B18: Technical Supplement for BRISM: A Structural Derivation of the SU(3) Layer from Internal 3-Stability and Born Invariance

This technical supplement closes a previously identified gap in the BRISM series by providing a structural derivation of the internal SU(3) symmetry layer used in the BRISM π-geometry. Starting from the Born-fixed interface setting and a precise internal 3-stability postulate, the supplement formulates the brane appearance as a minimal complex three-component fiber and requires invariance of the interface extraction under constant complex-linear internal basis changes. Under these conditions, Born-density preservation forces U(3) as the maximal internal symmetry group on the fiber. Since the global phase U(1) layer is already fixed independently by phase neutrality, the minimal non-abelian residual internal symmetry is SU(3). The argument is purely structural and does not invoke a dynamical gauge principle, grand unification, or renormalization-group running. In addition, the supplement explains why a canonical π³ normalization level is naturally associated with a ℂ³ internal fiber through the geometry of the unit sphere S⁵ ⊂ ℝ⁶. This clarifies the logical status of the SU(3) layer employed in the BRISM invariant X = 4π³ + π² + π. The result therefore upgrades the earlier BRISM use of SU(3) from hypothesis-language to an explicit conditional structural derivation: Born invariance + internal 3-stability ⇒ U(3) ⇒ SU(3) after separation of the already-fixed global U(1) phase direction. The supplement is intended as a reviewer-facing clarification note and as a citable logical anchor for later BRISM preprints and revisions. 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