FORK v5 – Dynamic Dark Energy and Stable k-essence Embedding B¨ ulent Kus¸c¸u Independent Researcher, Ankara, Turkey ORCID: 0009-0000-4160-1927 bulentkuscu@gmail.com September 2025 Abstract FORK v5 is a dynamic dark energy model based on the Chevallier-Polarski- Linder (CPL) parametrization, addressing three cosmological tensions: the Hubble tension (reduced from 5.2 σ to 0.87 σ), the S8 tension (reduced from 2.5 σ to 1.7 σ), and the JWST early galaxy excess (z =8–15). MCMC analysis using SH0ES, DESI Y3, JWST CEERS/JADES, and Planck 2018 datasets yields H 0 = 71.2 ± 1.8 km s −1 Mpc −1 , w 0 = −0.94 ± 0.08, w a = −0.21 ± 0.12. The z = 12 halo mass function exhibits 2.4 times the abundance of ΛCDM, aligning with JWST observations. The model ensures c 2 s > 0 and K > 0, preventing ghost instabilities while permitting phantom-like behavior at high redshift. Com- pared to wCDM and ΛCDM, FORK v5 is statistically competitive (Bayes factor ln B = −2.1), justifying additional parameters by resolving the three tensions. Testable predictions include atom interferometry (δa/a ∼ 10 −12 ), Casimir force shifts (∼ 1%), LHC dijet resonances (1–10 TeV), and a halved σ(w a ) with Euclid + DESI-5. This revision strengthens statistical analysis, JWST systemat- ics, ghost stability, simulation details, visualizations, and prediction method- ology based on referee feedback. 1 Introduction Despite the success of the ΛCDM model, three cosmological tensions remain un- resolved: the Hubble tension (a 5.2 σ discrepancy between local and CMB H 0 measurements), the S8 tension (a 2.5 σ discrepancy in matter clustering), and the JWST early galaxy excess (z =8–15 galaxies exceeding ΛCDM predictions). FORK v5 proposes a dynamic dark energy model with w(z )= w 0 + w a z/(1 + z ) via CPL parametrization, addressing all three tensions within a stable k-essence framework. While quintessence models are potential-driven (Ratra & Peebles 1988; arXiv:2501.18336), Horndeski general scalar-tensor theories encompass non-minimal coupling (Horndeski 1974; arXiv:2412.00931), and k-essence relies on non-standard kinetic energy (shift symmetry, technical naturalness, arXiv:2501.14366). Unlike Early Dark Energy (Poulin et al. 2019) or Interacting Dark Energy (Di 1