Coherence-Rupture-Renewal Multi-Room Explorer

Core Mathematical Framework

The Coherence-Rupture-Renewal (CRR) framework models agent behaviour through three coupled mathematical operators that construct temporality dynamically:

Where L(x,τ) represents memory density, φ(x,τ) is the historical field signal, Ω is the system temperature parameter, and Θ(t-τ) enforces causality.

Markovian Agent in Non-Markovian Field

The agent itself maintains only local, Markovian state (current position, immediate sensory information, discovered map). However, it is embedded in a coherence field that accumulates non-Markovian temporal dependencies:

• Local state: The agent "forgets" detailed history and acts based on current perception
• Field memory: Past experiences create weighted gradients in the coherence field that influence future decisions
• Emergent intelligence: I = tanh(C/Ω) grows as coherence accumulates, modulating exploration vs exploitation

Distinction from Standard Reinforcement Learning

This approach differs fundamentally from conventional RL methods:

• No prior training required: The agent begins with zero knowledge and learns entirely through real-time coherence accumulation
• No reward function: Behaviour emerges from coherence-rupture dynamics rather than external reward signals
• Non-stationary learning: Intelligence parameter I evolves continuously, creating adaptive temporal structure
• Rupture as feature: Loop detection triggers spatial memory suppression, preventing infinite cycles without external intervention
• Memory as landscape: Past experiences create gradients that guide future exploration through regeneration operator R

Biological and Philosophical Motivation

The CRR framework draws inspiration from biological memory systems:

• Memory consolidation: Coherence accumulation mirrors how experiences strengthen neural representations over time
• Attention switching: Rupture events parallel how biological systems break attentional fixation when stuck
• Plasticity: The regeneration operator implements a form of memory-guided exploration similar to hippocampal replay
• Temporal asymmetry: The causal constraint Θ(t-τ) enforces the "arrow of lived time" characteristic of biological systems

Observed Behaviours in This Simulation

The demonstration exhibits several emergent properties:

• Progressive room discovery: Agent systematically explores unmapped regions driven by frontier detection
• Loop breaking: Spatial suppression automatically prevents revisitation spirals without hand-coded rules
• Phase transition: Upon collecting all keys, behaviour shifts from exploration to goal-directed navigation
• Exit beaconing: Strong regeneration signal creates directed movement toward known goal location
• Adaptive intelligence: Decision quality improves as coherence accumulates, visible in reduced step counts over episodes

Applications Across Domains

Whilst this demonstration focuses on spatial navigation, the CRR formalism has been explored in multiple contexts:

• Ecological systems: Modelling moss growth patterns and ecosystem recovery after disturbance
• Neural dynamics: Perceptual switching, attention mechanisms, and memory consolidation
• Machine learning: Addressing catastrophic forgetting through metabolised rupture and selective regeneration
• Cultural evolution: Understanding how traditions accumulate, rupture, and synthesise through interference

Performance Characteristics

In this multi-room navigation task:

• Target performance: Completion in under 10,000 steps for 4-key configuration
• Progressive difficulty: Key count increases with successful completions
• No training phase: All learning occurs during task execution
• Emergent efficiency: Step count typically decreases across episodes as field memory accumulates

This implementation demonstrates that complex adaptive behaviour can emerge from simple mathematical principles governing coherence accumulation, rupture detection, and memory-guided regeneration—without explicit programming of navigation strategies or pre-training on examples.