BKT-37C1 Supplementary article to BKT–37C Source, geometric-informational, statistical, and validation apparatus for candidate residuals after SM/QCD/EW

BKT-37C1 is a supplementary article to BKT–37C, developing the mathematical, physical, statistical and validation framework for studying candidate residuals remaining after the application of a local SM/QCD/EW null model. The central question addressed in the work is whether, after subtracting known physical, systematic and covariance-controlled components, there may remain an ordered low-complexity residual structure that can be described by a restricted USC projection basis or by a positive-definite RKHS kernel. The tabular source of the analysed cases is the ATLAS/HEPData dataset for the process W+W− → e±νµ∓ν at √s = 13 TeV, based on the full Run 2 dataset with an integrated luminosity of 140 fb−1. The article clearly separates the experimental source data from the derived quantities introduced by the BKT-37C1 apparatus. ATLAS/HEPData provides bin-level data, reference templates, correlations and uncertainties, whereas SM residuals, orthogonal residuals, χ² values, Δχ², ΔBIC and residual-reduction coefficients are secondary computational quantities defined within the present framework. The aim of the article is not to replace the Standard Model, QCD, the electroweak sector or the SMEFT formalism. The Standard Model remains the local reference model, while BKT-37C1 introduces an additional test of the geometry of residuals after known physical components have been accounted for. In this sense, the document examines the possibility of a reproducible low-dimensional or low-complexity residual structure that could indicate a sectoral trace of a higher-order relational-informational layer within the LOM–GTSFC–USC–GTCW programme. The strongest thesis of the work is conditional. A local reduction of χ² is not treated as evidence for new physics. Structural-candidate status can only be assigned if the same frozen USC projection construction, or its explicitly defined kinematic transformation, reduces residuals in independent data, passes the global null test, the look-elsewhere control, full covariance control, comparison with SM/QCD/EW/SMEFT alternatives, and out-of-sample validation. BKT-37C1 therefore defines a falsifiable research pathway for the USC hypothesis. The document does not claim confirmation of new physics. It organizes the mathematical, statistical, logical and physical conditions under which an ordered residual after the Standard Model could be treated as a sectoral candidate trace of a higher-order relational-informational layer.