Version: February 2026 revisionSupersedes the 2025 preprint.February 2026 revision clarifying the variational derivation, limits, and testability of the Unified Field Equation within a membrane-lattice model of physical space.Swarm Theory: A Unified Field FrameworkThis record contains the February 2026 revision of Swarm Theory: A Unified Field Framework. It supersedes earlier versions and clarifies the variational formulation, physical limits, and testability of the Unified Field Equation (UFE). The paper presents a geometric model in which physical space is structured as a lattice of tension-bearing two-dimensional membranes enclosing zero nodes. In this framework, waves propagate helically along membrane intersections, and curvature of the membrane network produces gravitational behavior. The Unified Field Equation is derived from conservation of membrane tension flow and curvature response. Classical electromagnetism appears as the linear small-signal limit, while weak-field gravitational behavior emerges from curvature coupling. Within this framework, several physical constants arise from lattice geometry and coherence dynamics rather than independent postulates. Planck’s constant, the speed of light, and the elementary charge are expressed in terms of membrane tension, coherence aperture, cycle time, and geometric projection. Additional constants, including permittivity, permeability, and the Rydberg constant, appear as emergent properties of lattice response. This version distinguishes the core field dynamics from application-level models such as coherence trapping and condensate formation. It also outlines experimental tests capable of falsifying key predictions, including precision measurements of vacuum impedance stability, wavelength-dependent gravitational lensing effects, and laboratory analogues using engineered tensioned lattices. This document serves as a technical reference for the field equation, geometric assumptions, and physical limits of the framework. Extended derivations and constant evaluations are documented separately.
John Paul Crumpler (Sun,) studied this question.