Block Geometry: A New Mathematical Language Designed Exclusively for the Block Universe

This paper introduces Block Geometry, a new axiomatic framework and mathematical language constructed to provide a consistent mathematical description for the block universe ontology arising from general relativity. The framework is founded on three basic axioms: the Axiom of Global Existence, the Axiom of Symmetry Rigidity, and the Axiom of Global Constraint. Under these axioms, infinite mathematical objects are treated as globally pre‑existent static structures rather than stepwise constructive entities. Classical mathematics and logic remain valid as a special case within a restricted, classically constructible context. As a structural consequence of the global duality symmetry of the Riemann zeta function, the framework implies that all non‑trivial zeros of the zeta function are constrained to the critical line Re(s) = 1/2. The framework also offers a unified perspective on number theory, spacetime geometry, holographic duality, and self‑referential propositions, while leading to physically testable predictions compatible with cosmological and particle physics observations.