OFN II Dynamics, Reading Paths, and new σ‑Parameter of Consciousness

Abstract

This is the **revised and significantly expanded edition** of Part II of the Ontological Fundamental Network (OFN) series. The OFN framework proposes that reality is a static 4‑dimensional spinor network Ω, with spacetime, matter, and consciousness emerging from an iterative *reading process* along directed paths. ### What's New in This Version This revision addresses all critical feedback from the previous preprint: | Aspect | Previous Version | This Version | |--------|------------------|--------------| | **σ‑spectrum** | Phenomenological π/8, π/6, π/4, π/3 | **Rigorously derived** σ_crit = π/4 + φ‑scaling | | **Geometric calibration** | σ = 0 as baseline | **π/4 as absolute zero** of consciousness | | **Unit of coherence** | Not defined | **φ⁰ = 1** emerges from Φ_B = 2π | | **Localization measure** | Asserted | **Proved unique** (Table 1, Appendix D.5) | | **Normalization** | Implicit | **Explicit protocol** (Section 3.1.1) | | **Reproducibility** | None | **Full code + tests + Docker** (GitHub) | | **Figures** | Descriptions only | **8 publication‑ready figures** | ### Core Results 1. **Dynamics as Reading** Time emerges from sequential activation Φ(v,λ) along a reading path γ. 2. **The σ‑Parameter** A unique measure of activation localization: \[ \sigma(\lambda) = \left[\sum_{v\in\Gamma(\lambda)} |\Phi(v,\lambda)|^4\right]^{-1/4} \] 3. **Rigorous Critical Value** Three independent derivations yield σ_crit = π/4 (kink, Berry phase, cycle degeneracy). 4. **Geometric Calibration** - σ = π/4: **threshold of consciousness** (Φ_B = π) - σ = π/4 + 1 = π/4 + φ⁰: **full coherence / insight** (Φ_B = 2π) - φ‑scaling: φ² (dreaming), φ¹ (wakefulness), φ⁻¹ (psychosis threshold) 5. **Continuum Limit** Discrete dynamics → Soloviev equation, linking OFN to established consciousness models. 6. **σ‑Transitions** Mapped to avoided crossings in the non‑Hermitian spectrum of H(λ). 7. **Cognitive Interpretation** Complete mapping: vertices → qualia, edges → associations, reading path → stream of consciousness. 8. **Numerical Simulations** Sleep‑wake cycles, insight events, psychosis, meditation reproduced in silico. 9. **Philosophical Synthesis** Unifies eternalism, relationalism, and the hard problem via first‑person reading.