Hexacronon Score: A Metric for Temporal Recurrence in Human Cognition and Self-Improving AI Systems

The Hexacronon Score is a scalar metric designed to quantify structured temporal recurrence in both human cognition and self-improving AI systems. Based on the XChronos framework, the metric measures a system’s ability to reapply patterns, connect distant experiences, generalize across time, and reorganize itself through emergent meta-learning. It evaluates three components: hexacronal density, structural similarity, and normalized temporal reach. 

The Hexacronon Score ranges from 0 to 1 and captures temporal properties that traditional metrics—such as reward, loss, perplexity or BLEU—cannot measure. It is applicable to reinforcement learning agents, world models, multimodal architectures, symbolic cognition, and phenomenological analysis.

This work contributes to the emerging field of Computable Temporal Intelligence, offering a unified temporal metric for AI research, cognitive science, phenomenology, and symbolic systems.