The Thermal Bounce Action When the Bath Has a Maximum Temperature: S3 Near the Ceiling

Under the stated scaling the ratio S3/T is constant across the entire scan, taking the value 134.0 at a scale of 8.04e+07 GeV and the same value, 134.0, when the vacuum energy reaches a tenth of the ceiling. The constancy is the scaling symmetry of the toy construction made visible: with one scale in the problem, no dimensionless ratio can know where that scale sits relative to the ceiling. The ceiling therefore does not, by itself, move the nucleation condition in a single-scale potential. What it does is bound the domain: a potential whose symmetric-phase restoration would require temperatures above the maximum cannot be treated as thermally restored in the usual way, and its high-temperature history must be described as beginning at the ceiling rather than at arbitrarily high temperature. This study is simulated and computed from stated assumptions; it is not a measurement.