Resonant Etheric Dynamics (TDRE): A Covariant Lagrangian Model with Double-Vortex Solitons, Coulomb/Maxwell Sector and 8x12 Harmonic Quantisation

We present the Theory of Resonant Etheric Dynamics (TDRE): a covariant field-theoretic framework in which matter arises as stable (topological) excitations of a discrete physical substratum-the plenum. The model employs a complex CP1 doublet minimally coupled to a gauge potential Aμ, stabilised by a Skyrme-type term. We develop the Lagrangian formulation, establish energy positivity and local well-posedness, construct double-vortex solitons, and derive a discrete modal spectrum labelled by (n,m). We address two key technical criticisms: (i) reconciling the Bessel quantisation (model A) with the (n2+m2) law (model E) via an asymptotic homogenisation theorem and an explicit error bound; (ii) preparing the ground for a first-principles derivation of the stability cut-off n≤8 m≤12, to be completed in Part II. We also exhibit the Coulomb/Maxwell sector as an intrinsic low-energy limit of TDRE's gauge dynamics.