The k=2/k=3 Boundary Algebra and the Origin of Standard Model Mixing Parameters in Two-Sided Closure Theory

We identify the missing organising structure of Two-Sided Closure Theory (TSCT): the boundary algebra B₂₃ at the interface between Jones levels k=2 and k=3. This algebra, the centraliser of TL(k=2) in TL(k=3), has total dimension 29, with sub-dimensions 20 (gauge/curvature sector), 9 (colour sector), and EW carrier dimension 13. Every Standard Model parameter associated with mixing, CP violation, dark energy geometry, and quark isospin ratios is a projection of this single object. Specifically: sin²θ_W = N_C/dim_EW = 3/13; Ω_Λ = dim_gauge/dim_total = 20/29; A_CP(local)/A_CP(global) = dim_gauge/dim_colour = 20/9; m_u/m_d = 2N_C/dim_EW = 6/13. The Cabibbo angle, the √2/13 neutrino prefactor, and the Koide phase correction 9√2/320 follow as further projections. The colour charge N_C = 3 is a boundary invariant: N_C = (k₃+2) − [M:N]k₂ = 5 − 2 = 3. It is not a free parameter. This reduces eight independently stated Tier-2 identifications to a single algebraic claim: prove dim(B₂₃) = 29 from Jones bimodule theory. That is the central open obligation of this paper. Principle: the Standard Model mixing parameters are interface costs — the algebraic price of rendering two incompatible closure depths (k=2 and k=3) as one coherent physical world.