Our review
Checks the mathematical correctness of TDA results against known benchmarks and internal consistency checks.
Strengths
- Comprehensive validation checklist covering persistence diagrams, total persistence, null models, Wasserstein distances, and cross-era replication.
- Includes known benchmarks for direct comparison with established results from specific studies.
- Automates complex statistical tests and consistency checks that would be tedious to perform manually.
Limitations
- Requires deep TDA knowledge to interpret results correctly.
- Benchmarks are specific to certain datasets (e.g., trajectory_tda, BHPS, USoc) and may not generalize.
- Does not automatically fix errors, only detects them.
When rigorously validating TDA results against known benchmarks and consistency criteria after running analysis pipelines.
When you need a general-purpose validation tool without domain-specific benchmarks, or when results lack the structure required for comparison.
Security analysis
SafeThe skill is a static validation checklist and benchmark document. It contains no executable code, no tool invocations, and no instructions that could cause harm. It is purely informational.
No concerns found
Examples
/validate-topology trajectory_tda results/trajectory_tda_integration/04_nulls_wasserstein.json/validate-topology trajectory_tda results/trajectory_tda_h0_analysis.json/validate-topology — Validate Topological Results
Check mathematical correctness of TDA results against known benchmarks and internal consistency checks.
Usage
/validate-topology [domain] [result-file]
Example: /validate-topology trajectory_tda results/trajectory_tda_integration/04_nulls_wasserstein.json
Validation checklist
Persistence diagram sanity
- [ ] All birth values ≥ 0
- [ ] All death values > birth (finite features)
- [ ] H₀ has exactly one infinite feature (the final connected component)
- [ ] Feature counts are plausible for landmark count L: H₀ has L-1 finite features; H₁ count varies
Total persistence scaling
- [ ] Total persistence scales approximately linearly with L (±15% across a 2× range)
- [ ] Maximum persistence is stable across L values (should vary < 5%)
Null model consistency
- [ ] Label/cohort shuffle p-values are non-significant (negative control)
- [ ] Markov-2 null generates more total persistence than Markov-1 (higher-order Markov → more structured surrogates)
- [ ] Null distribution standard deviations are plausible (not near-zero, not huge)
Wasserstein-specific
- [ ] W(obs↔null) and W(null↔null) are of comparable magnitude (within ~3×)
- [ ] p-value = proportion of null-null distances ≥ mean(obs-null distances)
- [ ] 500 null-null pairs is sufficient for stable p-value at 3 decimal places
Cross-era replication
- [ ] BHPS-era order-shuffle H₀ p-value ≈ USoc order-shuffle direction (both significant or both not)
- [ ] BHPS-era Markov-1 direction ≈ USoc (both non-significant under total persistence)
Known benchmarks (trajectory_tda / P01)
| Test | Expected | Source | |---|---|---| | USoc order-shuffle H₀ (total persistence, L=5000) | p < 0.005 | P01 v5 Table 2 | | USoc Markov-1 H₀ (total persistence) | p = 1.000 | P01 v5 Table 2 | | USoc Markov-1 H₀ (Wasserstein, L=2000) | p = 0.002 | P01 v5 Table 2b | | BHPS order-shuffle H₀ | p = 0.000 | P01 v5 §4.7 | | BHPS Markov-1 H₀ | p = 1.000 | P01 v5 §4.7 | | GMM bootstrap ARI | 0.646 ± 0.086 | P01 v5 §3.5 |
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