Original verdict relied on IAAFT null calibration โ now prohibited by project policy. The finding needs to be re-derived from an approved null-calibration method before it can be used for decisions. Numbers below are preserved for the record.
Verdict: REPLICATED. The kyle_lambda_proxy non-linear dependence finding holds on BTCUSDT, ETHUSDT, and ADAUSDT โ IAAFT-validated REAL on all 6 (pair, symbol) combinations. The magnitude shrinks on smaller-cap symbols, but the signal stays decisively above its (also-shrinking) autocorrelation null. Not a BTC-specific artifact.
Hub trail: audit hub โ multi-symbol-robustness/
Why this test mattered
The Gate 3 calibration proved the BTC finding is "real, not noise". But maybe BTC is special โ maybe it has microstructure quirks that make this dependence appear. If we run the same test on Ethereum and Cardano (different liquidity, different traders, different market dynamics) and the finding doesn't replicate, then we've discovered something BTC-specific. If it does replicate, we've discovered something about how markets work, not just about BTC. This is the difference between a one-off curiosity and a generalizable result.
The 2 ORTHOGONAL-prior pairs tested against IAAFT null distributions on each symbol.
| Pair | Symbol | Observed ฮพ | Null max | Ratio | Verdict |
|---|---|---|---|---|---|
| kyle_lambda_proxy โ ofi | BTCUSDT | 0.715 | 0.065 | 11.0ร | REAL |
| kyle_lambda_proxy โ ofi | ETHUSDT | 0.297 | 0.041 | 7.3ร | REAL |
| kyle_lambda_proxy โ ofi | ADAUSDT | 0.232 | 0.023 | 10.3ร | REAL |
| kyle_lambda_proxy โ buy_volume | BTCUSDT | 0.652 | 0.069 | 9.5ร | REAL |
| kyle_lambda_proxy โ buy_volume | ETHUSDT | 0.164 | 0.026 | 6.3ร | REAL |
| kyle_lambda_proxy โ buy_volume | ADAUSDT | 0.079 | 0.018 | 4.3ร | REAL |
The "diminishing magnitude" pattern
You can see ฮพ shrinks as we go from BTC to ADA. But so does the null max. That's because BTC has more trades per bar (higher liquidity), which produces denser, less-noisy feature time series with stronger detectable structure. ADA at the same threshold has fewer trades per bar, so everything is noisier โ but the noise floor (null max) is also smaller. The ratio stays 4-11ร across the board, meaning we're seeing the same real phenomenon, just at different signal-to-noise ratios.
Pair-8 finding replicates on every tested symbol. The 3-axis verdict's "kyle is the most orthogonal feature" is substrate-generally correct under Pearson โ and substrate-generally incomplete under non-linear metrics.
Only 100 dbps tested. Coarser thresholds (250+) may flip the magnitude pattern.
Small ADA magnitudes might be statistically real but economically irrelevant. Orthogonality is upstream of utility.
Provenance: committed in f4235b13 ยท "multi-symbol robustness + Chatterjee broadening โ both validate"