A Constructive Calculation of Particle Mass from Substrate Inertia: Closing the SI Kilogram via a Frequency-Based Six-Field Framework

Mass is treated as an empirical parameter in contemporary fundamental physics. In the Standard Model, particle masses are introduced through fitted couplings and symmetry breaking, leaving unanswered whether mass can be calculated rather than measured, and whether its absolute value in SI units can be derived from first principles.

In this work, we present a fully constructive, bottom-up calculation of particle mass within the Six-Field framework. Starting from a single continuous substrate, persistent excitations are defined through admissibility and redundancy-invariant eigenmodes. Inertia emerges as a second-order response property of these modes, and mass is introduced as a projection of inertia into effective physics. A minimal quadratic eigenvalue spectrum fixes all dimensionless mass ratios without free parameters.

The absolute scale is not imposed but selected by an admissibility condition arising from finite propagation and resolvability, reinterpreting gravity as a constraint on spectral density rather than a fundamental force. This selection fixes a unique fundamental frequency. A dimensionless bridge to SI units is then defined via the cesium-133 hyperfine transition, and evaluated at leading order without empirical mass input.

The resulting construction closes the full chain from substrate dynamics to the SI kilogram. A boxed numerical illustration demonstrates that the derived electron mass appears at the correct SI and particle-physics order of magnitude, with remaining discrepancies attributable to identifiable higher-order corrections rather than calibration.

The framework is explicitly falsifiable: the existence of a stable fundamental particle whose inertial properties cannot be mapped to an isolated admissible eigenmode would invalidate the construction. The result is not a precision fit, but a proof of calculability—showing that mass, both relative and absolute, can arise as a derived quantity rather than an empirical primitive.