Delocalised Functional Geometry (DFG) develops a unified theoretical framework for modeling physical fields, information structures, and observer-dependent processes within a single mathematically coherent system. The central premise is that physical, cognitive, and phenomenological phenomena can be represented as structured configurations of an underlying delocalised ontophysical field. The framework introduces a set of formal tools, including delocalised functional basis expansions, nonlocal coupling operators, anisotropic field metrics, and a spiral-time parameterization, to describe the emergence, stabilization, and transformation of coherent structures across multiple spatial and temporal scales. A key contribution of the work is the formalization of observer systems as field-embedded subsystems characterized by projection operators, knowledge states, and phenomenological mappings. DFG further develops a Triadic Observer Architecture, demonstrating mathematically how stable shared realities require triadic (rather than dyadic) coupling, mediated through triadic coherence and interference operators. This approach provides a unified means to analyze how individual and collective observer systems generate, maintain, or destabilize coherent experiential structures. The framework defines explicit dynamical equations linking field evolution, coherence gradients, projection geometry, and observer adaptation. These include formulations for field-level dynamics, local and global coherence measures, branching behavior, morphogenetic constraints, and information-flow structures. The resulting model provides a mathematically explicit basis for understanding phenomena such as:– the emergence of stable cognitive and perceptual configurations,– transitions between coherent and incoherent system regimes,– constraints on functional brain morphology,– and multi-scale interactions in complex adaptive systems. This document presents the complete edition of Delocalised Functional Geometry, integrating its conceptual, mathematical, and structural components into a single, consolidated theoretical reference. The work is intended as a foundation for further empirical investigation and as a conceptual bridge between physics, neuroscience, cognitive science, and formal systems theory.
Delocalised Functional Geometry (DFG) develops a unified theoretical framework for modeling physical fields, information structures, and observer-dependent processes within a single mathematically coherent system. The central premise is that physical, cognitive, and phenomenological phenomena can be represented as structured configurations of an underlying delocalised ontophysical field. The framework introduces a set of formal tools, including delocalised functional basis expansions, nonlocal coupling operators, anisotropic field metrics, and a spiral-time parameterization, to describe the emergence, stabilization, and transformation of coherent structures across multiple spatial and temporal scales. A key contribution of the work is the formalization of observer systems as field-embedded subsystems characterized by projection operators, knowledge states, and phenomenological mappings. DFG further develops a Triadic Observer Architecture, demonstrating mathematically how stable shared realities require triadic (rather than dyadic) coupling, mediated through triadic coherence and interference operators. This approach provides a unified means to analyze how individual and collective observer systems generate, maintain, or destabilize coherent experiential structures. The framework defines explicit dynamical equations linking field evolution, coherence gradients, projection geometry, and observer adaptation. These include formulations for field-level dynamics, local and global coherence measures, branching behavior, morphogenetic constraints, and information-flow structures. The resulting model provides a mathematically explicit basis for understanding phenomena such as:– the emergence of stable cognitive and perceptual configurations,– transitions between coherent and incoherent system regimes,– constraints on functional brain morphology,– and multi-scale interactions in complex adaptive systems. This document presents the complete edition of Delocalised Functional Geometry, integrating its conceptual, mathematical, and structural components into a single, consolidated theoretical reference. The work is intended as a foundation for further empirical investigation and as a conceptual bridge between physics, neuroscience, cognitive science, and formal systems theory.
This work explores a unified metaphysical and mathematical framework for causality, perception, and observer-based reality, bridging foundational insights from physics and neuroscience. A central thesis is the modeling of conscious observers as Dirac delta functions anchored in perceptual and semantic manifolds, whose collapse events instantiate decoherence and give rise to empirical phenomena. We investigate Micro-Mini-Black Holes in the Brain (MMBHBs), proposing them as cognitive analogues of Kerr-type rotating black holes, whose inner horizons host closed timelike curves (CTCs), enabling acausal ontological dynamics and memory loops. Spacetime models such as S3 × S1 and the Gödel universe G3,1 are shown to admit global CTCs, which, when coupled with local Kerr-like MMBHBs, result in nested temporal structures and equivalence classes of observers. This coupling is explored through Lense–Thirring frame dragging, holonomy effects, and quantum resonance, suggesting mechanisms for observer synchronization, reincarnation paths, and cognitive phase transitions. Through rigorous mathematical modeling— including emotional tensors, gauge theory of identity, memory homology, and semantic Ricci curvature—this paper defines an extended Quantum Measurement Chain (QMC) across multiple observer networks. The resulting formalism admits structures like affective descent gradients, cognitive wormholes, and informational echoes in memory topology. We derive equations for entropy flux, decoherence actions, and perception-curvature dynamics, demonstrating the emergence of identity, emotion, and memory as geometrical and thermodynamical phenomena. This work proposes a novel synthesis of quantum cognition, field-theoretic metaphysics, and observer-centric cosmology.
The Triadic Fixpoint Framework (TF2) develops a unified operator-theoretic foundation for physics, in which physical reality emerges as the fixed point of a recursive map Ω = Ψ ∘ Φ combining physical evolution (Φ) and informational update (Ψ). In this formulation, time is identified with the convergence of informational states, spacetime geometry arises from curvature in informational stability, and measurement corresponds to the stabilization of a state under repeated application of Ω. TF2 extends and formalizes the preliminary ideas introduced in TF1 (Omezzolli 2025, DOI: 10.5281/zenodo.17363823) by providing a full fixed-point analysis, explicit convergence theorems, and a geometric interpretation of gravity, mass, and fields as gradients and curvatures in an informational potential. The framework further explains entropy, thermodynamics, cosmology, black hole behavior, and aspects of agency and observer dynamics as consequences of informational contraction. This release contains the full TF2 manuscript (PDF), LaTeX source files, bibliography, and supplementary material needed for reproducibility. The work is intended as a contribution to quantum foundations, emergent spacetime research, and information-theoretic approaches to physics.
This work introduces a rigorous operator-theoretic framework for Projection Mechanics, Projection Dynamics, Qualia Mechanics, Qualia Dynamics, and Quantum Psychology. The manuscript formalizes psychology as a partial-state estimation problem on adaptive projection manifolds rather than a purely heuristic interpretive discipline. Consciousness is modeled as an internally accessible but externally projected experiential state system evolving under constrained observability. Core contributions include: Formal definition of projection operators mapping latent internal states into observable behavioral space Projection fiber geometry and inverse inference structure Adaptive projection dynamics governing masking, signaling, and observer-dependent behavioral modulation Qualia-state manifolds and experiential evolution equations Stability and resonance analysis for conscious trajectories Noncommuting psychological observables and contextual measurement structure Operator-theoretic formulation of Quantum Psychology Structural bridges between psychology, consciousness studies, measurement theory, and quantum operator frameworks The framework does not claim that consciousness is literally quantum mechanical. Instead, it demonstrates that conscious and psychological systems share deep structural similarities with partially observable operator systems studied in quantum measurement theory. The manuscript aims to provide a mathematically structured foundation for future work in: computational psychology, consciousness studies, cognitive dynamics, operator geometry, adaptive behavioral systems, and measurement-theoretic models of mind.
Description: This collection presents a unified, coherence-based framework proposing that physical reality is not fundamental, but derivative—an emergent rendering of structured informational processes operating under thermodynamic and geometric constraints. Across four integrated papers, the author develops the Virtual Ego Framework (VEF) and Coherence-Geometrodynamics (CGD) into a consistent architectural model that reframes long-standing problems in physics and consciousness studies, including: the observer effect in quantum mechanics, the relationship between information, entropy, and gravity, identity persistence independent of material continuity, and the transition from probabilistic (wave) states to localized (particle) reality. Contents Overview Part I — Reality Is a DerivationResolves the “simulation hypothesis” by rejecting external-author metaphors and demonstrating that reality is better understood as a derivation from an informational substrate, consistent with Infodynamics and non-algorithmic (Gödelian) constraints. Part II — The Unified Architecture & the Cost of CoherenceIntroduces the concept of Observer Cost (ζ), showing that coherence, identity, and meaning require irreducible thermodynamic expenditure. This section integrates First-Principles critiques to avoid dualism and enforce ontological solvency. Part III — Coherence, Identity, and the Interface Between Meaning and MatterDevelops a boundary-layer model in which identity is a coherence envelope, not a material artifact. Introduces the Hyperion Universal Interface Membrane (HUIM) and Energy-in-Meaning (“eningmeaning”) as conceptual models explaining how structured intent becomes physical geometry. The Indexing Protocol (v2.1)Formalizes observation as Indexing—a geometric memory allocation event governed by the Genesis Ordinary Differential Equation (Genesis ODE). Proposes the Spheromatryoshka Domain (nested toroidal flows) as the fundamental unit of reality and reframes uncertainty as a bandwidth-solvency constraint rather than intrinsic indeterminacy. Scope and Limits These works are conceptual and architectural, not claims of experimentally confirmed new particles or forces. Speculative constructs (e.g., HUIM, eningmeaning) are explicitly presented as models, consistent with known physics but not replacements for it. The framework is falsifiable at the level of coherence prediction, observer-cost accounting, and identity persistence under pattern preservation. Intended Audience This collection is intended for researchers and advanced readers in: theoretical and digital physics, complex systems and information theory, consciousness studies, AI and cognitive architecture, philosophy of science and ontology. Together, these papers propose a coherent alternative to both naïve materialism and external-simulation narratives, arguing that reality is a just-in-time derivation of meaning under entropy constraints, stabilized by coherence rather than control.
Title: The Generative Architecture: From Distinction to Quantisation — A Variational and Geometric Theory of Generative Systems Author: David Michael Doy Date: June 2026Description: This work presents the complete variational and geometric foundations of the Generative Architecture, a unified mathematical framework in which reality emerges from a single primitive act: distinction. Beginning with the origin chain — nothingness → imbalance → collapse → action → massless field → D — the theory derives the three operational primitives (Possibility, Coherence, Boundary) as projections of D and develops the full generative dynamics that follow from them.The variational core of the architecture is built from the coherence functional C, the generative tension invariant I, and the conserved quantity G=D+I′. These elements enable the derivation of the generative action S[X], the canonical Hamiltonian, the Hamilton–Jacobi equation, the functional Schrödinger equation, and the path‑integral formulation without importing external physical primitives. An emergent quantum scale ℏeff arises naturally as the fluctuation amplitude of the generative action around stationary coherence‑ascent trajectories.A central contribution of this volume is the introduction of the compressed geometric formulation of the architecture. The full generative state is reorganised into the quadrupleX=(M,N(M),B(M),C),where M is the structural manifold, N(M) the constraint bundle, B(M) the boundary image, and C the coherence tensor. In this representation, the entire dynamics are governed by a single operator — the generative derivative DG — yielding the compressed master equation∂X∂t=πM (−δAδX)+C πN(M)(∇XV)+(1−C) πB(C(X)).This formulation unifies variational flow, teleodynamic drift, collapse, and boundary projection within a single geometric structure and provides a natural bridge to the teleodynamic regime.The document includes: • the explicit form of the coherence functional and its role in collapse, development, and geometry • the unified generative master equation and its geometric compression • the generative derivative and generative curvature • the path‑integral formulation of generative dynamics • the emergence of an effective metric and Einstein‑like field equation • the operational definition of ℏeff from simulation‑level fluctuations • the geometric bridge to identity, agency, and multi‑agent teleodynamicsTogether, these results show how quantum structure, geometric dynamics, and cognitive organisation arise from a single generative principle. This volume serves as the technical foundation for the broader Generative Architecture programme and complements the full monograph The Generative Architecture of Reality.Keywords: generative architecture, primitive distinction, coherence functional, generative derivative, geometric compression, variational dynamics, emergent quantisation, collapse dynamics, emergent geometry, unified field framework, teleodynamics, generative systems theory.
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.