The Bounce Assumed Round: Coleman's Symmetry, Asserted in One Sentence and Priced in a Deformation Family

Coleman's 1977 "Fate of the False Vacuum" founded the modern theory of vacuum decay: the rate is governed by a finite-action Euclidean solution, the bounce, and in the thin-wall regime the answer closes in form, B = 27\pi^2 S_1^4 / (2\varepsilon^3). The rate is an extremum over all field configurations, but the paper computes the round one, on an assertion printed in its own text: "I will assume that if there are any O(4)-noninvariant bounces, they have higher Euclidean action than the O(4)-invariant bounce, and thus can be safely ignored" — followed by a note added in proof promising the proof elsewhere. This paper evaluates the assertion. On a declared potential, a declared family of O(4)-breaking deformations (ellipsoidal thin-wall bubbles, semi-axis ratio \zeta) is extremized at fixed vacuum splitting: every deformation raises the action, by gaps from +4679.014003 at \zeta = 1.100000 to +343890.754365 at \zeta = 0.500000, and the family returns the round action exactly at \zeta = 1 (+0.000000). The direction is the one the 1977 sentence asserted; the content is an inequality over every non-round configuration in the theory, of which the 1977 paper computes none. The exact round bounce is also shot numerically: at \varepsilon = 0.400000 its action is 1246.895283 against the thin-wall formula's 1644.934067 — even on the ansatz, the headline number is a thin-wall reading, off by a relative -0.241979. Count: 1 symmetry assumption carrying 1 promissory note (redeemed 1978, single scalar field only); deformations computed in 1977: 0. Census headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.