This paper takes the limit structure of the natural logarithm as a mathematical prototype, elevates it to a Generalized Natural Scheme, and employs this as the sole foundation to unify the following theoretical systems: Functional Geometry, Arithmetic Rigid Kähler Geometry (ARKG), Curved Algebra, Relative Symmetry Groupoid, Gödel Oscillation, W-M Self-Similar String-Net Theory, and the Arithmetic Origin of Quantum Numbers. Core Breakthrough 1: The "Generalized Natural Limit" thoroughly resolves the self-referential paradox, transforming the self-referential fixed point U ≅ UU from a logical antinomy into a generative mechanism for physical fields. Core Breakthrough 2: Quantum numbers are not intrinsic particle properties but the objective counting N of physical exchange processes. One exchange equals one computation; since computation count must be integer, quantum numbers are necessarily integers. Quantization is not intrinsic discreteness of the world, but the inevitable projection of indivisible exchange counts under fixed scale. Core Breakthrough 3: The 126-dimensional Kervaire manifold rigidly splits as 126 = 6 + 120, where 6 dimensions correspond to visible fundamental dimensions and 120 dimensions correspond to the cyclic permutation space of these 6 dimensions --- the true ontology of dark matter. The entire paper contains only one mathematical structure: the Generalized Natural Scheme; only one ontology: the Natural Field; and only one total field equation: the Natural Field Equation. All physical objects---particles, interactions, the dark universe, the three-generation structure, quantum measurement, spacetime, and constants---possess no free parameters and are uniquely rigidified by the arithmetic of the Heegner point τ₁63.
Yaao Wang (Sat,) studied this question.