One Ceiling, Four Defect Classes: A Joint Bound on the Symmetry Scale from Strings, Walls, Monopoles, and Textures in a Bounced Cosmology

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. The ceiling scale is eta = 2.544e+09 GeV. Against it: the microwave string bound corresponds to a scale limit of 4.402e+15 GeV, a margin of 1.730e+06; the pulsar-timing level to 1.221e+14 GeV, a margin of 4.799e+04; the lensing-pair threshold to 2.398e+15 GeV, a margin of 9.426e+05; and the texture amplitude at the observed fluctuation level to 5.446e+15 GeV, a margin of 2.141e+06. For strings and textures every observational limit lies far above the ceiling: the framework is not merely allowed by those data, it is separated from them by large factors. Stable walls reverse the pattern: their formation-scale limit of 1.000e-03 GeV sits a factor 2.544e+12 below the ceiling, the single entry in the table where observation demands less than the ceiling permits, and therefore the single class where an extra ingredient, a vacuum bias, is mandatory. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.