Dimensional Closure Modes of the Four Fundamental Interactions

The four fundamental interactions are usually classified by source, mediator, range, symmetry group, and relative strength. This paper develops a complementary classification based on dimensional closure in the Quantized Dimensional Ledger (QDL), where physical quantities are represented on a 3L+2F integer-dimensional basis. Gravity, electromagnetism, the strong interaction, and the weak interaction are interpreted respectively as geometric-scale closure, propagation/readout closure, compact-binding closure, and transition/update closure. The central observation is that the Compton wavelength λC = h/(mc) and Compton frequency fC = mc²/h define a microphysical mass-frequency package satisfying λC fC = c and λC³ fC² = hc/m, with dimensional form L³F². This is the same Quantized Dimensional Cell (QDC) form that appears macroscopically in gravitational and Keplerian closure through GM and r³ω². The paper therefore argues that Compton localization supplies a microscopic realization of the QDC, while gravitational dynamics supplies a macroscopic realization. The paper does not claim to replace the accepted dynamical theories of gravity, electromagnetism, the strong interaction, or the weak interaction. Instead, it proposes an admissibility-level classification in which the four interactions are structurally related by closure compatibility rather than by sameness of dynamics. Gravity couples mass-frequency closure to geometric scale; electromagnetism propagates phase and supplies measurement readout; the strong interaction stabilizes compact localization regimes; and the weak interaction updates one admissible mass-frequency state into another. A modular SMEFT admissibility criterion is also proposed. Given a declared QDL projection and modular grade, an admissibility-preserving renormalization map should preserve operator grade. This yields a falsifiable selection rule: nonzero anomalous-dimension mixing is admissible only when the initial and final operators share the same declared QDL grade. Prospective falsification channels are identified through SMEFT operator mixing, gravitational clock-redshift residuals, beta-decay residual decomposition, nuclear-clock sensitivities, neutrino observables, and Compton-QDC scaling.