Irreducible Dimensional Cost in Heterogeneous Impedance Networks: Scaling Laws, Fractal Topology, and the Minimum Reflection Principle

Γ-Net (Gamma-Net) v3. 0. 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. v3. 0. 0 Highlights: Irreducibility Theorem • Dimensional Cost Irreducibility Theorem — A = Aᵢmp (t) + Acut, where Acut is invariant under all local impedance update rules at fixed topology• Negative scaling — τconv ~ N^−0. 91 (R² = 0. 95, N = 16–256): larger networks converge faster• Fractal control — DK = 0. 49γ + 1. 00: soft cutoff tunes K-space fractal dimension• Cost ceiling — Acut saturates at ~1386, revealing a natural geometric cost ceiling• Paper I — "Irreducible Dimensional Cost in Heterogeneous Impedance Networks" submitted to Physical Review E Core Equation: Γ (f) = (Zbrain (f) − Zbody (f) ) / (Zbrain (f) + Zbody (f) ) Pain is protocol collapse (|Γ| → 1. 0), learning is impedance matching (|Γ| → 0), emotion is instantaneous reflection energy. Scale: • 200 source files · 89, 400+ lines of Python• 2, 734 unit tests · 100% passing• 49 experiments · 18 body organs · 42 brain modules• 10+ clinical pathology models + computational pharmacology License: Code under AGPL-3. 0-or-later · Papers under CC BY-NC-SA 4. 0