Our review

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.

When to use it

Use after running a TDA pipeline to automatically verify that outputs meet expected mathematical and statistical properties.

When not to use it

Do not use for exploratory TDA without reference benchmarks, or when results are from non-standard methods not covered by the validation rules.

Examples

Validate a TDA result file

/validate-topology trajectory_tda results/trajectory_tda_integration/04_nulls_wasserstein.json

Check persistence diagram sanity

Run /validate-topology on my persistence results to verify that birth values are non-negative and death values exceed birth.

Benchmark comparison

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 |

Validate Topological Results

Recommended for