The Solid Rock of Everything: Universal Thermodynamic and Inertial Isomorphism Across Scales, the Fallacy of the Point-Mass Singularity, and the Hydrodynamic Bridge Between the Macro-Cosmos and the Subatomic Continuum

For over a century, modern theoretical physics has pursued an elusive "Theory of Everything" while remaining trapped in a foundational mathematical contradiction: the assumption that the ultimate constituents of nature are zero-dimensional geometric points (r = 0) moving through an empty receptacle. When pushed to short distances, this point-mass hypothesis inevitably produces mathematical infinities, forcing cosmology to invoke fictitious dark matter and softening lengths, and compelling quantum electrodynamics (QED) to rely on the ad-hoc accounting of renormalization. Written as a completely self-contained treatise for any reader approaching the 4D Continuum framework for the first time, this 41st paper establishes not a speculative "Theory of Everything," but The Solid Rock of Everything: the demonstration that fundamental physical laws—specifically the Laws of Thermodynamics, the Universal Principle of Inertia, Covariant Conservation, and Structural Isomorphism—hold unyieldingly across all 42 orders of magnitude of the physical universe, from the femtometer to the megaparsec. We demonstrate five core results in plain physical and mathematical terms: (1) The Impossibility of the Vacuum: both the measured electromagnetic wave impedance of free space (Z_0 = 376.73 Ohm) and the macroscopic integration of the intergalactic medium over 6.5 Gly prove that space is a real, continuous substrate; (2) Historical Metarcheology of the Point-Mass Dogma: how a convenient 17th-century calculation shortcut hardened into an uncritical 20th-century dogma; (3) Refutation of the Static "Zero-Brick" via Vortex Duality: a stable physical structure is neither a solid pebble nor an empty hole, but the dynamic symbiosis between a rotating kinetic crown and the central low-pressure baric cavity it excavates; (4) Structural Isomorphism (A-B-C <-> F-G-H): while physical ingredients change across scales, the relational architecture linking core excitation, medium polarization, and phase wake remains invariant; and (5) The Exact Madelung-Helmholtz Bridge: the time-dependent Schrödinger equation transforms algebraically without approximation into the continuity and Euler/Navier-Stokes momentum equations, resolving wave-particle duality as a compact core navigating its own interference wake along channels of minimum thermodynamic dissipation.