Complete Full BCR Theory Rerun: Independent Boundary-Conditioned Realization Audit of "Physics-Informed, Boundary-Constrained Gaussian Process Regression for the Reconstruction of Fluid Flow Fields"

This upload is an independent Boundary-Conditioned Realization (BCR) technical audit prepared by Alfred McBride. The reviewed source paper is “Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields” by Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, and Éric Savin, arXiv:2507.17582. This BCR review does not claim that the source-paper authors used, cited, adopted, or relied on BCR. It identifies technical convergence between the source paper’s boundary-constrained Gaussian-process method and the BCR realization-layer framework. The review applies BCR formulas numerically where reported data permit, including realization-law analysis, decrement/residual analysis, boundary-effect interpretation, visibility/transition logic, composite observability, residual drilldown, escalation gates, and solutional recommendations. The solutional BCR extension identifies open closure branches including no-slip boundary closure, pressure visibility, momentum residual closure, wall-shear and boundary-layer closure, morphology preservation, trajectory/no-crossing hard gates, numerical-conditioning gates, false-lock testing, domain-validity limits, and external witness validation. Boundary-Conditioned Realization (BCR), the BCR formulas, the BCR layer audit, the residual/no-noise classification, the visibility/transition analysis, and the solutional closure framework in this review are attributed to Alfred McBride. The source-paper authors are credited only as the authors of the reviewed source paper. They are not listed as authors, co-authors, contributors, reviewers, sponsors, or endorsers of this BCR audit unless they later provide written approval or formal acknowledgment.