TensorTrainAMEN fails when the RHS has an internal TT rank greater than one

@i3s93 is already working on this.

Since Sep 1, 2026.

BoBa’s scalar `TensorTrainAMEN` solver fails when solving a system whose right-hand side has a nontrivial internal TT rank. A minimal example of this is the system $Ax = b$ where

$$
A = I_{2} \otimes I_{2}, \qquad b = e_{1}\otimes e_{1} + e_{2}\otimes e_{2}.
$$

Using a rank-one initial guess such as $x_{0} = e_{1}\otimes e_{1}$ produces the error:

`Invalid contraction.: 1 == 2`

The likely cause is an index-ordering mismatch in `TensorTrainAMEN::project_phizy`. A left-to-right environment produced by compute_next_Phi is ordered as (r_z, r_y, 1), but scalar AMEn labels it as`{"rz", "one", "ry"}`. The correct indexing pattern should instead read `{"rz", "ry", "one"}`. The existing ordering is masked for rank-one RHS tensors because both exchanged axes have length one. BoBa’s block-AMEn implementation already uses the latter ordering.

AMEn should accept general valid RHS TT ranks and solve the identity example with $x = b$. A small rank-two RHS regression test in `test_tt_solvers.cpp` would likely demonstrate the failure and verify the proposed fix.