EEG-Based Estimation of Cortical Field Observables in Pediatric ADHD: Coherence Length ξ and Effective Control Parameter λ_eff as Robust Cross-Modal Discriminators, with a Methodological Note on C1 Estimation

This paper applies the Cortical Informational Field Theory (CIFT) Ginzburg-Landau framework to a publicly available 19-channel EEG dataset (IEEE DataPort; Mohammadi et al.; 61 ADHD + 60 neurotypical controls; ages 7–12 years; DSM-IV confirmed; 128 Hz) to estimate three cortical field observables: C1 = |⟨Φ⟩| (global integration), temporal coherence length ξ, and effective control parameter λ_eff = −D₀/ξ². Key findings (FDR-corrected, Benjamini-Hochberg): - ξ: ADHD 0.074 ± 0.022s vs Control 0.105 ± 0.028s · d=1.220 · p_FDR<0.001 ★ — largest effect size - λ_eff: ADHD −473 ± 515 vs Control −229 ± 191 · d=1.108 · p_FDR<0.001 ★ - C2 (Shannon entropy): emerges as significant after bandpass filtering (d=0.388 · p_FDR=0.049 ★) - C1: significant in raw signals (d=0.764 · p_FDR=0.0004) but NOT robust to bandpass filtering (d=0.172 · p=0.352 ns) — indicating that raw-signal C1 reflects low-frequency amplitude artifacts rather than genuine global field integration. Valid C1 estimation requires source-level EEG reconstruction or MEG. A systematic sensitivity analysis compares raw vs bandpass-filtered (1–40 Hz) signals for all observables. ξ and λ_eff survive filtering with large effect sizes; C1 does not.