tensor_inv rank-4 emit (blocks on numsim-cas exposing the contraction-index pair)

[petlenz]

Follow-up to #30 (Phase 1.1) and the tighten-rank-2-only decision in #42.

Summary

`tensor_inv` of rank ≠ 2 currently throws at emit time. The algebraic inverse is well-defined (and tmech can compute it), but emitting the correct `tmech::inv` template invocation requires knowing which contraction-index pair to invert against.

Example: a rank-4 elasticity-tangent inverse needs

```cpp
tmech::inv<tmech::sequence<1,2>, tmech::sequence<3,4>>(C)
```

— and the `<1,2>`/`<3,4>` choice is a property of the tensor's algebraic structure (minor-symmetric, major-symmetric, full, etc.), not a codegen-side default.

Where the work lives

Upstream (numsim-cas): add an accessor (e.g. `inv_contraction_pair()` returning two `sequence`-shaped index lists) on the `cas::tensor_inv` node. The factory `cas::inv(...)` already inspects the input tensor's space (`Symmetric`, `MinorMajor`, etc., via `tensor_inv.h:18-25`); deriving the natural index pair from that space is a small extension.

Downstream (numsim-codegen): once the accessor exists, the emit case in `tensor_code_emit.h` reads the pair and produces `tmech::inv<tmech::sequence<...>, tmech::sequence<...>>()`. The current rank-2 path stays (no template args).

Acceptance

• numsim-cas exposes the contraction-index pair on `tensor_inv`
• numsim-codegen emit case for rank-4 produces the right tmech template form
• New test in `tests/TensorCodeEmitTest.cpp` exercises a rank-4 `tensor_inv` (e.g. the natural inverse of a rank-4 elasticity tensor) and asserts the emitted sequence args
• The current rank-4 throw in `tensor_code_emit.h` is removed

Why it matters

This is on the critical path of #35 (Phase 3b algorithmic-tangent pass — D7 of the plan emits `tmech::inv(...)` at the rank-4 Jacobian inversion site). Without rank-4 inv, the tangent pass can't ship.

Refs

• Part of Phase 1.1 — Implement currently-stubbed emit cases #30 (Phase 1.1)
• Blocks part of Phase 3b — Algorithmic tangent + Kuhn-Tucker lowering #35 (Phase 3b)
• See the comment + throw in `include/numsim_codegen/code_emit/tensor_code_emit.h` at the `tensor_inv` override after Phase 1.1a: implement tensor_inv emit case (tmech::inv) #42 merges.

[petlenz]

Cross-repo dependency filed: NumSim-Stack/numsim-cas#248.

Found that the rank-4 question is unsettled upstream — closed numsim-cas #192 resolved by rejecting rank-4 at the `inv()` factory (not by supporting it), and the algorithmic-tangent use case (this issue + #35) wasn't on the table at that point.

NumSim-Stack/numsim-cas#248 lays out the two paths:

• Option A: add rank-4 support to `cas::tensor_inv` with an `inv_contraction_pair()` accessor — the original framing of this issue
• Option B: keep cas rank-2-only and let the algorithmic-tangent pass synthesise `tmech::inv<...>(...)` directly at emit time

This issue (numsim-codegen #43) will close once that decision lands upstream. If Option A wins, the implementation here is the original plan (read the pair, plumb into the template args). If Option B wins, this issue closes with no rank-4 work in numsim-codegen — the tangent pass owns it.

[petlenz]

Upstream decision (NumSim-Stack/numsim-cas#248): Option A — rank-4 tensor_inv support will land in numsim-cas in a future release. Estimate per the maintainers: "will take some time."

This issue stays open as the downstream tracker. Once cas exposes the inv-contraction pair on tensor_inv, the implementation is:

1. Drop the rank-4 throw in include/numsim_codegen/code_emit/tensor_code_emit.h operator()(cas::tensor_inv const &)
2. Add a branch that reads v.inv_contraction_pair() (or whatever the accessor lands as) and emits tmech::inv<tmech::sequence<...>, tmech::sequence<...>>(...) with the pair plumbed into the template args
3. Add a test for the rank-4 emit shape

No work to do until upstream lands. The source comment + throw message in #42 now point at numsim-cas#248 so anyone hitting the throw has the right pointer.