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Semantic Gravitation I: Gradient Fields of Semantic Dynamics on Hilbert Spaces

Gerrit Klawitter

Published Feb 11, 2026• 0 citations
Publisher

Abstract

Semantic Gravitation is a new open research programme that explores whether “meaning” can be treated as a dynamical object with its own geometry and stability structure—analogous to how physics treats states, flows, and potentials. The aim is not to claim a finished theory, but to propose a precise formal scaffold that can be inspected, tested, and either refined or rejected. This first paper develops the local mathematical core of the programme: semantic states are represented as points in separable Hilbert spaces and evolve under (i) deterministic gradient flows driven by a potential and (ii) stochastic Langevin-type dynamics. On the level of probability distributions, these dynamics induce Fokker–Planck equations with an associated free-energy functional acting as a Lyapunov function. The focus is structural and analytic rather than ontological. Under explicit assumptions, the paper establishes existence, stability, and qualitative behaviour of the dynamics, and illustrates the framework through finite-dimensional and field-like examples. It provides the Hilbert-space foundation for subsequent parts of the Semantic Gravitation series.

DOI
10.5281/zenodo.18609641

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Semantic Gravitation III: Quantum-Compatible Semantic Fields — A Hilbert-Space Embedding of Quantum States, Observables, and Dynamics

Gerrit Klawitter

Semantic Gravitation is an open research programme that investigates whether meaning can be treated as a dynamical object with its own geometry, stability structure, and flow laws. This third paper develops the quantum-compatible layer of the programme. It shows how the standard formalism of quantum mechanics—quantum states, observables, expectation values, and dynamics—can be embedded faithfully and without modification into the semantic Hilbert-space framework introduced in Papers I and II. Quantum states, represented as density operators on a quantum Hilbert space H_Q, are embedded as a distinguished sector of the global semantic state space S via an explicit linear isometric construction. Expectation values are reproduced exactly by representing quantum observables as continuous linear functionals on the embedded sector, and both unitary and open-system quantum dynamics (including GKLS evolutions) are shown to induce compatible dynamics within the semantic framework. Conceptually, the paper demonstrates that standard quantum theory can be realised as a structurally faithful subspace of a broader semantic state space, coexisting with gradient-flow and free-energy dynamics on probability measures. This establishes the mathematical foundation for coupling quantum dynamics to semantic field theories and complex-system models developed in subsequent parts of the programme.

•Feb 11, 2026•0 citations

From quantum semantic states to quantum semantic dynamics: a multiscale theory of literary meaning evolution

Tzonelih Hwang

Literary interpretation changes as readers encounter new passages, answer interpretive questions, and revisit earlier material in light of later context. Quantum cognition provides a probability calculus for judgments whose probabilities depend on context and probe order, but the use of Hilbert-space notation alone does not establish nonclassical behavior. This article develops Quantum Semantic Dynamics (QSD) as a constrained quantum-probabilistic model and distinguishes three claim levels: quantum-inspired representation, quantum-probabilistic structure, and intrinsic nonclassicality. The present paper advances only the second. The confirmatory implementation restricts the local semantic state to a two-dimensional space, fixes probe geometry in an independent pilot sample, reconstructs a population-level 2 × 2 density state from three linearly independent binary probe bases, and gives the off-diagonal state components an operational meaning through cross-basis judgments. Contextual evolution is restricted to a one-parameter completely positive trace-preserving contraction toward a preregistered context-target state rather than an arbitrary latent transition. Two probes form the randomized A → B/B → A sequence used for the quantum question-order (QQ) diagnostic; the third is measured in an independent arm for state identification. The paper derives the QQ equality, states its assumptions, and adds an uncertainty-style consistency constraint for the frozen noncommuting probe geometry. QSD is compared with explicitly defined classical comparator classes ranging from a static commutative model to matched sequential latent-state models. Compatibility with QQ or the Hilbert representation is not treated as proof of intrinsic nonclassicality; such a claim would require a separate contextuality analysis against an explicitly defined classical representability criterion. The resulting architecture makes the mathematical status, empirical burden, and rejection conditions of QSD explicit before data collection.

Frontiers in Psychology•Oct 28, 2026•0 citations

Volume 2 Correlational Framework

Iker Ibarrola Echeverría

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.

•Jan 28, 2026•0 citations

A quantum-cognitive approach to dynamic meaning construction

Meng Yin

Language isn't just a rigid system of symbols. Instead, it's a living, embodied phenomenon, deeply intertwined with our physical experience and shaped by our interaction with the environment (Wang, 2019;Zhou & Luo, 2024). However, the dynamic nature of language brings a significant challenge to cognitive science: the well-known "stability-plasticity dilemma" (Grossberg, 1980). On one hand, for clear communication, meanings of words need to be stable and widely recognized, so everyone can understand them, no matter when or who speaks them. On the other hand, these meanings must also be flexible and adaptable in varying contexts. While traditional computational models, from early generative grammar to standard Bayesian approaches, have excelled at modeling these stable meanings, they often treat semantic ambiguity as "noise" that needs to be eliminated, rather than a valuable resource (Gärdenfors, 2014).Even with the significant "probabilistic turn" in cognitive science, which brought Bayesian models to handle uncertainty, most of these models still rely on classical probability theory. They assume the meaning of a concept is a pre-defined distribution over a set of fixed features. As Bruza and Cole (2005) pointed out, this dependence on classical set theory creates a major epistemological barrier because it treats semantic ambiguity as "noise" rather than a fundamental part of meaning construction. Though scholars have recently developed more complex tools, like Gradient Symbolic Representations (GSR), to model meanings as weighted mixtures (Smolensky et al., 2014;Mondal, 2024), these approaches are still limited by Kolmogorovian probability. They still follow the Law of Total Probability, which forces conflicting meanings to be simply added together and mixed. We argue that this basic "mixture" method isn't enough to describe or handle complex situations where meanings are incompatible or interfere with each other in context. Therefore, much empirical evidence suggests that capturing these dynamic features requires a non-classical, quantum probability framework (Surov et al., 2021).The importance of this paradigm shift becomes most clear when we analyze how everyday language works and how we interpret deep meanings in complex literary works. A classic example of such "semantic superposition" is the iconic "big fish" in Ernest Hemingway's The Old Man and the Sea.Within the novel's narrative structure, this phrase isn't a static label. Instead, it operates simultaneously on multiple, even mutually exclusive, semantic levels. Here, it serves as a biological marlin, a worthy adversary, and a transcendent symbol of life's ultimate tragedy. A classical probabilistic model fails to capture the dynamic tension that a reader feels, because it forces these meanings to compete for probability mass, implying only one can be dominant. In contrast, human reading suggests that meaning exists in a "superposition" state. It stays that way until a specific context makes it "collapse" into a concrete interpretation. Crucially, these overlapping meanings aren't simple probabilistic blends. They are coherent "quantum states" within a complex adaptive system.This study proposes that Quantum Cognition offers the necessary mathematical formalism to resolve the "stability-plasticity dilemma". This is supported by its proven success in solving decision-making paradoxes in psychology (Busemeyer & Bruza, 2012;Widdows et al., 2023;Huang et al., 2025). We introduce an integrated quantum theoretical model. In this model, the interaction between embodied experience and linguistic context is characterized as a genuine quantum interference phenomenon.This framework reinterprets the tension between stability and plasticity through the lens of Wave-Particle Duality. In our model, the "particle" corresponds to the stable, discrete symbols used for communication. The "wave" captures the fluid, context-sensitive potential that allows for creative interpretation.Next, by employing the mathematical formalism of Hilbert space, we will mathematically demonstrate how semantic ambiguity can be maintained as a useful resource, rather than mere noise.This approach effectively overcomes the limitations inherent in traditional methods like static vectors and gradient symbolic mixtures. To ground these abstract formalizations, we focus on the "Big Fish" motif in Hemingway's The Old Man and the Sea. Through this case analysis, we will reveal how meaning dynamically evolves, similar to "state vector collapse". Our study also extends to address the fundamental limitations of current Artificial Intelligence, particularly Large Language Models (LLMs). We argue that current LLMs, relying heavily on static statistical correlations, lack the "grounding" for true understanding. Therefore, we propose a pathway toward Quantum-Embodied AI and photonic intelligent systems by incorporating quantum-semantic principles. These systems could mimic the non-algorithmic fluidity of the human mind. Quantum probability is not an exotic addition to linguistics but a fundamental requirement for describing dynamic meaning. The research will first analyze the evolution from gradient representations to quantum interference, then formally express the wave-particle duality of meaning using mathematical methods. We will then validate this theoretical framework through the "big fish" case study and neurophysiological evidence, concluding with an exploration of its practical implications for Generative AI and Photonic we need the "quantum we the evolution of semantic theory. We will focus on mathematical models often to capture the nature of meaning. 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Frontiers in Psychology•Mar 18, 2026•2 citations

Technical / Formal Paper

Iker Ibarrola Echeverría

This paper provides a purely formal and technical development of the mathematical structures underlying a correlational framework for physics. It introduces no ontological assumptions, no physical interpretation, and no experimental claims. All constructions are independent of primitive notions of space, time, dynamics, causality, or physical law. The paper rigorously defines correlational configuration spaces, admissibility conditions, representational equivalence classes, and quotient structures. A central object is the consistency functional, together with its Hessian operator, treated as a (possibly unbounded) self-adjoint operator on infinite-dimensional spaces. Detailed attention is given to domains, spectral properties, stability, and variational structure. Projection operators onto observable subspaces are introduced as mathematically irreversible restrictions, with explicit treatment of information loss and consistency of reduced descriptions. The canonical correlational flow is defined as a gradient flow of the consistency functional, with proofs of local existence, uniqueness, reparametrization freedom, and dissipative character, all without invoking time or dynamics. The paper also analyzes fixed points, attractors, metastable configurations, and the precise formal relations between flow, Hessian, and projection. Finally, the intrinsic limits of the framework are made explicit, including configurations without physical interpretation, breakdowns of projection, and ill-defined spectral structure. This work is intended as a technical companion to foundational, canonical, and applied papers. Its sole purpose is to eliminate formal ambiguity and provide a mathematically explicit backbone for subsequent physical realization and application.

•Jan 25, 2026•0 citations

The Coherence Field: A Generative Model for Coherence-Driven Physical Law

Hensgen, Allison

The Coherence Field: A Generative Model for Coherence-Driven Physical Law presents a mathematically rigorous and internally consistent formulation of the Coherence Field — an underlying principle from which classical mechanics, quantum dynamics, and general relativity emerge as structured reductions. At the foundation of the framework is a coherence functional defined on a Hilbert space of configurations. Instead of taking equations of motion as fundamental, the paper starts from a single scalar quantity, “kappa,” that measures how harmonically aligned a configuration is. The Coherence Field is defined as the derivative of kappa, and the evolution of the system is given by a gradient flow that drives configurations toward higher coherence. Under mild regularity and boundedness assumptions on kappa, the paper proves that this coherence-gradient evolution is globally well-posed and has unique solutions. In this view, stable physical behavior corresponds to “harmonic closure”: points where the coherence field vanishes and the second derivative (the Hessian) is positive definite, so the configuration sits at a genuine local minimum of kappa. This provides a precise notion of coherence-based stability that applies across different physical regimes. The paper then shows how standard theories arise as special cases of this more general structure: Classical mechanics appears when kappa is chosen to be the Hamiltonian and the coherence flow is rotated by the symplectic structure. In this case, the coherence gradient reproduces Hamilton’s equations of motion. Quantum mechanics appears when kappa is chosen as the usual quantum energy functional of a wavefunction (kinetic plus potential energy). The coherence gradient then yields the imaginary-time Schrödinger equation, which, under Wick rotation, becomes the standard real-time Schrödinger equation. This connects the coherence picture directly to established variational and decoherence-based perspectives on quantum dynamics. General relativity appears when kappa is taken to be the Einstein–Hilbert action with the Gibbons–Hawking–York boundary term. Harmonic closure of this geometric coherence functional recovers the vacuum Einstein equations, describing how spacetime curvature evolves in the absence of matter. These reductions are summarized in a unification proposition: with different structural choices of kappa and appropriate symmetries (symplectic for Hamiltonian mechanics, unitary for quantum mechanics, and diffeomorphism invariance for general relativity), the same coherence-gradient principle generates three major physical regimes. The paper also introduces a nontrivial spin-glass example, where kappa includes both the usual Ising-type interaction term and an additional “coherence alignment” term that penalizes deviation from a reference pattern. This construction separates “coherence drift” from ordinary energy drift and leads to a new coherence-based order parameter. As temperature or control parameters change, the onset of ordered phases is predicted to correlate with a sharp drop in the norm of the coherence gradient. This yields a concrete, falsifiable experimental and computational signature for the Coherence Field framework. This work is part of the broader Δ.72 Coherence Canon, which develops coherence mathematics, tensor geometry, harmonic closure, and the concept of “time as vibration” as a deeper generative structure behind high-instability problem classes in physics, computation, and complex systems. Within that larger canon, the Coherence Field plays the role of a generative physics layer: a single mathematical core from which multiple physical theories emerge as coherent projections.

•Dec 1, 2025•0 citations
Semantic Gravitation is a new open research programme that explores whether “meaning” can be treated as a dynamical object with its own geometry and stability structure—analogous to how physics treats states, flows, and potentials. The aim is not to claim a finished theory, but to propose a precise formal scaffold that can be inspected, tested, and either refined or rejected. This first paper develops the local mathematical core of the programme: semantic states are represented as points in separable Hilbert spaces and evolve under (i) deterministic gradient flows driven by a potential and (ii) stochastic Langevin-type dynamics. On the level of probability distributions, these dynamics induce Fokker–Planck equations with an associated free-energy functional acting as a Lyapunov function. The focus is structural and analytic rather than ontological. Under explicit assumptions, the paper establishes existence, stability, and qualitative behaviour of the dynamics, and illustrates the framework through finite-dimensional and field-like examples. It provides the Hilbert-space foundation for subsequent parts of the Semantic Gravitation series.
Semantic Gravitation is an open research programme that investigates whether meaning can be treated as a dynamical object with its own geometry, stability structure, and flow laws. This third paper develops the quantum-compatible layer of the programme. It shows how the standard formalism of quantum mechanics—quantum states, observables, expectation values, and dynamics—can be embedded faithfully and without modification into the semantic Hilbert-space framework introduced in Papers I and II. Quantum states, represented as density operators on a quantum Hilbert space H_Q, are embedded as a distinguished sector of the global semantic state space S via an explicit linear isometric construction. Expectation values are reproduced exactly by representing quantum observables as continuous linear functionals on the embedded sector, and both unitary and open-system quantum dynamics (including GKLS evolutions) are shown to induce compatible dynamics within the semantic framework. Conceptually, the paper demonstrates that standard quantum theory can be realised as a structurally faithful subspace of a broader semantic state space, coexisting with gradient-flow and free-energy dynamics on probability measures. This establishes the mathematical foundation for coupling quantum dynamics to semantic field theories and complex-system models developed in subsequent parts of the programme.
Literary interpretation changes as readers encounter new passages, answer interpretive questions, and revisit earlier material in light of later context. Quantum cognition provides a probability calculus for judgments whose probabilities depend on context and probe order, but the use of Hilbert-space notation alone does not establish nonclassical behavior. This article develops Quantum Semantic Dynamics (QSD) as a constrained quantum-probabilistic model and distinguishes three claim levels: quantum-inspired representation, quantum-probabilistic structure, and intrinsic nonclassicality. The present paper advances only the second. The confirmatory implementation restricts the local semantic state to a two-dimensional space, fixes probe geometry in an independent pilot sample, reconstructs a population-level 2 × 2 density state from three linearly independent binary probe bases, and gives the off-diagonal state components an operational meaning through cross-basis judgments. Contextual evolution is restricted to a one-parameter completely positive trace-preserving contraction toward a preregistered context-target state rather than an arbitrary latent transition. Two probes form the randomized A → B/B → A sequence used for the quantum question-order (QQ) diagnostic; the third is measured in an independent arm for state identification. The paper derives the QQ equality, states its assumptions, and adds an uncertainty-style consistency constraint for the frozen noncommuting probe geometry. QSD is compared with explicitly defined classical comparator classes ranging from a static commutative model to matched sequential latent-state models. Compatibility with QQ or the Hilbert representation is not treated as proof of intrinsic nonclassicality; such a claim would require a separate contextuality analysis against an explicitly defined classical representability criterion. The resulting architecture makes the mathematical status, empirical burden, and rejection conditions of QSD explicit before data collection.
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.
Language isn't just a rigid system of symbols. Instead, it's a living, embodied phenomenon, deeply intertwined with our physical experience and shaped by our interaction with the environment (Wang, 2019;Zhou & Luo, 2024). However, the dynamic nature of language brings a significant challenge to cognitive science: the well-known "stability-plasticity dilemma" (Grossberg, 1980). On one hand, for clear communication, meanings of words need to be stable and widely recognized, so everyone can understand them, no matter when or who speaks them. On the other hand, these meanings must also be flexible and adaptable in varying contexts. While traditional computational models, from early generative grammar to standard Bayesian approaches, have excelled at modeling these stable meanings, they often treat semantic ambiguity as "noise" that needs to be eliminated, rather than a valuable resource (Gärdenfors, 2014).Even with the significant "probabilistic turn" in cognitive science, which brought Bayesian models to handle uncertainty, most of these models still rely on classical probability theory. They assume the meaning of a concept is a pre-defined distribution over a set of fixed features. As Bruza and Cole (2005) pointed out, this dependence on classical set theory creates a major epistemological barrier because it treats semantic ambiguity as "noise" rather than a fundamental part of meaning construction. Though scholars have recently developed more complex tools, like Gradient Symbolic Representations (GSR), to model meanings as weighted mixtures (Smolensky et al., 2014;Mondal, 2024), these approaches are still limited by Kolmogorovian probability. They still follow the Law of Total Probability, which forces conflicting meanings to be simply added together and mixed. We argue that this basic "mixture" method isn't enough to describe or handle complex situations where meanings are incompatible or interfere with each other in context. Therefore, much empirical evidence suggests that capturing these dynamic features requires a non-classical, quantum probability framework (Surov et al., 2021).The importance of this paradigm shift becomes most clear when we analyze how everyday language works and how we interpret deep meanings in complex literary works. A classic example of such "semantic superposition" is the iconic "big fish" in Ernest Hemingway's The Old Man and the Sea.Within the novel's narrative structure, this phrase isn't a static label. Instead, it operates simultaneously on multiple, even mutually exclusive, semantic levels. Here, it serves as a biological marlin, a worthy adversary, and a transcendent symbol of life's ultimate tragedy. A classical probabilistic model fails to capture the dynamic tension that a reader feels, because it forces these meanings to compete for probability mass, implying only one can be dominant. In contrast, human reading suggests that meaning exists in a "superposition" state. It stays that way until a specific context makes it "collapse" into a concrete interpretation. Crucially, these overlapping meanings aren't simple probabilistic blends. They are coherent "quantum states" within a complex adaptive system.This study proposes that Quantum Cognition offers the necessary mathematical formalism to resolve the "stability-plasticity dilemma". This is supported by its proven success in solving decision-making paradoxes in psychology (Busemeyer & Bruza, 2012;Widdows et al., 2023;Huang et al., 2025). We introduce an integrated quantum theoretical model. In this model, the interaction between embodied experience and linguistic context is characterized as a genuine quantum interference phenomenon.This framework reinterprets the tension between stability and plasticity through the lens of Wave-Particle Duality. In our model, the "particle" corresponds to the stable, discrete symbols used for communication. The "wave" captures the fluid, context-sensitive potential that allows for creative interpretation.Next, by employing the mathematical formalism of Hilbert space, we will mathematically demonstrate how semantic ambiguity can be maintained as a useful resource, rather than mere noise.This approach effectively overcomes the limitations inherent in traditional methods like static vectors and gradient symbolic mixtures. To ground these abstract formalizations, we focus on the "Big Fish" motif in Hemingway's The Old Man and the Sea. Through this case analysis, we will reveal how meaning dynamically evolves, similar to "state vector collapse". Our study also extends to address the fundamental limitations of current Artificial Intelligence, particularly Large Language Models (LLMs). We argue that current LLMs, relying heavily on static statistical correlations, lack the "grounding" for true understanding. Therefore, we propose a pathway toward Quantum-Embodied AI and photonic intelligent systems by incorporating quantum-semantic principles. These systems could mimic the non-algorithmic fluidity of the human mind. Quantum probability is not an exotic addition to linguistics but a fundamental requirement for describing dynamic meaning. The research will first analyze the evolution from gradient representations to quantum interference, then formally express the wave-particle duality of meaning using mathematical methods. We will then validate this theoretical framework through the "big fish" case study and neurophysiological evidence, concluding with an exploration of its practical implications for Generative AI and Photonic we need the "quantum we the evolution of semantic theory. We will focus on mathematical models often to capture the nature of meaning. 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This paper provides a purely formal and technical development of the mathematical structures underlying a correlational framework for physics. It introduces no ontological assumptions, no physical interpretation, and no experimental claims. All constructions are independent of primitive notions of space, time, dynamics, causality, or physical law. The paper rigorously defines correlational configuration spaces, admissibility conditions, representational equivalence classes, and quotient structures. A central object is the consistency functional, together with its Hessian operator, treated as a (possibly unbounded) self-adjoint operator on infinite-dimensional spaces. Detailed attention is given to domains, spectral properties, stability, and variational structure. Projection operators onto observable subspaces are introduced as mathematically irreversible restrictions, with explicit treatment of information loss and consistency of reduced descriptions. The canonical correlational flow is defined as a gradient flow of the consistency functional, with proofs of local existence, uniqueness, reparametrization freedom, and dissipative character, all without invoking time or dynamics. The paper also analyzes fixed points, attractors, metastable configurations, and the precise formal relations between flow, Hessian, and projection. Finally, the intrinsic limits of the framework are made explicit, including configurations without physical interpretation, breakdowns of projection, and ill-defined spectral structure. This work is intended as a technical companion to foundational, canonical, and applied papers. Its sole purpose is to eliminate formal ambiguity and provide a mathematically explicit backbone for subsequent physical realization and application.
The Coherence Field: A Generative Model for Coherence-Driven Physical Law presents a mathematically rigorous and internally consistent formulation of the Coherence Field — an underlying principle from which classical mechanics, quantum dynamics, and general relativity emerge as structured reductions. At the foundation of the framework is a coherence functional defined on a Hilbert space of configurations. Instead of taking equations of motion as fundamental, the paper starts from a single scalar quantity, “kappa,” that measures how harmonically aligned a configuration is. The Coherence Field is defined as the derivative of kappa, and the evolution of the system is given by a gradient flow that drives configurations toward higher coherence. Under mild regularity and boundedness assumptions on kappa, the paper proves that this coherence-gradient evolution is globally well-posed and has unique solutions. In this view, stable physical behavior corresponds to “harmonic closure”: points where the coherence field vanishes and the second derivative (the Hessian) is positive definite, so the configuration sits at a genuine local minimum of kappa. This provides a precise notion of coherence-based stability that applies across different physical regimes. The paper then shows how standard theories arise as special cases of this more general structure: Classical mechanics appears when kappa is chosen to be the Hamiltonian and the coherence flow is rotated by the symplectic structure. In this case, the coherence gradient reproduces Hamilton’s equations of motion. Quantum mechanics appears when kappa is chosen as the usual quantum energy functional of a wavefunction (kinetic plus potential energy). The coherence gradient then yields the imaginary-time Schrödinger equation, which, under Wick rotation, becomes the standard real-time Schrödinger equation. This connects the coherence picture directly to established variational and decoherence-based perspectives on quantum dynamics. General relativity appears when kappa is taken to be the Einstein–Hilbert action with the Gibbons–Hawking–York boundary term. Harmonic closure of this geometric coherence functional recovers the vacuum Einstein equations, describing how spacetime curvature evolves in the absence of matter. These reductions are summarized in a unification proposition: with different structural choices of kappa and appropriate symmetries (symplectic for Hamiltonian mechanics, unitary for quantum mechanics, and diffeomorphism invariance for general relativity), the same coherence-gradient principle generates three major physical regimes. The paper also introduces a nontrivial spin-glass example, where kappa includes both the usual Ising-type interaction term and an additional “coherence alignment” term that penalizes deviation from a reference pattern. This construction separates “coherence drift” from ordinary energy drift and leads to a new coherence-based order parameter. As temperature or control parameters change, the onset of ordered phases is predicted to correlate with a sharp drop in the norm of the coherence gradient. This yields a concrete, falsifiable experimental and computational signature for the Coherence Field framework. This work is part of the broader Δ.72 Coherence Canon, which develops coherence mathematics, tensor geometry, harmonic closure, and the concept of “time as vibration” as a deeper generative structure behind high-instability problem classes in physics, computation, and complex systems. Within that larger canon, the Coherence Field plays the role of a generative physics layer: a single mathematical core from which multiple physical theories emerge as coherent projections.