Ontology of Orders: A Universal Hierarchy of Knowledge

Hierarchical model of knowledge with seven levels (0-6): from axiomatic foundation to innovation and epistemological barriers. Explains domain-specificity, prerequisite dependencies, irreversibility of foundational errors, and rarity of transfer/innovation. Theoretical framework for epistemology and cognitive science. This paper abandons the three-directional vector model (Version 5.0) and reconstructs the Ontology of Orders using Hilbert space mathematics. Knowledge is reframed not as intersecting vectors but as superpositions with finite collapse states. Each order represents a distinct quantum state: collapsed (determined), decoherent (constrained), coherent (possible), or impossible. The framework explains why knowledge propagates hierarchically, why certain combinations emerge only through domain interaction, why innovation exists at the frontier, and why some contradictions are forever impossible. Validated through mathematical structure and empirical observation (mathematics, chemistry, geography, Tesla's innovations). CC BY-NC-ND 4.0 (Creative Commons), C2PA, TDM Opt-Out