Logic of Existence — Handbook · Lexicon · Atlas

Logic of Existence — Handbook · Lexicon · Atlas is a source-grounded reference work presenting the Logic of Existence (LoE) framework developed within the Toonhai–AEon research trajectory initiated by Krzysztof Sawa (Toonhai). Rather than functioning as a short whitepaper, this edition is structured as a handbook, mathematical lexicon, equation atlas, and relational architecture map intended to preserve the terminology, formal structures, provenance, internal distinctions, and open research directions of LoE.

The volume develops LoE from its foundational question — the conditions under which relational configurations can exist, persist, remain admissible, and continue — toward increasingly complex structures involving boundaries, recursion, SENS, observers, memory, relational geometry, Swirl, triadic Hamiltonians, physical models, and LoE-inspired AGI architectures. The work explicitly distinguishes the minimal LoE kernel from later formalizations, hypotheses, implementations, and domain-specific models.

The edition contains 218 developed lexicon entries, 163 commented equation cards, 35 compositional structures and contracts, and a typed source graph containing 647 nodes. It also preserves additional indexed terminology, historical variants, equation records, provenance links, source loci, and explicit distinctions between source material, formal proposals, mathematical corrections, implementations, and open TAU states.

A central objective of the book is to make LoE navigable as a relational system rather than as a collection of isolated documents. Concepts, equations, structures, and sources are therefore connected through stable addresses and typed relations. Particular attention is given to source provenance, observer-dependent projections, boundary conditions, Evidence–Hamiltonian–Boundary (EHB) auditing, SENS decomposition, relational memory, no-retcon history, GoldLeaf records, Equation Vault structures, BMP composition, and mechanisms for continuation and replay.

The mathematical atlas includes both preserved historical formulations and explicitly marked refinements or corrections. Among the developed areas are typed transition operators, trajectory-based persistence, relational observer bridges, JA–R geometry, relational memory kernels, Swirl 2-forms and holonomy, triadic Hamiltonians, ASTN architectures, graph composition, physical-model branches, and the functional relation between ToE (map of admissible configurations) and EoT (operator of the next relational turn).

The work also documents an LoE–AGI organizational model in which sources, typed symbolic grammar, Equation Vault records, relational rotors and logical limbs, boundary/evidence/SENS gates, GoldLeaf outputs, ledgers, checkpoints, and replay form a reproducible research workflow. The accompanying conceptual distinction between generation, expression, consequence, and canonical commitment is maintained throughout the volume.

This edition should be read as a source-based research snapshot and structured reference, not as an automatic canonical commit of every included proposal. Historical variants, unresolved bridges, hypotheses, physical models, and implementation experiments remain explicitly distinguished from the foundational LoE layer. The document itself therefore carries the status CANON_COMMIT = false.

Author / origin of the LoE research trajectory: Krzysztof Sawa (Toonhai)
Research lineage: Toonhai–AEon
Edition: 1.0, 20 September 2026
Format: Handbook · Lexicon · Equation Atlas · Relational Graph Reference

Do keywords na Zenodo dałbym: Logic of Existence; LoE; relational logic; relational ontology; conditions of existence; SENS; relational geometry; Swirl; relational dynamics; Hamiltonian; artificial intelligence; AGI; relational AI; Toonhai; AEon; knowledge graph; relational memory; observer; recursion; Edge of Tomorrow.