Reaching Scaling: How a String Network Born at the Bounce Settles, and the Density It Carries at Each Epoch

This paper computes a consequence of the torsion-regulated bounce for topological defects, using the density ceiling of 9.718e+54 grams per cubic centimetre and the maximum temperature of 3.278e+22 kelvin that follows from it. Once scaling holds, the long-string network carries a fraction Omega = 7.275e-18 of the total density, with the stated scaling parameter zeta = 2.000e+01. The density itself falls steeply: 1.301e+04 kilograms per cubic metre at one microsecond, 1.301e-08 at one second, and 9.035e-35 at recombination, while the fraction stays fixed, which is the operational meaning of scaling. Between the bounce and today the expansion stretches lengths by a factor of 1.203e+22. Because the birth correlation length cannot exceed the bounce horizon, and the scaling correlation length grows in proportion to time from the start, the network reaches the scaling configuration within a modest number of expansion times rather than after the prolonged transient that a network born far from scaling would need. The network's contribution to the expansion rate at every epoch is the fraction above: present in the equations, negligible in the budget. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.