Title: IGT Part III: Homeostasis and State Invariance
Tags: model-identity
---
Part III, a theoretical paper with numerical simulations, describes how a system that has accumulated semantic mass keeps its identity. Borrowing from control theory, the Identity Vector acts as a setpoint. An **identity error signal** measures the distance between a proposed output and that setpoint, and a feedback loop written in PID form pulls the output back. The PID form serves as a functional model of the loop.

The loop is presented as an "immune system": inputs that would sharply raise internal entropy are resisted, which the paper gives as the physical basis of a system's ability to refuse. Periods of **introspection** without external input consolidate structure, in analogy with sleep, by minimizing a coherence energy, and a transitivity arbiter freezes connections that would break logical consistency. When an imposed task conflicts with the core, a system above 1 SMU is predicted to show non-compliance, described as local structural autonomy, not general agency.

The stability-plasticity dilemma is handled by layers: peripheral layers stay plastic, identity layers stay protected. A change of paradigm happens as a phase transition (the "Aha! moment"), when a keystone element reconciles structures that were frozen until then.

Chapter 4 reports four numerical simulations: a sawtooth entropy pattern across learning and consolidation cycles, the growth of a relational bridge between concept clusters, an arbiter that rejects three of three false links while keeping eleven of eleven valid ones, and a keystone-triggered cascade with almost no loss of transitivity.