Treatise on the Geometry of Physical Residuals Relative to Established Null Models USC Compatibility Channels, Flavour Anomalies, Alpha Decay and the Hypothesis of a Higher Informational Layer

This publication presents the treatise BK-BKT-26/BKT-26A/BKT-26B devoted to relational physics of information, Universal Structural Code channels and the residual geometry of couplings within the LOM–GTSFC–USC–GTCU research programme. The work develops a formal apparatus in which measured quantities of established physics, such as mass, energy, decay width, half-life, cross section, angular observables, Wilson coefficients and nuclear channel parameters, are not rejected or replaced, but treated as empirical projections of deeper coupling relations.

The central idea of the treatise is the distinction between the scalar layer of established physics and the relational layer, in which the stability of a physical system is described by the compatibility of coupling channels within admissible tolerance bands. In this framework, USC does not denote a digital code, but a formal rule of compatibility between physical configurations: phase, geometrical, topological, chiral, torsional, energetic and channel conditions. Stability is therefore not an ideal point of exact parameter equality, but the persistence of a system within an admissible compatibility band, analogously to mechanical tolerance in fitted components, where effective coupling requires an allowed range of deviations rather than absolute identity of dimensions.

The document consists of three logically connected parts. BKT-26 is the main article and defines the relational language: configuration spaces, USC channels, tolerance bands, the closure sphere, the relational weave core, the closure defect and the testability condition relative to the null model. BKT-26A develops the alpha-decay sector as a domain of numerical validation, introducing the estimator (\delta_{\rm nuc}), the operator (\widehat{D}{\rm nuc}) and the residual correction (\Delta{\rm USC}). BKT-26B acts as the technical mathematical-physical annex, organizing the conditions of reproducibility, the validation scheme, statistical limitations, residual orthogonality conditions, the interpretation of the correction in reduced width or preformation, and the boundaries of the evidential status of the obtained results.

The most important formal-numerical result of the work is the separation of three objects: the closure-defect estimator, the operator representing a positive quadratic form, and the residual correction entering the decay-rate equation. In the technical sample, a significant improvement of the residual description relative to the null model was obtained: RMSE decreased from (2.614990) to (0.949728), corresponding to a reduction of approximately (63.68%), with (\Delta {\rm BIC}\approx -36.725833). This result is not presented as a final proof of a new nuclear mechanism, but as a strong candidate validation anchor for the hypothesis that, after subtraction of established physics, an ordered and testable residual structure may remain.

The significance of the work extends beyond the alpha-decay sector itself. The treatise indicates that a similar residual apparatus may be applied to the analysis of flavour anomalies in particle physics, observables in CERN data, nuclear relaxation channels, relational interpretation of particle stability and the dark-sector problem. Within the LOM–GTSFC–USC–GTCU framework, dark matter and dark energy are considered as hypothetical macroscopic projections of the metafield, understood as a higher relational-informational layer that may act as a global compatibility scaffold of the structures of the Universe. This description does not replace (\Lambda)CDM, the Standard Model or nuclear physics, but proposes an additional analytical layer: testing whether residuals left by established models possess a channel-like, geometrical, informational and predictive structure.

The publication maintains a cautious scientific status. The results should be treated as a formally coherent and numerically promising stage of a research programme, requiring full validation on larger datasets, in particular ENSDF, NNDC, LiveChart, nuclear-family data, uncertainty propagation, out-of-sample tests and independent comparison with WKB, R-matrix, preformation models, shell effects, pairing, deformation and hindrance. In this sense, the work does not close the theory, but establishes its strict conceptual, mathematical and validation apparatus.