Unified Theory of Semantic Symmetry: Mathematical Foundations of Coherent Reality

Evert Willem Beth

Helder Fernando Passos Soares

Ediverso Theory: A Unified Theory of Possibility, Choice and Reality Ediverso Theory proposes a new mathematical and conceptual framework for describing how realities emerge from fields of admissible possibilities. While classical mathematics, logic and physics primarily study realised states, determined values and observed outcomes, Ediverso Theory introduces possibility itself as a fundamental object of formal investigation. The framework is built upon four primitive concepts: Possibility (E) — the field of admissible states; Choice (Ω) — the operator that transforms possibility into reality; Memory (H) — the accumulated history of realised states; Coherence (C) — the structure that constrains consistent evolution. From these primitives emerges a unified formal architecture spanning geometry, topology, information theory, observer theory, computational systems, physics, logic, mathematics, consciousness, evolution and collective dynamics. At the core of the theory lies the Ediverso operator: ╠╬╣ which represents a structured field of admissible possibilities rather than a single realised value. Classical mathematics appears as a limiting case when the possibility field collapses to a single point. The work develops: • A Geometry of Possibility• A Topology of Admissible Realities• An Information Theory of Choice• A Formal Theory of Observers• Computational Ediverso Systems for Artificial Intelligence• Possibility-Based Physical Models• Ediverso Logic and Mathematical Foundations• Theories of Consciousness, Evolution and Civilizational Dynamics• The Irreducibility Theorem of Ediverso Systems The central question motivating the entire research programme is: What exists before reality becomes reality? Rather than treating possibility as ignorance, uncertainty or incomplete information, Ediverso Theory investigates the hypothesis that possibility possesses its own independent mathematical structure and that reality emerges through admissible selection within that structure. This manuscript presents the first complete formulation of the Ediverso Research Program and is intended as an open scientific framework subject to mathematical analysis, criticism, refinement, extension and falsification. If successful, Ediverso Theory may provide a common language for describing decision, emergence, information, observation and reality across disciplines traditionally studied in isolation. Reality is not the beginning. Reality is the consequence. Possibility is the beginning. Keywords: Ediverso Theory, Possibility Mathematics, Choice Theory, Emergence, Information Theory, Observer Theory, Mathematical Foundations, Logic, Artificial Intelligence, Consciousness Studies, Complexity Science, Theoretical Physics, Philosophy of Mathematics, Foundations of Reality.

Alexey V. Yakushev

Аll actual versions оf YUCT, you can get it at theDOI 10.5281/zenodo.18444598 or website https://yuct.org/This DOI represents all versions, and will always resolve to the latest one of Yakushev Unified Coordination Theory. This work introduces a paradigm shift in fundamental physics: coordination of states among distributed components is ontologically prior to both spacetime and matter. We formalize this through three interlocked mathematical constructs: 1. **Dictionary Manifolds** ℳ_𝒟 – Riemannian manifolds whose points represent dictionaries mapping compact indices to complex actions, equipped with a semantic distance metric. 2. **YPSDC Protocol** (Yakushev Protocol for Synchronous Distributed Coordination) – achieving coordination efficiency K_eff = H(𝒜)/H(κ) > 1 without violating causality, through separation of coordination (dictionary distribution) from data transmission (index activation). 3. **D+I•R Triad** – the ontological primitive Reality = Dictionary + Information × Resonance, providing a unified framework across physical, biological, and information systems. The complete structure is a fiber bundle π:ℰ→ℳ with spacetime as base and dictionary manifolds as fibers. This geometric and information-theoretic foundation enables subsequent derivation of physical laws from coordination principles, resolving long-standing paradoxes such as the EPR problem through K_eff → ∞ and offering testable predictions for gravitational and quantum systems. This is an overview of the framework. The complete mathematical formulation with full derivations and experimental predictions is available in the complete version.

Claudio Garola

G. Fáy

Philip Lilien

This paper completes the core layered architecture of the Unified Coherence Closure Framework by formalizing the observer/consciousness polarity as explicit operators. Paper 1 identified the observer-function (reduction of coherence into locally determinate form) and the complementary consciousness-function (reintegration and symmetry enhancement) as ontologically primitive irreducibilities required for any world in which stable entities, transformations, and intelligibility can arise. Papers 2–4 carried this polarity forward as paired reduction and reintegration maps within the axiomatic requirements and coherence mathematics, and realized it physically through spectral decomposition in Closure Physics. The present paper elevates these maps to full operator status: the Asymmetry Resonance Operator (ARO) and the Symmetry Coherence Operator (SCO), which together constitute the Meta-Operator. These operators are not introduced externally or as ad hoc additions. They are the disciplined formal expression of the same closure dynamics already operative in the ontological, axiomatic, mathematical, and physical layers. The ARO and SCO are shown to be complementary, to satisfy the four axiomatic requirements of Paper 2, and to be consistent with the Seed Tetrad (0⁰ = 1, 0! = 1, −e^(iπ) = 1, ∞⁰ = 1) as the primitive disclosure architecture. The Meta-Operator therefore completes the operator-theoretic stage of the framework while preserving strict ontological grounding. The deeper foundations of ontological mathematics the generative ground from which mathematics itself discloses reality are acknowledged as fundamental and reserved for dedicated later treatment. This paper focuses on the formalization of the observer/consciousness polarity already compelled by the preceding stages. Keywords: Meta-Operator; Asymmetry Resonance Operator (ARO); Symmetry Coherence Operator (SCO); Unified Coherence Closure Framework; observer-function; consciousnessfunction; reduction; reintegration; Seed Tetrad; ontological mathematics; coherence mathematics; Closure Physics