General Unified Electro-Gravitation (GUEG): One Derivative Further Toward Einstein's Vision

This manuscript represents the Version 1.0 submission of the General Unified Electro-Gravitation (GUEG) framework and accompanies the reproducibility materials to be released under the same DOI family. We present General Unified Electro-Gravitation (GUEG), a geometric unification of General Relativity (GR) and Maxwell electrodynamics (EM) in a four-dimensional, torsion-free, globally static spacetime regulated by the cosmological constant Λ set to one-half its ΛCDM value (Einstein 1915; Maxwell 1865; Einstein 1917). Electromagnetism emerges from the time-varying Weyl tidal field (“tidal jerk”) through an antisymmetric projection of the derivative of the Weyl tensor along a physical congruence, yielding the electromagnetic tensor Fμν with ∇·F = 0 and standard gauge freedom (Weyl 1918; Jackson 1999). The Maxwell stress-energy feeds back into curvature within a single field equation (Wald 1984; Misner, Thorne & Wheeler 1973). The construction reduces to GR in static spherical vacua, recovers Newtonian, special-relativistic, and Maxwell limits, and remains perturbatively stable for small coupling kGEM (Wald 1984). For observables, we retain baryons-only GR as the lensing baseline and add a calibrated tidal-jerk correction (Planck Collaboration 2020; ACT Collaboration 2023). For redshift, we replace Doppler expansion with an additive line-of-sight term JLOS = |κ| × τeff using a sparse event model (Neff, γ, Nmax) (Górski et al. 2005; Planck Collaboration 2020). Across nine sightlines we fit a single coupling kz on the training set and forecast the holdout sample using Planck MV convergence synthesized to Lmax = 1024, obtaining kz = 4.737, R²Train = 0.990, RMSETrain = 0.065, and RMSEHoldout = 0.837. Phase-randomized and randomized-right-ascension nulls (N = 2000 each) yield p ≈ 0.33 and p ≈ 0.32 (Planck Collaboration 2020; Astropy Collaboration 2013, 2018; Virtanen et al. 2020; Harris et al. 2020). A late-time CMB anisotropy operator for the nine sightlines is provided without monopole claim (Planck Collaboration 2020; Peebles 1993). All inputs and a minimal Colab/worksheet recipe accompany the paper (Gumucio 2025, Zenodo; Python Software Foundation 2024). This work is distributed under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0), permitting unrestricted use, distribution, and reproduction provided the original author is credited. This is the initial preprint release of General Unified Electro-Gravitation (GUEG): One Derivative Further Toward Einstein’s Vision, containing the complete theoretical and mathematical development. Supporting data files and the fully formatted LaTeX version will be released in a forthcoming update (Version 2). This version is published to establish authorship, DOI certification, and public visibility of the core results.