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
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
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
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 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
We present the Interference-First Reality (IFR) framework, in which physical objectivity is not assumed as primitive but is operationally characterized through the stabilization of observer-induced probability distributions under redundant observation. Within this framework, emergent shared reality is identified with the Fréchet barycenter of an ensemble of observer-induced probability distributions in Jensen-Shannon geometry. A consistency theorem shows that empirical barycenters converge almost surely to their population counterpart as the number of independent observers grows, grounding objectivity in standard metric barycenter theory rather than in additional physical postulates. Alongside this variational construction, we introduce a complementary weighted geometric-overlap estimator and analyze its relation to the barycentric formulation. We instantiate the framework across five physical domains: cosmic microwave background (CMB), heart-rate variability (HRV), JWST spectroscopy, large-scale structure (LSS), and gravitational-wave open data (GWOSC). Across all domains, we find reproducible multi-observer collective summaries, bounded Jensen-Shannon distances consistent with stabilization, and a cross-domain distinguishability hierarchy stable under bootstrap resampling and insensitive to the choice between arithmetic and geometric aggregation. Permutation-based null tests further show that the observed clustering structure exceeds domain-specific random baselines. The empirical scope is nevertheless domain-specific: the GW cross-event comparison mainly reflects observational context and noise geometry, while the JWST case probes structured instrumental heterogeneity within a common observing program rather than independent platforms. Finally, we outline an extension in which time is defined as cumulative informational arc-length between successive stabilized collective states, leaving its full development to a companion study.
This document presents a self-contained formulation of Return Theory — Projection, developed within the broader framework of Return Theory (RT) doi:10.5281/zenodo.17857410. In RT, observation is not treated as passive access to an observer-independent reality, but as a constrained geometric projection from a higher-dimensional state manifold to an observer-accessible space. Building on this principle, the present work formalizes the structure of projection, explicitly distinguishing between observable dimensions, latent observables, and intrinsically non-instrumentable degrees of freedom defined by the kernel of the projection map. The concept of narrative stability is introduced as an operational criterion for observational coherence under increasing data accumulation, emphasizing that stability and interpretability may arise from projection geometry rather than intrinsic physical equilibrium. This document is independent of any specific physical domain or instrumental implementation. It provides a general, falsifiable framework applicable across astrophysics, cosmology, and signal analysis, while remaining fully consistent with the geometric foundations of Return Theory as established in the core RT formulation doi:10.5281/zenodo.17857410.
We present the Interference-First Reality (IFR) framework, in which physical objectivity is not assumed as primitive but is operationally characterized through the stabilization of observer-induced probability distributions under redundant observation. The emergent shared reality is identified with the Fréchet barycenter in Jensen-Shannon geometry. Framework instantiated across five physical domains: CMB, HRV, JWST spectroscopy, large-scale structure (LSS), and gravitational-wave data (GWOSC). Published in Journal of Applied Mathematics and Physics, 14, 1627-1674 (2026). DOI: 10.4236/jamp.2026.144077