/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

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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 |