Microwave-Background Anisotropy from Strings in a Bounced Cosmology: The Predicted Fraction and Its Distance from the Planck Bound

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 capped tension the predicted string fraction is f_10 = 1.227e-27, against a bound of 0.011: the prediction is below the bound by the square of the tension ratio, an enormous margin. The corresponding root-mean-square contribution to the sky is about 1.051e-12 microkelvin, and the temperature step across a single moving string, by the Kaiser-Stebbins relation at typical network velocity, is delta T over T = 6.275e-19. The tension would have to rise to 1.300e-07 for strings to reach the present bound, a factor in symmetry scale of 1.730e+06 above the ceiling scale. Microwave anisotropy, the historically strongest string probe, therefore has no reach into this framework's allowed range: even a future experiment improving the f_10 bound by several orders of magnitude would remain far from the predicted fraction, because the fraction falls with the square of an already small tension. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.