Overview
This article proposes a structural interpretation of superconductivity based on projective phase locking of stable composite configurations in a fiber-constrained geometric framework. Rather than introducing a material-specific pairing interaction as the primary principle, the mechanism identifies superconductivity with the stabilization and phase locking of a topological $w=2$ composite class, which can be realized through different microscopic channels. In conventional superconductors this stabilization is mediated by phonons, consistent with BCS theory, while in strongly correlated systems it arises from real-space frustration minimization.
The framework connects conventional and strongly correlated regimes within a single constraint-based picture. Pairing symmetry is selected by minimizing a lattice-constrained raccordement cost functional under a dominant frustration channel and the lattice symmetry group.
Core contributions
- Unified mechanism: superconductivity interpreted as projective phase locking of stable w=2 composites.
- Real-space origin: pairing driven by frustration reduction and fiber raccordement minimization, not an assumed interaction kernel.
- Symmetry selection: gap symmetry obtained from a lattice-constrained minimization principle under a dominant frustration channel.
- Material predictions: d-wave ($d_{x^2-y^2}$) in cuprates and extended $s^\pm$ in nickelates.
- Scaling: $T_c$ linked to independently measurable $\delta$, $J$, and a frustration amplitude proxy $r_F$.
- Falsifiability: decisive tests via symmetry probes, phase stiffness scaling, disorder response, and pressure dependence.
Conventional vs strongly correlated regimes
In conventional superconductors, mediator-assisted binding stabilizes the composite class and the framework recovers London electrodynamics and the Ginzburg–Landau structure as long-wavelength consequences of phase locking.
In strongly correlated materials such as cuprates, pairing emerges from real-space frustration reduction. The framework naturally separates amplitude and phase scales, providing a structural interpretation of pseudogap behavior as local composite formation without global phase coherence.
Nickelates: symmetry, disorder, and pressure tests
Infinite-layer nickelates exhibit reduced and partially isotropized antiferromagnetic frustration relative to cuprates. Within the present framework this shifts the minimization landscape away from B1g and favors an extended s± class.
The predicted s± state implies intermediate sensitivity to non-magnetic disorder. Pressure dependence is constrained through independently measurable evolution of the exchange scale J(P) and the frustration proxy $r_F(P)$. A mismatch between Tc(P) and the measured evolution of J(P) and $r_F(P)$ would falsify the mechanism.
Relation to the Cosmochrony program
This article focuses on superconductivity. It is presented as a constraint-based framework for symmetry selection and scaling across material families. Companion works develop broader structural motivations and related bounded-response dynamics, but they are not required to follow or evaluate the superconductivity results presented here.
References
Jérôme Beau. A Unified Real-Space Frustration Mechanism for Superconductivity. Preprint, Zenodo. 10.5281/zenodo.18718224