The Anisotropy Contest in Einstein-Cartan Cosmology: The Exact Bianchi I Condition for the Spin-Density Bounce

The homogeneous Einstein-Cartan dust model with an unpolarised Weyssenhoff spin fluid gives H^2 = (8piG/3) rho (1 - rho/rho_A) with rho_A = 9.72e54 g/cm^3, so a contracting homogeneous universe turns over at rho_A. In a Bianchi I universe the shear contributes a positive density scaling as a^-6, identically to the negative spin term, so survival of the turnover under anisotropy is decided by coefficients alone. This paper computes that contest exactly. Writing the shear density at the homogeneous minimum as a fraction r of rho_A, a turning point exists if and only if r < 1; it is displaced to bare density rho_b = rho_A/(1-r), and it is a genuine minimum of the scale factor for every 0 <= r < 1. Equivalently, at every epoch the shear fraction must satisfy f_sigma < x = rho/rho_A. At big-bang nucleosynthesis densities x is between 1e-48 and 1e-50, while observation permits a shear fraction of order unity there: the required shear fraction lies some 47-49 orders of magnitude below what observation permits (shortfall 49.1 orders at 1 MeV, 47.2 at 3 MeV). The bouncing set r in [0,1) is not measure-zero in coefficient space, but under any smooth measure on initial data specified at a dilute epoch the bouncing subset is vanishingly small (fraction ~1e-49 of the observationally allowed range at BBN), and the model contains no shear-suppression mechanism. For r >= 1 there is no turning point and the contraction proceeds to a singular, anisotropy-dominated approach. This work was prepared with the assistance of an AI assistant (Dave), including computation and drafting support; all results were checked against the accompanying computation script.