Silent failure modes in three-dimensional two-band time-dependent Ginzburg–Landau simulations of geometric superconducting diodes

We present a three-dimensional two-band time-dependent Ginzburg–Landau solver for mesoscopic superconductors under transport current, the protocol used to measure with it, and eighteen failure modes the protocol detects: each produces a converged, plausible number that does not measure what it is reported as, and each has a test. The central one concerns current injection with zero scalar potential: a phase imposed uniformly on the link variables of a contact face cancels in the discrete curl and in the Neumann condition, so the solver integrates the zero-current problem. Self-field (Ampère) injection is odd in the current, and the voltage is read from the Josephson relation on the gauge-invariant phase, unwrapped line by line. Further modes concern averaging windows that set a threshold, the memory of a current ladder, convergence floors counted in iterations, coefficients whose names mislead, and heat generated where injected normal current converts into supercurrent. Complex conjugation composed with the mirror along the direction of vortex motion maps +J onto −J, so a mirror-symmetric sample has zero diode efficiency, exactly in exact arithmetic and to a few parts in 10^11 away from bifurcations. The solver reproduces a reference implementation bit for bit, the lattice Landau level within 1.6% and H_c3/H_c2 within 0.05%. In equilibrium the screening measures the total stiffness of the two condensates, and the functional caps the π-band upper critical field by the stiffness partition. Under current a notched box rectifies with a sign that survives changes of mesh, thickness and padding; the magnitude falls from −47% with one cell of padding to −21% [−33, −7] with eight cells, and no converged value is quoted.