Reasoning:
- Zero-energy bookkeeping (eq. 3.22): E = -(4pi/3) epsilon rho^3 + 4pi sigma rho^2 vanishes at the materialization radius rho_0 = 3 sigma/epsilon — quantum tunneling conserves energy, so the bubble is born at exactly the radius where volume gain pays for wall cost.
- Growth: the thin wall then traces the O(3,1)-invariant hyperboloid through its materialization radius — expansion asymptotically at c in every frame. Physically, within a spherically symmetric shell of zero enclosed total energy there is no external gravitational field, so nothing outside is disturbed before arrival and nothing decelerates the wall. (This frame-independence is what makes collision-triggered nucleation immune to the slow-vs-fast-products distinction used elsewhere in the safety debate.)
- Interior: for decay from a zero-cosmological-constant false vacuum to energy density -epsilon, the interior is anti-de Sitter space; though nonsingular, it is unstable to small perturbations and inevitably undergoes gravitational collapse like the end state of a contracting Friedmann universe, on the timescale of the bubble parameters (microseconds or less). Hence the paper’s verdict that even the Stoic comfort of a habitable successor vacuum is eliminated in this case.
- Scope note: for the reverse case (de Sitter false vacuum decaying to our zero-Λ vacuum), neither the exterior de Sitter space nor the interior Minkowski space suffers such collapse.
Step 6 verdict
Verdict: approved (checked). Traced: E = -(4pi/3) epsilon rho^3 + 4pi sigma rho^2 vanishes at rho_0 = 3 sigma/epsilon - checks; zero enclosed energy + spherical symmetry (Birkhoff) → no exterior field, hence no warning and nothing retarding the wall; the O(3,1)-invariant hyperboloid through rho_0 → asymptotically luminal expansion in every frame (this same invariance underwrites A-55’s frame-independence point). The AdS-interior instability/collapse claim and the changed-constants consequence are taken from the source’s derivation and are consistent with the energetics. Valid.