The Phase Relational Field Framework (PRFF) presents a unified process ontology intended to connect quantum measurement, gravitational source accounting, and cosmological response as scale-dependent manifestations of a single, continuously maintained process. It does not replace the predictive formalisms of quantum mechanics or general relativity. In a checked constitutive specialization, the interaction-supporting carrier is represented as a continuous, lossless distributed LC medium with phase speed 1/√(L₀C₀) and characteristic phase impedance Z₀ = √(L₀/C₀). The familiar value Z₀ ≈ 377 Ω follows only when L₀ and C₀ are identified with the measured electromagnetic-vacuum response; Z₀ alone does not constitute an absolute load or capacity bound. The central ontological proposition is that a localized entity is maintained through a reaction surface and that the same maintaining process continues beyond its localization boundary as an Omnidirectional Spherical Process-Load Domain (OSPLD). Its Gauss-surface process-load invariant is unsigned and additive. Microscopic quantum interactions may return signed, phase-, polarity-, and orientation-sensitive relational projections, whereas gravitational source accounting retains the unsigned cumulative magnitude. The signed-interaction/unsigned-gravity distinction therefore describes two coupling channels of one continuous process rather than separate quantum and gravitational substrates. The dynamical carrier-to-metric map remains to be derived; Einsteinian curvature, geodesics, and geodesic deviation are retained as macroscopic representation targets. The framework identifies three linked research programmes: Quantum Statistics and Entanglement: PRFF proposes that topological repartition does not erase the relational phase organization of the parent process. Bell-type correlations may consequently arise from contextual, spatial-geometric sampling of an extended joint OSPLD rather than from action at a distance. A complete realization must derive a non-factorizable joint-response kernel and recover the Born rule, singlet correlations, the maximal CHSH value, and no-signalling under a setting-independent sampling measure. Horizon Dynamics and Coalescence: Event horizons are treated as candidate null reaction-surface limits at which local admission, phase relation, and carrier loading become extremal. Bilateral impedance matching and the condition ΓH = 0 provide a conditional, mode-resolved description of reflectionless horizon coupling, while the symmetric Z₀/2 + Z₀/2 partition remains a constitutive ansatz. Binary coalescence is interpreted as a reciprocal phase-commutation transition between complete OSPLDs. The resulting carrier-stress transient is proposed as the source-level process whose transverse-traceless projection is represented macroscopically by the + and × gravitational-wave polarizations. Cosmological Background and the Hubble Tension: Under an Olbers-type shell accumulation model, an unsigned common-mode matter contribution may diverge with increasing sampling radius unless a separate nonlinear carrier-saturation law intervenes. Its large-scale asymptote could be represented gravitationally as an effective cosmological term rather than as a fundamental local repulsive force. Because cosmic dilution changes the cumulative load distribution, the associated saturation radius and effective cosmological response may drift with the scale factor. This supplies a concrete ontological mechanism to investigate as a possible contribution to the Hubble tension, rather than claiming its resolution in advance. By separating derived relations, constitutive interpretations, working hypotheses, and theorem targets, PRFF establishes an explicit and falsifiable research architecture. Its principal open requirements are the derivation of a covariant carrier and boundary action, the carrier-to-metric map, the nonlinear saturation law, the joint quantum-response kernel, and quantitative confrontation with gravitational-wave and cosmological observations.
The Phase Relational Field Framework (PRFF) presents a unified process ontology intended to connect quantum measurement, gravitational source accounting, and cosmological response as scale-dependent manifestations of a single, continuously maintained process. It does not replace the predictive formalisms of quantum mechanics or general relativity. In a checked constitutive specialization, the interaction-supporting carrier is represented as a continuous, lossless distributed LC medium with phase speed 1/√(L₀C₀) and characteristic phase impedance Z₀ = √(L₀/C₀). The familiar value Z₀ ≈ 377 Ω follows only when L₀ and C₀ are identified with the measured electromagnetic-vacuum response; Z₀ alone does not constitute an absolute load or capacity bound. The central ontological proposition is that a localized entity is maintained through a reaction surface and that the same maintaining process continues beyond its localization boundary as an Omnidirectional Spherical Process-Load Domain (OSPLD). Its Gauss-surface process-load invariant is unsigned and additive. Microscopic quantum interactions may return signed, phase-, polarity-, and orientation-sensitive relational projections, whereas gravitational source accounting retains the unsigned cumulative magnitude. The signed-interaction/unsigned-gravity distinction therefore describes two coupling channels of one continuous process rather than separate quantum and gravitational substrates. The dynamical carrier-to-metric map remains to be derived; Einsteinian curvature, geodesics, and geodesic deviation are retained as macroscopic representation targets. The framework identifies three linked research programmes: Quantum Statistics and Entanglement: PRFF proposes that topological repartition does not erase the relational phase organization of the parent process. Bell-type correlations may consequently arise from contextual, spatial-geometric sampling of an extended joint OSPLD rather than from action at a distance. A complete realization must derive a non-factorizable joint-response kernel and recover the Born rule, singlet correlations, the maximal CHSH value, and no-signalling under a setting-independent sampling measure. Horizon Dynamics and Coalescence: Event horizons are treated as candidate null reaction-surface limits at which local admission, phase relation, and carrier loading become extremal. Bilateral impedance matching and the condition ΓH = 0 provide a conditional, mode-resolved description of reflectionless horizon coupling, while the symmetric Z₀/2 + Z₀/2 partition remains a constitutive ansatz. Binary coalescence is interpreted as a reciprocal phase-commutation transition between complete OSPLDs. The resulting carrier-stress transient is proposed as the source-level process whose transverse-traceless projection is represented macroscopically by the + and × gravitational-wave polarizations. Cosmological Background and the Hubble Tension: Under an Olbers-type shell accumulation model, an unsigned common-mode matter contribution may diverge with increasing sampling radius unless a separate nonlinear carrier-saturation law intervenes. Its large-scale asymptote could be represented gravitationally as an effective cosmological term rather than as a fundamental local repulsive force. Because cosmic dilution changes the cumulative load distribution, the associated saturation radius and effective cosmological response may drift with the scale factor. This supplies a concrete ontological mechanism to investigate as a possible contribution to the Hubble tension, rather than claiming its resolution in advance. By separating derived relations, constitutive interpretations, working hypotheses, and theorem targets, PRFF establishes an explicit and falsifiable research architecture. Its principal open requirements are the derivation of a covariant carrier and boundary action, the carrier-to-metric map, the nonlinear saturation law, the joint quantum-response kernel, and quantitative confrontation with gravitational-wave and cosmological observations.
# Project Description: The Relational Closure Framework (RCF) ## 1. Project Purpose and Background (研究目的与背景) Modern fundamental physics faces deep structural crises, primarily manifested in the mathematical and conceptual incompatibilities between General Relativity (space-time geometry) and Quantum Mechanics (probability amplitudes and non-locality). Most contemporary attempts at unification (such as String Theory or Loop Quantum Gravity) retain the classical paradigm of "objects" (e.g., strings, loops, points) or pre-existing spacetime backgrounds as their ontological starting point. The purpose of this research project is to develop and formalize the **Relational Closure Framework (RCF)**, a radical, background-independent, and purely relational foundation for physics. RCF operates on the core philosophical and mathematical premise that **relations are ontologically prior to objects**. Objects, spaces, fields, and particles do not possess inherent existence; instead, they are emergent phenomena. The framework systematically models how stable physical entities and laws arise from self-consistent, discrete cyclic relations called **closures**. When discrete relations close upon themselves, they generate topological invariants (**holonomies**) that act as structural anchors. The ultimate goal of this project is to provide a rigorous mathematical derivation of the core pillars of physics—including conservation laws, the principle of least action, Born’s rule, the speed of light, and the emergence of continuous spacetime—directly from the discrete algebraic properties of these closure networks. ## 2. Methodology and Theoretical Architecture (方法论与理论架构) The project proceeds axiomatically by establishing four primary structural axioms and one fundamental derived theorem, utilizing tools from abstract algebra, higher category theory, operator algebras (von Neumann algebras), and quantum information theory: * **Axiom 1 (Primacy of Relations):** Pure distinction forms the precursor to all relations. There are no pre-existing entities or backgrounds. * **Derived Theorem 1 (Non-Commutativity):** Because relations must occur sequentially to establish distinction, non-commutativity is a mathematically derived necessity, providing the foundational algebra for quantum observables. * **Axiom 2 (Closure-Induced Invariance):** Stable structures exist if and only if relations form self-consistent cyclic configurations. These closures generate topological invariants (holonomies) across different topological scales. * **Axiom 3 (Chirality from Order):** Spatial and structural chirality (such as the \mathbb{Z}_3 minimal non-trivial chiral closure) emerges inherently from the algebraic ordering of relations. * **Axiom 4 (Bidirectional Group Exchange):** Observation and physical measurement are modeled not as passive recordings, but as bidirectional group-theoretic exchanges between overlapping relational systems forming a joint closure. ## 3. Expected Outcomes and Key Derivations (预期数学成果与推导) The primary expected outcome of this project is a self-consistent mathematical physics framework that derives standard physics as a macroscopic statistical limit of the discrete network. Specifically, the framework delivers the following five principal theoretical results: * **A Generalized Noether Theorem:** The project proves that physical conservation laws are equivalent to the non-trivial kernel of the relational exchange map. In the continuous limit, this reduces to standard Noether currents, but in the discrete regime, it predicts strictly discrete, quantized conserved numbers. * **Derivation of the Least Action Principle:** The action functional (S) is derived as a direct function of the network’s closure invariants (holonomies). The classical principle of least action (\delta S = 0) is shown to be equivalent to a non-Abelian Kirchhoff's law enforcing relational consistency across the network, recovering Maxwell and Yang-Mills fields in the continuous limit. * **Emergence of the Speed of Light (c) and Causality:** Utilizing the **Lieb-Robinson bound** on discrete networks, the project demonstrates that the propagation of structural constraints has a finite, maximum velocity (v_{LR}). This maximum velocity is identified as the physical speed of light (c = v_{LR}). Consequently, causal consistency (the absence of closed timelike curves) emerges as a mathematical corollary of network locality. * **Derivation of the Born Rule:** Quantum randomness is explained via the **Nakajima-Zwanzig projection method** acting on the information limits of localized observers. By applying the **Gleason-Busch theorem**, the quadratic probability rule (|\alpha|^2) is derived rigorously from finite additivity and non-contextuality within the closure space. * **Origin of Spacetime and Wave Functions:** Physical spacetime is reinterpreted as a "pseudo-continuity"—a statistical artifact arising from mutually constraining discrete closures. Similarly, wave functions and the Schrödinger equation are derived as the statistical envelopes of underlying discrete constraint-gap dynamics. ## 4. Empirical Predictions and Observational Significance (经验预测与实验检验) While primarily a foundational and theoretical physics project, RCF yields distinct, falsifiable empirical predictions that differentiate it from standard quantum mechanics and general relativity, providing a clear pathway for future experimental validation (e.g., via multi-ion traps or superconducting qubit benchmarks): * **Observer-Capacity Dependent Decoherence:** RCF predicts that a quantum system's phase dephasing rate (\gamma_{deph}) is explicitly bounded by, and scales non-linearly with, the total information storage/processing capacity (C) of the local physical observer. * **The Quantum "Locking Phase Transition":** The framework predicts that when the information required to specify a quantum state (I_{req}) approaches the maximum capacity of the environment/observer (C), the system will undergo a sharp, non-linear phase transition, dramatically freezing its lifetime within its pointer basis. * **Non-Linear S-Shaped Trigger Curves:** In quantum erasure or interferometry tracking experiments, the interference visibility (V) as a function of information saturation (\Delta = I_{req} - C) is predicted to follow a distinct Sigmoid (S-shaped) curve, rather than the linear or pure exponential decay predicted by standard environmental decoherence models. * **Cosmological Entropy Bounds:** The framework provides a localized, boundary-driven explanation for de Sitter space entropy, predicting the maximum cosmological observer complexity to be bounded near S_{dS} \approx 10^{122} based on the global finiteness of the constraint network.
A Unified Algebraic-Informational Ontology of the Universe Substrate Independence, Distance Geometry, and the Crossed Product Resolution of von Neumann Algebras Driven by Dean A. Kulik September 2026 Introduction to the Relational Universe The enduring pursuit of theoretical physics has been to reconcile the continuous, geometric scaffolding of general relativity with the discrete, probabilistic, and algebraic nature of quantum mechanics. Historically, this reconciliation has faltered because both paradigms impose an a priori ontological framework upon the universe: classical mechanics assumes a pre-existing continuous spacetime manifold, while quantum mechanics presupposes a globally defined Hilbert space. However, a profound synthesis of modern algebraic quantum field theory (AQFT), constructor theory, Euclidean distance geometry, and discrete operator logic suggests that neither space nor continuous state vectors are fundamental. Instead, the universe functions as a closed transformation domain of purely relational, substrate-independent distinctions. In this unified paradigm, information is the foundational bedrock of physical reality. Constructor theory asserts that the laws of physics are not strictly predictive equations of motion, but rather exact specifications of which transformations of physical systems are possible and which are impossible. Because these transformations govern the flow of information independently of the underlying micro-physical medium, reality itself is substrate-independent. A quantum bit, or any physical correlate of information, can be abstractly modeled as a set of allowable operations—such as continuous reversibility and the prohibition of simultaneous encoding—without reference to whether the system is implemented via trapped ions, superconducting circuits, or the vacuum of spacetime. When these allowable physical transformations are formally mapped, they generate a stringent "Operator Grammar". This grammar constitutes the absolute minimum set of constraints dictating how elemental distinctions are addressed, separated, preserved, and subsequently re-read. Crucially, the physical manifestation of spatial geometry does not exist as a prior stage for these operations. Rather, geometry emerges algebraically as a constraint-satisfaction rendering of purely relational distances between distinctions, governed mathematically by the Cayley-Menger determinant. As the system scales to the continuum limit, the localized regions of these transformations map precisely to the local observable algebras of quantum field theory. These algebras are intrinsically pathological von Neumann factors of Type III, which lack well-defined traces or density matrices due to infinite boundary entanglement across localized causal diamonds. The resolution to this algebraic pathology—and the exact mathematical mechanism by which measurable reality, finite thermodynamic entropy, and macroscopic observers emerge—is found in the crossed product of the Type III algebra with its modular automorphism group. This operation yields a well-behaved Type II algebra, effectively restoring the observer to the physical system. This report provides an exhaustive, multi-disciplinary synthesis of this unified paradigm, demonstrating that the universe functions as an infinitely extendable field of non-destructive transformations where spacetime geometry is merely the "read head" interface, and the macroscopic observer is mathematically isomorphic to the modular flow that regularizes quantum entanglement. Substrate Independence and the Operator Grammar To construct a universe from the bottom up, without smuggling in assumptions of space, time, or mass, one must begin with the absolute primitives of logic and transformation. This requires identifying the fundamental constraints—the laws—that govern any distinguishable state. In a purely informational ontology, the universe is governed by an Operator Grammar consisting of fourteen irreducible physical constraints (identified sequentially as C0 through C13), which collectively establish the mechanisms by which a state space can evolve. The absolute floor of this reality is the principle of distinction, defined as C0. For anything to exist, there must be at least two states that are not identical (). Without this primary distinction, there is no substrate to transform, select, bound, relate, or render. Building upon this, C1 dictates the law of continuation: every admissible state must admit a successor distinct from itself, explicitly excluding absolute terminals and self-loops. Mathematically, for every distinction , there must exist a transformation such that . Consequently, the object itself is not the fundamental entity; rather, the object is merely a temporarily stable rendering of a continuous transformation process. These distinctions are governed by the law of independent continuation (C1a). If two distinctions are genuinely independent, the transformation of one cannot secretly consume the other's capacity to continue. In the language of quantum mechanics and operator algebras, this independence requires that the operators commute, such that . If this commutator fails to vanish, the operations are coupled, meaning they share a reference point and cannot be treated as separate informational channels. The Conservation of Reachability and Non-Subtraction Classical physics generally allows for the destruction or annihilation of states (e.g., inelastic collisions, dissipative friction), but in a substrate-independent informational universe, true destruction violates the continuity of the state space. The grammar enforces this through C2, the preservation of reachable history. A lawful transformation cannot annihilate a distinction; it can only alter, detach, bound, merge, or re-address the accessibility of that distinction. The history of the state is conserved within the topological arrangement of the system. This leads directly to C3, the law stipulating that no transformation is a subtraction. In this framework, all change is equal in its obligation to preserve information. A cut or division of a continuous object does not reduce the total payload (); rather, every cut is the birth of two distinct entities, producing a relation . If material is lifted from an active field, it transitions to a "bench" state (), where represents the detached continuation state. The lifted distinction loses its active location but fundamentally retains its existence and relational history. Consequently, C3 is not an arbitrary law but is mathematically derivable as C2 applied specifically to the lift operator. Orthogonal Waves: Selection and Boundary Any physical operation necessitates two orthogonal waves of action: one that dictates what part of the field is acted upon (Decay/Selection), and one that dictates what reality becomes after the action occurs (Boundary). These two waves cannot be collapsed into a single mechanism without freezing the state space entirely. The first wave, Selection (C4), establishes an address into the admissible transformation space, denoted as . The selector does not create the distinction; the distinction was already an admissible potential within the substrate . Selection merely instantiates which specific continuation path is taken. The second wave, Boundary (C5), changes the topology of continuity. A boundary creates a new condition of continuation without requiring new physical payload. For example, if a symbol is lifted from a sequence, the resulting gap can either close (collapsing the prior address and establishing new adjacency) or persist (creating two bounded regions). According to the Wall Theorem, a distinction is physically "alive" if and only if at least one of these two channels (value/selection or relation/boundary) remains unfrozen. Collapsing Decay into Boundary freezes both channels in a single event, resulting in a strictly forbidden configuration. When boundaries are introduced, they possess the unique capacity to create new origins (C6). A continuous sequence evaluated as a whole produces a single macroscopic magnitude. However, if that sequence is sectioned into multiple bounded segments, those segments become independent origins for new computations, despite remaining entangled by their shared substrate history. This sectioning is the primary mechanism for non-linear computational growth in the universe. The Rendering Interface and Constraint Satisfaction The final layer of the Operator Grammar separates the underlying relational data from its macroscopic observation. According to C7, results are rendered rather than merely read. The final observed state is a complex function of the substrate , the geometry of the interaction , the selection criteria , and the boundary topology . It is not the simple linear accumulation of hidden objects. Crucially, Geometry is defined as the "Read Head" (C8). The substrate itself does not inherently possess a Euclidean or curved shape. Geometry controls how the transformation encounters the distinctions. A linear read head defines a one-dimensional adjacency, while a circular, grid, or cyclical step-pattern defines entirely different neighborhood relations. Therefore, physical bases (such as positional notation or coordinate systems) are simultaneously available representations (C9). The selected base does not create the underlying substance; it merely acts as a coordinate system for rendering the preexisting relations. This culminates in the Value-to-Shape constraint satisfaction law (C10). The numbers or data points in the universe do not need to physically resemble a shape. If a relation among rendered values satisfies the constraints of a specific geometry—for example, if they satisfy —then those values instantiate a right-triangle relation. Shape exists purely as a potential admissible structure before it is instantiated, and measurement tests this constrain
ZETA: Identity Theory I Unifying Scalar Quantum Recurrence and 1PN Gravity One Exponential Admissibility Operator with One Parent Action derives Schrödinger and the Mercury Perihelion from Identity, predicting non-singularity at the extremes Preliminary paper of the ZETA Unification Programme Kirk Zavieh · ZETA Research Programme · London · 21 May 2026 SCOPE STATEMENT This paper establishes the founding ontology of ZETA Identity Theory and derives the admissibility operator’s two domain-specialisations — the Born density from the phase domain and Mercury’s 1PN perihelion advance from the loading domain — and names a 2PN candidate empirical separator from general relativity. In ZETA, the Primum is the continuous energetic medium of physical reality. Identity is the configuration of the Primum preserved across continuation — what of the past continues forward, what is admissible into the next moment. U is the local loading of the Primum at any point. We present the ZETA admissibility operator, where each identity continues via ∆ζ: ∆ζ(U) = e−U From this operator, read within the loading-as-ti-boost identification from the contracting identity–transmission eigenmode and then checked by the loading-domain composition conditions on observable attenuation, the operator has two domain-specialisations: loading (Sections 5–8) and phase (Section 9). Quantum recurrence (Section 9): stable phase- recurrence in the phase domain forces the complex amplitude representation ψ ∈ C, gives the loaded Schrödinger equation by narrow-band envelope reduction, and yields the Born density |ψ|2 as the projected conserved scalar of the U(1) Noether current within the positive- frequency narrow-band sector. 1PN gravity (Section 10): Mercury’s anomalous perihelion advance ∆π = 6πGM/[a(1 − e2)c2] = 42.98′′/century is fully derived within the stated ZETA weak-field reduction (static spherical source, test-body limit, 1PN order), with no Mercury-specific fitted coefficient. 2PN discriminators (Section 11): the gauge-invariant expansion ∆K = x2 +O(x3) is a candidate empirical separator from general relativity within the test-particle / circular-orbit approximation class. Beyond 2PN, the exponential structure of ∆ζ motivates a non-singular strong-field programme: because the loading operator remains finite under repeated formal differentiation and integration, ZETA predicts that the full nonlinear Primum sector may avoid horizons, central singularities, and boundary pathologies of the general-relativistic type. The proof is not contained in Paper I and is companion-paper material. Programme content named explicitly but not closed in this paper — master-action completion, Standard Model numerical content (fine-structure constant, Yukawa couplings, CKM/PMNS), full Born-rule branch-probability closure, measurement collapse, Yang-Mills extension, Pauli/Fock from identical-particle topology, relativistic Dirac structure, non- canonical Density Sphere channel, loop-level EFT naturalness audit — is companion-paper material (Foundations II and the technical companion). This is the unification claim of the framework: one Primum, one admissibility operator, one reciprocal parent action, with two derivational reductions (weak-field gravity and quantum-core recurrence) carried at the depth of this paper, and the strong-field reduction plus the full Lorentz EFT naturalness audit named as open programme content. The broader master manuscript embeds this reciprocal parent action in a seven-sector master-action programme with structural- forcing closure under a binary admissibility-character grading (Section 6); Paper I uses only the scalar / loading and bound-recurrence sectors needed for the worked results. The framework’s distinctive ontological commitment is the non-materialisation discipline (Section 13): only the Primum materialises; S3 does not bend, universal time does not dilate, the operator algebra is not a substance. The framework reinterprets relativistic effects traditionally ascribed to spacetime curvature or time dilation as effects on matter and radiation under loading, wherever the corresponding Primum-energy reduction has been derived. The paper does not claim a completed unified theory; it establishes the priority architecture and the worked derivational core.
Abstract Relativity describes the structure of a world once definite reality is in play. This paper proposes a complementary shift in perspective: that definite reality itself is constituted by physical encounter at the quantum boundary. Where Einstein showed that properties are relative to a frame of reference, this framework proposes that existence is relational—forged through interaction, not given in advance. The paper advances two claims of differing epistemic weight. The first is ontological: that relatedness is fundamental, meaning definiteness arises through encounter, not prior to it. The second is a metaphysical proposal: that consciousness, as known in integrated biological organisms, is best understood as the intrinsic interior of recursively organised relational actualisation. An empirical programme is proposed, centred on the Integration-Dissipation Ratio (RID = Sprod / CL), with explicit failure conditions. Independent computational validation on real human EEG (OpenNeuro ds005620, Bajwa et al. 2024, 21 subjects, propofol sedation) confirms the framework’s central prediction: RID is statistically invariant between wakefulness and light propofol sedation with preserved dreaming (p = 0.48, BF = 178.60), and collapses significantly under deep propofol where consciousness is abolished (p = 0.0065). The scalar proxy does not recover window-level linear coupling (r = 0.003); this is expected, as the proxy compresses spatially distributed, directed tensor structure into a single undirected scalar. Cross-species validation on rat neocortical LFP (DANDI 000041, Watson et al.) confirms magnitude consistency with human values (KR1–KR4 all pass). Human sleep deprivation EEG (OpenNeuro ds004902, 21 paired subjects) confirms elevated waking RID under homeostatic debt (p = 0.033). Overnight polysomnography (Sleep-EDF, 152 recordings) reveals a methodological boundary of the histogram-based entropy production proxy, suggesting that the thermodynamic signature of consciousness may require multi-dimensional operationalisation. Four datasets, two species, and three recording modalities are reported with full transparency. The scalar proxy analysis was not designed to test the full tensor equation; its role was to test whether an aggregate projection of the framework carried empirical signal. It did (p = 0.48, BF = 178.60). The framework’s fundamental equation, derived from a Nakajima-Zwanzig coarse-graining of quantum relative entropy (Appendix F), is the Relational Tensor: Σμν(t) = Π ∫ K(t−τ) (dCμν/dτ) dτ + Λμμδμν, where Σμν is the directed thermodynamic flux tensor, Cμν is the directed relational complexity tensor (identified as classical transfer entropy under decoherence), Π = αkBln 2 is the Landauer-bounded thermodynamic cost constant (α ≥ 1), K is a causal memory kernel, and Λμμδμν is the strictly diagonal local bath dissipation baseline. The empirical RID is formally recovered as the macroscopic scalar projection (global spatial summation) of this tensor. The proper test of the elementwise equation requires spatially resolved, directed, temporally filtered network analysis on high-density data. PC algorithm causal discovery confirms three robust causal edges (Sprod–CL, Sprod–Conscious, CL–Conscious), with the Sprod–CLcoupling persisting within conscious and unconscious states independently (r ≥ 0.995). A formal coarse-graining reduction establishes the mathematical chain from quantum relational entropy to macroscopic transfer entropy via the Nakajima-Zwanzig formalism, diagonal trapping of bath correlations, and decoherence-induced projection, with full dimensional consistency against the Landauer bound. The thermodynamic structure of the tensor equation is shown to belong to the same family as emergent gravity: when evaluated on a Bekenstein-saturating system at a local Rindler horizon, it reproduces both inputs to Jacobson’s (1995) thermodynamic derivation of Einstein’s field equations, establishing the framework as a specific instance of the information-geometry correspondence. The core theorems have been independently verified by two formally distinct proof kernels: Lean 4 (v4.14.0) and Rocq/Coq (v9.1.1), with zero placeholders in either verification. A matrix of sixteen falsifiable predictions defines the precise conditions under which the framework would be disconfirmed. Keywords: Relational Ontology, Quantum Decoherence, Consciousness, Ontological Resolution, Thermodynamic Irreversibility, Hard Problem of Consciousness, Integration-Dissipation Ratio, Relational Tensor, Nonequilibrium Brain Dynamics, Quantum Darwinism, Pixel Tax, Causal Discovery, Bayesian Model Comparison, Dual Formal Verification, EEG Validation
We develop the quantum layer of the finite ring cosmology framework: observation as the interaction of a Subject and an Object, phase-coherent cyclic subsystems of a common finite Carrier shell. Four identifications carry the construction, each a derivation rather than an interpretation. The wave function is phase: pure states are windings of the Object's cycle, selected by stationarity under the global drive, with E=hf an identity. The probability amplitude is Object-to-Subject projection onto a forced orthogonal basis, so that completeness, the selection rules, and the Lüders update are finite character theory rather than postulates. Probability is a coincidence count in the Subject's ledger - the group ring Z[i] of the shared quarter-turn core - which derives the Born rule below the coherence horizon and forces complex amplitudes. Composition is conservation: the single drive conserves the relative offset of a pair, synchronised orbits are the Bell states, and the framework saturates the Tsirelson bound exactly, S=2(ζ8+ζ8−1)=22, while reproducing the network behaviour of the real-versus-complex discrimination. The same conservation makes gravity an entangling channel whose distinctive parameter-free signature is equal force but unequal entanglement - a source gravitates by its full mass yet entangles only through its coherent fraction --- with entanglement forming at the Newtonian rate under the complementarity V2+C2=1. Every claim is verified by exact arithmetic in three worked configurations (eleven validation suites, eighty-nine checks), and the experimental confrontation closes in a single falsifiability ledger on one committed carrier scale.
Based upon the static-substrate local-perturbation unified paradigm, this paper elaborates a homologous-origin perturbation phase-locking mechanism to give an ontological account for non-local correlation manifested in quantum entanglement. Building on the axiomatic skeleton established in the paradigm’s foundational preprint, this work bridges microscopic quantum phase behaviour to macroscopic substrate homeostatic self-reversion dynamics. We first review conceptual limitations of major mainstream quantum interpretations, including the Copenhagen interpretation, many-worlds interpretation, and Bohmian mechanics. Under the substrate-perturbation framework, Bell-type experimental statistics are fully reproduced without postulating superluminal signal propagation. Entanglement correlation originates from inherited locked-phase relations established at the moment when a composite homologous perturbation splits, rather than ongoing real-time information exchange between spatially separated particle-like fragments. Non-local correlation is an intrinsic holistic property of the original unified perturbation source system, not an interaction transmitted across spatial distance. The mechanism naturally respects Lorentz invariance and circumvents conceptual pathologies common to non-local hidden-variable constructions. We analyse decoherence as environmental perturbation-driven erosion of inherited phase relations. Within this picture we interpret double-slit interference and quantum-eraser observations without invoking observer-dependent collapse or retrocausality. We further point out the structural isomorphism between microscopic spin and large-scale galactic rotation originating from universal substrate perturbation dynamics. This manuscript remains primarily ontological-qualitative; concrete quantitative dynamical derivation and discriminative experimental proposals are reserved for follow-up dedicated work. This article forms a micro-physics branch within the serial research programme The System of Static-Substrate and Local-Perturbation Universe. It unifies microscopic quantum correlation and macroscopic gravitational convergence as two distinct-scale manifestations of the substrate’s inherent homeostatic self-reversion tendency.