Information as Geometric Trajectories in Cube State Spaces

This paper proposes a novel cryptographic construction called Cube-Gematria Fractal Cryptography, which integrates permutation group dynamics, numerical encoding, and fractal-inspirednonlinear transformations.The core idea is to map symbolic input strings into a structured state evolution on a Rubik’sCube configuration space, where each elementary operation is represented as a permutationacting on a 54-element state vector. This discrete dynamical system is further combined with agematria-like encoding scheme that transforms operation sequences into numerical representations.To enhance nonlinearity and diffusion, the model introduces modular arithmetic-based compression functions and a fractal-inspired scaling layer motivated by the self-similarity propertiesof the Koch curve. Additionally, an optional wave-modulated parameter extension is proposedto introduce controlled dynamical variability into cryptographic parameters.The resulting system forms a hybrid construction combining elements from group theory,discrete dynamical systems, nonlinear arithmetic, and fractal geometry. While the functionexhibits strong structural diffusion and high sensitivity to input perturbations, it is not claimedto satisfy formal cryptographic security proofs under standard adversarial models.This work is intended as a theoretical framework exploring the interaction between combinatorial group actions and nonlinear cryptographic transformations, rather than a finalizedindustrial cryptographic primitive.