Add comprehensive tensor space-annotation preservation matrix

[petlenz]

Summary

PR #108 added three lock-in tests for Skew annotation preservation through negation, scalar-mul, and tensor_mul-as-child. The full preservation matrix is much wider — five space tags × every tensor composition node. A property-style test that walks the matrix would lock in the contract end-to-end and catch the platform-specific loss tracked by #93 if it ever recurs.

Scope

Space tags (perm × trace combinations):

• Skew × AnyTraceTag
• Symmetric × AnyTraceTag
• Symmetric × VolumetricTag
• Symmetric × DeviatoricTag
• Symmetric × HarmonicTag
• No annotation (control)

Composition nodes to walk (tensor → tensor):

• tensor_negative (unary)
• basis_change_imp / trans (unary)
• tensor_inv (unary)
• tensor_pow (binary tensor × scalar)
• tensor_scalar_mul (binary scalar × tensor)
• tensor_add (n-ary)
• tensor_mul (n-ary)
• inner_product_wrapper (binary tensor × tensor)
• outer_product_wrapper (binary tensor × tensor)
• tensor_to_scalar_with_tensor_mul (cross-domain)
• tensor_projector ⊕ inner_product (the skew() / sym() / vol() / dev() projection paths)

For each (space, node) pair, the test should check:

1. The annotation that should be preserved (e.g. Symmetric through inv → Symmetric).
2. The annotation that should be downgraded (e.g. Deviatoric through inv → Symmetric, since tr(D^{-1}) ≠ 0).
3. The annotation that should be dropped (e.g. Skew through pow with odd exponent → can't determine, drop).
4. The annotation that should be derived (e.g. trans(A) − A → Skew even if A had no annotation).

Why a single matrix vs many individual tests

• Each pair could be its own gtest, but the matrix is ~60 cells. Parameterised (TEST_P with a value-parameterised fixture) is far less repetitive.
• A property-style walker (loop in code, accumulate failures with context) is more maintainable than 60 hand-written tests.
• The matrix doubles as documentation of the annotation contract.

What this catches

• The platform-specific Skew loss tracked by Investigate platform-dependent Skew space annotation loss inside tensor_mul #93 (if it recurs).
• Future regressions in any composition path that affects any space tag.
• Asymmetries in the propagation rules (e.g. if tensor_negative preserves Symmetric but basis_change_imp doesn't).

Acceptance criteria

• Test fixture or helper that takes a (space_annotation, composition_callable) pair and runs it.
• Coverage of all pairs in the scope above (or explicit "deliberately unsupported" markers for cells where the algebra doesn't define the propagation).
• Documented expected-behavior table either in the audit doc or as a comment block in the test file — the test enforces the table.
• Failure messages include the (space, node) coordinates so a regression points at the specific cell that broke.

Not blocking

The current three tests in PR #108 catch the most common cases. This is the comprehensive next step that would replace those three.

References

• PR Investigate #93: lock in Skew preservation (cannot reproduce original loss) #108 — current narrow coverage.
• Investigate platform-dependent Skew space annotation loss inside tensor_mul #93 — platform-specific Skew loss the comprehensive matrix would catch.
• include/numsim_cas/tensor/skew_classification.h — current structural fallback.
• include/numsim_cas/tensor/functions/tensor_inv.h — example of preservation/downgrade rules.
• tests/TensorSpacePropagationTest.h — existing partial coverage that this matrix would consolidate.

[petlenz]

Triage (2026-05-16): Open and tracked. Status summary across recent issues:

• Closed via PR chain when it merges (tagged Closes #N in the PR body):

  • Fuzzy tensor diff seeds skipped due to underlying CAS bugs #89 (fuzz seeds) → PR Remove flaky tensor diff seed skip list by fixing underlying bugs #90.
  • n_ary_sub_dispatch::dispatch(add, add) has unguarded coeff add and uses + instead of - #91 (n_ary_sub_dispatch bug) → PR Audit simplifier dispatchers and fix n_ary_sub_dispatch(add, add) bug #98.
  • Add deterministic regression for merge_or_insert transitive collision loop #92 (merge_or_insert regression) → PR Add merge_or_insert iteration-counter instrumentation and lock-in tests #106.
  • Add tensor pow simplifier (missing entire family) #96 (tensor pow simplifier) → PR Add tensor pow simplifications for pow(I, n) and pow(inv(A), n) #105.
  • Add n_ary_mul_mul_dispatch (LHS=mul) sibling for the mul dispatcher family #97 (n_ary_mul_mul_dispatch) → PR Correct #97 audit claim; lock in existing mul × mul merge behavior #103.
  • Centralize trivial-result collapse pattern from simplifier dispatchers #99 (collapse pattern centralisation) → PR Centralize trivial-result collapse as finalize_add<Traits> helper #100.

• Partial work in flight (issue stays open):

  • Investigate platform-dependent Skew space annotation loss inside tensor_mul #93 (Skew space loss) — partial work in PR Investigate #93: lock in Skew preservation (cannot reproduce original loss) #108; cannot reproduce on current platform; structural detection in skew_classification.h is the defensive fallback.
  • tensor_evaluator rebuilds t2s_eval per tensor_to_scalar_with_tensor_mul visit #94 (t2s_eval rebuild) — partial work in PR Lock in correctness of t2s_eval rebuild (partial work on #94) #107; full optimization deferred per Roadmap: execute t2s_eval optimization (post-bench) #112 roadmap.
  • Unify simplifier dispatchers across add/sub/mul/pow and across domains #95 (simplifier-unification umbrella) — audit landed in PR Audit simplifier dispatchers and fix n_ary_sub_dispatch(add, add) bug #98; consolidation follow-ups are Consolidate scalar and t2s mul × mul merge into a generic n_ary_mul_mul_dispatch #104, Unify tensor pow simplifier with the dispatcher pattern used by scalar/t2s #109, others.

• Filed during review but not yet implemented:

  • Audit *DispatchSmoke / *ConstructionSmoke tests for missing value assertions #101 (smoke-test audit) — sweep tracked by Execute smoke-test audit sweep per #101 #113.
  • constant_sub_dispatch::dispatch(add) has same unguarded-coeff + push_back bug pattern #102 (constant_sub_dispatch bug) — fix shape documented in the issue body.
  • Consolidate scalar and t2s mul × mul merge into a generic n_ary_mul_mul_dispatch #104 (mul × mul consolidation) — design space documented.
  • Unify tensor pow simplifier with the dispatcher pattern used by scalar/t2s #109 (tensor pow dispatcher) — design space documented.
  • Add microbenchmark for tensor_evaluator (prerequisite for #94 optimization) #110 (microbenchmark) — prerequisite for Roadmap: execute t2s_eval optimization (post-bench) #112.
  • Add comprehensive tensor space-annotation preservation matrix #111 (annotation preservation matrix) — design space documented.

No code change planned from this triage; each item has its own tracking ticket and an implementation path.