Generalize first Jacobi–Trudi identity to independent M and N

[faabian]

Summary

• separate the partition/determinant size M from the alphabet/variable count N
• add the rectangular tableau and path APIs needed for independent dimensions
• generalize the full LGV nonintersection/east-step-height bridge to rectangular path tuples
• prove the unconditional independent-M/N first Jacobi–Trudi identity
• preserve the existing equal-dimension API through compatibility results

Validation

• full lake build passes (8079 jobs)
• targeted JacobiTrudiMN module build passes without warnings
• no new sorry, admit, or axiom

The new main result is jacobiTrudi_h_mn; jacobiTrudi_h_mn_self verifies compatibility with the existing M = N theorem.