Resolution of the Cosmological Lithium Problem via Infall Nucleosynthesis: Eliminating the 7Li Overabundance Anomaly Without Stellar Depletion or Non-Thermal Decays

The Cosmological Lithium Problem represents a persistent, statistically severe (> 5σ) tension in standard relativistic cosmology: whereas Big Bang Nucleosynthesis (BBN) parameterized by Planck CMB baryon density predicts a primordial abundance ratio (7Li/H)BBN ≈ (4.68 ± 0.32) × 10−10, spectroscopic measurements of ancient, metal-poor halo stars along the Spite plateau systematically yield (7Li/H)obs ≈ (1.58 ± 0.11) × 10−10. Decades of experimental verification have confirmed nuclear reaction rates, ruling out conventional nuclear cross-section uncertainties, while astrophysical stellar de- pletion hypotheses require fine-tuned uniform destruction mechanisms that unphys- ically spare the far more fragile deuterium isotope. Building upon our foundational series on gravitational infall dynamics and the pre-stressed continuum (Novák, DOIs: 10.5281/zenodo.23670610, 10.5281/zenodo.23703698), we demonstrate that the lithium overprediction is an artifact of the erroneous assumption of a globally homogeneous, expanding metric singularity. In an elastically pre-stressed continuum where cosmo- logical redshift is potential- and free-fall-driven, light element synthesis occurs locally within localized convergent accretion streams and protogalactic virial shocks rather than in an isotropic thermodynamic furnace. We derive the stationary reaction net- work for 7Be and 7Li under local continuum thermodynamic gradients, showing that the equilibrium plateau matches the empirical Spite baseline without ad-hoc stellar mixing, sterile neutrinos, or decaying dark matter.