A Static, Eternal Universe: Geometric Resolution of Cosmological Anomalies Without Dark Components or the Big Bang

We present a complete cosmological framework in which the universe is static, eternal, and non-expanding, yet reproduces all key observations currently attributed to the Big Bang paradigm. Redshift is not Doppler re- cession but a path-dependent accumulation along null geodesics in a Finsler– Randers geometry. Dark matter and dark energy are eliminated, their ef- fects emerge from velocity-dependent modifications to geodesics and geo- metric energy loss, respectively. The CMB is not a relic of a hot dense phase but a thermalized background with anisotropies imprinted by fundamental geometric anisotropy. The Karlsson redshift periodicity ∆ log(1 + z) = 0.089 is derived from first principles via anomaly cancellation, yielding κ = H0fa/mec 2 = 0.0891 ± 0.0003. JWST’s “impossibly mature” high- z galaxies are naturally accommodated in eternal time. Crucially, the framework is falsifiable. It predicts: • Weak Equivalence Principle violation at ∆a/a ∼ 10−15, detectable by • Redshift-dependent BAO scale evolution d ln rs/dz ≈ 0.005z If any of these fail at predicted thresholds, the framework is excluded. If they hold, the Big Bang paradigm is in existential crisis. We also identify the primordial helium abundance as an open quantitative problem and propose AGN nucleosynthesis as the candidate mechanism, distinguishing this from ad hoc patching by grounding it in the substrate physics. Keywords: Finsler–Randers geometry · static cosmology