Quantify the effect of timeframe-ladder length

Determine how much of the cross-panel variation in the descriptive and forecasting relationships of the Kuramoto coherence measure is attributable to using three-rung versus four-rung timeframe ladders rather than to genuine asset-class differences.

Background

Three of the eight data panels use three-rung timeframe ladders because of provider-side intraday-history limits, whereas the other five use four-rung ladders. Because the order parameter has different discretization properties for different numbers of timeframes, ladder length may affect cross-panel comparisons.

The paper identifies this as unresolved and does not quantify the extent to which ladder length, rather than asset-class characteristics, explains variation in the reported descriptive and forecast results.

References

A related, structural limitation is that three of the eight panels (yfinance-sourced, limited by provider-side intraday history caps) use a 3-rung timeframe ladder against the other five panels' 4-rung ladder; Section~\ref{sec:results-discretization} explains why this affects the order parameter's discretization, but we have not separately quantified how much of the cross-panel variation in Tables~\ref{tab:descriptive}--\ref{tab:forecast} is attributable to ladder length versus genuine asset-class differences, a natural target for follow-up work once longer intraday history becomes available for those instruments.

— Synchronization Reveals Market Structure That Classical Randomness Tests Cannot Detect  (2610.11028 - Le, 8 Oct 2026) in Section 4, Discussion, paragraph 3