The Cosmological Lithium Exhaust: Differential Diffusion and the Navier-Stokes Fallacy in Standard Big Bang Nucleosynthesis

Standard Big Bang Nucleosynthesis (SBBN) models consistently overpredict the primordial abundance of Lithium-7 by a factor of approximately three relative to observations of low-metallicity halo stars (the Spite plateau). This tension, known as the Cosmological Lithium Problem, is conventionally treated as a failure of nuclear reaction rates or as an indicator of exotic decay channels. In this paper, we demonstrate that the anomaly is a structural consequence of the Navier-Stokes continuum assumption: treating the relativistic primordial plasma as an idealized, infinitely smooth FLRW fluid across first-order phase transitions. By inverting the reaction network and treat-ing the observed Lithium-7 deficit as an empirical boundary constraint, we solve the coupled differential diffusion and nuclear reaction rates across the nucleosynthesis window (T ∼ 0.8 × 109 K to 0.3 × 109 K). We demonstrate that the 3× deficit is the direct physical consequence of differential neutron transport across localized baryonic density fluctuations. Solving the critical timescale intersection τspall ≈ τdiff while enforcing observational bounds on Yp and D/H uniquely isolates an initial density contrast δ = 42.6 ± 8.4 and a characteristic comoving spatial scale `turb ≈ (1.8 ± 0.5)× 104 cm at T = 1 MeV. The Spite plateau is therefore not an astrophysical anomaly, but a high-fidelity diagnostic of primordial fluid turbulence.