MKL Pardiso ComplexF64 test fails on Julia 1.13 pre-release (Zero pivot error)

[ChrisRackauckas-Claude]

Description

The Pardiso ComplexF64 test (test/pardiso/pardiso.jl line 47) fails on Julia pre-release (1.13.0-beta2) with a "Zero pivot, numerical fact. or iterative refinement problem" error from MKL Pardiso.

Error

LoadError: Zero pivot, numerical fact. or iterative refinement problem.
Stacktrace:
  [1] check_error(ps::Pardiso.MKLPardisoSolver, err::Int32)
     @ Pardiso ~/.julia/packages/Pardiso/GVB44/src/mkl_pardiso.jl:83
  [2] ccall_pardiso(ps::Pardiso.MKLPardisoSolver, N::Int64, nzval::Vector{ComplexF64}, ...)
     @ Pardiso ~/.julia/packages/Pardiso/GVB44/src/mkl_pardiso.jl:75

Context

• This test passes on Julia 1 (stable) and Julia LTS
• Only fails on Julia pre (currently 1.13.0-beta2)
• The failing algorithm is MKLPardisoIterate() with a ComplexF64 sparse matrix
• CI run: https://github.com/SciML/LinearSolve.jl/actions/runs/21811499819

Workaround

Pardiso tests have been excluded from pre-release Julia CI in the test matrix to keep CI green.

Action Items

• Investigate if this is a Julia 1.13 regression or MKL compatibility issue
• Re-enable Pardiso pre-release tests once Julia 1.13 is stable or the issue is resolved