Cross-Domain Coherence Analysis

We extended the DPCC framework to a multiscale setting by integrating electroencephalographic (EEG) data with geomagnetic activity indices (Kp) obtained from NOAA.

Signals from both domains were aligned in time and projected into a shared relational space using mutual information. Structural invariants were computed across all variable combinations, enabling the detection of coherence breakdowns both within and across domains.

Results

Comparison between EEG-only and multiscale DPCC signals (Figure 1) reveals systematic differences:

• The multiscale configuration exhibits higher variability in $D(t)$, indicating sensitivity to cross-domain interactions.
• The difference signal (Figure 2) highlights periods where geomagnetic contribution alters the structural coherence landscape.

Exception detection (Figure 3) shows that:

• Multiscale DPCC identifies additional coherence breakdown events not present in EEG-only analysis.
• These events are temporally clustered, suggesting structured rather than random interference.

Interpretation

These results suggest that:

Incorporating geomagnetic data modifies the relational structure of EEG-derived invariants, producing detectable shifts in coherence dynamics.

However, no causal inference is claimed. The DPCC framework identifies:

• structural coupling signatures
• coherence breakdown synchronization

rather than direct physical influence.