Information as Geometric Trajectories in Cube State Spaces
Ren Matsuoka · Zenodo (CERN European Organization for Nuclear Research) · 2026
This work proposes a unified framework in which digital information is represented as discrete geometric trajectories over finite configuration spaces generated by cube rotation groups. In this model, binary data is mapped into sequences of group operations and interpreted as paths on a structured geometric system based on a 2×2×2 cube state space. The framework extends this geometric representation into a cryptographic setting by introducing state-dependent transformations and history-sensitive key generation mechanisms. Unlike conventional encryption schemes that rely on algebraic operations over fields, this approach encodes information in the structure of motion within a non-commutative geometric system. The resulting system treats information as dynamic trajectories rather than static symbols, allowing encryption to be interpreted as a deformation of paths in a finite geometric space. While the model exhibits strong structural complexity and nonlinear behavior, it remains constrained by the finite nature of the underlying state space and is therefore not intended as a formally secure cryptographic primitive, but rather as a geometric information transformation framework with cryptographic resistance properties.