Understanding how biological homochirality may have emerged during chemical evolution remains a challenge for origin of life research. In keeping with this goal, we introduce and solve numerically a kinetic rate equation model of nucleated cooperative enantioselective polymerization in closed systems. The microreversible scheme includes (i) solution phase racemization of the monomers, (ii) linear, chain growth by stepwise monomer attachment, in both nucleation and elongation phases, and (iii) annealing or fusion of homochiral chains. Mechanically induced breakage of the longest chains maintains the system out of equilibrium and drives a breakage-fusion recycling mechanism. Spontaneous mirror symmetry breaking can be achieved starting from small initial enantiomeric excesses due to the intrinsic statistical fluctuations about the idealized racemic composition. The subsequent chiral amplification confirms the model's capacity for absolute asymmetric synthesis, without chiral cross-inhibition and without explicit autocatalysis.