Cuprate Superconductivity — Mechanism Identification

Strong correlation intractability. Cuprate superconductors are strongly correlated electron systems: the interactions between electrons are large enough that they cannot be treated as small perturbations to a non-interacting system. This makes exact theoretical treatment computationally intractable for systems of realistic size. Every theoretical framework for cuprate superconductivity is therefore an approximation, and different approximation schemes produce different predictions. The identification problem is partly a computational problem: even if the correct microscopic Hamiltonian is known, extracting predictions from it is not straightforward. This is a structural resistance mechanism — it is not specific to any proposed theory, it constrains all of them.

Absence of a decisive distinguishing experiment. Competing theoretical frameworks often make overlapping predictions for measurable quantities, making clean discrimination difficult. The d-wave symmetry evidence (IN-003) strongly constrained viable descriptions but did not identify the microscopic pairing interaction. The field therefore still lacks a single experimental result whose interpretation has produced broad mechanism-level convergence.

Identification requires convergence across theory and experiment, not the existence of an individual proposal. The claim requires a mechanism to be accepted as explaining the relevant superconducting behaviour with sufficient predictive and experimental support. No single framework has yet reached that threshold across the cuprate evidence base. The bottleneck is therefore evidential convergence: candidate descriptions must survive discriminating tests and account for the major empirical constraints well enough to support stable community identification.

Controlled simulation as a potential resolution path. More accurate classical calculations, cold-atom simulators, and future quantum simulations of Hubbard-type models at experimentally relevant parameters could test whether those models reproduce the key cuprate phenomena and distinguish among proposed microscopic explanations. IN-007 advances this trajectory by localising the net d-wave pair-forming contribution within a two-dimensional Hubbard-model calculation to frequencies set by the superexchange interaction. This increases the discriminating value of controlled calculations, but a model result does not by itself establish that the same interaction uniquely causes pairing in real cuprate materials. The attractor remains a discriminating computational capability rather than a predetermined theoretical outcome.