The microscopic mechanism driving high-temperature superconductivity (HTS) in cuprate materials remains one ofthe central unsolved problems in condensed matter physics. We present the Pressure-Mediated Pairing (PMP) framework, in which Cooper pairing is mediated by emergent collective lattice pressure gradients arising from chargeinhomogeneity introduced by chemical doping. The pressure field P (r) is derived from a Ginzburg-Landau free energyfunctional whose parameters are anchored by elastic and thermodynamic measurements on YBa2Cu3O7. Theresulting screening length xiP is of order a few nanometres, comparable to the superconducting coherence lengthinferred from STM. The pairing coupling constant lambdaP scales with strain variance in a disordered elasticmedium, following from second-order perturbation theory. The matrix element carries an explicit momentum-spaced-wave form factor following from the tetragonal D4h symmetry of the CuO2 plane; the s-wave channel vanishes bygroup-theoretical orthogonality of irreducible representations. A doping-dependent isotope exponent alpha (delta) =MO/2 (MO + Mₑff (delta) ) and a universal pressure scaling ratio kappa = 1/ (1 + lambdaP - mu*) emergenaturally and agree quantitatively with existing Raman and transport data across five cuprate families, yielding kappa= 0. 513 +/- 0. 018. The pseudogap is proposed to arise as a percolative onset of local pressure coherence. PMP isdistinguished from preformed-pair theories by its identification of a specific lattice mediator, and from standardelectron-phonon theory by coupling to strain variance and a doping-dependent interaction range. Five falsifiableexperiments are proposed.
Mo Jerrow (Wed,) studied this question.