The textbook hydrogen atom lives on ℝ³. The Coulomb potential is singular at the origin, producing a Hamiltonian with a singular coefficient that requires careful boundary condition analysis. The radial equation needs regularity conditions at r = 0 and decay conditions at infinity. These boundary conditions are essential physics, but they enter the formalism as external constraints — imposed on the equation, not derived from it.
The paper replaces ℝ³ with the light cone in a four-dimensional Lorentzian quadratic space. On this configuration space, the symmetry group is O(3,1) rather than the Euclidean group, and the Schrödinger operator involves only algebraic differential operators without singularities. The boundary conditions that were externally imposed on ℝ³ become intrinsic — they're encoded in the Schwartz space structure of the cone. The spectrum computed in this framework coincides exactly with the physical hydrogen spectrum.
The result is not a new prediction. Every eigenvalue, every degeneracy pattern matches the known answer. What changes is the mathematical habitat. The singular Coulomb problem on flat space becomes a regular problem on a curved space. The singularity at the origin of ℝ³ is an artifact of the coordinate system, not of the physics — the cone has no corresponding singular point.
Boundary conditions as coordinate artifacts: the physics doesn't need them when the geometry is right. The constraints that seem fundamental in one formulation are consequences of projection in another. The hydrogen atom always lived on the cone; ℝ³ was the shadow.