Our review

Checks the mathematical correctness of topological data analysis results against known benchmarks and internal consistency requirements.

Strengths

Enforces a rigorous checklist for persistence diagram sanity.
Compares results against known P01 benchmarks to catch errors.
Verifies null model consistency and Wasserstein distance validity.

Limitations

Specific to the trajectory_tda / P01 pipeline and its benchmarks.
Flags issues but does not automatically fix them.
Requires trusted reference values for meaningful checks.

When to use it

When you need to validate TDA results from trajectory analysis before reporting or relying on them.

When not to use it

When validating non-topological analyses or when domain-specific benchmarks are unavailable.

Examples

Validate trajectory TDA results

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

Check persistence diagram sanity

Run topology validation on the persistence diagram file for the USoc dataset.

Cross-era replication check

Validate topology results comparing BHPS and USoc eras against the known benchmarks.

/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 |

Topology Validation

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