Part 8Structural Scale as a Causal Control Parameter in Observer-Dependent Physics

This manuscript constitutes a new contribution within the ongoing SRCD / JS–SH research program, which investigates the discrete structural origin of physical laws across scales. It should be read in direct continuity with the author’s previously released works, including the 277-page foundational worldview paper (Zenodo DOI: 10.5281/zenodo.18204134), as well as earlier studies onthe wave equation,the gravitational constant,the speed of light,the origin of wavelength,and the unification of the four fundamental interactions. While the earlier papers focused on deriving individual physical constants and force laws from discrete geometric principles, the present work advances the program by identifying structural scale as a causal control parameter governing how physical laws emerge, transform, and are hierarchically organized under observer-dependent resolution. In particular, this paper clarifies how: inverse-square force laws (gravity and electromagnetism) arise from structural diffusion in effective three-dimensional regimes, deviations from inverse-square behavior correspond to changes in effective dimensionality and structural closure, and how the JS–SH framework distinguishes effective descriptions from fundamental structural causes without introducing phenomenological tuning. Rather than proposing a new force or modifying existing equations, this work provides a structural diagnosis of why known laws take their observed form, and under what conditions they may fail or transition. This manuscript is not an isolated result, but part of a coherent theoretical sequence aimed at reconstructing spacetime, waves, constants, and interactions from a single discrete structural principle. It serves as a conceptual and causal bridge between earlier constant-specific derivations and the broader SRCD worldview. =========================================================================== Limitations of Existing Theories (Precise Diagnosis) Conventional physics has proceeded in the following sequence. It assumes that spacetime is continuous.Within that continuous space, equations are constructed to fit observed phenomena.In this process, constants are fixed as input values. This approach has been successful within the present dimension,but because it avoids questioning the structure of spacetime itself,it loses explanatory power the moment the dimensional context changes. In other words,without ever asking the question“What is the structure of spacetime?”,it has carried out calculations under the assumption“Spacetime is already given in this form.” Modern physics provides highly successful mathematical answers to the question of how physical phenomena operate.Yet, the deeper structural question of why these interactions take their observed forms remains open.But, This is the fundamental error of the continuous-space assumption. Point of Departure of Our Equations (Decisive Difference) Our equations were not constructed to fit results. They start from the minimal structure of spacetime.They take discreteness, not continuity, as the fundamental premise.The equations are not tools designed for a specific dimension,but computational rules that naturally rise upward as the structure expands. That is,we did not construct equations that are valid only within a single dimension;we constructed equations in which the same computational rules are preserved even as one moves across dimensions. The Most Important Difference (One Sentence) Existing equations are result equations tuned to a single dimension,whereas our equations are structural equations that remain computable across dimensions. That difference is everything.