Extended Hinge–Entropy Framework: Testable ZIT Roadmap for Emergent Multi-Scale Forces

This dataset presents an extended hinge–entropy framework for modeling small-scale microstructures as interacting hinges governed by elastic constraints and configurational (geometric) entropy. The framework is mathematically explicit and numerically testable, providing a minimal system for exploring how microstructure and entropy can produce emergent forces at larger scales.Key Features:Variationally consistent force laws for hinge networksStable, finite equilibria for minimal hinge systemsEmergent 1/r forces arising from coarse-graining hinge clustersExtensions toward electromagnetic, quantum, and short-range interactionsA roadmap for multi-scale, ZIT-inspired modeling, linking microstructure to emergent macro behaviorApplications: This framework provides a rigorous starting point for:Testing scale-dependent dynamics in structured systemsInvestigating emergent forces from minimal microstructural rulesExploring concepts aligned with Zero Inversion Theory (ZIT) in a testable, mathematical contextAccess and Testability: All equations are fully defined and suitable for numerical simulation or analytical investigation of small hinge networks. Associated materials and prior versions are available via Figshare.DOI: https://doi.org/10.6084/m9.figshare.30996139