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 II₁ Program, DOI 10. 5281/zenodo. 21321125. We demonstrate that the four-term Lagrangian of Retrocausal Unified Field Theory reduces to two independent terms: L̃EH (dressed Einstein–Hilbert) and LSM (Standard Model), with Lₐmor 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, pbootstrap = 0. 0004). Null specificity control (N = 55, 303, 141. 9 h): Pearson ρ (gcr₁₆₀, gcr₁₆₀+1440 s) ≈ 0 vs ρ (qᵣ, hw, qᵣ, hw+1440 s) = +0. 727, confirming τₙode 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.