Volumetric Syntax for Formal Mathematics -- Audigé Youmbi, Salomon Emmanuel (2026).

This work studies mathematical writing itself as a geometric inscription rather than as a linear symbolic discourse. The basic object is a derivation-graph encoding logical and algebraic dependencies. It is shown that certain derivation-graphs cannot be rendered faithfully on any planar support due to unavoidable semantic collisions, independently of the chosen layout. A constructive result proves that every finite derivation-graph admits a collision-free realization in a three-dimensional writing domain. The framework is not restricted to R^3: writing domains may be higher-dimensional, complex, quaternionic, p-adic, adelic, or metric-measure spaces of non-integer Hausdorff dimension. Classical two-dimensional textual mathematics is preserved as a valid but non-universal writing regime.