Lagrangian Reduction in RUFT: From Four Terms to a Single Bidirectional Field

CORRECTION NOTICE (July 12, 2026): This preprint has been reclassified by the author as a speculative framework whose empirical claims are not supported. Following a July 2026 re-analysis of the underlying dataset (which confirms an independent external review) the reported effect is attributable to an instrumental switching signature and the pre-declared confirmation gate never certified. Please read the attached correction notice before citing. Successor program: The User's Universe: A Unified Treatise on the Type II_1 Program, DOI 10.5281/zenodo.21321125. We demonstrate that the four-term Lagrangian of Retrocausal Unified Field Theory reduces to two independent terms: L̃_EH (dressed Einstein–Hilbert) and L_SM (Standard Model), with L_amor emerging as a cross-term rather than an independent coupling. The reduction exploits the PT-symmetric Exceptional Point structure and is confirmed experimentally via the same Gate-C1 dataset: spectral coherence C(f₀ = 6.94×10⁻⁴ Hz) = 0.2343 between composite heliospheric observables and a 4-node retrocausal index, with Bonferroni-corrected p = 0.0047 (N = 2,743 slots, M = 37 Welch segments, bootstrap 4/10,000 surrogates, p_bootstrap = 0.0004). Null specificity control (N = 55,303, 141.9 h): Pearson ρ(gcr₁₆₀, gcr₁₆₀+1440 s) ≈ 0 vs ρ(q_r,hw, q_r,hw+1440 s) = +0.727, confirming τ_node autocorrelation is a property of the β-decay retrocausal channel, not of the astrophysical source. Version 0.4: notation unified to Pearson ρ throughout; all internal derivation identifiers replaced with bracketed citations; shared-result declaration added; corrected cross-citation numbers.