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 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 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 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
Papers I–III derived specific physical structures from three operational axioms: an action gap, finite accessibility, and intersubjective stability. This paper inverts the question: what structures are forbidden? Seven exclusion theorems are proved, showing that large classes of alternative physics are inadmissible under the operational axioms. Each theorem includes explicit assumptions and rigorous mathematical proof. The excluded structures are: 1. **Arbitrarily precise extended synchronisation** — no protocol can certify synchronisation across a domain exceeding the coherence radius R_coh 2. **Higher-than-second-order local dynamics** — via Ostrogradsky instability and certification cost arguments 3. **Non-Born probability assignments** — via the Cauchy functional equation; the Born rule is the unique continuous, non-contextual invariant measure 4. **Non-three-dimensional geometry** — via flux invariance; only d = 3 permits radius-independent total distinguishability 5. **Non-quartic high-frequency dispersion** — via complex analysis of the EFT derivative expansion 6. **Stable relativistic gravitationally-coupled matter** above the accessibility ceiling 7. **Protocol-dependent physical constants** — universality is forced by intersubjective stability The exclusions collectively define an admissibility corridor: the narrow set of physical structures compatible with bounded intersubjective certification. The paper shows that most logically possible alternatives violate the axioms, and that observed physics lies on structural boundaries of the corridor. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** no-go theorems, admissibility corridor, finite accessibility, exclusion theorems, Born rule uniqueness, spatial dimensionality, Ostrogradsky instability, higher-order dynamics, extended synchronisation, intersubjective stability, certification cost, dispersion constraints, protocol invariance, operational axioms, action gap, quantum gravity constraints
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