A Simplified Physical Foundation: The Lorentz-Invariant Universe Resulting from Two Constraints

We present a simplified physical foundation based on only two constraints: a finite propagation speed $C$ and an energy density saturation threshold $P_{0}$. Together these constraints define a Lorentz-invariant wavespace substrate in which nonlinear compression is dynamically redistributed through saturated eigenmode geometry. Under sustained energy influx, this redistribution enforces global standing-wave organization across both nonlinear and linear regimes. The simultaneous enforcement of these constraints establishes a global resonant scale $R_{0}$ and a microscopic saturation scale $r_{0}$, imposing a discrete spectrum of stable eigenmodes.

Two fundamental geometric families emerge within this constrained substrate: a saturated spherical reservoir and a cylindrical or toroidal transport channel. Their interaction yields two independent coupling invariants, identified with the fine-structure constant $\alpha$ and the Rydberg constant $R_{\infty}$. In this framework, mass, charge, and coupling strengths arise as emergent features of boundary geometry and mode structure rather than as fundamental inputs. Infinitesimal boundary leakage at the global scale couples back to local modes, producing a persistent attractive effect identifiable with gravitation in the weak-field limit.

Established physical theories are recovered as effective descriptions of these constrained geometric dynamics within their respective domains of validity. The framework is not constructed by fitting numerical values to known constants, but as a closed physical system whose eigenmode structure yields dimensionless couplings and scale relations as natural outcomes of the underlying constraints. As such, it offers a physically grounded starting point with the potential to clarify longstanding conceptual gaps and unexplained relationships in fundamental physics.