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 = A_imp(t) + A_cut, where A_cut is invariant under all local impedance update rules at fixed topology• Negative scaling — τ_conv ~ N−0.91 (R² = 0.95, N = 16–256): larger networks converge faster• Fractal control — D_K = 0.49γ + 1.00: soft cutoff tunes K-space fractal dimension• Cost ceiling — A_cut 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) = (Z_brain(f) − Z_body(f)) / (Z_brain(f) + Z_body(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