One Contracting Branch for the Einstein-Cartan Bounce: Horizon, Flatness, Entropy and Reheating Ledgers for an Explicit Two-Component History

The homogeneous Einstein-Cartan dust model gives a turning point of the scale factor, H = 0 with a-double-dot > 0, at the fermion density rho_A = 9.72e54 g/cm^3, but specifies no contracting history that arrives there. This paper writes out one explicit pre-bounce history in full - a two-component branch of fermion dust and radiation, tracked separately throughout (spin variable x built from the fermion density only), beginning at the present-day mean matter density as a stated initial condition - and re-runs the horizon, flatness, entropy and reheating ledgers on that single branch in one set of definitions. The branch contracts through 64.90 e-folds over 17.23 Gyr and reaches a genuine minimum displaced by its radiation content to a fermion density of 1.0099 rho_A. Its ledgers do not close: contraction delivers 33.14 equivalent e-folds of causal contact against a requirement of 46.8 (shortfall 13.6 e-folds; meeting it would require a starting density of 4.97e-67 g/cm^3, 36.7 orders below the present mean density); it suppresses curvature by 28.19 orders against the 42.84 orders required (shortfall 14.65 orders; the starting curvature must already be below 2.24e-15); the entropy arriving at the bounce is 1.39e-11 k_B per carrier against roughly 6e9 k_B per baryon observed, with the low entropy stated as an unexplained initial condition and entropy production at reheating excluding any exactly periodic or past-eternal cyclic reading (single bounce or nothing). The named reheating channel, decay of the carrier fermions to radiation, produces a thermal bath above 1 MeV before nucleosynthesis for lifetimes in the window 2.9e-25 s to 0.98 s, but it sets the baryon-to-photon ratio to at best 1.55e-2, a factor 2.53e7 above the observed 6.1e-10, at every lifetime in the window; the free neutron lifetime of 879 s lies outside the window. The isotropy assumption is adopted at the price priced by the companion anisotropy result (DOI 10.5281/zenodo.24113527): shear fraction below the local x at every epoch, i.e. below 2.77e-85 at the branch start. Conclusion: on this branch the Einstein-Cartan bounce is a turning point of one solution, not a cosmology. 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.