Absolute Kinematics and the Geometry of the Cosmos

Core Thesis This work proposes that the physical content of spacetime is governed by a single fundamental scale: a universal, ineliminable proper acceleration modulus α₀ > 0, shared by all observers; Analytically, α₀ ≈ 1.7036 × 10⁻¹⁰\ m/s². This is not a denial of general relativity, but rather a natural completion of the equivalence principle on the global scale. This paper asserts that "motion" is not an attribute of a physical object, but its very essence. The worldline ensemble, taken as the fundamental physical substratum, and motion itself are two inseparable facets of the same mathematical-physical object. On this basis, time and space are emergent, not a priori. The kinematics of a worldline is reduced to a three-term equation of motion: d² x^μ/dτ² = α₀ r^μ + i∇^μφ + W^μ, where the first term encodes the absolute inertial frame, the second represents gravitational perturbations, and the third emerges from topological-matter couplings. The α₀-postulate forces spacetime to be de Sitter with Λ = 3α₀²/c⁴ and transverse slices H³; the real acceleration background α₀ r^μ and imaginary perturbation i∇^μφ together yield a Kähler cone geometry. The path integral over closed worldline knots is rendered finite by the horizon cutoff, and the cohomological long exact sequence yields a rigid holographic correspondence. General relativity is recovered as the high-acceleration (a α₀) limit; in the low-acceleration regime (a α₀), the theory yields the MOND critical acceleration a₀ ≈ 1.2× 10⁻¹⁰\,m/s², with H₀ ≈ 70.14\,km·s⁻¹Mpc⁻¹. Fermion masses are expressed through analytic formulas anchored by the topological mass reference Mₜₒₚₒ ≈ 4.137\,MeV. The W, Z and Higgs boson masses are derived as macroscopic spectral-geometric projections, yielding MW ≈ 80.39\,GeV, MZ ≈ 91.24\,GeV, and MH ≈ 125.22\,GeV. The fine-structure constant is locked to a purely topological expression: α⁻¹ = 4π³ + π² + π ≈ 137.036. Core Conclusions Inertia is geometry. The α₀ modulus is the geometric ground state of spacetime itself: it generates time as an irreversible fiber flow and space as a negatively curved transverse slice. Gravity and inertia are conjugate. The global product Gα₀² = const locks the entropic thrust (α₀) with the stress restorative force $(G)$. The observed dark energy effect is merely the geometric projection artifact of the holographic entropy budget when projected from the discrete bare geometry onto the continuous observational layer. Holography is cohomology. The bulk-boundary relation is rigidly governed by the long exact sequence in relative cohomology, yielding the discreteness of boundary Chern-Simons levels and the conservation of total entropy. Matter is topology. Fermions are prime knots in H³; their mass, charge, and chirality are determined by knot invariants, braiding-induced couplings, and Berry phases. The three generations are forced by the dimension of the $SO(3)$ frame projection. The Standard Model is geometrically inevitable. Its gauge group SU(3)c × SU(2)L × U(1)Y, chiral coupling, and boson mass spectrum are the projected outputs of the α₀ geometry under horizon regularization and discrete algebraic closure. Wave-particle duality is an observational representation. It is the distinction between time-averaged slice-intersection statistics (waves) and single-event phase-locked projection (particles), unified by the topological structure of the holographic boundary. Experimental Falsifiability A 10 m drop-height dual-isotope Bose–Einstein condensate Mach-Zehnder atom interferometer can detect the α₀-induced sidereal-time signal. If no characteristic amplitude-modulated signal with amplitude ≥ 2.74\,mrad (corresponding to α₀ ≥ 1.7× 10⁻¹⁰\,m/s²) is detected, the entire framework is strictly falsified.