Improve test verification for math crates

[marvin-hansen]

Improve tests for:

• [ ]: deep_causality_algebra (deep_causality_unified_math/deep_causality_algebra)
• [ ]: deep_causality_calculus (deep_causality_unified_math/deep_causality_calculus)
• [ ]: deep_causality_fft (deep_causality_unified_math/deep_causality_fft)
• [ ]: deep_causality_haft (deep_causality_unified_math/deep_causality_haft)
• [ ]: deep_causality_homology (deep_causality_unified_math/deep_causality_homology)
• [ ]: deep_causality_linear (deep_causality_unified_math/deep_causality_linear)
• [ ]: deep_causality_metric (deep_causality_unified_math/deep_causality_metric)
• [ ]: deep_causality_multivector (deep_causality_unified_math/deep_causality_multivector)
• [ ]: deep_causality_num (deep_causality_unified_math/deep_causality_num)
• [ ]: deep_causality_num_complex (deep_causality_unified_math/deep_causality_num_complex)
• [ ]: deep_causality_num_dual (deep_causality_unified_math/deep_causality_num_dual)
• [ ]: deep_causality_num_rational (deep_causality_unified_math/deep_causality_num_rational)
• [ ]: deep_causality_rand (deep_causality_unified_math/deep_causality_rand)
• [ ]: deep_causality_stats (deep_causality_unified_math/deep_causality_stats)
• [ ]: deep_causality_tensor (deep_causality_unified_math/deep_causality_tensor)
• [ ]: deep_causality_topology (deep_causality_unified_math/deep_causality_topology)
• [ ]: deep_causality_uncertain (deep_causality_unified_math/deep_causality_uncertain)

[marvin-hansen]

For all math crates

Class	Raw count	Share	Scanner meaning
single-input	4,792	70.2%	No loop or table was recognized.
cherry-picked	1,222	17.9%	One input, literal expected value, and no recognized provenance.
circular	192	2.8%	Arithmetic used to construct the expected value.
tautology	73	1.1%	Only a weak predicate such as is_ok, is_some, or is_finite was recognized.
no-assertion	46	0.7%	No assertion was recognized in the function body.

Recommended order, prioritizing confirmed defects over raw scanner percentages:

1. deep_causality_topology

   • Known Hodge-star implementation failure.
   • Confirmed assertion-free test.
   • Multiple gauge, point-cloud, and gradient-flow tests that do not inspect results.
   • Largest suite and broad downstream impact.
   • Treat the Hodge-star repair as a separate architectural change from test cleanup.

2. deep_causality_uncertain

   • Confirmed ineffective sampling, seed-reset, and conditional-branch tests.
   • 92.9% single-input and 24.1% cherry-picked.
   • Small enough for a focused, high-value repair.

3. deep_causality_num_complex

   • Confirmed circular quaternion transcendental tests.
   • Highest substantial circular count: 66 candidates, 12.4%.
   • Replace copied formulas with independent reference values and algebraic identities.

4. deep_causality_tensor

   • Confirmed finite-only Gaussian-density assertions.
   • Large numerical surface with 367 single-input and 58 cherry-picked candidates.
   • Prioritize statistical extensions and decomposition/indexing kernels.

5. deep_causality_num_dual

   • Highest cherry-picked rate: 61.1%.
   • Only 90 explicit tests, making it a relatively quick mutation-testing target.

6. deep_causality_calculus

   • Small suite with high raw rates: 93.3% single-input and 43.3% cherry-picked.
   • Preserve independent analytic-derivative comparisons; investigate with targeted mutations.

7. deep_causality_linear

   • Large absolute backlog: 203 cherry-picked and 17 circular candidates.
   • Many flagged tests are actually independent exact or cross-algorithm controls, so mutation testing must drive repairs.

8. deep_causality_multivector

   • 104 cherry-picked and 17 circular candidates.
   • Focus on non-symmetric inputs, signs, grade selection, and cross-product/geometric-product identities.

9. deep_causality_num

   • Largest absolute candidate count: 255 cherry-picked tests.
   • Lower urgency because many are legitimate differential checks against standard-library operations.
   • Audit numeric kernels before trait-delegation tests.

10. deep_causality_algebra

    • Fix the vacuous f64::NAN test immediately.
    • The 22 no-assertion flags are otherwise helper, panic, or compile-time checks.

11. deep_causality_rand

    • Modest raw signal. Prioritize distribution boundaries and deterministic seeded behavior.

12. deep_causality_metric

13. deep_causality_haft

14. deep_causality_num_rational

15. deep_causality_homology

    • Mostly single-input or low-volume candidates without confirmed high-severity examples.

16. deep_causality_stats

    • Strong table/helper-driven suite; its no-assertion flags were false positives.

17. deep_causality_fft

    • Best scanner result: no tautology, circular, cherry-picked, or assertion-free candidates.

In practical batches: topology → uncertain/num_complex/tensor → num_dual/calculus → linear/multivector/num → remaining crates. Mutation survivors should determine the order within each batch.