A Classification Theorem for Physical Constants

Static and Dynamic Uniqueness Arc — Paper II

A Classification Theorem for Physical Constants
Admissibility-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:

1. Minimal Conditions for Admissible Construction

2.  The Structure of Admissibility