Our review

Checks topological data analysis outputs against benchmark expectations and internal consistency rules, including persistence diagrams, null models, and Wasserstein distances.

Strengths

Covers multiple validation layers (diagrams, total persistence, null models, Wasserstein, cross-era replication).
Includes concrete expected benchmarks from known studies, making deviations easy to spot.
Provides a clear, structured checklist with quantitative criteria.
Checks statistical behavior of null models, an often overlooked aspect.

Limitations

Only validates against a specific trajectory_tda / P01 benchmark set.
Requires result files in the expected format.
Does not automatically fix detected issues.

When to use it

Use after running TDA computations to confirm results are mathematically and statistically sound before reporting.

When not to use it

Do not use for exploratory TDA pipelines that do not follow the trajectory_tda benchmark structure, or when only visual inspection is needed.

Examples

Validate trajectory TDA Wasserstein results

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

Validate USoc TDA summary

/validate-topology USoc results/usoc_tda_summary.json

Check BHPS replication results

/validate-topology BHPS results/bhps_tda_final.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 |

Validate Topological Results

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