This paper formulates the Relational Recoverable Reality Principle, a strengthened extension of the Recoverable Reality Principle in which physical realization is described as observer-relative recoverable compression rather than as a single global description of reality. The framework replaces a universal compression map with relational compression maps between interacting subsystems. A physical state is treated as realized when it can be compressed into an effective description, reconstructed up to the equivalence class accessible to a reference subsystem, and protected against singular, nonregular, or information-erasing failure modes. The paper introduces coarse-grained information-geometric reconstruction distances, running recovery couplings, an emergent-time construction from recursive realization events, and sector templates for quantum measurement, gravitational geometry, black-hole horizons, cosmology, and numerical graph-based implementation. In the quantum sector, Born weights are interpreted as minimally lossy measurement records under recoverable compression. In the gravitational sector, smooth geometry is treated as an effective compression of relational substrate data, while singularities are interpreted as nonrecoverable boundary failures. The resulting theory is presented as a relational, computable, and empirically oriented architecture for studying physical realization, rather than as a final microscopic theory of all sectors.
This paper formulates the Relational Recoverable Reality Principle, a strengthened extension of the Recoverable Reality Principle in which physical realization is described as observer-relative recoverable compression rather than as a single global description of reality. The framework replaces a universal compression map with relational compression maps between interacting subsystems. A physical state is treated as realized when it can be compressed into an effective description, reconstructed up to the equivalence class accessible to a reference subsystem, and protected against singular, nonregular, or information-erasing failure modes. The paper introduces coarse-grained information-geometric reconstruction distances, running recovery couplings, an emergent-time construction from recursive realization events, and sector templates for quantum measurement, gravitational geometry, black-hole horizons, cosmology, and numerical graph-based implementation. In the quantum sector, Born weights are interpreted as minimally lossy measurement records under recoverable compression. In the gravitational sector, smooth geometry is treated as an effective compression of relational substrate data, while singularities are interpreted as nonrecoverable boundary failures. The resulting theory is presented as a relational, computable, and empirically oriented architecture for studying physical realization, rather than as a final microscopic theory of all sectors.
This paper is the seventh in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of objects independently existing within spacetime. Two prior results set up its question. The third paper (Uchida, 2026c) characterized public finality—recoverability of a committed fact by many mutually independent accessors, non-disturbingly and repeatably—as a broadcast redundancy: an effectively classical pointer value proliferated across many disjoint environmental fragments, approximately in the form of spectrum broadcast structure. The fourth paper (Uchida, 2026d) read the evaporating black hole as the regime in which a committed interior record crosses, at the Page time, from hidden to recoverable encoding, reconstructible from the radiation through entanglement-wedge reconstruction; and the parent framework (Uchida, 2026a, §10) had flagged holographic quantum error correction as a place its language of protected, redundantly encoded, locally recoverable records might find content. The present paper makes that content precise as a structure theory of recoverable records, kept separate from any claim of new physics or any suggestion that the framework derives the underlying results. The central claim is conditional and structural. The framework does not claim that every recoverable piece of information is a code, that the universe is literally a quantum error-correcting code, or that AdS/CFT describes our universe. It claims that when information qualifies as an erasure-recoverable record because an encoding preserves a logical degree of freedom—or a logical operator algebra—against a specified family of physical erasures, then that recoverability is formalized as an exact or approximate quantum error-correcting structure, in which each correctable erasure leaves an authorized complementary region supporting a recovery map. That formalization is itself an established mathematical classification; the paper's interpretive contribution is to read the series' recoverable record through it, and to set it against a second, distinct architecture. Broadcast redundancy makes the same effectively classical value legible from many disjoint fragments; erasure-correcting redundancy protects noncommuting logical quantum information by keeping each correctable erased region ignorant of—approximately private with respect to—the protected logical content, while suitable remaining regions recover it. The formal engine of this distinction is the duality between correctability and privacy (the information–disturbance tradeoff), not the no-cloning theorem; no-cloning, with the access structure of quantum secret sharing, survives as the reason independently usable recovery regions for arbitrary unknown logical quantum information must overlap. Three commitments keep the reading honest. First, it separates three senses of "record"—protected logical quantum information, a committed classical record, and a publicly final record—and insists that recovery or decoding restores access to logical quantum information but does not, by itself, commit a classical value; commitment additionally requires measurement, pointer imprinting, decoherence, and stabilization (Uchida, 2026f), and public finality a still later broadcast. Second, holographic quantum error correction is offered as the sharpest worked model of the distinction, with exactly solvable tensor-network toy codes (exact within the model) kept distinct from realistic semiclassical holographic reconstruction beyond those limits (generally treated as approximate), and both from the further question of state-dependence. Third, code-recoverability does not by itself imply public finality: protected quantum information can be recoverable from authorized regions while remaining non-public. The framework relabels code structure as the architecture of recoverability and derives none of it, making no independent empirical prediction. Its disciplined thesis is that codes protect recovery; broadcasts create publicity—different architectures that a single physical history may nonetheless realize in sequence.
This paper proposes Causal Bandwidth Reconstruction as a finite-information framework for interpreting physical reality. The central claim is that an observer-like physical system does not access the complete instantaneous state of the universe, but reconstructs an effective reality from causally available information constrained by light-speed delay, channel bandwidth, source capacity, memory, and processing limits. The paper introduces a causal bandwidth bound combining propagation delay, effective information bandwidth, source information capacity, and observer integration capacity. It then defines observer-relative effective reality as a reconstruction map acting on information from the past light cone. Within this framework, classical physical laws are interpreted as stable compression rules: position, velocity, mass, temperature, pressure, rigidity, friction, optical objects, and field values are treated as low-dimensional variables that remain stable after inaccessible microscopic distinctions are removed. The revised version adds a conditional Born-rule stabilization argument. It does not claim to derive the Born rule from light speed alone. Instead, it shows that if stable quantum records form an orthogonal event algebra and the reconstruction map is positive, normalized, additive on orthogonal channels, unitarily invariant, noncontextual, and stable under finite-bandwidth coarse-graining, then Gleason-type reasoning selects the squared Hilbert amplitude as the unique stable record probability. In this interpretation, the Born rule is treated as the probability measure naturally selected by stable finite-bandwidth record reconstruction. The paper also adds testable directions. These include finite-bandwidth delayed-choice quantum eraser experiments, bandwidth-controlled decoherence and record-stabilization studies in macroscopic quantum systems, finite-time Wigner-type record synchronization, and numerical estimates using photon-counting detector bandwidths, sensory bandwidths, and integration capacities. A curved-spacetime extension is outlined by replacing the flat delay r/c with retarded causal time in a general metric and by interpreting horizons as extreme causal-bandwidth boundaries. This work is theoretical and interpretive. It does not replace standard quantum mechanics, relativity, thermodynamics, or statistical mechanics. Rather, it provides a unifying finite-information lens through which classical laws, thermodynamic coarse-graining, optical perception, field descriptions, quantum measurement, Born-rule stabilization, and observer-relative record formation can be understood as different regimes of causal information reconstruction. Interdisciplinary fields crossed by this work include theoretical physics, special relativity, quantum foundations, Born-rule studies, decoherence theory, quantum measurement theory, information theory, Shannon communication theory, statistical mechanics, thermodynamics, black-hole information theory, holographic principle research, philosophy of physics, information geometry, cognitive science of observation, artificial observer theory, AI systems, virtual embodiment studies, and complex-systems modeling.
This paper develops a conditional first-principles architecture for reconstructing the Born rule from delayed recoverable geometry and recoverability–fidelity rigidity. The framework is organized in two layers. The first layer, Delayed Recoverable Geometry Completion, begins from stabilized distinction, delayed history, closure-defect suppression, and recoverable compression rather than from primitive spacetime, instantaneous time evolution, or measurement probability. Within this layer, physical realization is treated as a stable and observer-relative recoverable compression of deeper relational structure. The second layer, Recoverability–Fidelity Rigidity under Unitary Retarded Probability Dynamics, reconstructs the Born rule inside the projective quantum sector. Instead of postulating an additive probability measure over projectors, the theory introduces a recoverability functional between physical rays. Ray invariance, unitary covariance, orthogonality annihilation, tensor multiplicativity, and local ray-reconstruction calibration force this recoverability functional to become squared projective fidelity. Stable record cells then generate branch projectors, branch recoverability becomes the standard Born weight, and large-record frequency stabilization converts these weights into observed probabilities. A revised ray-quotient reconstruction loss is introduced to clarify that the quadratic exponent is fixed by intrinsic projective reconstruction error rather than by assuming the Born probability rule. The paper also includes a kernel-deformed decoherence example, showing how a delayed memory kernel can produce a concrete visibility-suppression prediction relative to ideal pure-state Born predictions while preserving the trace rule for the effective delayed state. The result is not presented as an unconditional derivation of all physics from no assumptions. Rather, it is a closed conditional architecture showing that, once delayed recoverable physical realization compresses into a reversible projective quantum sector, the Born rule can be reconstructed as the stable frequency law of recoverable quantum branches.
Relational Theory of Expression (RTE) proposes a new conceptual framework in which physics is understood not primarily as a theory of independently existing objects, but as a theory of the conditions under which physical content becomes expressible within a quasilocal domain. The central idea is that the physically accessible object is not an isolated state x, but an operational equivalence class [x]ᴰ, induced by an expression map Eᴰ : Sphys → Sobs(D). This naturally leads to x₁ ∼ᴰ x₂ ⇔ Eᴰ(x₁) = Eᴰ(x₂) and to the factorization of physical descriptions through operationally meaningful quotient spaces. The framework separates definitions, theorems, physical postulates, hypotheses, and interpretations, allowing philosophical motivation and mathematical structure to evolve independently while remaining logically consistent. Beyond operational equivalence, RTE introduces a rigorous distinction between manifestation, reconstruction, and ontology. Past and future are treated as compatible reconstructions, represented by the space of histories Γᴰ(d) rather than directly observable entities. Local physical descriptions are organized through presheaf and sheaf structures, where restriction maps connect overlapping domains and failures of gluing provide a natural mathematical language for contextuality, boundary effects, and reconstruction limits. Within this framework, auxiliary constructions such as B⁴ are treated with explicit type discipline: they may exist as mathematical fillings or variational tools without being promoted to physically existing regions of spacetime. The programme therefore distinguishes mathematical existence from physical existence in a precise and operationally useful way. The present work is intended as the foundational paper of a broader research programme connecting quasilocal cosmology, information theory, observer-dependent reconstruction, and categorical mathematics. Rather than proposing a new dynamical law, it establishes a minimal structural language in which later developments—such as the DRD information framework, quasilocal B⁴ cosmology, boundary variational principles, and observational cosmology—can be formulated within a common conceptual architecture. The guiding principle is that physics studies invariant structures of expressibility, while the objects of physics emerge as stable relational manifestations rather than self-subsistent entities. This first version is therefore conceived as the opening movement of a larger mathematical programme, providing a disciplined foundation for subsequent theoretical and empirical developments.
We develop a pregeometric reconstruction framework in which quantum theory, entanglement structure, gauge symmetry, locality, Lorentzian spacetime geometry, gravitation, and effective physical constants emerge from recursively stabilized coherent relational organization. The framework begins from a primitive relational substrate consisting of compositional accessibility processes endowed with complex coherent transport amplitudes. No background spacetime manifold, metric geometry, particle ontology, or external classical time parameter is assumed fundamentally. The central proposal is that coherent compositional structure is more fundamental than spacetime geometry. Hilbert organization emerges from consistency requirements on coherent relational composition. Observable physical sectors arise through projection stabilization: a dynamical stability-selection process acting on coherent relational transport. Decoherence partitions coherent accessibility structure into approximately factorizable sectors, producing emergent locality and classical persistence. Gauge symmetry emerges naturally as redundancy in coherent transport representation. Lorentzian geometry arises statistically from stabilized accessibility organization, while gravitation appears as thermodynamic relaxation of projected coherent geometry. The framework is formulated as a reconstruction program rather than a completed unified theory. Its aim is not to replace existing physics at the phenomenological level, but to explain why physical reality organizes itself through Hilbert structure, gauge redundancy, locality, relativistic spacetime, and thermodynamic gravitational dynamics. Particular emphasis is placed on the possibility that quantum nonseparability is more fundamental than spacetime locality.
Quantum mechanics represents physical states through complex amplitudes, state vectors, and density operators, yet the ontological status of these objects remains interpretation-dependent. This paper develops a closure-based formulation in which a quantum state is interpreted as a representation of contextually partial relational closure: the state possesses definite mathematical and relational structure while remaining unresolved relative to one or more observational contexts. Within this language, decoherence differentiates closure channels and redistributes locally accessible coherence into relational structure; environmental redundancy stabilizes records; and classical facts emerge as approximately fixed, effectively commuting, redundantly recorded structures. Measurement is separated into three problems—context, weight, and outcome—so that decoherence, Born weighting, and unique outcome selection are not conflated. The paper then distinguishes two stronger research programs from the exact reformulation. First, it asks whether Hilbert-space quantum mechanics can be reconstructed from primitive closure, incompatibility, composition, and consistency principles. Second, it formulates a falsifiable closure-history extension in which physically relevant information might exist beyond the present density operator. Quantum Partial Closure Theory is therefore presented as a relational interpretation and information calculus, a reconstruction program, and a prospective experimental framework rather than as an established replacement for quantum mechanics. Keywords: quantum foundations; closure; wavefunction ontology; coherence; entanglement; decoherence; measurement; classical emergence; quantum information; Hilbert-space reconstruction The wavefunction question Quantum theory is operationally clear about what a wavefunction does. For a normalized pure-state vector ψ∈H and a projective measurement with alternatives {Π_i}, the Born weights are p_i=Tr(ρ_ψ Π_i ), ρ_ψ=ψψ^†. For a rank-one outcome Π_i=e_i e_i^†, this reduces to p_i=|e_i^† ψ|^2. Yet the mathematical clarity of the formalism does not by itself settle what the state vector is ontologically. Interpretations of quantum theory differ over whether the state should be regarded as physical, epistemic, relational, branch-relative, dispositional, or otherwise. The present paper proposes a specific interpretive and reconstructive language: partial relational closure. The central claim is not that the wavefunction is literally a new material substance called closure. Rather, ▭(ψ "is interpreted as a Hilbert-space representation of coherent partial relational closure" .) The word partial is crucial. It does not mean that a state is a scalar fraction of being real or complete. It means that information and constraint are distributed across local, coherent, and relational sectors, and that closure is always specified relative to a context. A Bell state, for example, can be locally indefinite while being relationally exact. A decohered state can be closed with respect to one effective macroscopic context while retaining a larger quantum embedding. A selective outcome can be locally definite without implying that every larger-scale relation in the universe is globally closed. This formulation is motivated by three observations. First, projective dephasing is naturally closure-like because it is idempotent. Second, modern quantum information already supplies exact measures for local coherence, correlations, and record redundancy. Third, the quantum-to-classical transition is naturally relational: local coherence can disappear from a subsystem while information migrates into system-environment correlations. The paper has three epistemic layers. Layer A uses established quantum mathematics. Layer B derives exact information identities and interprets them in closure language. Layer C states reconstruction conjectures and an explicitly speculative beyond-QM closure-history hypothesis. These layers are kept separate throughout. A quantum system is not structureless before measurement. Its amplitudes, phases, conservation relations, and correlations are tightly organized. What remains unresolved is how that structure will become locally definite relative to a chosen measurement context. The partial-closure view therefore distinguishes three broad regimes: Coherent partial closure. Alternatives remain phase-related and can interfere. Contextual differentiation. Interaction or dephasing suppresses coherence between alternatives relative to a context without necessarily choosing one. Selective local closure. A particular outcome is conditioned or realized relative to the measurement relation. In this language, wave-like behavior corresponds to spatially or otherwise contextually unresolved coherent closure, while particle-like detection corresponds to localized closure. Entanglement is closure stored in relations rather than in isolated subsystems. Decoherence is not simply destruction: in a globally pure description it can be a transfer of local coherence into relational entanglement. Classical objectivity appears when relevant records become stable and redundantly accessible. The framework does not assign consciousness a privileged dynamical role. An observer is a partial closure process for constraining possibilities. Explainer video Watch on YouTube (Roots of Reality): https://www.youtube.com/watch?v=UYx_omk3h3A The video, its thumbnail and description are included in this record.