R01: BRISM Status 3M: Three-Month Review, Logical Consolidation, and Claim Hierarchy

This note presents the three‑month consolidation review of the BRISM (BRane Interface Substrate Model) program following its initial phase of public dissemination across multiple preprints. Its purpose is not to reduce scope, but to clarify logical status, claim hierarchy, and domain of validity. The central outcome is that BRISM should be read as a stratified framework rather than a flat top‑down construction. The hard current core consists of the readout architecture: under explicit interface assumptions, the Born density is structurally selected, and global phase neutrality yields a minimal U(1) symmetry. A second layer remains structurally meaningful but explicitly conditional: SU(2) is retained under rotational interface stability, and SU(3) is retained under internal 3-stability together with Born-invariant internal mixing. A third layer is preserved as a working layer rather than a theorem-level result: the quantities ε₀ = 1/π² and X = 4π³ + π² + π are treated as BRISM working invariants, with their strongest present support arising in micro-scale sectors. A key addition of the present review is an explicit scale hierarchy. Micro-scale manifestations—such as Casimir structure, the infrared fine-structure sector, and the UV minimal-length construction—are interpreted as closer probes of the bare microscopic interface anchor. By contrast, large-scale sectors, including cusp–core regularization, low-ℓ CMB structure, global curvature scaling, and near-horizon phenomenology, are reclassified as effective or exploratory projections anchored in the same underlying geometry. The result is a methodological consolidation: BRISM is reformulated as a graded logical architecture distinguishing hard core results, conditional structural extensions, working invariants, and effective or exploratory sectors. This clarification allows future developments to build on a transparent hierarchy of claims, while preserving the cross-scale structural coherence that motivates the framework. A structured consistency analysis of the underlying BRISM interface framework is provided in the accompanying Supplement (DOI: 10.5281/zenodo.19296467) All BRISM papers on Zenodo >> SearchlistSupplementary structural material, dependency maps, and reproducibility notes are available in an accompanying public repository: https://github.com/swencarloheinze/brism-framework