The Black and White Rabbits Model: A Dynamic Symmetry Framework for the Resolution of Goldbach’s Conjecture

This paper introduces the Black and White Rabbits Model as a dynamic interpretation of Goldbach’s Conjecture, extending previous frameworks based on density–localization duality. The model represents even numbers as a field of dual motion: a white rabbit starting from 0 and a black rabbit starting from E, both advancing through the integer continuum toward the midpoint E/2. Their synchronized motion symbolizes the counter-propagation of primes on the number line, where one sequence decreases and the other increases until they meet at a common equilibrium (p, q) such that p + q = E. The meeting point corresponds to the equal-likelihood zone derived in earlier studies on the Unified Prime Equation [Bahbouhi Bouchaiba-b, preprints.org, 2025]. This work formalizes the metaphor into a deterministic and reproducible mathematical system, showing that the apparent randomness of primes hides a hidden symmetry of approach. By combining motion equations with local probability fields, the Black and White Rabbits Model offers a new geometric and intuitive framework capable of explaining why Goldbach’s conjecture holds true across all tested scales. The resulting model unifies visualization, computation, and analytical reasoning into a single conceptual structure bridging classical number theory and dynamic equilibrium. By modeling prime interactions as dual trajectories converging within a finite variance wall, the Black and White Rabbits Model advances Goldbach’s Conjecture to a near-complete analytical resolution, revealing it as a direct consequence of density–localization symmetry.