Stability and Mode Transition of Rotating Standing-Wave Solitons: A Structural-Isomorphism Argument within the Wave-Ontology Framework

The E×B-T theory of rotating standing-wave solitons takes "wave existence" as its sole postulate. Rotation, revolution, and radial oscillation describe the modes of the wave's evolution; at any instant the wave is a one-dimensional waveform—not a fundamental string—and this waveform is the state of the wave at that instant. Under phase-locking conditions, these instantaneous states coalesce into a standing-wave state as the wave evolves, i.e., a rotating standing-wave soliton. The central qualitative claim of the theory is that a soliton exists stably only above a certain frequency threshold: below the threshold the structure breaks up; at the threshold phase locking closes; beyond the threshold a mode transition occurs; and a phase-locked standing wave does not radiate a net energy flux outward. This paper does not derive new quantitative formulas for E×B-T; instead, taking as references a number of verifiable, established results in modern nonlinear dynamics, wave theory, and condensed-matter physics, it argues, step by step, for the structural plausibility of this qualitative picture and translates it into language testable by the physics community. Section 3 draws on the locking region of the Adler equation, experimental observations of Arnold tongues in breathing-soliton lasers, the critical frequency of vortex nucleation in rotating Bose–Einstein condensates (BECs), nucleation below the thermodynamic threshold in rotating optical lattices, the stability of Hasegawa–Mima modons, and the modulation of coherent-structure rotation by gradient fields in tokamaks, to establish the dynamical basis of phase-locking stability and experimental anchors for threshold behavior. Section 4 draws on the Sommerfeld radiation condition, the domain of validity of the Larmor formula, the Vakhitov–Kolokolov (VK) slope criterion and its limitations, PT-symmetry breaking and the real/complex nature of eigenvalues in non-Hermitian systems, and the parameter sensitivity of stability domains in moiré photonic lattices, to argue that "phase-locked standing waves do not radiate; departure from phase locking entails radiation/decay" can be restated as computable criteria within several scholarly frameworks. Section 5 draws on supercritical and subcritical pitchfork bifurcations, experimental verification of bifurcations and critical slowing down in dissipative solitons, and the Hopf bifurcation and synchronization locking of breathing dissipative solitons, to argue that the instability following threshold crossing can be differentiated into two classes of fate. Section 6 discusses spherical Bessel zeros and radial closure modes, the stability parameter boundaries of azimuthons, and the hierarchical differences in laboratory reproduction. The conclusion is that the qualitative picture of E×B-T is structurally isomorphic to the quantitative behavior of established theories, which provides independent circumstantial evidence for its possible correctness; however, the dedicated cutoff-frequency formula, the E×B-T formalization of the radiation criterion, the quantitative relation between spherical Bessel zeros and the threshold, the explicit correspondence between the two-dimensional frequency structure and the Adler-equation quantities ψ, ν, and ν_c, and the temperature-gradient correction term together with the energy-budget calculation remain to be supplied.