The Infinite Gap ($\varepsilon_\infty$) as a Model-Dependent Structural Principle in Physics: Conceptual Framework, Dynamical Bounds, and Experimental Signatures
#Description: This work introduces the concept of the *Infinite Gap* ($\varepsilon_\infty$) as a model-dependent structural principle capturing the fundamental mismatch between idealized mathematical descriptions and physically realized states. Rather than defining $\varepsilon_\infty$ as a single universal observable, we formulate it as a family of gap functionals whose explicit representation depends on the physical framework under consideration. The concept is developed across multiple domains, including cosmology, quantum mechanics, and information theory, providing a unifying perspective on discrepancies between theoretical predictions and empirical observations. In the quantum context, the Infinite Gap is directly related to measurable quantities such as state purity, defined by $1 - \mathrm{Tr}(\rho^2)$, and is shown to obey dynamical inequalities under Lindblad evolution, reflecting the irreversible growth of decoherence. This establishes a direct bridge between the conceptual framework and experimentally accessible systems. We further introduce a structural contribution, $\delta_{\text{struct}}$, representing an irreducible component of the gap that cannot be attributed to noise, entropy, or decoherence. This term is proposed as a hypothesis capturing intrinsic limitations in the representation of physical reality by mathematical models. The framework also provides testable implications in controlled quantum systems, where deviations from idealized purity can be experimentally quantified, as well as in cosmology, where large-scale observational tensions may be interpreted within this perspective. Overall, this work aims to establish a conceptual and semi-quantitative bridge between ideal theoretical constructs and the limitations inherent in their physical realization, positioning the Infinite Gap as a candidate structural feature of physical theory. # Keywords: * Infinite Gap * Structural Principle in Physics * Quantum Decoherence * Density Matrix * Purity * Entropy * Lindblad Equation * Cosmology * Model-Dependent Framework * Effective Theories * Information Theory * Foundations of Physics
The Infinite Gap (ε∞) as a Model-Dependent Structural Principle in Physics: Conceptual Framework, Dynamical Bounds, and Experimental Signatures
#Description: This work introduces the concept of the Infinite Gap (ε∞) as a model-dependent structural principle capturing the fundamental mismatch between idealized mathematical descriptions and physically realized states. Rather than defining ε∞ as a single universal observable, we formulate it as a family of gap functionals whose explicit representation depends on the physical framework under consideration. The concept is developed across multiple domains, including cosmology, quantum mechanics, and information theory, providing a unifying perspective on discrepancies between theoretical predictions and empirical observations. In the quantum context, the Infinite Gap is directly related to measurable quantities such as state purity, defined by 1−Tr(ρ2), and is shown to obey dynamical inequalities under Lindblad evolution, reflecting the irreversible growth of decoherence. This establishes a direct bridge between the conceptual framework and experimentally accessible systems. We further introduce a structural contribution, δstruct, representing an irreducible component of the gap that cannot be attributed to noise, entropy, or decoherence. This term is proposed as a hypothesis capturing intrinsic limitations in the representation of physical reality by mathematical models. The framework also provides testable implications in controlled quantum systems, where deviations from idealized purity can be experimentally quantified, as well as in cosmology, where large-scale observational tensions may be interpreted within this perspective. Overall, this work aims to establish a conceptual and semi-quantitative bridge between ideal theoretical constructs and the limitations inherent in their physical realization, positioning the Infinite Gap as a candidate structural feature of physical theory. # Keywords: * Infinite Gap * Structural Principle in Physics * Quantum Decoherence * Density Matrix * Purity * Entropy * Lindblad Equation * Cosmology * Model-Dependent Framework * Effective Theories * Information Theory * Foundations of Physics
Modern physics has achieved extraordinary predictive success, yet it continues to face unresolved conceptual tensions concerning the role of the observer, the nature of information, and the origin of physical structure. From quantum measurement to cosmology, the assumption of an observer-neutral reality increasingly appears insufficient to fully account for empirical phenomena and theoretical inconsistencies. This manifesto proposes an Informational Observer-Centered Framework, in which information is treated as a fundamental ontological substrate and observation as an active, structured process rather than a passive act of measurement. Within this perspective, physical systems, observers, and informational exchanges form a unified dynamics, where state reduction, decoherence, and emergent classicality arise from informational interactions and constraints. Rather than introducing a new closed theory, this manifesto establishes a conceptual foundation unifying several complementary models—including Informational State Dynamics, observer-dependent informational compression, and informational interpretations of quantum and cosmological phenomena—into a coherent research program. The framework is explicitly non-dogmatic, open to falsification, and intended as a guiding structure for further theoretical development and empirical testing. The aim of this document is not to replace existing physical theories, but to clarify their conceptual boundaries and propose an integrative lens through which unresolved problems in quantum foundations, cosmology, and cognitive systems may be systematically explored.
This work presents a conceptual and representational framework aimed at clarifying the structural relationships among established physical theories across relativistic, quantum, and cosmological regimes. Rather than proposing new dynamical laws, particles, or experimentally testable predictions, the manuscript focuses on how existing physical descriptions may be consistently interpreted within a unified representational structure. The proposed Dual-Spacetime Projection Framework distinguishes between an underlying descriptive domain and an observed effective spacetime, connected through a scale-dependent projection. This distinction is intended as a formal and interpretative tool, not as an ontological claim about the existence of multiple physical spacetimes. Within this perspective, several foundational features of modern physics—such as Lorentz invariance, finite signal propagation, quantum uncertainty, and large-scale cosmological behavior—are discussed as consequences of representational structure rather than as independent postulates. The manuscript is positioned as a contribution to the foundations of theoretical physics, offering a coherent conceptual lens for organizing and interpreting existing theories. It is intended for readers interested in foundational questions, conceptual unification, and the representational aspects of physical law, and does not rely on experimental data or numerical simulation.
This paper introduces and formalizes the Principle of Structural Non-Neutrality: In a coherent system, no part can be structurally neutral. Beginning from the quantum limits of measurement—where informative observation necessarily disturbs the observed system—we argue that this apparent "strangeness" of quantum mechanics is not an anomaly but a minimal requirement for any system in which the observer is physically embedded. Classical physics, by contrast, implicitly assumes an external observer who can extract information without interaction—a privilege that no physical theory can consistently grant. From this insight, we derive a sharp distinction between systems and models: A system is that which cannot be known without being changed A model is that which can be known without being changed This distinction yields our central principle: in a genuinely coherent system, every part must contribute to the global structure. Structural neutrality—the presence of a part that makes no difference to the system's state space—is logically incompatible with coherence. Key Contributions Formal definition of structural relevance using mutual information: R(p, S) = I(p; S \ {p}), with exact neutrality defined as R = 0 Proof by contradiction demonstrating that coherent systems (as defined) cannot contain structurally neutral elements Unification of existing frameworks: reliability theory's "component relevance," quantum non-separability, and Integrated Information Theory's irreducibility are shown to be instances of a single structural requirement Resolution of apparent counterexamples: redundant components, silent genes, weakly coupled systems, and gauge degrees of freedom are analyzed and shown to be compatible with the principle Connection to quantum interpretations: the principle constrains (without adjudicating among) many-worlds, decoherence-based, QBist, and relational interpretations Applications: epistemology (coherentist justification), reliability engineering, biological networks, and ecological systems Theoretical Framework The paper traces a conceptual path: Quantum measurement limits → Observer embeddedness → Systems vs. models distinction → Structural non-neutrality principle → Applications across domains The principle is offered not as a revolutionary discovery but as a unifying formulation that makes explicit what several frameworks already imply, while grounding this shared requirement in the impossibility of genuinely external observation. Keywords quantum measurement; observer problem; coherent systems; structural non-neutrality; systems theory; integrated information; reliability theory; quantum foundations; philosophy of physics; mutual information; non-separability; decoherence Academic Context This work bridges quantum foundations, general systems theory, and philosophy of science. It is relevant to researchers in: Foundations of quantum mechanics Philosophy of physics Complex systems theory Integrated Information Theory Reliability engineering Theoretical biology Epistemology (coherentism) Note: This paper underwent multiple rounds of peer review and revision, addressing concerns about scope, mathematical formalization, relation to existing literature, and applicability limits. The final version includes a graded measure of structural relevance, explicit comparison with IIT and reliability theory, treatment of apparent counterexamples, and open questions for future research.
This monograph establishes a unified ontological and mathematical framework for understanding discrete state transformations across mathematics, physics, and complex systems. The work identifies a fundamental gap in binary logic regarding developmental dynamics and proposes the Primarcode domain \mathcal{P} = \{0, 1, +1\} as the minimal necessary extension to accommodate state change. The central claim is that every realized transition requires a minimal act of realization, formalized as a Surplus Operator (+1), which acts upon a structured space of potentials to compel a unique outcome. By developing this distinction axiomatically, the work demonstrates that the universal increment x = y + 1 is not a domain-specific assumption but a structural necessity of any discrete system capable of change. Key Applications & Results: Quantum Mechanics: Reinterprets Schrödinger dynamics as the evolution of potential structures and provides a formal resolution to the measurement problem via the Observer-Modulator Framework, aligning with experimental decoherence data. Prime Number Mechanics: Introduces an arithmetic resonance framework where prime gaps act as frequencies. It presents a deterministic prime generation algorithm and a geometric embedding (the Prime Helix) that reveals the underlying mod-6 structure of the prime sequence. Riemann Hypothesis: Proposes the Leue Map and the Residual Whiteness Condition, establishing a computationally testable equivalence between the Riemann Hypothesis and the spectral completeness of prime-gap residuals. Topology & Cosmology: Provides a constructive proof for the 3-sphere as the necessary resonance arena for physical and arithmetic processes, offering new insights into the nature of space and Dark Energy. This work renders long-standing conceptual tensions—particularly in quantum measurement and number theory—transparent as necessary consequences of ontological structure.
This monograph establishes a unified ontological and mathematical framework for understanding discrete state transformations across mathematics, physics, and complex systems. The work identifies a fundamental gap in binary logic regarding developmental dynamics and proposes the Primarcode domain \mathcal{P} = \{0, 1, +1\} as the minimal necessary extension to accommodate state change. The central claim is that every realized transition requires a minimal act of realization, formalized as a Surplus Operator (+1), which acts upon a structured space of potentials to compel a unique outcome. By developing this distinction axiomatically, the work demonstrates that the universal increment x = y + 1 is not a domain-specific assumption but a structural necessity of any discrete system capable of change. Key Applications & Results: Quantum Mechanics: Reinterprets Schrödinger dynamics as the evolution of potential structures and provides a formal resolution to the measurement problem via the Observer-Modulator Framework, aligning with experimental decoherence data. Prime Number Mechanics: Introduces an arithmetic resonance framework where prime gaps act as frequencies. It presents a deterministic prime generation algorithm and a geometric embedding (the Prime Helix) that reveals the underlying mod-6 structure of the prime sequence. Riemann Hypothesis: Proposes the Leue Map and the Residual Whiteness Condition, establishing a computationally testable equivalence between the Riemann Hypothesis and the spectral completeness of prime-gap residuals. Topology & Cosmology: Provides a constructive proof for the 3-sphere as the necessary resonance arena for physical and arithmetic processes, offering new insights into the nature of space and Dark Energy. This work renders long-standing conceptual tensions—particularly in quantum measurement and number theory—transparent as necessary consequences of ontological structure.
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.