BKT-32: Relational Analysis of the Emergence of Hadron Mass in Jefferson Lab Data

Publication Introduction — BKT-32 This document presents the BKT-32 module devoted to the relational analysis of the emergence of hadron mass in the context of Jefferson Lab results. The starting point is an established problem in strong-interaction physics: the dominant part of the proton and neutron mass does not originate from the current masses of light quarks, but from non-perturbative QCD dynamics, known as the emergence of hadron mass. In the standard language of hadron physics, this problem is analysed through QCD, strongly coupled QCD, continuum Schwinger function methods, reaction models, nucleon-resonance descriptions, GPD and Regge approaches. The purpose of BKT-32 is not to replace these descriptions. The document proposes a narrower and testable thesis: after subtracting the best available null model, an ordered relational residual may remain, which can be described in the USC language as a scalar-projection defect, a closure channel, coupling tolerance and a compatibility operator. In this formulation, hadron mass, probing depth, persistence of CLAS/CLAS12 resonance structures and the absence of full factorization in the KaonLT sector are treated as related manifestations of one problem: the transition from scalar description to channel-relational description. The document develops a mathematical-physical apparatus including the observables space, the null model, the orthogonal USC residual, the Mahalanobis metric, covariance matrices, uncertainty propagation, PCA/ICA/FastICA reduction, the BIC criterion, the full Bayes factor and out-of-sample validation. The parameter (G_^ USC, OOS) plays a central role. It measures whether a frozen USC residual reduces the covariance-weighted predictive error of the null model on data not used during calibration. The numerical results presented in the document have the status of model-derived working values and formal-numerical demonstrators. They do not constitute full empirical validation of the Jefferson Lab sector. Full PASS status requires raw binned CLAS12/KaonLT data, complete experimental covariance matrices and computation of the USC residual out of the calibration sample. The document therefore maintains a cautious formal-diagnostic status: it shows that the USC apparatus can be formulated as a falsifiable residual hypothesis, not as a completed empirical resolution. The publication forms part of the PJM–GTWSSF–USC–GTCW / LOM–GTSFC–USC–GTCW research programme, in which observed scalar values are treated as projections of deeper coupling relations, tolerance channels and closure conditions. BKT-32 shows how this idea can be translated into mathematically and statistically controlled language, with a clear separation between empirical data, null model, numerical result, interpretation and conditions for future validation. Keywords: LOM; GTSFC; USC; GTCW; BKT-32; Jefferson Lab; emergence of hadron mass; EHM; QCD; CSM; CLAS12; KaonLT; nucleon resonances; GPD; Regge; dressed-quark mass; scalar-projection defect; null model; covariance matrix; PCA; ICA; FastICA; Bayes factor; out-of-sample validation; PASS/FAIL.