TitleStructural Observability: A Framework for Quantum Measurement and Probability This paper proposes the Structural Observability (SO) framework for interpreting quantum measurement and probability. The framework distinguishes between a Complete Relational Configuration (CRC), representing the full relational structure of reality, and the Limited Observational Reference Frame (L-ORF), representing the restricted observational perspective available to observers embedded within spacetime. Within this structure, definite outcomes arise when components of a system’s state become associated with distinguishable physical records in spacetime, a condition termed Structural Observability. Quantum probabilities then arise from the structural limitations imposed by the L-ORF description rather than from fundamental randomness in the underlying configuration. The framework preserves the standard mathematical formalism of quantum mechanics—Hilbert space, unitary evolution, and the Born rule—while providing a structural account of why these elements appear in the observational description. Version 2 — What's new: This version represents a substantial development of the framework presented in Version 1. Major additions include: a formal mathematical structure section with five axioms for the accessibility map Λ, a causal context space (Σ, ≤) making the temporal structure of the framework explicit, and a three-part Structural Observability condition stated as a formal definition with a proof that decoherence is necessary but not sufficient for SO. Six worked examples are included, replacing the purely conceptual treatment of Version 1. Two novel experimental predictions are introduced: a first prediction concerning a critical stability threshold τ below which raw unpost-selected interference is directly observable, and a second prediction concerning a retrievability timescale τR* identified with the quantum information scrambling time, above which interference may again become observable. Together, these define a three-regime non-monotonic structure of interference visibility with no analogue in standard quantum mechanics. A full Statement on AI Assistance has been added, documenting the role of AI language models in the development of the work.* Keywords Quantum foundationsQuantum measurementBorn ruleDecoherenceRelational physics Structural observabilityQuantum interpretation
This revised version (v1.1) introduces several major improvements compared to the previous release: 1. Added a physically consistent open-system model The qubit–bosonic–mode system is now described using a full Lindblad master equation, including: relaxation (T1), non-geometric dephasing, bosonic-mode damping, realistic mode–reduction from a Gaussian scalar field. This makes the model experimentally testable and physically grounded. 2. New coherence-stabilization mechanism validated in an open system We demonstrate that the proposed Energy-Balance Manifold(Δlog=0) acts as a true coherence sweet-spot,even when dissipation is present. The previous version only discussed this at a conceptual level. 3. Improved numerical simulations All figures have been recomputed using the new codebase: 2D manifold maps, analytic suppression law, 3D coherence surface, Ramsey and Spin-Echo simulations. All numerical scripts are now included in /Code and all datasets in /Data,making the results fully reproducible. 4. Added figure references, cross-citations and expanded physical explanation The manuscript now contains: figure-by-figure captions, in-text references to Figures 1–10, an expanded physical motivation for the bosonic-mode reduction, a new section 4.5 Open-System Extension and Realistic Decoherence Channels. 5. Complete package archive with checksums The ZIP now contains: report, code, figures, data, checksum file, README file. This enables independent verification of all results.
EE_V05 represents a significant refinement and extension of the continuum‑geometric framework for electron entanglement within the Monistic Continuum Model (MCM). Compared to EE_V04, this version improves the mathematical clarity, structural consistency, and conceptual accessibility of the model. The continuum field, operator definitions, and correlation structures have been streamlined and unified across all sections. The main updates include : • A revised and more coherent formulation of the continuum field 𝐶 and the organization space ΛΩ.• A clearer and more precise description of the nonlocal operator 𝐷nl and its role in generating non‑separable kernel structures.• An expanded and reformulated main theorem, providing a transparent spectral argument for continuum‑induced entanglement.• A newly added abstract summarizing the core contributions of EE_V05.• A comprehensive glossary of symbols and concepts to support readability and formal consistency.• Refined discussion and conclusion sections, offering improved comparisons with QM, QFT, GR, GRW, Everett, and relational QM.• Harmonized LaTeX structure and section ordering aligned with the conventions of the MCM series. EE_V05 therefore provides a more complete, coherent, and technically precise presentation of electron entanglement as a geometric and dynamical phenomenon emerging from the continuum substrate of the MCM. MCM – Master Document (10.5281/zenodo.22128163)