Meta‑Discoveries of Discrete Sampling Geometry and Their Implications

Abstract: Based on the previously established “He‑Luo Geometry — Discrete Sampling Geometry” system, this paper extracts several meta‑discoveries from the foundational level. Starting from one Meta‑Axiom (the unit sphere together with a rotation ) and one First Principle (Symmetry First, Structural Minimality, Parameter Uniqueness), the system necessarily yields the number , the dihedral group , the orbit stratification , the curvature spectrum , the continuous emergence via the refinement limit, and the most striking spectral splitting — exactly the dimensional decomposition of the Standard Model gauge group. This paper reveals that discreteness is essential and continuity is a limiting appearance; the Symmetry-First principle has a powerful filtering capability; the Standard Model gauge group may originate from discrete geometry; the principle of least action arises from discrete minimality; Form‑Qi Conservation is a geometric prototype of the unity of opposites; and mathematics and physics are unified at the level of necessity. As a concluding meta‑discovery, it is shown that Being itself together with the fundamental action is uniquely locked by the three rules, and they are inseparable. Ultimately, the nature of the universe is a Turing machine running on a discrete geometric grid with a minimal action. Keywords: Discrete Sampling Geometry; He‑Luo Geometry; Symmetry First; Gauge group; ; Meta‑discovery; Unique locking of Being and action; Universe as Turing machine