Once the substrate crosses the modal threshold, its potential is no longer a bowl with a single bottom: it is a sombrero, and the lowest points form a whole ring, the vacuum manifold 𝒱 ≅ S¹. The configuration must sit somewhere on that ring, and the two directions it can move in are not alike. That asymmetry is where mass and orbital motion both come from. Push the marble and find out.

• Radial kick — the massive direction. Shove the marble across the valley and the wall pushes back: it climbs, stalls, and falls into an orbit that breathes about r₀, never escaping. That restoring force is mass. The radial fluctuation of this vacuum is the physical Higgs field, and m_h² = 4ε is just the steepness you can see.
• Angular kick — the flat direction. Shove it around the ring and nothing resists: the new speed persists forever, because every point on the ring is an equally good vacuum: no preference, therefore no force. That costless direction is the massless (Goldstone) mode left behind by symmetry breaking, the phase later eaten by the gauge field.
• And L never budges. Through both kicks the radius and the angular speed visibly change, yet L = 2r²θ̇ stays exactly constant. That is Noether’s theorem in a single number: a perfect symmetry always forces some quantity to be conserved, and the ring’s rotational symmetry conserves angular momentum by construction. Orbital motion, from electrons to planets to galaxies, is not an initial condition anyone had to set. It is the only stable state the vacuum’s topology permits.