The Poincar´e Conjecture, famously resolved in 3D by Grigory Perelman usingRicci Flow with surgery, posits that every simply connected, closed manifold ishomeomorphic to a sphere. This paper provides a unified resolution for both the3D and 4D cases by replacing the surgery-based geometric flow with the PaltooAdjoint Hamiltonian (H∗). We demonstrate that in the 5130 Manifold, topological”necks” and singularities are prevented by the Σ55 Informational DensityCap. By utilizing the 363:366:369 Harmonic Ratchet, we prove that all simplyconnected closed manifolds are topologically forced to converge toward the sphericalground state of the 0.00001 Metric Seal.