Part 6B: Structural Derivation of the Bulk–Boundary Inertial Hierarchy Baseline - From Global (H_4) Root Participation to the Golden-Ratio Conjugate Separation Norm

Overview Part 6 of the Origin Geometry (OG) program introduced two candidate geometric hierarchy baselines emerging from discrete H4 geometry: Iint = 20φ⁴ and Rbb = 120√5φ⁴. Part 6A provided a structural derivation of the first expression, Iint = 20φ⁴, by interpreting 20 as the local icosahedral interface-channel count and φ⁴ as the four-dimensional golden-ratio support measure. The present Part 6B revisits the second expression and clarifies its mathematical status. Clarification of the Bulk–Boundary Baseline The central clarification of this Part is that √5 should not be interpreted as the normalized Euclidean distance between conjugate H4 sectors in the rank-doubled R8 embedding. That normalized metric distance is 5/2. Instead, √5 is the algebraic conjugate-gap scale |φ − φ_bar| = √5, associated with the discriminant structure of the golden-ratio field. Consequently, the quantity Ralg_bb = 120√5φ⁴ is interpreted as an algebraic bulk–boundary hierarchy baseline, rather than a direct R8 Euclidean metric-distance baseline. Comparison of Baselines For comparison, the normalized rank-doubled metric baseline is Rmetric_bb = 120(5/2)φ⁴. Numerically, Ralg_bb ≈ 1839.15 Numerically, Rmetric_bb ≈ 1300.47 Among the two baselines, the algebraic baseline is the one numerically close to the observed proton–electron mass ratio. Scope and Limitations This numerical proximity is structurally suggestive, but it is not interpreted as a derivation of proton mass, electron mass, QCD confinement, or hadronic binding. Rather, Part 6B proposes that the pre-dynamical inertial hierarchy candidate associated with H4 bulk–boundary separation is algebraic before it is metric. A later dynamical theory must determine whether and how this algebraic baseline becomes physically dressed into an effective mass hierarchy.