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CVFT - Programmatic Extension

Iker ibarrola

Published Feb 27, 2026• 0 citations
Publisher

Abstract

We present a closed axiomatic formulation of a multiscale correlational framework (CVFT 3.0). No spacetime, metric, or geometric structure is postulated at the fundamental level. Instead, physical structure is encoded in an algebra of observables endowed with a refinement semigroup, an internal relational flow, and a positive spectral generator. We formally delimit the structural consequences derivable from the axioms and explicitly state the boundaries of the framework.

DOI
10.5281/zenodo.18806317

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We present an operational formulation of Correlational Variational Field Theory (CVFT) in which physical structure is described by a positive correlational kernel defined over a relational domain. In this framework the fundamental ontological object is a multiscale kernel Ks(x,y)K_s(x,y)Ks​(x,y) encoding the strength of relational connectivity between degrees of freedom. Contact: ibarrolaiker@gmail.com
This work presents the complete and final canonical closure of the Universal Correlational Lattice (UCL) framework. All ontological primitives, structural assumptions, and dynamical principles required to define the theory are stated explicitly and exhaustively within this document. No additional axioms, foundational postulates, or hidden assumptions are introduced beyond those formalized here. The UCL framework is closed in the strict mathematical and conceptual sense: the space of admissible configurations, the correlational degrees of freedom, the variational structure, the selection criteria for physical realizability, and the operational definition of observables are fully specified. As a consequence, the theory is self-contained and internally complete at the foundational level. After this closure, any further development of the framework necessarily belongs to one of the following categories: (i) applications of the formalism to specific physical systems, (ii) phenomenological instantiations and numerical implementations, or (iii) effective or emergent descriptions derived from the closed correlational base. No subsequent work modifies, extends, or supplements the foundational structure established here. This document therefore constitutes the definitive structural reference of the UCL framework. Its role is not to predict particular phenomena, but to delimit unambiguously the theoretical domain within which all predictions, models, and comparisons with empirical data must be constructed. In this sense, the closure presented here marks the transition from foundational formulation to systematic deployment.
This document presents the Universal Correlational Lattice (UCL) as a general theoretical framework for constructing physical models directly from correlational structures, without assuming spacetime, fields, or quantum states as fundamental entities. The UCL formalism is built around a universal correlational kernel defined over relational sites, from which effective notions of dynamics, observables, uncertainty, and emergent geometry arise through explicit variational and coarse-graining procedures. Rather than postulating equations of motion or quantization rules a priori, the framework provides a model-building methodology: physical laws appear as effective descriptions of stable correlational configurations. This document is not a phenomenological fit nor a proposal of a specific new particle or interaction. Instead, it serves as a theoretical construction manual, showing how to: Define correlational degrees of freedom and their internal parameters, Construct effective observables from correlational averages, Derive emergent dynamics through functional variation, Identify classical, quantum-like, and geometric regimes as limits of the same underlying structure, Build toy models and progressively refine them toward empirical applicability. Uncertainty, probabilistic behavior, and apparent quantum effects are treated as emergent properties of incomplete access to correlational information, not as fundamental axioms. Likewise, time is introduced through internal correlational evolution and synchronization, rather than assumed as an external background parameter. The goal of the UCL framework is to provide a unified, internally consistent base from which models relevant to particle physics, gravity, and cosmology can be constructed and compared with existing theories such as Quantum Field Theory and General Relativity, while remaining agnostic about their ultimate empirical success. This work is intended for researchers interested in: Foundations of physics, Emergent spacetime and dynamics, Alternative formulations of quantum theory, Correlational and relational approaches to physical law. Empirical validation is not claimed at this stage; instead, the emphasis is placed on conceptual completeness, internal consistency, and explicit model-building capability.
This work presents a two-stage first-principles construction for foundational physics. In the first stage, an axiomatic framework is introduced in which physical objecthood is defined exclusively through participation in observation–feedback (OF) processes. At this axiomatic level, no background spacetime, metric, Hilbert space, or symmetry group is assumed a priori. In the second stage, a minimal faithful realization of this framework is adopted, consisting of a set of explicitly stated, controlled algebraic choices that support finite operational distinguishability. Within this minimal realization, a hierarchy of physically significant structures is consistently represented: an internal O(3) symmetry with oriented SO(3) sectors; a Lorentz-type kinematical structure with invariant group SO⁺(3,1) (the proper orthochronous Lorentz group) and an associated invariant propagation scale that occupies the structural role of the conventional speed c; and a minimal closure scale that, under standard action-dimensional normalization, plays a structural role analogous to that of the reduced Planck constant ℏ. This construction thus provides a unified relational setting in which the core kinematical architectures of special relativity and quantum mechanics admit a consistent, operationally grounded representation, realized under explicitly stated minimal assumptions. No derivation of dynamical equations or direct identification with empirical spacetime geometry is claimed.