Shell Selection of Proton–Neutron Pairing as a Nuclear Anchor of the Relational Interpretation of USC. BKT-31

The BKT-31 publication presents a formal analysis of the CaFe result on shell-selected short-range proton–neutron pairing in atomic nuclei as a candidate anchor for the relational interpretation of the Universal Structural Code within the LOM–GTSFC–USC–GTCW framework. The point of departure is the observation that the intensity of short-range nucleon correlations cannot be reduced to a simple count of protons, neutrons or mass number alone, but depends on occupied shell orbitals and on the admissible compatibility of quantum channels. The document does not treat the CaFe result as a conclusive validation of LOM–GTSFC–USC–GTCW. The result is treated as an empirically significant test case in which the standard counting description is insufficient, while a controlled analysis requires a null model, an operator residual, a shell-channel compatibility matrix, non-closure and closure estimators, and a PASS/FAIL procedure. In this sense, BKT-31 does not replace nuclear physics with a new interpretation. It builds a formal relational language anchored in standard tools such as chiral effective field theory, the generalized contact formalism, orbital graphs, Fisher–Rao information geometry, Quantum Fisher Information and the Bures metric. The central element of the publication is the transition from a scalar description of constituent numbers to an operator description of state compatibility. A short-range proton–neutron pair is described as the observable projection of a stable channel node whose formation depends on shell, spin-isospin, geometric, topological and tolerance-based compatibility. The USC hierarchy introduced in the article — cubiton, polmeton, polmeta, informational weave and stable informational node — is not treated as a postulate of new particles, but as a formal-interpretive layer for describing admissibility conditions and stabilization of coupling relations. Version v16 contains the main article and technical appendices covering chiEFT anchoring, discrete orbital-graph geometry, USC-estimator calibration, QFI/Bures information geometry and an MC/QFI/Bures demonstrator. The numerical results indicate a sign change of the residual relative to the counting model: the transition (^40Ca ^48Ca) gives a channel-blocking structure, while the transition (^48Ca ^54Fe) gives a channel-enhancement structure. This requires replacing a simple damping filter by a two-mode operator that distinguishes channel non-closure from channel closure. The epistemic status of the publication remains controlled. BKT-31 has the status of a formal-interpretive hypothesis, a mathematical-physical demonstrator and a test programme, not of completed empirical validation. A stronger status requires further ab initio calculations, derivation of reduced proton–neutron density matrices, computation of QFI/Bures metrics, inclusion of experimental uncertainties and out-of-sample validation on nuclei beyond the CaFe calibration set without parameter retuning. The proper contribution of the publication is the rigorous formulation of the USC apparatus: relational concepts are rewritten into mathematical objects, inserted into a null-model framework and subjected to a falsifiable research procedure.