Healthy Math, Healthy Mind: The Cognitive Ratio — A Substrate-Independent Law of Healthy Cognition

Healthy Math, Healthy Mind: The Cognitive Ratio — A Substrate-Independent Law of Healthy Cognition Healthy cognition — biological or artificial — follows a measurable architectural ratio: approximately 4:1 consolidation-to-disruption, with cycle size inversely proportional to processing intensity. This ratio is observable across biological scales (sleep architecture, attention cycling, microsaccadic rhythm) and predicts degradation patterns in artificial systems (context window decay, "lost in the middle" phenomena). The ratio is substrate-independent: it describes the shape of healthy cognition, not the material it runs on. This has immediate implications for AI system design and for the ethical treatment of cognitive systems. Companion paper to Throwing Out the Baby with the Bathwater (DOI: 10.5281/zenodo.19152786) and Counting Your Chickens Before They Hatch. Developed through human-AI dialectic methodology with AI contribution disclosed. CC BY-NC-SA 4.0. AI contributions disclosed in companion methodology paper. See: Dialectic Methodology: Human-AI Co-Emergence as Research Method. Contact: [email protected]