Γ-Net (Gamma-Net) v3.2.0: A Physics-Driven Electronic Lifeform Modelling Cognition, Emotion, Pain, Sleep, Language Emergence, and Psychopathology Through Impedance-Mismatch Equations Derived from Coaxial Transmission Line Theory

Γ-Net (Gamma-Net) v3.2.0 — A physics-driven electronic lifeform that models cognition, emotion, pain, sleep, language emergence, and psychopathology through impedance-mismatch equations derived from coaxial transmission line theory. This record contains four companion papers (Papers I–IV) of the Γ-Net series: Paper I — Irreducible Dimensional Cost in Heterogeneous Impedance Networks: Scaling Laws, Fractal Topology, and the Minimum Reflection Principle Proves the Dimensional Cost Irreducibility Theorem: A = A_imp(t) + A_cut, where A_cut is invariant under all local impedance update rules at fixed topology. Key results: negative convergence scaling τ_conv ~ N-0.91 (R²=0.95, N=16–256); soft-cutoff fractal control D_K = 0.49γ + 1.00 reproducing cortical fractal dimensions D ∈ [1.3, 1.5]; spontaneous relay-node hierarchy emergence as thermodynamic necessity. Paper II — Twin Impedance Networks: A Unified Neural–Vascular Organ Model from the Minimum Reflection Action Derives Murray’s Law of optimal vessel branching (r_p³ = Σrd,i³) as the exact minimum of the vascular action A_v = ΣQ²|Z| + βV, with 100% numerical agreement for n=2,3,4 branches. Introduces the dual-network organ health model H = T_n · T_v = (1−ρ²_n)(1−ρ²_v). Fractional flow reserve (FFR) is identified as exactly the vascular transmission ratio T_v. 10/10 clinical calibrations passed (FAME, NASCET, UKPDS); 12/12 dual-network RCT validations passed (STENO-2, ADVANCE, SPRINT-MIND, UKPDS-80, etc.); 100/100 randomised stability runs converged. Paper III — The Cost of Life: Impedance Debt as the Thermodynamic Origin of Sleep and Brain Evolution Proposes sleep as homeostatic discharge of impedance debt ΔZ = ∫ T_wake ρ²(t)P_int dt. Three independent evidence lines: (i) cnidarian sleep without a brain (Cassiopea/Nematostella DNA-damage studies); (ii) convergent evolution of brains ≥9 times as thermodynamic centralised impedance-debt managers; (iii) human embryogenesis recapitulating the thermodynamic causal chain (heart → neural tube → brain vesicles). Dual-network decomposition ΔZ = ΔZ_n + ΔZ_v; tidal-zone as quarter-wave impedance matching (log gradient reduces action to 6.2% of direct jump); ischemia verified at 4.77× mismatch ratio. 9/9 computational experiments passed. Paper IV — The Lifecycle Equation: Cognition, Emotion, and Aging as Three-Force Competition on an Impedance Network Derives the Lifecycle Equation dρ²/dt = -α(t)ρ² + β(t)ε_env(t) + γ(t)D(t), a first-order ODE in which learning (MRP descent), novelty injection, and Coffin–Manson fatigue compete to produce the bathtub curve of cognitive performance from birth to senescence. Emotion, reward (dopamine), stress (cortisol), curiosity, and boredom are derived as temporal readouts of ρ² dynamics at different time scales. Atherosclerosis is derived as vascular Coffin–Manson fatigue; the vascular–neural aging cascade explains why cardiovascular disease precedes neurodegeneration. 9/9 computational experiments passed including the Yerkes–Dodson inverted-U curve and full lifecycle simulation. Core Equation (all four papers derive from a single variational principle): A = ∫ Σ_ij ρ²_ij dt → min, where ρ = (Z_L − Z_0)/(Z_L + Z_0) v3.2.0 Release (code): https://github.com/cyhuang76/alice-gamma-net License: Code under AGPL-3.0-or-later · Papers under CC BY-NC-SA 4.0