Mathematics as the Self-Descriptive Grammar of Being: A Relational Ontology from the Hetu

This paper reframes the foundations of mathematics, arguing that its true ground is not a domain of abstract objects but the relational logic of representability itself—to be is to relate. Formalized through a minimal symbol system (●, ○, ⊙, →, ↔, ∟, ⊥) inspired by the archaic Chinese H-e-t-u（河图）, the theory shows that any determinate phenomenon (⊙X) must be dually constrained by a one‑dimensional (→) and a two‑dimensional (∟) relative‑to relation. Applying this dual constraint recursively generates exactly five primordial phenomena in a closed, self‑determining loop. As a direct consequence, each phenomenon acquires two irreducible logical names—the decimal digits 0–9 emerge necessarily as the expression of this dual‑naming structure. Furthermore, by formalizing the indescribable relational background (○), the system derives the imaginary unit i and the relation i² = −1, unifying the ontological basis of natural and complex numbers. In the end, mathematics is revealed as the intrinsic syntax through which existence articulates itself in pure relation. （These articles are just records of places I’ve passed by. Don’t take them too seriously, my friend — they may be full of mistakes. Trust yourself. If you want to find my recent location, please check the pinned post or updates on my homepage.）