Volume I of the TF2.5 Trilogy develops the informational core of the Triadic Fixpoint Framework. It introduces the triadic structure of observer, system, and informational environment, formalizes the fixpoint dynamics of quantum measurement, and derives emergent spacetime geometry from informational constraints.
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.
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 volume develops the formal mathematical representation of the correlational ontology introduced in Book I. Without adding new ontological assumptions, the framework is translated into a precise formal language based on configuration spaces, equivalence classes, order structures, functionals, and operators. Key structures such as the consistency functional, canonical correlational flow, Hessian operator, and projection to observable subspaces are defined rigorously. The mathematical role of gradients, variational structures, spectral analysis, and stability is clarified, while maintaining the non-ontological status of time, dynamics, and laws. The volume emphasizes representational freedom, gauge equivalence, and the distinction between structural objects and effective physical descriptions. It establishes the formal core from which all subsequent physical realizations and predictions are derived. This book functions as the technical backbone of the framework, independent of any particular physical regime.
This volume presents the canonical physical realization of the correlational framework. Starting from the formal structures defined previously, it shows how familiar physical notions—such as effective time, dynamics, locality, geometry, and field equations—emerge in specific regimes. The emergence of physical operators, propagators, and effective actions is derived from spectral properties of the Hessian operator under projection and restriction. Gravity, quantum-coherent dynamics, open-system behavior, and dissipative regimes are treated as contextual realizations rather than fundamental structures. The volume demonstrates how classical, relativistic, and quantum descriptions arise as effective limits, clarifying their domain of validity and breakdown conditions. No regime is ontologically privileged. This book establishes how known physical theories are recovered and unified within the correlational program without modifying its foundational assumptions.
This volume introduces the canonical realization mechanism that connects correlational ontology and formal structure to effective physical description. A universal correlational flow is defined as a non-ontological ordering principle acting on correlational configuration space, without invoking time or dynamics. From this realization mechanism, an emergent structural action and fundamental emergent equations are derived. The volume develops the emergence of time, dynamics, space, geometry, quantum and classical regimes, and physical laws as regime-dependent effective descriptions. Known physical theories—quantum mechanics, classical mechanics, and relativity—are recovered as distinct realization regimes. The volume makes explicit the non-fundamental status of action principles, equations of motion, and spacetime geometry. This volume constitutes the physical core of the framework.
This work introduces the foundations of an observer-dependent informational theory of physics.Rather than proposing a closed or final model, the paper establishes the conceptual and methodological architecture of a unified research program in which physical phenomena are described through observer-accessible informational states. The theory treats the observer as an integral component of physical description, rather than as an external disturbance or purely abstract entity.Information is defined operationally, as a relational construct linking observation, structure, and temporal coherence. The paper does not present new mathematical derivations.Instead, it provides a stable foundational framework that unifies a set of modular technical works, each addressing specific physical, cognitive, or interpretative problems. Mathematical formulations, empirical models, and testable predictions are delegated to the corresponding modular papers, allowing the theory to evolve through falsification and refinement without requiring repeated foundational revision. This contribution is intended as a foundational reference for an evolving observer-centered informational approach to physics.