The Quantahedron as a Pre-Gravitational Unified Geometry: A Null-Centered Framework for Mass–Energy–Time without Fundamental Gravity

The Quantahedron as a Pre-Gravitational Unified Geometry proposes a geometric framework in which mass, energy, and temporal delay emerge from angular deviation within a normalized quanta lattice rather than from gravitational curvature as a fundamental interaction. The Quantahedron is defined as a convex L¹ simplex centered on a null symmetry state, providing a minimal geometric substrate for propagation, interaction, and conservation without requiring gravity as a primitive force.

Within this framework, observable physical quantities arise as functions of propagation geometry. Angular deviation encodes mass emergence, directional propagation components encode energy, and asymmetric propagation produces temporal delay. A mapping to relativistic invariants demonstrates compatibility with Lorentz kinematics, while a geometric action formulation frames particle trajectories as constrained optimization paths within the simplex manifold. Physical dimensionality is introduced through a characteristic lattice scale, enabling connections to Compton and Planck regimes and yielding explicit scaling relations linking geometric deviation to measurable quantities.

The Quantahedron therefore functions as a pre-gravitational geometric substrate in which gravitational phenomena are interpreted as emergent macroscopic effects of angular deviation gradients and collective symmetry deformation. This perspective aligns with emergent gravity approaches while offering a unified geometric interpretation of mass–energy–time relationships grounded in convex topology, normalization constraints, and information-geometric structure.

The manuscript outlines formal definitions, relativistic correspondences, a geometric Lagrangian formulation, dimensional scaling relations, and potential experimental implications, including discrete mass quantization, modified scattering geometry, and null-propagation stability. The framework is intended as a conceptual and mathematical foundation for further development of geometry-first unification approaches and connections to positive geometry, discrete spacetime models, and emergent interaction theories.