Function solve_resolved_scalar_elliptic_cartesian 

pub fn solve_resolved_scalar_elliptic_cartesian(
    program: &KernelProgram,
    resolved: &ResolvedRealization,
    backend: &dyn LinearSolverBackend,
) -> Result<(ScalarEllipticCartesianModel, ResolvedScalarEllipticCartesianSolution), Diagnostic>

Execute one resolved plan against a canonical Cartesian scalar elliptic model with essential conditions on every box side.

The same model lowering feeds Q1 FEM or cell-centered TPFA. Generated mesh density, quadrature, solver, and backend are read only from the resolved Realization; they never enter canonical meaning.

Errors

Returns EQ0807 for revision/dimension mismatch, nonessential boundary data, or an unsupported plan, and preserves lowering/numerical diagnostics from the selected path.