Field Equations of Formal Causation: Deriving Structure-Residual Dynamics from Quantum Vacuum Geometry

This work provides field-theoretic completion of Papers 1–3, deriving modified Einstein equations from formal-cause Lagrangian and demonstrating scale unification across 36 orders of magnitude. Starting from a quantum measurement in 9-qubit GHZ states (δ = 0. 014009 ± 0. 001472), we predict: Galactic rotation curves: β = 0. 668 ± 0. 024 (SPARC, N=175 galaxies, 0. 15% agreement) CMB parity asymmetry: A₃₀ = -0. 011 ± 0. 003 (perfect match with Planck observation) Dark matter density: ΩDM ~ 0. 27 (consistent with Planck 0. 268 ± 0. 005) The theory proposes that "dark matter" phenomena arise from formal causation—quantum vacuum geometry coupled to spacetime—rather than undiscovered particles. This constitutes the first field-theoretic formulation connecting Aristotelian metaphysics to modern physics through experimentally falsifiable predictions. Related works: Paper 1: Even-Odd Vacuum Structure in N-Qubit GHZ Structural Coherence (Zenodo 17649694) Paper 3: CMB Even-Odd Parity Asymmetry as Quantum Structural Coherence (Zenodo 17660391) For peer review and community feedback.