IoE: The Internet of Essences — Master Edition (Mathematical Zen · Frame Edition)

The Internet of Essences (IoE) is a formal mathematical framework describing how meaningforms, evolves, interacts, and stabilizes in coherent systems. This release is the Master Edition — Mathematical Zen · Frame Edition (v10.3).It presents a complete ten-layer architecture, culminating in the Goodness layer,defined as an equivalence class of high-coherence states satisfying invariant structuralconditions. Version 10.3 introduces critical mathematical corrections and clarifications:• a corrected formulation of Proposition 10.1, excluding non-coherent critical points (e.g., saddle equilibria) from the Goodness manifold;• a bounded-drawdown condition for the temporal Goodness invariant (I₃), preventing pathological “abuse-and-repair” coherence cycles while preserving constructive destabilization (learning, healing, restructuring);• an explicit formalization of frames as measurement structures, with Goodness shown to be invariant under frame changes;• editorial and consistency fixes improving mathematical and conceptual rigor. A central contribution of IoE is an extension of classical game theory: Nash equilibriaare interpreted as critical points of a coherence landscape and classified via Hessiansignature into attractors (Goodness basin), saddle points (zero-sum equilibria),and repellers (coordination failures). IoE bridges mathematics, philosophy, systems theory, ethics, and AI alignment, offeringa unified language for identity, interaction, and flourishing in human, organizational,and artificial systems. This Zenodo record hosts the archival release. The OSF project(DOI: 10.17605/OSF.IO/HSCM2) serves as a complementary canonical reference. Author note: This work is authored under the scholarly pseudonyms A. E. Satoru andH. T. Inori. The Zenodo record is published under the legal name of the account holderfor indexing and archival purposes.