S.P.A.R.K.: Spatial Propagation And Relativistic Kinematics

Standard 4D relativistic kinematics relies on continuous Minkowski spacetime to dictate mass dilation and time contraction, utilizing algebraic postulates that inevitably collapse at macroscopic singularities. Building upon the 6D (3s+3t) discrete topological framework established in earlier letters, this manuscript demonstrates that continuous relativity is a macroscopic illusion generated by discrete trigonometric frame rotations of the 6D Vielbein. I analytically derive the Lorentz factor () strictly as the secant of the orthogonal frame rotation (=), extracting macroscopic spatial momentum as its pure geometric tangent and temporal momentum as its cotangent, thereby proving the Weak Equivalence Principle (mᵢ = mg) is a strict trigonometric identity (). By defining the 6D thermodynamic potential of these conjugates, I geometrically derive Color Confinement as the absolute minimum of the spatial lattice at 45^, natively proving why the observable macroscopic universe geometrically projects exactly three spatial dimensions (3). Expanding this rotational limit to the 90^ event horizon natively resolves the singularity paradoxes for both static and spinning black holes, mathematically defining deterministic Hawking Radiation and rotational superradiance. Applying the space-evolved Korteweg-de Vries (KdV) fluid equation to the discrete lattice, I mathematically derive the active kinematic dressing of the W boson (+106. 86 MeV) without arbitrary parameters. Furthermore, the second derivative of this KdV progression exposes a cosmic rectifier, proving that Dark Energy is the unidirectional thermodynamic feedback of Dark Matter shedding geometric friction, projecting an explicitly falsifiable Cosmological Constant resonance at 11. 3 keV. Finally, by introducing the 91-state Hamilton Mass Sieve O. R. A. C. L. E. , the framework exposes profound, scale-invariant bridges unifying the entirety of the Standard Model. I mathematically demonstrate that the Top Quark is the relativistically dilated bare Higgs Boson (mₜ = ₐₔ₀ₑ₊ mH), the Tau lepton is the exact geometric remainder of Electroweak symmetry breaking, and the stable Baryon and Lepton are strict inverse geometric foldings of the exact same Weak vacuum fracture. Ultimately, this framework derives the absolute equation of Quantum Gravity (mₚ = 512 ₀⁹ MP), proving that the stable proton is a classical Planck Mass topologically unspooled across the 12 edges of the 3D spatial grid.