The Stochastic Gravitational-Wave Background from String Loops at Capped Tension: A Prediction Far Below the Pulsar-Timing Signal

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 G mu = 4.342e-20, the plateau amplitude is Omega_gw h^2 = 6.589e-13 in the nanohertz band, a factor 6.589e-05 of the 10^-8 level associated with the reported pulsar-timing process. The corresponding characteristic strain at one cycle per year is 2.181e-17. Matching a background of 10^-8 with the same loop model would require G mu = 1.000e-11, and matching twice that amplitude would require 4.000e-11, because amplitude grows only as the square root of tension. A loop born at a tenth of the bounce horizon, 1.286e-17 metres, lives for about 1.976e-08 seconds against gravitational radiation at the capped tension, which is long compared with the bounce time and short compared with later cosmological epochs. The framework's statement is therefore sharp: a string-loop interpretation of the nanohertz signal at its commonly discussed tensions is incompatible with the tension ceiling, by roughly nine orders of magnitude in G mu. The calculation is performed from stated assumptions with all arithmetic deposited, and it is a computation, not a measurement.