Automated summary
Validates topological data analysis results by checking persistence diagrams, total persistence scaling, null model consistency, and cross-era replication against known benchmarks.
Strengths
- Comprehensive checklist covering diagram sanity, scaling, null models, and Wasserstein metrics.
- Provides known benchmarks from published studies for reproducibility.
- Catches subtle inconsistencies in TDA pipelines.
Limitations
- Requires pre-computed TDA results in specific JSON format.
- Only validates against provided benchmarks; not a full TDA framework.
- Assumes fixed parameters (e.g., landmark count L) from the referenced study.
Use after running a TDA pipeline to automatically verify that outputs meet expected mathematical and statistical properties.
Do not use for exploratory TDA without reference benchmarks, or when results are from non-standard methods not covered by the validation rules.
Security analysis
SafeThe skill is a static validation checklist with no executable commands, destructive actions, or data exfiltration instructions. It poses no security risk.
No concerns found
How this analysis is madeExamples
/validate-topology trajectory_tda results/trajectory_tda_integration/04_nulls_wasserstein.jsonRun /validate-topology on my persistence results to verify that birth values are non-negative and death values exceed birth.Use /validate-topology to compare my BHPS order-shuffle H0 p-value against the known benchmark from the P01 study./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 |
From the file to a first result
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