Arc II — Observation Paper 4 Title Correlation Degradation, Rank Collapse, and Operational Horizons in Observational Physics Zenodo DOI 10.5281/zenodo.18188547 Description This paper develops a general operational theory of correlation loss in physical observation, showing how finite accessibility leads to systematic degradation of correlation rank across measurement channels. Rather than treating decoherence, noise, or irreversibility as dynamical effects, the analysis reframes them as consequences of constrained inference under finite observational capacity. Using rank as a protocol-independent measure of accessible correlation, the paper demonstrates that successive observations generically induce rank collapse: a reduction in the dimensionality of distinguishable joint states accessible to observers. When rank collapse becomes irreversible, an operational horizon forms, beyond which no experimental refinement can recover lost correlations. The framework applies uniformly to quantum measurement, classical signal processing, and cosmological observation. It clarifies why certain observational limits appear absolute despite differing experimental designs, and why increased resolution or repeated measurement cannot bypass fundamental accessibility constraints. By identifying horizons with rank collapse rather than spacetime boundaries, the paper unifies measurement limits, decoherence, and observational irreversibility within a single operational structure. Keywords correlation rank; decoherence; measurement limits; operational horizons; information loss; observational physics Notes Arc II — Observation (core synthesis paper) Introduces rank collapse as a universal operational phenomenon Horizons defined by irrecoverable correlation loss Applies to quantum, classical, and cosmological observations Bridges measurement theory and horizon physics
Arc II — Observation Paper 4 Title Correlation Degradation, Rank Collapse, and Operational Horizons in Observational Physics Zenodo DOI 10.5281/zenodo.18188547 Description This paper develops a general operational theory of correlation loss in physical observation, showing how finite accessibility leads to systematic degradation of correlation rank across measurement channels. Rather than treating decoherence, noise, or irreversibility as dynamical effects, the analysis reframes them as consequences of constrained inference under finite observational capacity. Using rank as a protocol-independent measure of accessible correlation, the paper demonstrates that successive observations generically induce rank collapse: a reduction in the dimensionality of distinguishable joint states accessible to observers. When rank collapse becomes irreversible, an operational horizon forms, beyond which no experimental refinement can recover lost correlations. The framework applies uniformly to quantum measurement, classical signal processing, and cosmological observation. It clarifies why certain observational limits appear absolute despite differing experimental designs, and why increased resolution or repeated measurement cannot bypass fundamental accessibility constraints. By identifying horizons with rank collapse rather than spacetime boundaries, the paper unifies measurement limits, decoherence, and observational irreversibility within a single operational structure. Keywords correlation rank; decoherence; measurement limits; operational horizons; information loss; observational physics Notes Arc II — Observation (core synthesis paper) Introduces rank collapse as a universal operational phenomenon Horizons defined by irrecoverable correlation loss Applies to quantum, classical, and cosmological observations Bridges measurement theory and horizon physics
Arc II — Observation Paper 2 Title Measurement as Horizon Activation Zenodo DOI 10.5281/zenodo.18188427 Description This paper reframes quantum measurement as the activation of an operational horizon rather than as wavefunction collapse, branching, or decoherence driven by environmental dynamics. Measurement is defined as the moment when accessible correlations saturate, forcing an irreversible projection of observational structure. Within the finite-accessibility framework, a measurement outcome is not a revelation of a pre-existing value but the stabilization of an inference boundary. Once this boundary forms, further refinement of the measured observable becomes operationally impossible, regardless of improvements in apparatus or control. The horizon is informational, not geometric, and need not coincide with any spacetime boundary. The paper demonstrates that standard features of quantum measurement—outcome definiteness, irreversibility, and apparent randomness—follow directly from accessibility limits without invoking collapse postulates or many-worlds branching. Born-rule statistics emerge as the unique stable weighting compatible with horizon activation and correlation degradation. By treating measurement as a structural transition in accessibility, the work unifies measurement theory with thermodynamic irreversibility and horizon physics. It also clarifies why measurement problems persist when accessibility constraints are ignored. Keywords quantum measurement; wavefunction collapse; horizons; irreversibility; Born rule; operational quantum mechanics Notes Arc II — Observation (core conceptual paper) Measurement defined as horizon formation Collapse reinterpreted as accessibility saturation Born rule emerges structurally Bridges thermodynamics, measurement, and horizons
Arc II — Observation Paper 1 Title Thermalization Without Equilibrium Zenodo DOI 10.5281/zenodo.18180820 Description This paper demonstrates that thermal behavior does not require equilibrium ensembles, microscopic ergodicity, or underlying statistical assumptions. Instead, thermalization is shown to arise from the progressive degradation of accessible correlations under finite observational capacity. The analysis reframes temperature, entropy production, and apparent equilibration as operational phenomena: when observers lose the ability to resolve fine-grained correlations, remaining observables converge toward thermal statistics regardless of the underlying dynamics. Thermal distributions therefore emerge as inference-fixed points under accessibility constraints, not as properties of microscopic phase space. By constructing thermalization without reference to microstates or equilibration timescales, the paper resolves long-standing conceptual tensions between thermodynamics and unitary dynamics. It clarifies why thermal behavior appears robust across systems with vastly different microscopic laws. This framework applies equally to classical, quantum, and gravitational settings, including horizon-induced thermality and detector responses in curved spacetime. Thermal behavior is shown to be a consequence of observational saturation rather than dynamical relaxation. Keywords thermalization; entropy production; irreversibility; operational thermodynamics; accessibility limits; non-equilibrium physics Notes Arc II — Observation (foundational) Thermal behavior derived without equilibrium assumptions Temperature as an inference artifact Applies to classical, quantum, and gravitational systems Conceptual bridge between entropy (Arc I) and measurement
Arc VI — Experiment Paper 3 Title Diagnostic and Therapeutic Guidelines for Conceptual Pathologies in Quantum Mechanics Zenodo DOI 10.5281/zenodo.18226039 Description This paper serves as a diagnostic and interpretive guide to longstanding conceptual pathologies in quantum mechanics, reframed through the lens of finite accessibility. Rather than proposing new dynamics or interpretations, it provides a systematic classification of common conceptual failures—such as nonlocality paradoxes, wavefunction realism, and observer-dependent inconsistencies—and traces them to implicit violations of accessibility constraints. Quantum phenomena traditionally regarded as paradoxical are reinterpreted as artifacts of treating geometrical or ontological structures as fundamental in a regime where only operational accessibility is well-defined. Measurement collapse, contextuality, and observer-relative state assignments are analyzed as predictable consequences of horizon activation and algebraic restriction, not physical discontinuities. The paper introduces a set of “diagnostic criteria” for identifying when a quantum argument has exceeded its domain of operational validity, alongside “therapeutic prescriptions” that restore consistency by removing surplus structure. These guidelines are illustrated across canonical examples including Bell tests, Wigner’s friend, Schrödinger’s cat, and delayed-choice experiments. By systematizing these corrections, the paper functions both as a conceptual reference for researchers and as a pedagogical tool, enabling practitioners to recognize and avoid interpretive errors that arise from illicit geometric importation. Keywords quantum foundations; measurement problem; contextuality; nonlocality; operational interpretation; conceptual diagnostics Notes Arc VI — Experiment (conceptual diagnostics and interpretation) No new dynamics or formalism introduced Identifies accessibility violations as root cause of QM paradoxes Provides practical criteria for evaluating quantum arguments Intended as both reference and pedagogical guide
Arc V — Gravity & Quantum Theory Paper 6 Title Accessibility, Thermodynamics, and the Quantum Gap:Why Purification Is the Minimal Structural Upgrade Zenodo DOI 10.5281/zenodo.18225996 Description This paper addresses the structural gap between classical accessibility-based physics and quantum theory. While finite accessibility accounts naturally for horizons, thermodynamic irreversibility, and emergent geometry, it does not by itself explain quantum coherence, entanglement, or unitary evolution. This discrepancy is identified as the quantum gap. The analysis shows that classical accessibility dynamics generically lead to mixed states and irreversible information loss. To recover quantum phenomena, an additional structural principle is required. The paper argues that purification—the requirement that every mixed state arise from a larger pure state—is the minimal and unique upgrade capable of closing this gap without introducing geometric or ontological assumptions. Thermodynamic behavior is reinterpreted as accessibility collapse within a larger purified state space. Entropy emerges from marginalization over inaccessible degrees of freedom rather than from microscopic counting. The paper demonstrates that purification restores reversibility and coherence while remaining fully compatible with operational constraints. By isolating purification as the sole necessary extension beyond finite accessibility, the work sharply constrains possible routes from classical operational physics to quantum theory. Any alternative upgrade is shown to either over-assume structure or fail to recover core quantum features. Keywords purification; quantum foundations; thermodynamics; entropy; accessibility collapse; mixed states; operational quantum theory Notes Arc V — Gravity & Quantum Theory (structural bridge to quantum theory) Identifies the “quantum gap” in accessibility-based physics Purification isolated as the minimal necessary structural upgrade Thermodynamics reinterpreted as marginalization over inaccessible degrees Sets the foundation for post-geometric quantum mechanics
Arc V — Gravity & Quantum Theory Paper 8 Title Quantum Mechanics Without Geometry Zenodo DOI 10.5281/zenodo.18226024 Description This paper presents a fully non-geometric formulation of quantum mechanics, completing the quantum arc of the finite-accessibility program. Building on the purification-based reconstruction of Paper V.7, it shows that quantum theory neither requires nor benefits from geometric ontology at the fundamental level. Measurement, collapse, and nonlocality are reinterpreted as changes in operational accessibility rather than physical processes occurring in spacetime. Observables are defined as elements of context-dependent accessible algebras, and measurement is treated as the activation of an accessibility horizon that selects a subalgebra without invoking wavefunction realism or spacetime projection. Within this framework, Bell inequality violations arise from the impossibility of embedding incompatible operational contexts into a single geometric structure, rather than from nonlocal dynamics. Similarly, Wigner-type paradoxes and observer-dependent state assignments are resolved as bookkeeping conflicts between distinct accessibility horizons. The paper demonstrates that all empirical predictions of quantum mechanics are preserved exactly, while the conceptual pathologies associated with geometric interpretation are eliminated. Quantum mechanics is revealed as a theory of constrained inference and context activation, with geometry appearing only later as a classical, intersubjective record structure. This work closes the quantum-reconstruction arc by showing that purification-complete quantum mechanics is intrinsically post-geometric. Keywords quantum foundations; non-geometric quantum mechanics; measurement problem; Bell inequalities; operational horizons; contextuality Notes Arc V — Gravity & Quantum Theory (quantum foundations) Quantum mechanics reformulated without spacetime ontology Measurement as accessibility-horizon activation Bell violations explained without nonlocal causation Conceptual closure of the quantum arc of the program
Arc IV — Structure Paper 2 Title Intersubjective Stability: Objective Reality as the Limit of Multi-Agent Inference Zenodo DOI 10.5281/zenodo.18225913 This paper addresses the origin of objective physical reality from the standpoint of finite accessibility by modeling objectivity as a limit of convergent inference across multiple agents. Rather than assuming observer-independent facts as primitive, the framework defines objectivity operationally: a property is objective if it is stable under variation of observers, protocols, and inference strategies constrained by finite access. Using tools from information theory and operational equivalence, the paper formalizes intersubjective stability as a fixed point of multi-agent inference. Physical quantities that persist across observers are shown to be those that survive accessibility filtering and protocol variation, while observer-dependent quantities fail to stabilize and cannot serve as reliable elements of physical law. This approach reframes long-standing debates in the philosophy of physics concerning realism, observer dependence, and measurement. Objectivity emerges not from a privileged ontology but from the convergence properties of constrained inference networks. The paper establishes the structural conditions required for shared physical descriptions and prepares the ground for the emergence of intersubjective geometry in the subsequent work. Keywords intersubjectivity; objectivity; multi-agent inference; finite accessibility; operational equivalence; philosophy of physics; foundations Notes (Optional / Internal) Arc IV — Structure (core conceptual paper) Bridges constants-as-bounds to emergent geometry Conceptual backbone for later geometry and gravity papers