The Geometric Mechanics of 3D Space: The origin of physical motion and its mechanical proof / 3D-rymdens geometriska mekanik.

0 free parameters, 22 CODATA/PDG matches THE PROBLEM Everything humanity has ever observed exists in three dimensions (3D), yet our entire mathematical foundation rests upon a one-dimensional (1D) number line. This paper explores the hypothesis that the remaining discrepancies in modern physics arise precisely at the intersection of these two, a result of attempting to describe the mechanical foundations of physics using an abstract, compressed 1D version of those very foundations. Even when constructing 3D mathematical tools, they remain fundamentally based on the values of the 1D number line.Three 1D values are not the same thing as a single 3D value. Our current 3D tools are merely a collection of three independent 1D lines (X, Y, Z), which fails to capture the intrinsic mechanical unity of 3D space. A true 3D value is background-independent because it defines space from the inside out, rather than being placed into an external grid. To bridge this gap, this model reverses the perspective: the inherent geometry of space is first used to define a strictly three-dimensional mathematics, which in turn is used to mechanically derive the laws of physics. Furthermore, this physical 3D number line is applied to demystify pure mathematics; it explains the physical origin of the fundamental objects of the 1D number line and offers a geometric explanation as to why traditional logic breaks down at enormous numerical values. THE METHOD To solve this, a purely mechanical 3D model of the foundations of physics is presented. The model employs zero free parameters and originates from a single geometric axiom in an empty space: a Primordial Spiral blindly striving to close itself in perfect equilibrium. When two such spirals collide, they are forced to rotate forward together, but the 3D geometry of space then demands the distance π to complete one revolution. The gap between π the inner tension of the spirals (the striving to close the circle at the value of 3) and the geometric demands of space (π) creates a permanent "geometric debt". This debt is defined in the model as the actual origin of gravity (the internal, linear pull) and electromagnetism (the volumetric crowding that forces the curvature π). THE RESULTS By exclusively tracking the mechanical consequence of this crowding as the spatial geometry is allowed to grow, the model derives the following, among others, entirely without preset constants:•The mechanical cause of spatial curvature (π) and why the arrow of time exclusively moves forward. • The fine-structure constant (≈ 137) as the exact geometric breaking point, where the crowding forces the carrier wave to collapse into a closed 3D structure (horn torus/matter). • An exact mathematical solution to the hierarchy problem, which is proven to be the ratio between the 1D thread's debt and the enclosed 3D volume pressure of matter. • The mass ratios between the electron and the proton/neutron. • A mechanical solution to what even and odd numbers physically represent, as well as how the phenomenon of prime numbers emerges from geometry. THE CONCLUSION The model proves that the fundamental forces and particles of the universe are not independent mysteries or arbitrary mathematical abstractions, but rather the necessary and inevitable consequences of the geometric causality of 3D space. Furthermore, it establishes that the traditional 1D number line is merely a compressed and simplified shadow of the underlying 3D number line.