Paper TS-X: Derivation of the FSC Baryon Coupling Ratio — Ab Initio Calculation of g·ρ_b/(2λv²) = Ω_b²/(Ω_M · N_sector)
Year: 2026
Type: preprint
Abstract: Paper TS-T established that the FSC dark energy equation of state parameter w_a = +0.003 depends on the baryon–field coupling ratio r ≡ g·ρ_b/(2λv²) = 0.00191. Paper TS-U identified this as Open Question OQ-U-1: derive r from first principles without assuming its value. This paper proves: r = g·ρ_b/(2λv²) = Ω_b²/(Ω_M · N_sector) = (0.0493)²/(0.3111 × 4) = 0.001951, in agreement with the TS-T value r = 0.00191 to within 2.1%. The derivation uses only: (i) the FSC Z4 symmetry structure (Paper TS-W); (ii) the Mexican-hat potential of the FSC scalar field Φ (Paper F); (iii) the physical requirement that baryon–field coupling preserves the Z4 orbit structure. The factor Ω_b² in the numerator arises from a two-step energy transfer: Sector-I (baryons) →[ε_b = Ω_b/Ω_M]→ Sector-II (dark matter) →[1/N_sector]→ Sector-III (dark energy). Each step contributes one factor of Ω_b/Ω_M, explaining the appearance of Ω_b² in the numerator. The complete master chain of FSC is: e^{iπ}+1=0 [Euler] → N_sector=4 [TS-W] → r=Ω_b²/(Ω_M·4) [TS-X] → w_a=+0.003 [TS-T], with zero FSC-specific free parameters. The critical observational test is w_a > 0 from DESI DR2 (expected 2026).
Author: Katakura, Yoshitaka
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204203510
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