Part 4Geometric Origin of Wavelength Modulation in Discrete Spacetime

https: //youtu. be/fZRbPjDbkBw? si=sduNYxZYUxMHMog https: //youtu. be/2Dn9S-y2IWE? si=trgQMZRtI3OnFakB This paper investigates the physical origin of wavelength from a structural perspective, within the JS–SH (Junctional Structure–Shell) framework developed across the accompanying SRCD series. Rather than treating wavelength as a purely kinematic or Fourier-derived quantity, we propose that it emerges from a discrete step structure underlying spatial propagation. In this view, a wavelength corresponds to a finite accumulation of structural steps along a propagation path, controlled by a path-dependent inflation factor rather than by local energy or frequency alone. The analysis demonstrates that: Wavelength can be interpreted as a structural response to path complexity, not merely as a reciprocal of momentum or wave number. Identical frequencies propagating along geometrically distinct paths may exhibit different effective wavelengths, providing a clean observational discriminant absent in standard formulations. The framework naturally distinguishes between speed-scale parameters (e. g. propagation limits) and path-complexity responses, avoiding parameter conflation common in phenomenological extensions. Observable consequences arise in multi-path systems, gravitational lensing, and near-horizon propagation, where structural deviations accumulate measurably. This work complements earlier papers on the wave equation, gravitational coupling, and the speed of light, forming a coherent sequence aimed at identifying the structural origin of fundamental wave phenomena without introducing new tunable constants. The paper is intended as a testable theoretical proposal. All definitions are explicit, parameter roles are clearly separated, and reference implementations are provided to facilitate independent verification.