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.
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.
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
This paper develops a theoretical framework that seeks to unify the foundational principles of quantum mechanics, general relativity, and thermodynamics by extending spatial geometry to include a compactified fourth spatial dimension. The central proposal is that many counterintuitive features of quantum systems—such as wave function collapse, superposition, entanglement, tunneling, and decoherence—emerge as phenomena from the projection of four-dimensional quantum states into observable three-dimensional space. Within this formulation, apparent quantum randomness is reinterpreted as a consequence of observing only a lower-dimensional slice of a higher-dimensional structure. A key innovation of the framework is the introduction of a scalar degree of freedom, termed the entropion field, which governs decoherence and encodes the thermodynamic arrow of time. The entropion field couples directly to both quantum fields and spacetime curvature, leading to modified Einstein field equations and an entropic extension of quantum field dynamics. This mechanism provides a consistent account of classicality emerging from quantum substrates, links entropy growth to projection dynamics, and clarifies how spacetime geometry constrains quantum evolution. The theory is presented through a structured progression of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular emphasis is placed on testable deviations from standard theories, including altered interference signatures in 4D-projected systems, entropion-modulated decoherence rates, and revised mechanisms of tunneling and entanglement. Broader implications are explored for quantum information theory, cosmology, condensed matter, and computational theory. Collectively, these results establish a geometrically grounded unification scheme that integrates the three major pillars of modern physics into a consistent and falsifiable framework.
This derivationally self-contained sector connection instantiates Return Theory (RT): Foundations 1.0.0 (doi:10.5281/zenodo.23286579) in finite-dimensional quantum-record systems. It studies a friend–Wigner laboratory, general two-branch systems, and an exactly solvable branching environment. Quantum mechanics remains the unchanged host law. The RT connection explicitly separates candidate generation, record admission, validation reference, representation reference, observer access, image fibres, inter-observer agreement, and operational objectivity. The release establishes four mathematical results: complementarity for one access, complementarity for two disjoint systems, agreement bounds for jointly realised admitted records, and the equal-tolerance threshold for disjoint content and phase observers. Nine host-law consequences include the friend’s exact content record, Wigner’s exact phase record and content non-identifiability, persistence of internal agreement with loss relative to an outside record, the exact cost of a partial inter-observer copy, agreement without a record, fragment admission and redundancy, phase exclusion from fragments, the classical mutual-information plateau, and an overlapping-observer code construction. The discriminating RT-connection prediction class is explicitly empty in version 1.0.0: every observable distribution in the declared systems is fixed by quantum theory together with the stated preparations, channels, and measurements. Four prospective protocols, V1–V4, are therefore classified as tests of host-law consequences and calibrations rather than as independent RT physical predictions. The reproducibility package contains the release PDF and LaTeX source, exact state-vector code, fixed-seed validation calculations, JSON results, generated tables and figures, machine-readable B1–B10 declarations, the three-way result ledger, checksums, and release-audit scripts. No external data are required. This release continues the earlier public Quantum Records record (doi:10.5281/zenodo.23282709), which is cited only for lineage and timestamping and is not used as a premise.
We introduce Interference-First Reality (IFR), a theoretical framework in which physical objectivity is not assumed as a primitive property of the world, but is derived as a stable multi-observer limit of an underlying interference structure. The fundamental object of the theory is a pre-spatiotemporal interference state Ψ defined on an abstract configuration space X, together with a family of operational observer maps projecting Ψ into observer-accessible representation spaces. Agreement between observers is quantified by an information-geometric redundant dispersion functional. Within IFR, objective structures are defined as stable Fréchet-type centers of observer projections, and physical configurations are selected by a variational principle involving interference dynamics, informational curvature, and redundant multi-observer contraction. The parameter λ is not identified with physical time. Instead, temporal order is defined as the ordered succession of stable minima of redundant dispersion, while effective spacetime geometry arises when the underlying information geometry admits a low-dimensional metric representation. The framework derives objectivity, time, space, and gravitation from a single variational structure. Contents of this deposit. Alongside the complete-formulation preprint, the archive contains the consolidated information-geometry module ifr_core, implementing Jensen–Shannon divergence and distance, geometric and arithmetic barycenters, and the redundant-dispersion functional, together with its verification routines, the full set of analysis scripts, and self-configuring ready-to-run launcher packages for Windows, macOS, and a flat code archive. The ifr_core module is byte-identical across all packages and hash-verified, and reproduces all reported JSD/KL values with a maximum numerical discrepancy below 1e-13. The packages are strictly code-only. Data directories contain only .gitkeep or README.md placeholders, and the public re-downloadable datasets used in the analyses, including Planck, GWOSC, JWST/JADES, and PhysioNet, are intentionally excluded from the deposit. Citation. The Concept DOI 10.5281/zenodo.20528552 is the stable DOI to be used for citation and resolves to the most recent version. Each deposit mints a version DOI for archival versioning only; version DOIs should not be used in manuscripts. Peer-reviewed publication. This document is the complete and unified formulation of the IFR framework, subdivided into six parts for peer-reviewed publication in the Journal of Applied Mathematics and Physics (JAMP). The empirical validation referenced here has been published in Bianchi (2025), JAMP 13, 4355–4378, and Bianchi (2026), JAMP 14, 1627–1674. Part I of the series has been published as Bianchi, M. (2026) Interference-First Reality Theory: Foundations and Objectivity, JAMP 14(7), 2735–2772, DOI 10.4236/jamp.2026.147137. Part II is under peer review; Parts III–VI are in preparation for sequential submission.
This publication presents an extended axiomatic revision of the Probability-Space Axiomatic Foundation. The original minimal logical core (K1–K4), governing realization, temporal asymmetry, and constrained selection among unrealized possibilities, is preserved verbatim and unchanged. This revision introduces an Extended Core (v2.0) consisting of three additional axioms (K5–K7) that are additive rather than revisionary. These axioms are required to support observer-dependent projection of observables, non-signaling correlation via shared collapse ancestry (entanglement), and the emergence of persistent relational deformation interpreted as effective curvature. The extended axioms do not modify the original logical foundation; instead, they constrain how realized structure is accessed, correlated, and stabilized when instantiated as a physical system. The work is structured as a strict in-place extension of the original manuscript. All original text, numbering, and logical development are preserved word-for-word. New material is inserted only where logically required, and is explicitly labeled as part of the Extended Core. No experimental claims are made. No force-based or field-first primitives are introduced. Physical quantities such as mass, energy, or spacetime curvature are not assumed at the axiomatic level. This axiomatic framework is intended to function as a constraint layer for physical theories built on Probability-Space concepts, ensuring compatibility with observer locality, non-signaling correlation, and emergent large-scale structure without altering the minimal logical basis. The framework is falsifiable in principle: any physical realization must recover standard quantum statistics and empirically tested gravitational behavior in appropriate limits. This record supersedes and extends the author’s prior Zenodo publication by providing a formally defined Extended Core (v2.0), while maintaining full continuity with the original axiomatic foundation.
This publication develops the geometric interpretation of the Resonance-Based Subspace Dynamics (RBS-D) framework, extending the conceptual foundation introduced in Publication 01. It establishes a structural description in which physical reality is modeled as a continuous subspace, where particles and observable properties emerge from stable resonance configurations and relational mode structures. This publication (No. 02 / 24) defines the geometric interpretation layer of the RBS-D framework and provides the transition from conceptual hypothesis to structurally interpretable subspace geometry. Core Contributions: • Introduction of a structural vision for a unified physical description based on resonance dynamics • Definition of physical entities as:Stable, phase-coherent mode configurations within a continuous subspace • Conceptual shift from particles to:Relational, geometry-dependent structures • Interpretation of physical properties as:– emergent from internal structure– dependent on phase relations and coupling geometry • Structural hypothesis:Mathematical state spaces represent projections of deeper relational subspace structures Motivation and Conceptual Position: Modern physics provides highly accurate predictions, yet often relies on abstract mathematical frameworks with limited direct structural interpretation. Phenomena such as:• high-dimensional quantum states• nonlocal correlations• wave-particle duality suggest that an underlying structural layer may exist. RBS-D introduces a framework that:• preserves empirical validity• while offering a more physically interpretable structural description Core Principles: • Physical reality is continuous at the foundational level • Stable physical entities correspond to resonance states with phase coherence • Observable properties emerge from internal geometric and relational structure • Mathematical representations correspond to projections of deeper subspace relations Within the RBS-D framework, physical systems are described in terms of: • continuous subspace structures• phase-coherent mode configurations• relational geometry between interacting components• resonance-based stability conditions RBS-D CONTENT MAP (Series Navigation) • Core Focus:Conceptual and geometric vision of subspace-based physical description • Key Contribution:Transition from conceptual hypothesis (P01) to geometric interpretation • Extends:→ Publication 01 (Foundational Concept and Structural Framework) • Leads to:→ Publication 03 (Mathematical Operator Formalization)→ Publication 04 (Stability Theory of Resonance Structures) • Application Context:Conceptual physics, geometric modeling, interpretation of quantum and field structures Recommended Entry Path: → Publication 01 (Conceptual Foundation)→ Publication 03 (Mathematical Formalization)→ Publication 04 (Stability Theory) Series Context: This publication is part of the 24-part framework"Resonance-Based Subspace Dynamics (RBS-D)". The series develops a unified structural approach across: • theoretical physics• applied mathematics• nonlinear dynamics• plasma and fluid systems• astrophysical structures The framework progresses from conceptual foundations (P01–P03)to geometric and stability analysis (P04–P07),and further toward applied resonance engineering (P15–P24). Scientific Position: RBS-D does not replace established physical theories, but provides a structural interpretation that connects them through resonance-based dynamics and relational geometry. Abstract (English) This publication develops the geometric interpretation of the Resonance-Based Subspace Dynamics (RBS-D) framework, in which physical reality is described as a continuous subspace structured by resonance and phase relations. Physical entities are interpreted as stable, phase-coherent mode configurations, while observable properties emerge from internal geometric and relational structure. Mathematical state spaces are understood as projections of deeper subspace dynamics. This work establishes the transition from conceptual foundation to geometric interpretation and provides the basis for subsequent mathematical formalization and stability analysis within the RBS-D series.