Spin Cancellation Between Species: How Precisely Must Opposing Spin Populations Balance to Postpone a Bounce by a Given Factor?

An imbalance of one part in a hundred between the opposing populations postpones the bounce by a factor of 1.000e+04 in density. An imbalance of one part in ten thousand postpones it by 1.000e+08. Inverted, the requirement is severe: postponement by a factor of 10 needs the populations balanced to an imbalance of 0.316; by a factor of 100, to 0.100; and by a factor of a million, to 1.000e-03. At that last level the balance must be held against Poisson fluctuations of the spin carriers themselves, which requires of order 1.000e+06 carriers per relevant volume before random statistics alone would be expected to leave a residual imbalance of the permitted size. The study is a computation from stated assumptions, performed by the accompanying script; it is simulated, not measured.