EEG-Based Estimation of Cortical Field Observables in Pediatric ADHD: Coherence Length ξ and Effective Control Parameter λₑff 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 λₑff = −D₀/ξ². Key findings (FDR-corrected, Benjamini-Hochberg): - ξ: ADHD 0. 074 ± 0. 022s vs Control 0. 105 ± 0. 028s · d=1. 220 · pFDR<0. 001 ★ — largest effect size - λₑff: ADHD −473 ± 515 vs Control −229 ± 191 · d=1. 108 · pFDR<0. 001 ★ - C2 (Shannon entropy): emerges as significant after bandpass filtering (d=0. 388 · pFDR=0. 049 ★) - C1: significant in raw signals (d=0. 764 · pFDR=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 λₑff survive filtering with large effect sizes; C1 does not.