Minor-symmetric consistent tangents (#35 follow-up)

[petlenz]

Minor-symmetric consistent tangents (#35 follow-up)

Resolves the one open MINOR from the PR #80 review (math finding Q3): the emitted consistent tangent lacked minor symmetry.

Problem

∂(2μ ε)/∂ε emitted the non-symmetrized rank-4 identity δ_ik δ_jl (tmech::otimesu(eye,eye)). The contraction C:ε is correct for symmetric ε, but the tangent object lacks minor symmetry C_ijkl = C_ijlk that a Voigt/Mandel FE assembler expects. Root cause: codegen tensor inputs carried no tensor_space, so cas::diff fell back to the bare identity instead of P_sym.

Fix

add_tensor_input now sets a symmetric tensor_space ({Symmetric, AnyTraceTag}) for symmetric-role rank-2 inputs (e.g. roles::Strain). cas::diff then returns the symmetric rank-4 identity, so the tangent emits minor-symmetric:

// dσ/dε for σ = 2μ ε, eps declared roles::Strain:
auto t2 = 0.5 * (tmech::otimesu(tmech::eye<double,3,2>(), tmech::eye<double,3,2>())
                 + tmech::otimesl(tmech::eye<double,3,2>(), tmech::eye<double,3,2>()));
auto t3 = t0 * t2;   // 2μ · ½(I⊗ᵘI + I⊗ˡI) = 2μ I⁴ˢ

Why it's safe / narrow

• Opt-in via the role. Plain add_tensor_input (roles::Other) stays unconstrained — backward compatible. (New test PlainInputTangentStaysNonSymmetrized locks this.)
• No CSE/hash ripple. The tensor space is metadata, not part of the leaf hash_value(), so non-derivative outputs and temp numbering are byte-identical. Confirmed: of 209 prior tests, exactly one changed — the minor-symmetry lock test I wrote in PR Phase 3b-1: AlgorithmicTangentPass scaffolding (#35) #80 round 2 specifically to catch this transition. Every other recipe (MOOSE/Integration/Newton using roles::Strain) emits identically.
• Aligns with TensorSpaceConsistencyPass, which already cross-checks Role.is_symmetric against the tensor space.

Tests

Full suite 210/210 (the round-2 ElasticTangentEmitsNonSymmetrizedIdentityForNow lock is superseded by ElasticTangentIsMinorSymmetric; added PlainInputTangentStaysNonSymmetrized).

🤖 Generated with Claude Code

[petlenz]

Critical review — 2 lenses (correctness/blast-radius + CAS/continuum-mechanics semantics)

Both lenses came back clean — no CRITICAL/MAJOR findings. The three load-bearing claims (space propagates, zero hash/CSE ripple, exactly one prior test changed) were each verified by static tracing and an empirical revert-probe.

Correctness / blast-radius — all claims confirmed

• Propagation is real and load-bearing. expression_holder::data() mutates the shared leaf node (holder is a shared_ptr), so the stored m_tensor_symbols copy and the returned handle share the space. Decisively, cas::diff's leaf rule reads the space from its argument handle (m_arg), not from the leaf inside the forward expression — so the CAS "2-arg ctors drop space" / move-ctor caveats are irrelevant to this path. Empirically proven: disabling only the set_space block makes ElasticTangentIsMinorSymmetric fail (emission reverts to bare otimesu). Not a no-op passing for the wrong reason.
• Hash claim confirmed. symbol_base::update_hash_value() combines only m_name; m_tensor_space is never hashed → no CSE/leaf-match shift.
• Blast radius confirmed. With the change, exactly one prior test flips; the other 201 pass unchanged. MOOSE/standalone roles::Strain emit tests are unaffected (stress is not a derivative).
• Rank guard correct. rank==2 aligns with the CAS leaf handler, which only synthesizes a projector for a rank-2 argument; rank-4 symmetric inputs are correctly skipped.

CAS / continuum-mechanics semantics — correct

• AnyTraceTag is the only correct trace tag (the crux). Strain has a non-zero volumetric part, so it must carry no trace constraint. DeviatoricTag/VolumetricTag would map ∂ε/∂ε to P_dev/P_vol and silently project the volumetric (bulk/pressure) response out of the tangent — physically wrong. Verified against classify_space + the diff leaf rule.
• P_sym = the correct minor-symmetric identity ½(δ_ik δ_jl + δ_il δ_jk), lowered to 0.5*(otimesu+otimesl). ∂(2με)/∂ε = 2μ·P_sym is exact.
• The forward stress 2με is unchanged (space is hash-invariant metadata; it propagates as a tag through 2μ·ε only to enable the diff, not to rewrite the value).

Two MINOR notes (both independently raised; addressed in 70bd111)

• The guard is keyed on is_symmetric && rank==2, so it also covers a (rare) roles::Stress input — which is correct (stress is symmetric). Documented the breadth + intent.
• Documented the AnyTraceTag rationale and that propagation rides on the diff-argument handle (so a future reader isn't misled by the CAS "drops space on copy" caveat). Noted the σ=2με tangent is in fact major-symmetric too (the PR claimed only the load-bearing minor symmetry).

Verification

Full suite 210/210 after the doc clarifications. No code-behavior change in this round — comments only.

Verdict

Semantically and mechanically correct; claims accurate and independently verified. Ready to merge.