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 $\alpha_0 > 0$, shared by all observers; Analytically, $\alpha_0 \approx 1.7036 \times 10^{-10}\ \text{m/s}^2$. 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: $$\frac{d^2 x^\mu}{d\tau^2} = \alpha_0 r^\mu + i\nabla^\mu\varphi + \mathcal{W}^\mu,$$ where the first term encodes the absolute inertial frame, the second represents gravitational perturbations, and the third emerges from topological-matter couplings. The $\alpha_0$-postulate forces spacetime to be de Sitter with $\Lambda = 3\alpha_0^2/c^4$ and transverse slices $\mathbb{H}^3$; the real acceleration background $\alpha_0 r^\mu$ and imaginary perturbation $i\nabla^\mu\varphi$ 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 $(a \gg \alpha_0)$ limit; in the low-acceleration regime $(a \lesssim \alpha_0)$, the theory yields the MOND critical acceleration $a_0 \approx 1.2\times 10^{-10}\,\text{m/s}^2$, with $H_0 \approx 70.14\,\text{km·s}^{-1}\text{Mpc}^{-1}$. Fermion masses are expressed through analytic formulas anchored by the topological mass reference $M_{\text{topo}} \approx 4.137\,\text{MeV}$. The W, Z and Higgs boson masses are derived as macroscopic spectral-geometric projections, yielding $M_W \approx 80.39\,\text{GeV}$, $M_Z \approx 91.24\,\text{GeV}$, and $M_H \approx 125.22\,\text{GeV}$. The fine-structure constant is locked to a purely topological expression: $$\alpha^{-1} = 4\pi^3 + \pi^2 + \pi \approx 137.036.$$ Core Conclusions Inertia is geometry. The $\alpha_0$ 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 $G\hbar\alpha_0^2 = \text{const}$ locks the entropic thrust $(\alpha_0)$ 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 $\mathbb{H}^3$; 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 $SU(3)_c \times SU(2)_L \times U(1)_Y$, chiral coupling, and boson mass spectrum are the projected outputs of the $\alpha_0$ 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 $\alpha_0$-induced sidereal-time signal. If no characteristic amplitude-modulated signal with amplitude $\geq 2.74\,\text{mrad}$ (corresponding to $\alpha_0 \geq 1.7\times 10^{-10}\,\text{m/s}^2$) is detected, the entire framework is strictly falsified.