The Co-Moving Elastic Bubble Profile: A Natural Solution of the RTE Wave Equation and Two Distinct γ Effects

Paper 4 of this series (Colombo 2026e) proposed the elastic equilibrium bubble as a conceptual mechanism for inertial-frame equivalence. This paper provides the first quantitative bubble profile by solving the RTE wave equation, with explicit source term, for a uniformly moving source. A co-moving solution U(r − vt) is sought without imposing any Lorentzian geometry. The result — derived, not assumed — is an ellipsoidal profile with longitudinal semi-axis a_L = k (fixed at the rest-frame value, velocity-independent) and transverse semi-axis a_T = kγ (growing with velocity). A fundamental distinction is maintained throughout: this ellipsoidal deformation is the physical state of the elastic lattice field, not the Lorentz contraction of measurements. Lorentz contraction, in the RTE model, is hypothesized to emerge separately from the local temporal dynamics (Papers 3 and 6 of this program). The paper thus identifies two distinct physical mechanisms that both carry the factor γ but act in opposite geometric directions: the co-moving bubble's transverse expansion (elastic field deformation) and the measurement effect's longitudinal contraction (temporal tick-rate asymmetry). Whether these two mechanisms share a common dynamical origin is identified as the central open question.