TRIDENT-Z0 Diagnostic Framework: High-Tc Cuprate Superconductivity as a Mechanistically Underdetermined Quantum Coherence System (PHYS-HTSC-001.v1)

This technical note applies the TRIDENT-Z0 diagnostic framework to high-Tc cuprate superconductivity. Cuprate materials exhibit reproducible macroscopic superconducting coherence below Tc, including zero DC resistance, Meissner response, d-wave gap symmetry, and a doping-dependent superconducting dome. However, the microscopic pairing mechanism and the governing constraint field remain contested. --- SCOPE INVERSION --- This case deliberately inverts the scope boundary used in PHYS-BCS-001.v1. Cuprates were excluded from the conventional BCS node due to strong-correlation effects and mechanistic ambiguity. Here they are explicitly included to test whether the framework can resist forcing a PASS outcome on a system that shares macroscopic coherence vocabulary with BCS but lacks its microscopic closure. Scope inclusion: layered copper-oxide superconductors with strong electronic correlations and doping-dependent phase diagrams. Scope exclusion: claims of a uniquely settled pairing glue, phenomenological models treated as closed microscopic derivations, and generalization to all unconventional superconductors. --- EMPIRICAL STATUS --- G1 PASS: The superconducting phase itself is reproducible across material families (LSCO, YBCO, Bi-2212, Hg-1201). Tc is a thermodynamic boundary scalar. d-wave order parameter symmetry is experimentally established. Phase stiffness rho_s is measurable. --- MECHANISTIC STATUS --- G2 PARTIAL: Competing candidate mechanisms include spin-fluctuation pairing, strong-correlation emergent models (e.g., RVB-type proposals), and mixed-channel interactions. Multiple mechanisms reproduce overlapping subsets of the data without uniquely discriminating predictions. No single agreed microscopic parameter plays the role of lambda_ep in BCS. --- QUANTITATIVE STATUS --- G3 PARTIAL: Empirical scaling relations exist (Uemura relation Tc proportional to rho_s(0); Homes scaling rho_s proportional to sigma_dc times Tc). These provide quantitative structure but do not constitute a closed constraint field derivable from first principles across material families and doping levels. --- COHERENCE BOUNDARY STATUS --- G4 OPEN: Tc defines a sharp thermodynamic boundary. However, the governing constraint field linking microscopic interaction to Tc is not uniquely mapped across doping regimes and cuprate families. The relationship between pseudogap onset T* and superconducting coherence onset Tc remains experimentally contested. The coherence boundary exists; the constraint field governing it is not closed. This node functions as a stress test within the PHYS branch. A forced PASS would constitute framework inflation. The OPEN outcome is the correct diagnostic result under current evidence. Keywords High-Tc superconductivity Cuprate superconductors d-wave pairing Strongly correlated electrons Pseudogap phase Spin fluctuation pairing RVB theory Uemura relation Homes scaling Superfluid stiffness rho_s Thermodynamic phase transition Constraint field closure Boundary-defined coherence Quantum coherence TRIDENT diagnostic framework SHRF corpus Evidence-bound analysis Mechanistic underdetermination Open gate classification