Coherent Ordering Dynamics (COD): A Unified Attractor Framework for Measurement Distortion, Gravity, and Gauge Structure
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2026
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| _version_ | 1866902092425199616 |
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| author | Trumble, Ray |
| author_facet | Trumble, Ray |
| contents | <p>Coherent Ordering Dynamics (COD), a nonlinear attractor-based framework in which physical structure emerges from the evolution of a coherence tensor Ψ under a single master equation:</p> <p> </p> <p>dΨ/dτ = O[Ψ]·Ψ</p> <p> </p> <p>The document unifies and refines the current COD program across three major sectors:</p> <p> </p> <p>1. Observer / measurement sector</p> <p> An explicit saddle-node fixed-point structure is developed, with derived critical exponent ν = 1/2 and sensitivity f(r*) ≈ -0.3609. A coupled observer-sector model with a smooth thresholded auxiliary variable produces measurement distortions of the form p(1-p) and related antisymmetric variants, providing a concrete dynamical mechanism by which observer coupling can modify Born-style probabilities.</p> <p> </p> <p>2. Gravity sector</p> <p> A tightened compatibility theorem is presented showing that COD attractor constraints strongly favor General Relativity within the class of pure massless conserved second-order tensor theories. Fractal scaling selects the second-order operator class, algebraic consistency favors conserved rank-2 tensors, and luminal propagation favors the massless tensor branch. This work does not claim strict uniqueness over all modified gravity models, but establishes a strong dynamical preference for General Relativity as the canonical representative of the surviving class.</p> <p> </p> <p>3. Gauge sector</p> <p> The internal generator sector of the COD operator is of Yang–Mills type and supports compact non-abelian gauge structure. A minimal internal decomposition into phase, binary sealing, and three-channel exchange sectors yields a Standard Model-like generator count (1 + 3 + 8 = 12), providing a structural route to a minimal U(1) ⊕ SU(2) ⊕ SU(3) gauge algebra. This is presented as gauge compatibility and structural preference rather than a unique derivation.</p> <p> </p> <p>The master document also consolidates the COD fixed-point formalism, the observer/measurement program, PhiGuardian vector-attractor AI safety results, the adversarial refinement dialogue, and mathematical foundations.</p> <p> </p> <p>Current status: This version is a consolidated research record presenting explicit normal forms, toy-model derivations, stress-tested theorem statements, and clearly stated limitations. The framework does not yet establish strict uniqueness of General Relativity, a full derivation of the Standard Model gauge group, or a complete particle mass spectrum. Instead, it defines a coherent and testable dynamical program in which measurement distortion, spacetime curvature, and internal gauge structure emerge as projections of a shared attractor geometry.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19195130 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Coherent Ordering Dynamics (COD): A Unified Attractor Framework for Measurement Distortion, Gravity, and Gauge Structure Trumble, Ray <p>Coherent Ordering Dynamics (COD), a nonlinear attractor-based framework in which physical structure emerges from the evolution of a coherence tensor Ψ under a single master equation:</p> <p> </p> <p>dΨ/dτ = O[Ψ]·Ψ</p> <p> </p> <p>The document unifies and refines the current COD program across three major sectors:</p> <p> </p> <p>1. Observer / measurement sector</p> <p> An explicit saddle-node fixed-point structure is developed, with derived critical exponent ν = 1/2 and sensitivity f(r*) ≈ -0.3609. A coupled observer-sector model with a smooth thresholded auxiliary variable produces measurement distortions of the form p(1-p) and related antisymmetric variants, providing a concrete dynamical mechanism by which observer coupling can modify Born-style probabilities.</p> <p> </p> <p>2. Gravity sector</p> <p> A tightened compatibility theorem is presented showing that COD attractor constraints strongly favor General Relativity within the class of pure massless conserved second-order tensor theories. Fractal scaling selects the second-order operator class, algebraic consistency favors conserved rank-2 tensors, and luminal propagation favors the massless tensor branch. This work does not claim strict uniqueness over all modified gravity models, but establishes a strong dynamical preference for General Relativity as the canonical representative of the surviving class.</p> <p> </p> <p>3. Gauge sector</p> <p> The internal generator sector of the COD operator is of Yang–Mills type and supports compact non-abelian gauge structure. A minimal internal decomposition into phase, binary sealing, and three-channel exchange sectors yields a Standard Model-like generator count (1 + 3 + 8 = 12), providing a structural route to a minimal U(1) ⊕ SU(2) ⊕ SU(3) gauge algebra. This is presented as gauge compatibility and structural preference rather than a unique derivation.</p> <p> </p> <p>The master document also consolidates the COD fixed-point formalism, the observer/measurement program, PhiGuardian vector-attractor AI safety results, the adversarial refinement dialogue, and mathematical foundations.</p> <p> </p> <p>Current status: This version is a consolidated research record presenting explicit normal forms, toy-model derivations, stress-tested theorem statements, and clearly stated limitations. The framework does not yet establish strict uniqueness of General Relativity, a full derivation of the Standard Model gauge group, or a complete particle mass spectrum. Instead, it defines a coherent and testable dynamical program in which measurement distortion, spacetime curvature, and internal gauge structure emerge as projections of a shared attractor geometry.</p> |
| title | Coherent Ordering Dynamics (COD): A Unified Attractor Framework for Measurement Distortion, Gravity, and Gauge Structure |
| url | https://doi.org/10.5281/zenodo.19195130 |