The Latent-Heat Fraction Has a Ceiling: Maximum Transition Strength as a Function of Temperature

At 100 GeV the envelope permits alpha up to 1.19e+28, an enormous figure that excludes nothing proposed for the electroweak epoch. The envelope tightens as the fourth power of inverse temperature in relative terms: at 10^6 GeV the maximum has fallen to 1.19e+12, and the crossings occur at 3.30e+08 GeV for alpha = 100 and 1.05e+09 GeV for alpha = 1. Above the latter temperature, even a transition that converted the entire permitted energy density into latent heat could not reach alpha of order unity, because radiation at that temperature already carries a comparable share of the ceiling. Strong transitions, in the conventional sense of alpha above one, are therefore a low-temperature phenomenon under the ceiling, with a definite upper temperature at which they cease to be available at all. This study is simulated and computed from stated assumptions; it is not a measurement.