Static and Dynamic Uniqueness Arc — Paper II A Classification Theorem for Physical ConstantsAdmissibility-Fixed, Quotient-Dependent, Effective, Transport-Defined, and Presentation-Dependent Roles By Amos Jay Maley This manuscript is the second paper in the Static and Dynamic Uniqueness Arc, a sequence of works analyzing admissibility-preserving uniqueness, invariant transport, standing-bearing continuation structure, and fixed-domain constraint architecture in physical theory construction. Building on the fixed-domain standing-fixity results established in Paper I, this paper develops a formal role-classification theorem for physical constants and constant-like quantities under admissibility-preserving comparison. The central result is a five-role exhaustion theorem: admissibility-fixed, quotient-dependent, effective, transport-defined, and presentation-dependent. The manuscript argues that these are not discretionary interpretive categories, but the complete admissibility-bearing loci available to constant-like quantities inside a fixed physical domain. The paper establishes that physical constants do not form a homogeneous parameter ontology merely because they appear numerically in equations. Instead, constant-like quantities perform structurally different admissibility roles depending on whether they function as: domain anchors, quotient invariants, effective envelope coefficients, lawful transport coordinates, or representational presentation structure. The manuscript develops: fixed admissibility domains, anchor/tensor/skin decomposition, role profiles, constant-continuation loci, family-level role discipline, transport-closure constraints, and target-domain retyping conditions for parameter families and ensemble comparisons. Detailed classifications are provided for: gauge groups and symmetry structure, dimensionful and dimensionless constants, gauge couplings, RG trajectories, fine-structure-constant structure, Yukawa matrices, CKM and PMNS transport structure, CP phases, EFT coefficients, Wilson coefficients, replicated sectors, and formal parameter scans. The paper further develops: a no homogeneous constant-space result, a role-before-explanation principle, a no default selector theorem for pre-admissible parameter spaces, and a formal error taxonomy for fine-tuning, anthropic, and multiverse role compression. The analysis remains explicitly compatible with: renormalization-group running, effective field theory, empirical parameter fitting, controlled parameter scans, beyond-Standard-Model construction, and ensemble modeling, while denying that formal parameter multiplicity automatically inherits standing-bearing explanatory authority. The central conclusion is that admissibility role classification is logically prior to variation, fine-tuning, anthropic conditioning, multiverse comparison, or explanation. Before a constant-like quantity can be meaningfully varied or explained, its admissibility role, comparison structure, continuation locus, and target domain must first be fixed. This paper is downstream of: Minimal Conditions for Admissible Construction The Structure of Admissibility