hackett–Pefkou–Shanahan gives a mechanical radius of 0.752475 fm; replacing the dipoles with tripoles preserving their values and slopes at zero gives 0.868883 fm, an increase of 15.4701%. This is a difference between reconstructions, not a new measurement of proton size. For a selected parameter point of the conditional dipole-coherence model, the calculated electric-polarizability change is −0.121082 × 10⁻⁴ fm³, with a leading change in the differential Compton cross section of +0.035219 nb/sr at a photon energy of 100 MeV and an angle of 90°. The limitations of the low-energy approximation and the combined statistical–systematic test budget are specified. The complete response of the five-parameter model considered is also shown to depend on at most three independent parameter combinations, so increasing the number of measurement frequencies alone does not identify the proposed geometry. The formalism includes compatibility and non-closure estimators and a logarithmic diagnostic, distinct from probabilities of decay or hypothesis truth. The empirical context consists of the ATLAS results, lattice form-factor calculations, dispersive reconstructions, and A2/MAMI Compton measurements discussed in the article. The ATLAS observation at 6.0 sigma concerns the dependence of partonic response on nuclear geometry, not the helical structure of an individual proton. Helical–torsional geometry is a specified variant of the coupling hypothesis in this work; its microscopic realization and additional fundamental dynamics have not been empirically established. The publication’s contribution is to connect closure conditions with multi-operator response, stability analysis, and identifiability. Its formal and numerical results strengthen the proton sector of the LOM program by explicitly restricting admissible models and the scope of inference. Their relevance extends beyond an individual proton profile: they provide criteria for assessing when a reduced description preserves equilibrium and predictions, and when it obscures relations essential to the study of a complex structure.