https://youtu.be/8B6ohIwoiTc?si=5s3DfS8CgTFAZVhL https://youtu.be/zbMdeQ3eRj0?si=PTN5bKCX1KDjbNX4 This work presents a fully analytic derivation of the wave equation from a discrete structural framework based on the JS–SH (Junctional Sphere–Structural Hub) geometry.Rather than assuming the continuum a priori, the continuum wave equation is shown to emerge as a necessary limit of discrete structural dynamics. The approach is equation-first and parameter-free: no phenomenological fitting, ad hoc assumptions, or empirical tuning are introduced. Starting from minimal discrete structural constraints, the model leads uniquely to a coupled dynamical system whose continuum limit reproduces the standard wave equation with an unavoidable quartic correction term. The analysis clarifies the structural origin of wave propagation, showing that the conventional continuum formulation can be interpreted as an effective description arising from deeper discrete dynamics. In this sense, the wave equation is not postulated but derived as a structural consequence of discrete spatial interactions. The framework provides a unified structural interpretation of wave dynamics that is compatible with standard continuum physics while extending it by identifying the discrete mechanisms underlying continuum behavior. The results are fully analytic and reproducible, and they offer explicit criteria for comparison with conventional formulations. This work is intended as a foundational contribution to discrete-to-continuum physics and structural approaches to fundamental equations, with potential implications for quantum theory and gravitational models where the emergence of continuum behavior from discrete structures plays a central role.
Seunghyun Hong (2026) studied this question.