A Unified Real-Space Frustration Mechanism for Superconductivity: Projective Phase Locking from Conventional to Strongly Correlated Systems

We propose a structural framework for superconductivity in which pairing is identified with the formation of stable $w=2$ composite configurations that minimize real-space frustration and enable global phase coherence.The mechanism does not assume a specific pairing interaction; instead, the superconducting symmetry and phase stiffness follow from a minimization of a fiber raccordement cost functional under lattice and frustration constraints.In conventional superconductors, mediator-assisted binding stabilizes the composite class, recovering the London and Ginzburg--Landau structure.In strongly correlated systems, pairing emerges from the reduction of staggered (π,π) frustration, naturally separating amplitude and phase scales and accounting for pseudogap phenomenology.The symmetry of the order parameter is selected geometrically: the framework predicts dx²-y² symmetry in strongly staggered cuprates and extended s^± symmetry in nickelates, where antiferromagnetic frustration is reduced and partially isotropized.To leading order, the critical temperature scales as Tc ~ π/2,δ J f(rF), linking Tc directly to independently measurable exchange and frustration amplitudes.The theory yields falsifiable predictions for gap symmetry, phase stiffness scaling, disorder sensitivity, and pressure dependence in nickelates.It provides a unified constraint-based description of low- and high-Tc superconductivity within a common geometric framework.