Part 11_A Structural Definition of Effective Interaction Range from Phase-Open Dynamics and JS–SH Discrete Geometry

https://youtu.be/wzIexVZxl7Y?si=gUVjvirWoIMiTLX7 https://youtu.be/km6lksFPEO8?si=ESxv22pn414hea5f In standard continuum physics, fundamental interactions such as gravity, electromagnetism, and nuclear forces are formally infinite in range. While mathematically consistent, this description obscures a physically meaningful question: at what distance does space stop responding to a finite source? This paper introduces a structural definition of effective interaction range, formulated within the framework of Phase-Open Dynamics, JS–SH discrete geometry, and Self-Regulated Curvature Dynamics (SRCD). Rather than modifying established force laws or introducing new mediators, interaction range is reinterpreted as a consequence of structural phase accumulation and saturation in a discrete substrate. The central result is a universal phase-saturation criterion Δϕ(reff)=Δϕmin⁡,Δ φ(reff) = Δ φₘᵢₙ,Δϕ(reff)=Δϕmin, which defines the effective influence radius reffreffreff across all four fundamental interactions. Despite spanning more than thirty orders of magnitude in energy and distance scales, nuclear, weak, electromagnetic, and gravitational interactions all converge to the same saturation threshold under a single SRCD-covariant calibration. Key contributions of this work include: A structural reinterpretation of interaction range as finite structural relevance, not force extinction A universal shell structure with an invariant non-integer shell count Nshell≃3.2Nₛₕₑₗₗ 3.2Nshell≃3.2, independent of interaction type Identification of Hill radii, nuclear force ranges, atomic scales, and weak interaction lengths as manifestations of the same phase-saturation mechanism Demonstration that gravity is mathematically infinite-range but structurally finite-range due to environmental phase competition A falsifiable, non-tuned universality test collapsing all four interactions under a single threshold No coupling constants are altered, no new fields are introduced, and standard quantum field theory and general relativity remain intact within their domains of validity. The framework operates at a structural level beneath force laws, explaining why effective interaction domains emerge without invoking arbitrary cutoffs. This work provides a unifying geometric and topological explanation for interaction range, force saturation, and cross-scale consistency, and serves as a structural bridge between microscopic forces and astrophysical domains. The paper also predicts intermediate transition regimes where partial phase saturation may lead to observable deviations from single-scale behavior, offering concrete avenues for future experimental and numerical tests.