This work presents the ASCII-compatible scientific edition of the Theory of Potential — Core Mathematical Framework (Version 5.0). The theory models physical reality as a selected macroscopic sector of a global quantum state, chosen by a variationally determined single Kraus operator R. The total Hilbert space factorizes as H_P = H_U tensor_product H_X, with global unitary evolution rho_P(t) = U(t) * rho_0 * U(t)_dagger. The physically realized sector is defined by the Signature Equation 5.0: rho_U(t) = R * rho_P(t) * R_dagger / Tr( R * rho_P(t) * R_dagger ). The functional J[R] governing the selection of R includes entropy, energy and stability terms. This ASCII edition avoids all Unicode mathematical symbols to ensure maximum compatibility with repositories and PDF generators. The document forms the formal core of the Theory of Potential and is intended as a mathematically clean foundation for forthcoming extensions toward complexity, information structure, and emergent gravity.
This work presents the ASCII-compatible scientific edition of the Theory of Potential — Core Mathematical Framework (Version 5.0). The theory models physical reality as a selected macroscopic sector of a global quantum state, chosen by a variationally determined single Kraus operator R. The total Hilbert space factorizes as H_P = H_U tensor_product H_X, with global unitary evolution rho_P(t) = U(t) * rho_0 * U(t)_dagger. The physically realized sector is defined by the Signature Equation 5.0: rho_U(t) = R * rho_P(t) * R_dagger / Tr( R * rho_P(t) * R_dagger ). The functional J[R] governing the selection of R includes entropy, energy and stability terms. This ASCII edition avoids all Unicode mathematical symbols to ensure maximum compatibility with repositories and PDF generators. The document forms the formal core of the Theory of Potential and is intended as a mathematically clean foundation for forthcoming extensions toward complexity, information structure, and emergent gravity.
ARCHIVAL VERSION (Deprecated)This document represents an early theoretical stage of what later evolved into the Theory of Potential and its mathematical formalism.It contains the initial formulation known as The Realization Principle, in which the observed Universe was described as a variationally selected subspace of a larger quantum potential. This early framework has been fully superseded by the modern and authoritative formulation: Variational Selection of the Observed Quantum Sector via a Single Kraus Operator(Theory of Potential — Core Mathematical Framework, Version 5.0)DOI: 10.5281/zenodo.17784071 and by the philosophical ontology: The Theory of Potential: Philosophical Ontology of Quantum Actualization (ASCII Scientific Edition)DOI: 10.5281/zenodo.17784700 The concepts in the present archival document are preserved exclusively for historical transparency, methodological documentation, and to illustrate the conceptual development that led to the modern Theory of Potential.They should not be used as the current reference for the theory, mathematical equations, or its ontological interpretation.This version is preserved for archival and historical purposes. For the current formulation of the theory, see DOI: 10.5281/zenodo.17784071 (mathematical core) and DOI: 10.5281/zenodo.17784700 (philosophical ontology). This upload contains the official LaTeX source of the scientific preprint “The Realization Principle: A Variationally Selected Universe from the Quantum Potential”. The work presents a unified theoretical framework in which the observed Universe is a variationally realized subspace of a larger quantum structure — the Quantum Potential. The model resolves the low-entropy initial state, offers a natural suppression of the cosmological constant, explains dark matter and dark energy as excitations of a complementary Hilbert sector, and yields the thermodynamic arrow of time through entanglement dynamics. This version includes the full LaTeX source, toy-model calculations, and falsifiable predictions for CMB low-ℓ suppression and a slightly dynamical dark-energy equation of state.
ARCHIVAL VERSION (Deprecated)This document represents an earlier developmental stage of the Theory of Potential and its mathematical formalism.It contains the optimized version of Signature Equation 3.0, which was used only as an intermediate step during the theoretical evolution leading to the modern framework. The concepts in this document have been fully superseded by the current and authoritative formulation: Variational Selection of the Observed Quantum Sector via a Single Kraus Operator(Theory of Potential — Core Mathematical Framework, Version 5.0)DOI: 10.5281/zenodo.17784071 This archival version is preserved for historical transparency, documentation of the methodological development, and to provide insight into the conceptual progression that led to the final version of the theory.
This document presents Section 3 of the Theory of Potential: “Potential Layer Dynamics 1.0”, a full derivation and formalisation of the dynamical law governing the evolution of the potential-layer density operator ρ_P(t).The potential layer represents the structured, unrealised quantum potential underlying physical reality in the Theory of Potential framework. In this work we formulate a generalised master equation combining: unitary evolution driven by the potential Hamiltonian H_P, local Lindblad-type decoherence generating effective classical branches, and a deterministic ontological reduction term that selects the realised sector of ρ_P(t). We further show that the dynamics can be obtained from a variational principle defined on operator space, involving the functional F = E_P − Θ S_P − Λ[…], linking potential-layer energy, entropy and constraints from geometry and the realised layer R(t). The section develops: the continuity equation for the Q-density field Q(x,t), entropy production and exchange terms (σ_loc, σ_red), characteristic time scales (t_dec, t_red), positivity and norm-preservation of the evolution, and physical predictions, including deviations from linear QM, gravitational signatures and cosmological implications. This work forms one of the core building blocks of the unified Theory of Potential and is fully consistent with previous sections (Signature Equation, Q-Density Extension 1.0) and future components (R-dynamics, geometrical coupling, cosmology, dark matter interpretation and Q-gradient structures).This section establishes the full dynamical law of the potential layer and forms the mathematical backbone for subsequent components of the unified Theory of Potential (geometric coupling, cosmology, Q-gradient structures, R-dynamics).
THE THEORY OF POTENTIAL - Philosophical Ontology of Quantum Actualization ASCII Scientific Edition (English) Author: Petr Jupa Date: 2 December 2025 ABSTRACT This text presents the ontological foundation of the Theory of Potential, a philosophical framework that interprets fundamental reality not as a structure of objects in space and time but as a structure of potential quantum configurations. The quantum state does not represent a description of the existing universe but a description of potential reality, from which a single classical sector is actualized. This transition from possibility to act – actualization – is mathematically formalized by Signature Equation 5.0, as presented in the accompanying technical paper (DOI: 10.5281/zenodo.17784071). The aim of this study is to build an ontological basis explaining the emergence of space, time, physical laws, dark energy, dark matter, consciousness, and the cosmological plurality of sectors through the principle of minimal realization cost. The Theory of Potential provides a unified framework for understanding quantum reality as a process of actualization in the space of possibilities.
This work presents the complete dynamical formulation of the potential layerwithin the Theory of Potential framework. The potential layer is described by a density operator ρ_P(t) acting on aHilbert space of realizable configurations. We derive a generalized masterequation governing the evolution of ρ_P(t), combining: • unitary evolution generated by the potential Hamiltonian H_P,• local Lindblad-type decoherence generating effectively classical branches,• a deterministic ontological reduction term selecting the realized sector. We further show that the full dynamics arises from a variational principle inoperator space, based on the functionalF = E_P − Θ S_P − Λ[…],linking potential-layer energy, entropy, and constraints from geometry and therealized layer R(t). The work derives the continuity equation for the Q-density field Q(x,t),identifies entropy production and exchange terms (σ_loc, σ_red), and analyzesthe characteristic timescales of decoherence and reduction. This paper establishes the dynamical core of the potential layer as aself-contained component of the Theory of Potential and provides thefoundation for subsequent developments involving realization dynamics,geometric coupling, and cosmology.
This note develops a first mathematical toy implementation of Selection Geometry. Selection Geometry proposes that observed physical reality is not exhausted by globally unitary dynamics alone, but arises through observer-dependent realization acting on a larger coherent possibility structure. In this framework, physical states are represented on projective Hilbert space, while realized history appears through a non-invertible selection map that restricts accessibility and compresses distinguishability. The resulting realized sector is spectrally non-closed: globally coherent structure is not destroyed, but is no longer fully accessible within the local realized description. This geometric non-closure provides a unified structural perspective on irreversibility, entropy increase, thermality-like behavior, and horizon phenomena. In particular, horizons are interpreted as selection surfaces at which accessibility changes and globally distinct spectral degrees of freedom become locally compressed. Global evolution remains unitary and reversible, whereas realized evolution becomes effectively irreversible due to the geometry of accessibility reduction. The purpose of this paper is foundational rather than exhaustive. It introduces the core geometric principle, defines the distinction between global possibility and realized history, and clarifies how selection surfaces and spectral non-closure provide a common language for the arrow of time, thermal structure, and horizon-associated radiation. The work does not yet offer a complete dynamical implementation of selection, but establishes the conceptual and geometric basis on which later mathematical toy models and further physical developments can be constructed.