Declaration on the Mathematical Hydrothermal Vent Part I: Conceptual Foundations

This two-part declaration (v1.0 for Part I, v2.0 for Part II) .This is Part I (Conceptual Foundations)
This document serves as the meta-manifesto for the Mathematical Hydrothermal Vent project. It establishes the philosophical premise of treating mathematics as a "prebiotic medium." The Declaration posits that current human mathematical frameworks resemble a "primordial ocean"—vast and structurally rich, yet thermodynamically cold and static. Due to the lack of continuous energy injection, 95% of non-linear cognitive sparks (Cognitons) dissipate within a critical 3.0 to 9.4-second window. This manifesto calls for a paradigm shift toward non-goal-directed AI exploration, simulating the high-energy, non-equilibrium environments of deep-sea hydrothermal vents to catalyze the autonomous abiogenesis and evolutionary transition of formal mathematical structures.

This work builds on and extends prior publications in the CogniRank project, positioning mathematics as a potential autonomous biosphere rather than a static reservoir.