Part 7: Provisional Physical Identification of Interface and Algebraic Bulk–Boundary Hierarchy Baselines From Geometric Invariants to Candidate Phenomenological Correspondence

Overview The Origin Geometry (OG) program proposes that discrete aperiodic four-dimensional geometry can generate structurally distinguished dimensionless baselines prior to empirical fitting, field-theoretic dynamics, or particle-specific interpretation. Earlier Parts established the geometric substrate, dimensionless baseline structure, interaction-regime taxonomy, attractor stability, dynamical screening, and the emergence of hierarchy candidates from H4 geometry. Review of Geometric Baselines Part 6 introduced two hierarchy candidates associated with discrete H4 organization. Part 6A clarified the structural origin of the interface baseline I_int = 20φ⁴, where 20 is the local icosahedral interface-channel count and φ⁴ is the four-dimensional golden-ratio support measure. Part 6B clarified the status of the bulk–boundary hierarchy candidate by distinguishing the algebraic baseline Ralg_bb = 120√5φ⁴ [6, 8, 23, 24, 25, 26] from the normalized rank-doubled metric baseline Rmetric_bb = 120(5/2)φ⁴. Provisional Physical Identification The present Part performs a single task: provisional physical identification. No new geometry, no new numerical derivation, no dynamical field equation, and no empirical fitting are introduced. Instead, we examine how the previously derived geometric baselines may be cautiously associated with phenomenological structures such as electromagnetic coupling hierarchy, stable baryon-to-lepton inertial hierarchy, and gravitational weakness. Core Claims The central claim is deliberately limited: Boundary-supported geometric organization provides a candidate structural setting for electromagnetic-like phase coherence, while the interface baseline I_int may be interpreted as a candidate inverse electromagnetic coupling hierarchy baseline. The algebraic bulk–boundary baseline Ralg_bb may be interpreted as a candidate inertial hierarchy baseline associated with stable bulk-supported versus boundary-supported excitation classes. The metric baseline Rmetric_bb is retained as a mathematically valid comparison, but it is not the baseline numerically close to the proton–electron mass ratio. Gravitational weakness is interpreted more cautiously as a possible consequence of distributed bulk stress response and aperiodic anti-resonance. Scope and Limitations This Part does not derive electromagnetism, U(1) gauge theory, proton mass, electron mass, QCD confinement, General Relativity, or Newtonian gravity. It proposes candidate correspondences between geometric baselines and physical hierarchy classes, while preserving the distinction between structural identification and completed physical derivation.