Kinetic Pairing via Spin-Bubble Formation in Doped Antiferromagnets: A Real-Space Restatement of String Pairing and a Materials Roadmap for Three-Dimensional High-Tc

A single hole moving through an antiferromagnet is basically stuck. Every hop it makes leaves a trail of overturned spins and the energy cost keeps growing. It cannot go anywhere. Two holes paired as a spin singlet are a different story. They share a small local disturbance of the magnetic order and move it through the lattice together. The order closes back behind them. No trail, no debt building up. Moving as a pair is cheaper than moving alone and that is the whole point. This is not attraction. This is kinetic energy savings. The paper turns that picture into something precise. Two failure modes cap Tc: phase chaos, where pairs form but lose coherence before condensing, and lattice melting, where heat destroys the magnetic order the pairing depends on. Both pin Tc to the antiferromagnetic coupling J. Higher Tc needs higher J, not better doping or thinner films. A 3D network should beat cuprates on phase coherence because thermal depletion of superfluid density scales as T in 2D and T^2 in 3D. But moving to 3D costs you coordination: J_3D needs to be at least (2/3) J_2D to match cuprate per-site magnetic energy. That threshold comes out of one line of algebra. The chemistry does not cooperate. No known 3D oxide or oxyfluoride hits undistorted 180 degree bonds and the right J/t ratio at the same time. Octahedral tilting kills J. Fluorine localizes the electrons and kills t. The paper names both problems precisely and lays out what any synthesis has to solve to break the cuprate ceiling.