The Primordial Lithium Problem in the Einstein–Cartan Bounce Frame: A Null Result with the Arithmetic Shown

Standard big bang nucleosynthesis, at the baryon density measured by the cosmic microwave background, predicts a primordial lithium-7 abundance of 7Li/H = (4.72 +/- 0.70) x 10^-10, while the Spite plateau in metal-poor halo stars gives (1.6 +/- 0.3) x 10^-10 -- a factor of 2.95, a 4.1-sigma discrepancy on the tabulated errors, standing for decades. This paper tests whether the Einstein-Cartan bounce frame -- the frame whose counting rule, applied to vacuum mode sums, dissolves the magnitude of the vacuum catastrophe, and whose torsion correction replaces the initial singularity with a bounce at a density rho_A = 9.720 x 10^54 g/cm^3 -- bears on the discrepancy through either of its two mechanisms. It does not. The counting rule governs vacuum mode sums and is, by its own statement, identical to the standard computation below its independence crossing E_ind = 3.02 x 10^9 GeV; the nucleosynthesis network contains no vacuum mode sum, every energy in it lies at or below 3 MeV -- 9.9 x 10^-13 of the crossing -- and the collective density of the plasma, the rule's own trigger quantity, never exceeds 6.8 x 10^-48 of the bound, so the rule changes no network input, exactly. The torsion correction to the expansion rate, evaluated at nucleosynthesis densities, satisfies delta H/H <= 3.4 x 10^-48 throughout the era, against the order-unity change a solution would require; the baryon-to-photon ratio is a post-bounce constant that the frame does not split between the nucleosynthesis and recombination epochs; and the neutron lifetime is shifted by a fraction below 10^-47, where even the full experimental beam-bottle disagreement moves the neutron budget by less than one percent. The frame neither solves, reduces, nor worsens the lithium problem. The discrepancy stands at its full size, untouched by this framework, and the null result has a boundary value: it excludes, by the margins printed in Section 5, this class of mechanism as the discrepancy's source.