The Homeostasis Theorem: Unifying Mechanics, Gravity, and Cognition via Geometric Stiffness

Current physical theories treat stability as a consequence of conserved quantities (energy, mo-mentum) derived from continuous symmetries (Noether’s Theorem). We propose a complementaryprinciple: The Homeostasis Theorem. This theorem posits that physical existence is not merelya state but a dynamic process of error correction, maintained by the vacuum’s “Geometric Stiffness”(β). We define the “Associator Anomaly” as the fundamental error term of physical geometry anddemonstrate that systems across all scales—from mechanical pendulums to astrophysical black holesto cognitive neural networks—persist only by actively suppressing this anomaly. We present compu-tational verification of this theorem via three distinct simulation engines, establishing β ≈ 1.91 as theuniversal critical point for complexity.