The Quantized Dimensional Ledger for Metrology: Dimensional Closure, QMU Ledgers, and the Ontology of Physical Constants

This work introduces the Quantized Dimensional Ledger (QDL), a unified dimensional framework based on a 3L + 2F basis of length-like and frequency-like primitives. The QDL constructs a closed algebra of physical dimensions in which mass, time, and all derived quantities emerge from combinations of five operational axes: three geometric scales (L1, L2, L3) and two frequency scales (F1, F2). Within this basis, the Quantum Measurement Unit (QMU) is defined as a standardized ledger cell for energy, momentum, and action, enabling a structured representation of physical constants and observables. The framework yields a 20-entry dimensional ledger (Appendix B) spanning mechanics, electromagnetism, gravitation, thermodynamics, and quantum observables. This ledger provides a consistent classification system that clarifies which constants are dimensionless invariants and which are dimensional couplings whose exponents are fixed by the 3L + 2F structure. A key feature of QDL is dimensional closure, ensuring that the Einstein–Hilbert action, Maxwell action, and classical mechanical quantities share a common underlying exponent structure. This enables a unified interpretation of constants such as c, ℎ, G, and the fine-structure constant α as ledger invariants or as ratios of ledger entries. A quantitative demonstration is included, showing how ledger ratios reconstruct the structural dependence of Planck’s constant, the Rydberg constant, and vacuum impedance, with comparison to CODATA values. The purpose of this work is conceptual and metrological rather than dynamical: QDL does not propose new field equations, but offers an internally consistent dimensional ontology supporting the interpretation, classification, and potential reduction of physical constants.