Arc V — Gravity & Quantum Theory Paper 7 Title Purification as the Structural Seed of Quantum Theory:Minimal Axioms Beyond Finite Accessibility Zenodo DOI 10.5281/zenodo.18226009 Description This paper presents a full axiomatic reconstruction of quantum theory starting from finite accessibility augmented by a single additional structural principle: purification. Building on the identification of the quantum gap in Paper V.6, it demonstrates that purification is not merely sufficient but structurally generative—acting as the seed from which the full architecture of quantum mechanics emerges. The analysis shows that when purification is imposed on an accessibility-limited operational framework, core quantum features arise necessarily rather than by assumption. These include superposition, entanglement, reversible dynamics, and the tensor-product structure of composite systems. No geometric ontology, wavefunction realism, or microscopic state postulates are introduced. The paper carefully distinguishes purification from interpretational assumptions. It is treated not as a metaphysical claim about reality, but as a constraint on admissible descriptions: all apparent irreversibility must be explainable as loss of access to a larger, pure structure. From this requirement alone, the mathematical formalism of quantum mechanics is shown to follow. By identifying purification as the minimal axiom beyond finite accessibility, the paper sharply limits the space of possible quantum theories. Any alternative framework lacking purification is shown to fail to reproduce essential quantum phenomena, while any stronger assumption introduces surplus structure. Keywords quantum reconstruction; purification axiom; entanglement; superposition; operational quantum mechanics; axiomatic foundations Notes Arc V — Gravity & Quantum Theory (axiomatic quantum reconstruction) Purification elevated from repair mechanism to generative principle Quantum structure derived without geometry or microstates Strong separation between operational axioms and interpretation Direct precursor to non-geometric formulations of quantum mechanics
Arc V — Gravity & Quantum Theory Paper 7 Title Purification as the Structural Seed of Quantum Theory:Minimal Axioms Beyond Finite Accessibility Zenodo DOI 10.5281/zenodo.18226009 Description This paper presents a full axiomatic reconstruction of quantum theory starting from finite accessibility augmented by a single additional structural principle: purification. Building on the identification of the quantum gap in Paper V.6, it demonstrates that purification is not merely sufficient but structurally generative—acting as the seed from which the full architecture of quantum mechanics emerges. The analysis shows that when purification is imposed on an accessibility-limited operational framework, core quantum features arise necessarily rather than by assumption. These include superposition, entanglement, reversible dynamics, and the tensor-product structure of composite systems. No geometric ontology, wavefunction realism, or microscopic state postulates are introduced. The paper carefully distinguishes purification from interpretational assumptions. It is treated not as a metaphysical claim about reality, but as a constraint on admissible descriptions: all apparent irreversibility must be explainable as loss of access to a larger, pure structure. From this requirement alone, the mathematical formalism of quantum mechanics is shown to follow. By identifying purification as the minimal axiom beyond finite accessibility, the paper sharply limits the space of possible quantum theories. Any alternative framework lacking purification is shown to fail to reproduce essential quantum phenomena, while any stronger assumption introduces surplus structure. Keywords quantum reconstruction; purification axiom; entanglement; superposition; operational quantum mechanics; axiomatic foundations Notes Arc V — Gravity & Quantum Theory (axiomatic quantum reconstruction) Purification elevated from repair mechanism to generative principle Quantum structure derived without geometry or microstates Strong separation between operational axioms and interpretation Direct precursor to non-geometric formulations of quantum mechanics
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 TheoryPaper 9 Title Compatibility of Accessibility and Purification:Existence and No-Go Results Zenodo DOI 10.5281/zenodo.18234636 Description This paper examines the internal consistency of the finite-accessibility framework when augmented by the purification principle, addressing a critical foundational question: under what conditions can accessibility limitations and purification coexist without contradiction? Building on the axiomatic reconstruction of quantum theory in Paper V.7, the analysis treats purification and accessibility as independent structural constraints and studies their joint realizability. The paper proves several existence results demonstrating that nontrivial operational theories satisfying both principles do exist, while also establishing sharp no-go theorems that rule out broad classes of seemingly plausible models. In particular, the work shows that purification cannot be imposed arbitrarily on accessibility-limited theories. Certain accessibility profiles are incompatible with global purification, leading to unavoidable irreversibility or breakdown of compositional structure. Conversely, when compatibility conditions are satisfied, purification enforces strong constraints on allowable dynamics, correlations, and system composition. These results clarify the logical status of purification within the program: it is neither optional nor universally admissible, but a structurally selective principle that dramatically narrows the space of consistent theories. The paper therefore functions as a consistency checkpoint for the Gravity & Quantum Theory arc, delineating exactly where the program can and cannot be extended. Keywords finite accessibility; purification; no-go theorems; operational quantum theory; axiomatic consistency; irreversibility Notes Arc V — Gravity & Quantum Theory (consistency and constraints) Sharp existence and no-go results for accessibility–purification coexistence Clarifies when quantum reconstruction is structurally possible Constrains admissible accessibility profiles and dynamics Logical bridge between axiomatic reconstruction and non-geometric quantum theory
Arc V — Gravity & Quantum TheoryPaper 10 Title Falsifiable Signatures of Accessibility–Purification Interaction:Interaction Signatures Without New Dynamics Zenodo DOI 10.5281/zenodo.18234688 Description This paper identifies concrete, falsifiable experimental signatures arising from the interaction between finite accessibility and the purification principle, without introducing any new fundamental dynamics. Rather than modifying equations of motion or postulating additional fields, the analysis shows that the coexistence of accessibility limits and purification alone imposes observable constraints on information flow, coherence recovery, and correlation structure. Building on the consistency results of Paper V.9, the paper derives operational signatures that distinguish accessibility–purification theories from both classical metric gravity and standard quantum mechanics. These signatures appear as deviations in recoverability, correlation scaling, and compositional behavior in regimes where purification is enforced but accessibility is nonuniform or partially collapsed. Crucially, the predicted effects do not rely on speculative microscopic mechanisms. They arise purely from structural incompatibilities and boundary conditions implied by the joint axioms. As a result, the signatures function as null tests: their absence constrains the accessibility–purification framework, while their presence falsifies theories that treat purification or accessibility as emergent or approximate. The paper emphasizes experimental contexts in which such effects could be probed, including interferometric coherence recovery, composite-system purification tests, and controlled-accessibility laboratory systems. In this way, it closes the Gravity & Quantum Theory arc by translating axiomatic structure into empirical consequences. Keywords finite accessibility; purification; falsifiability; operational tests; quantum structure; coherence recovery Notes Arc V — Gravity & Quantum Theory (experimental signatures) Falsifiable predictions without introducing new dynamics Signatures arise from structural interaction, not microscopic modeling Null-test framework constraining both quantum and gravitational theories Bridges axiomatic reconstruction to experimental accessibility tests
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
This work presents an axiomatic and structural reconstruction of core elements of quantum mechanics. Starting from minimal principles — symmetry under vanishing preference, normalization, consistency of probability assignments, and coherence-preserving dynamics — we derive several central features of the quantum formalism rather than postulating them. Key results include: A geometric derivation of the constants 1/21/\sqrt{2}1/2 and 1/21/21/2 from symmetry and normalization. A theorem-level derivation of the Born rule (including the qubit case) from noncontextuality and additivity. A reconstruction of Schrödinger dynamics from reversible norm-preserving structure. A derivation of the tensor-product structure for composite systems from composition axioms and local tomography, with entanglement emerging as a necessary consequence. Formal treatment of Bell–CHSH nonlocality, Tsirelson’s bound, and no-signalling. A conditional reconstruction of complex Hilbert space structure from intrinsic phase dynamics and compositional consistency. The manuscript is self-contained and framed in standard mathematical-physics language. It does not propose modifications to quantum mechanics, but instead clarifies why many of its defining structures arise inevitably from deeper structural constraints. Prior computational and model-based work by the authors (including diagnostic toy models exploring phase locking, coherence stabilization, and recursive-time dynamics) is acknowledged but intentionally not reproduced here, in order to keep the present work focused on axiomatic structure rather than model-specific architecture. This upload is intended as a foundations and reconstruction contribution, suitable for readers interested in the mathematical and conceptual structure of quantum theory.
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