Unified Geometric Wave Theory: Brane Interface Module — Canonical Closure, Dimensional Consistency, and Portal Constraints

We present the locked Brane Interface Module of the Unified Geometric Wave Theory (UGWT), a five-dimensional covariant framework in which quantum collapse is driven by a geometric entropy-wave mechanism. This module closes the variational, canonical, and dimensional gaps identified in prior UGWT drafts. The key deliverables are: (i) a dimensional convention lock assigning the entropy scalar S dimensionless status and the Lagrange multiplier field λ mass dimension three in five-dimensional natural units, with the bookkeeping constant χ dimensionless; (ii) the correct Israel trace-reversal coefficient 1/(d−1) = 1/3 for a four-dimensional brane worldvolume embedded in a five-dimensional bulk, derived from first principles and replacing a previously incorrect statement; (iii) fully explicit Robin-type jump conditions for the normal derivatives of λ and S at the brane, sourced by universal trace portals with dimensionally consistent coupling constants; (iv) the closed exchange law relating the divergence of the brane stress tensor to bulk-to-brane energy transfer; (v) canonical closure of the embedding sector via the extended phase space of brane position and momentum fields X^A(y), P_A(y), including explicit verification of both Poisson brackets; and (vi) a notation bridge resolving the symbol collision between the entropy scalar S and the brane surface stress S_ij present in earlier UGWT appendices. Constraints from the MICROSCOPE equivalence-principle test, Eöt-Wash fifth-force exclusions, and Oklo-class alpha-variation bounds are used to rank portal choices and identify the universal trace coupling as the least-constrained option in the short-range regime.