Temporal Geometry of Entropy Evolution

This preprint introduces a temporal geometry framework that models how entropy, symbolic manifolds, and state transitions interact across time. The work treats temporal flow as a structured, measurable system rather than a passive background, using large‑scale hexagram datasets to analyze how states evolve, tunnel, or drift under changing entropy conditions. The manuscript develops a symbolic manifold architecture that allows temporal states to be represented, compared, and transformed with machine‑like precision, giving a way to study nonlinear temporal dynamics without relying on traditional probabilistic or Markov assumptions. The core idea is that time has an internal geometry shaped by entropy gradients, and that this geometry can be mapped, measured, and modeled. The paper presents the underlying theory, the computational method, and the dataset used to test the system, including more than one million generated hexagrams. The goal is to provide a foundation for a new interdisciplinary field that connects complexity science, nonlinear dynamics, symbolic systems, and entropy‑driven modeling. This work is intended for researchers interested in emergent structure, temporal modeling, entropy behavior, and cross‑domain theoretical frameworks. If you want to explore the system further, the preprint includes examples, diagrams, and dataset references that show how temporal geometry behaves under different entropy conditions and how symbolic manifolds can be used to track transitions across time.