The Kibble Correlation Length at a Density Ceiling: Defect Spacing When the Hot Phase Has a Maximum Temperature

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. At the bounce the thermal length is 6.986e-26 metres and the horizon distance is 1.286e-16 metres. Between them sits a third length that the ceiling itself supplies: the smallest correlation length consistent with the energy budget, xi_min = 7.757e-26 metres, below which a string network with length density one per correlation area would carry more than the ceiling density and so cannot form. The allowed window for the correlation length therefore runs from xi_min to the horizon, a span of 9.220e+00 orders of magnitude, wide in length but bounded at both ends by the framework rather than by taste. For a scalar coupling lambda = 1 the microphysical correlation length equals xi_min and the string fraction at formation is of order unity by construction; for lambda = 0.1 it is 2.453e-25 metres with string fraction 1.000e-01, and for lambda = 0.01, 7.757e-25 metres with fraction 1.000e-02. At the causal extreme, one correlation length per horizon, the point-defect density is 4.701e+47 per cubic metre and the string fraction falls to 3.637e-19. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.