This preprint introduces a discrete-continuous duality framework where singularities in black holes and the Big Bang are resolved by replacing infinite curvatures with finite combinatorial structures. The Core Idea: , Geometric objects (circles, spheres) are approximated by discrete structures (squares, cubes) through a discretization functor T: 𝐌𝐚𝐧 → 𝐒𝐢𝐦𝐂𝐨𝐦, where this transformation preserves topological and metric properties with convergence dH (K_ε, M) = O (ε²). Mathematical Foundation: The framework is rigorously grounded in category theory (smooth manifolds vs. simplicial complexes) and discrete differential geometry (Desbrun et al. , 2005). Three Key Validations: 1. Geometric packings ->Discrete grids achieve ±1. 3% accuracy vs. continuous optimality2. Cosmic topology -> Poincaré dodecahedral space naturally explains CMB anomalies (ℓ=2, 3 suppression) 3. Discrete equations -> Regge calculus and Schrödinger equations emerge from simplicial networks Implications: Singularities resolve as finite configurations. The framework unifies fundamental forces, explains dark matter/energy, resolves wave-particle duality, and provides testable predictions (gravitational wave echoes, CMB anisotropies, discrete Hawking radiation). This work invites collaboration from researchers in quantum gravity, discrete geometry, cosmology, and mathematical physics.
Florian Gisbert (Sat,) studied this question.