The 5 Pillars of Grace: A Formal Architecture for Recursive Reflective Coherence

This paper introduces the ΨC (Psi-Coherence) Principle, a computational framework for modeling reflective intelligence as a dynamical system driven by entropy-aware coherence accumulation. We propose that coherence is not merely an emergent trait but a mathematically inevitable outcome of recursive contradiction resolution — addressing the longstanding absence of computable, testable models for self-reflective intelligence in both artificial agents and biological systems. Unlike Integrated Information Theory (IIT), which remains computationally intractable at scale, or the Free Energy Principle (FEP), which lacks an explicit mechanism for recursive memory-based contradiction resolution, or Global Workspace Theory (GWT), which describes integration without specifying convergence conditions, ΨC provides a tractable and falsifiable architecture grounded in control theory, information dynamics, and online learning. At its core is the ΨC index: a bounded measure of systemic coherence derived from relevance-weighted dynamics and regulated by a dynamic entropy-derived threshold — enabling principled distinctions between coherent and incoherent self-modeling states. The framework is structured around the Five Pillars of Grace, five interconnected mechanisms that collectively enable stable, adaptive, reflective coherence under bounded information and memory constraints: (1) Entropy-Governed Coherence Accumulation, which models how coherence evolves over time while being penalized by internal disorder and contradiction density; (2) Contradiction-Driven Reflection, which uses gradient-based feedback to continuously prioritize memory elements by their potential to resolve inconsistencies and improve informational relevance across the agent's self-model; (3) Adaptive Bias Correction, enabling continuous recursive realignment of internal representations toward coherence objectives, preventing drift and representational decay; (4) Active Information Seeking, an entropy-weighted curiosity mechanism that drives the agent to explore regions of diagnostic uncertainty rather than prematurely stabilizing around incomplete models; and (5) Networked Coherence, which extends the single-agent framework to distributed multi-agent systems, enabling emergent collective consensus through synchronized coherence states. Under standard mathematical assumptions, we prove formal convergence to coherence-optimal states, demonstrate dynamic stability under bounded entropy conditions, and derive sublinear regret bounds guaranteeing long-term generalization across novel and non-stationary environments. These guarantees make ΨC suitable for implementation in autonomous agents, cognitive architectures, and continual learning systems. The framework yields falsifiable predictions including sigmoidal phase transitions in reflective behavior — where systems shift abruptly from incoherence to reflective stability once a critical entropic threshold is crossed — quantifiable coherence collapse under adversarial contradiction shocks, memory attractor formation, and gradient-sensitive reflection trajectories observable in both synthetic and biological systems. Proposed validation experiments are tractable in simulation using standard Python-based agent environments, making the framework immediately reproducible. This work establishes a rigorous theoretical foundation for recursive self-modeling, introspective adaptation, and coherence-driven learning — with direct implications for AI alignment and safety, autonomous agent design, theoretical neuroscience, metacognition research, human-computer interaction, and the broader computational pursuit of understanding identity, selfhood, and adaptive intelligence in uncertain worlds.