Fossil Gravity: A Parameter-Free Derivation of the Dark Energy Equation of State from the Z_S Term via LIGO GWTC-3

AbstractDESI DR2 (March 2025, 4.2σ) finds w₀ = −0.752 ± 0.059 and rules out a cosmological constant.We present the first parameter-free derivation of the dark energy equation of state w(z) withinfossil gravity theory (Wartenberg 2026). The Zₛ term of the theory describes spacetimecurvature through causal condensation in Zone 0 - without a mass source term. FromSupplement VII, Eq. VII-29, follows the scaling G^BHμν ∝ M², implying a cosmological energydensity ρ_ZS(z) = (4πG/ℏc³)·⟨M²⟩·n_SL, where ⟨M²⟩ is the mean squared total mass and n_SL isthe comoving number density of stellar black holes. Both quantities are directly computablefrom gravitational-wave catalogues - without fitting to cosmological data. The effective equationof state w_ZS(z) = −1 + (1/3)·dlnρ_ZS/dlna deviates structurally from −1 without freeparameters; this prediction follows from the M² scaling alone. Using the LIGO-Virgo-KAGRAGWTC-3 catalogue (81 BBH events, z = 0.05-0.83), we compute ρ_ZS(z) and derive w_ZS(z)directly from observations. Current results are limited by LIGO selection effects.Selection-corrected results with LIGO O4 data (∼200 events) are identified as the decisivequantitative test. Falsifiable prediction: if w_ZS(0) lies outside the DESI band, the Zₛinterpretation of dark energy is ruled out. Note on this version (v2): The first version of this paper (May 2026) carried an incomplete andmisattributed entry in the reference list (“Kehle, C. & Unger, R. 2026” for DOI 10.1103/gbg1-pjgq).This DOI belongs to the paper “Violation of the Third Law of Black Hole Mechanics in VacuumGravity” by Crump, Gadioux, Reall and Santos (2026); the entry has been corrected accordingly.The content and results of this paper are unaffected by the correction.