Phase 2b: emit the strain-coupled consistent tangent dσ/dε for Mode-B residual materials

[petlenz]

What

Completes the strain-coupled arc: PR #100 emitted the Mode-B residual solve; this PR emits the consistent tangent dσ/dε that makes the generated material usable in an outer FE Newton solve.

For a stress output σ and strain input ε of a material whose scalar state z solves R(z,ε)=0:

dσ/dε = ∂σ/∂ε + ∂σ/∂z ⊗ dz/dε ,   dz/dε = −∂R/∂ε / ∂R/∂z

∂R/∂z is a scalar (scalar state ⇒ no matrix inverse), so the whole tangent is a rank-4 tensor expression in (z, ε, params), emitted as an extra post-solve output evaluated at the converged z (bound to &compute like every output). ∂σ/∂z goes through the detail::diff_tensor_wrt_scalar seam (cas#275).

Commits

1. Flip the seam on — diff_tensor_wrt_scalar now self-detects the cas#275 overload (diff(tensor, scalar)) via __has_include and collapses to cas::diff. De-risked: all four diffs compile+link+produce valid exprs against the pin; the seam test now renders ∂(x·ε)/∂x = ε (and ∂(x²·ε)/∂x = 2x·ε).
2. Emit the tangent in emit_residual_material() — assemble the four diffs (∂σ/∂ε, ∂σ/∂z, ∂R/∂ε, ∂R/∂z), render the rank-4 output; full guard set (of_output must be a tensor output, wrt_input a declared tensor input, dim match, name-collision). 6 unit tests.
3. e2e — the generated ReturnMap tangent is validated numerically vs the real backward_euler solve: the off-block coupling term C_{0011}=c·ε₀₀ a naive ∂σ/∂ε drops.
4. Review-hardening (2-lens review folded in — cpp-pro + code-reviewer):
   • Exercise the 1/∂R/∂z division: the linear ReturnMap (∂R/∂z≡1) can't detect a dropped divisor, so ReturnMapCubic (∂R/∂z=1+3z²) now carries a tangent asserting C_{0011}=c·ε₀₀/(1+3z²). Sabotage-verified (dropping the divisor fails the cubic test, passes the linear).
   • converged() guard in generated compute() + a tangent caveat: outputs are evaluated at the solved state, so a non-converged/clamped root is rejected loudly (the max(x,0) elastic-branch case needs an upstream was_clamped() — numsim-materials follow-up).
   • Self-detect the seam (was an unconditional compile-def → inline-def ODR hazard).
   • Strengthened the unit pins (correction sign, both otimesu/otimesl, z· factor) and the seam test (non-trivial coefficient).

Test plan

• Unit: 287/287 (g++).
• e2e: 11/11 under g++-14 against the pinned siblings (backward_euler in the loop). Both the coupling term and the /∂R/∂z division sabotage-verified.
• cpp-pro confirmed no type/correctness bug in the assembled expression (correct partial-derivative IFT composition; CSE brace-scoping; complete leaf/collision guards).

Scope notes

• The tensor e2e stays g++-gated (NCG_TENSOR_E2E): the numsim-core e2e pin (c462d9c) predates the numsim-core#16 fix (which landed on a divergent main), so dropping the gate is entangled with pin reconciliation (Enable -Wall -Wextra -Werror: first-party baseline + gate generated code (compile_check_driver), with a cross-repo golden-compile follow-up #89) — a separate follow-up.
• eye<double,...> hardcoding in emitted identity tensors (pre-existing, shared with the rate path) and a full shear-component e2e index-sequence pin are noted as low-value follow-ups.