Electromagnetism: An EET Structural Realization: From Constraint Network Dynamics to the Classical Maxwell Equations

This document is a REAL (Structural Realization Paper) within the Energy-Efficiency Theory (EET) framework. It does not introduce new EET constitutional concepts. Electromagnetism is constitutionally defined in Interaction v2. 1 as Mechanism-1 (edge-weight modulation) on an open U (1) ₄₌ constraint subnetwork with Ec=0 bosons (photons). The present document provides the classical continuum limit structural realization: the derivation of the -modulated Maxwell equations from constraint network dynamics, the graph-theoretic foundation of U (1) ₄₌ gauge symmetry as Type~II edge phase consistency, the dual-channel electromagnetic wave damping framework, and the five-channel electromagnetic thermodynamics operationalization. Five core academic contributions are established. (i) ~-Modulated Maxwell equations. The standard Maxwell equations are extended to include -dependent constitutive parameters () = ₀/ () and () = ₀/ (), derived from the coupling constant -modulation framework. At =1, the standard Maxwell equations are recovered in full. The speed of light acquires the modulation c () = c/ (), with c () c for 1, bounded above by the Lieb-Robinson velocity v_ = _ d_. (ii) ~Dual-channel electromagnetic wave damping. The constraint-network dual-channel damping framework is instantiated for electromagnetic waves. The elastic channel (1- (), reversible) vanishes at =1, producing dissipation-free EM wave propagation in vacuum --- parallel with gravitational wave propagation (Gravitation v3. 1 3. 3. 3). The plastic channel (C₄₌ (t) ₖ/₁, irreversible) captures cumulative attenuation in aged or high-C (t) media. (iii) ~U (1) ₄₌ ₆₀ₔ₆₄ ₒₘ₌₌₄ₓₑₘ ₄₌₄ₑ₆₄₍₂₄ --- ₂₎₌₏₋₄ₓ₄ ₃₄ₑ₈ₕ₀ₓ₈₎₍ ₂₇₀₈₍. The full derivation chain from discrete graph connection ₈₉ = e^i₈₉ and the discrete Bianchi identity to the continuous field strength tensor F_ and the classical Maxwell equations is established. (iv) ~Five-channel electromagnetic thermodynamics. The five-channel complete constraint Second Law is instantiated for electromagnetic systems, with each channel receiving a specific EM-domain physical process identification. The EM five-ratio diagnostic fingerprint is provided as domain instantiation of the Interaction v2. 1 constitutional framework. (v) ~Photon zero-mass constitutional necessity. The photon's zero mass is derived as the constitutional consequence of the EM subnetwork's open topology combined with the free propagation of the graph zero-mode, contrasted with the QCD gluon (Ec=0 but jammed). This document is the electromagnetic parallel of Gravitation v3. 1. Where Gravitation v3. 1 establishes the classical continuum limit of the gravitational force (Einstein field equations, CONJECTURE), this document establishes the classical continuum limit of the electromagnetic force (Maxwell equations, Ring~1 STANDARD). Both are structural realizations of the same underlying constraint network dynamics in two distinct topological regimes: universal geometric coupling (gravitation, Mechanism-3) and open-subnetwork edge-weight modulation (electromagnetism, Mechanism-1). Four falsifiable predictions are provided with full PM-9 statistical specification. The document registers three academic priority claims and responds to fourteen open problems in classical and quantum electromagnetism from the EET constitutional perspective.