# content
A7-HBM–ΩΦ: An Integrated Seven-Band

Neurogeometric Model of Cognition Combining

Computational Simulations, Neurogeometry, and Experimental Frameworks

Abstract

The Al-Olofi Seven-Band Hierarchical Brain Model (A7-HBM–ΩΦ) presents an integrative neurogeometric and computational architecture describing multiscale brain oscillations through seven hierarchically organized frequency bands: δ (0.5–4 Hz), θ (4–8 Hz), α (8–12 Hz), σ (12–16 Hz), β (13–30 Hz), γ (30–80 Hz), and Ω (80–200 Hz).

The framework applies nonlinear coupled-oscillator dynamics, phase–amplitude coupling (PAC), and golden-ratio scaling (Φ ≈ 1.618) to define optimal cross-band relations. Using fourth-order Runge–Kutta simulations with Lyapunov stability analysis, the system self-organizes into Φ-consistent clusters with robust PAC coherence and globally negative Lyapunov exponents, confirming dynamic stability.

Each band corresponds to a specific geometric primitive, neural substrate, and cognitive role, forming a neurogeometric pyramid from interoceptive integration (δ) to metacognitive resonance (Ω). A proposed EEG/MEG experimental protocol tests predicted σ–Ω and β–γ PAC interactions.

The A7-HBM–ΩΦ thus unites mathematics, neural dynamics, and cognition within a single testable model, with implications for neuro-inspired AI, brain–computer interfaces, neuromodulation, and clinical diagnostics.

DOI: doi.org/10.21203/rs.3.rs-806...

# source.content
A7-HBM–ΩΦ: An Integrated Seven-Band

Neurogeometric Model of Cognition Combining

Computational Simulations, Neurogeometry, and Experimental Frameworks







**Abstract**

The Al-Olofi Seven-Band Hierarchical Brain Model (A7-HBM–ΩΦ) presents an integrative neurogeometric and computational architecture describing multiscale brain oscillations through seven hierarchically organized frequency bands: δ (0.5–4 Hz), θ (4–8 Hz), α (8–12 Hz), σ (12–16 Hz), β (13–30 Hz), γ (30–80 Hz), and Ω (80–200 Hz).

The framework applies nonlinear coupled-oscillator dynamics, phase–amplitude coupling (PAC), and golden-ratio scaling (Φ ≈ 1.618) to define optimal cross-band relations. Using fourth-order Runge–Kutta simulations with Lyapunov stability analysis, the system self-organizes into Φ-consistent clusters with robust PAC coherence and globally negative Lyapunov exponents, confirming dynamic stability.

Each band corresponds to a specific geometric primitive, neural substrate, and cognitive role, forming a neurogeometric pyramid from interoceptive integration (δ) to metacognitive resonance (Ω). A proposed EEG/MEG experimental protocol tests predicted σ–Ω and β–γ PAC interactions.

The A7-HBM–ΩΦ thus unites mathematics, neural dynamics, and cognition within a single testable model, with implications for neuro-inspired AI, brain–computer interfaces, neuromodulation, and clinical diagnostics.





DOI: [doi.org/10.21203/rs.3.rs-806...](https://doi.org/10.21203/rs.3.rs-8060417/v1)



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