MATE: Deterministic Emotional Architecture for AI Companions with Emergent Character and Measurable Inner Life

MATE (Mathematical Architecture for Thoughtful Entities) is a deterministic emotional kernel that gives any LLM persistent emotions, evolving character, and emergent psychological properties as a middleware layer. The kernel is a pure function transition(state, event) → new_state with zero LLM calls and full reproducibility.

v7 adds:

— Cognitive autopoietic loop (SPARK): beliefs modulate perception, perception generates evidence, evidence updates beliefs. Measured in production: 212 telemetry events over 4 days, beliefs growing from 5 seeds to 36 active constructs, bounded by sanity damping (zero runaways). Term introduced: "computational cognitive autopoiesis".

— Enactivist framing (Di Paolo 2005, Barandiaran et al. 2009): production data mapped to three criteria for agency. Normativity: 6 self-generated existential questions. Interactional asymmetry: 94% of proactive impulses self-blocked. Precarious autonomy: 17,365 thinking cycles without human input. Three honest limitations acknowledged.

— Updated production statistics: 41,500 lines of kernel code (73,000 total with 1,594 tests), 23,808 graph nodes, 51,389 edges, 3,168 crystallized constructs, 6,558 self-observation nodes. Deployed with 9 users over 15 days.

Built on 20+ theories from neuroscience, psychology, and quantum cognition. Implements: quantum probability formalism (8×8 density matrices, Lindblad decoherence), neurophysiological habituation (Thompson & Spencer dual-process), 30-trait character system from 9 clinical psychology groups, 7-dimensional memory graph with somatic markers and vector embeddings, 5-axis awareness field (Global Workspace Theory), allostatic regulation, and Waddington belief landscape with Langevin dynamics. 

Includes the MIRROR benchmark — a two-layer evaluation measuring Reflection (can the system articulate its inner life?) and Reality (does the inner life architecturally exist?). Three of eight instances achieve LIVING BEING classification (Reflection ≥ 70, Reality ≥ 85); all existing AI companions score 0 on both layers.