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
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
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 (R_ID = S_prod / C_L), with explicit failure conditions. The thermodynamic cost of ontological resolution is formalised as the Pixel Tax, grounded in Tank's (2025) Functional Information framework for Quantum Darwinism. The core mathematical theorems have been formally verified using Lean 4 (version 4.14.0) against Mathlib4, with zero sorry placeholders. Combined proof corpus SHA-256: 46aacdfaf77ffbae5e23ce7be10516f29d435f52d49f0075c2ccc3bc527302e3.
This paper proposes that definite reality is constituted through physical encounter at the quantum boundary, not given in advance. Where Einstein showed that properties are relative to a frame of reference, this framework proposes that existence is relational: forged through interaction. Two claims of differing epistemic weight are advanced. 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. All results have been independently reproduced three times using separately authored analysis code, and are fully reproducible from public datasets using standard tools. The Coin invariant, 4ħ ln 2 · G · ρ_rev = c³, ties gravitational coupling, information density, and entropy bookkeeping into one exact constraint. Four headline measurements confirm the constitutive coupling across regimes: R_ID is invariant across conscious states (Bayes Factor 178.60; collapse p = 0.0065 under deep anaesthesia); α·k_B ln 2 is uniform across 26 gate voltage settings in a single-electron quantum dot at 10 mK, where the Onsager coefficient M = p(1−p) holds to machine precision and sech²(A/2) is an exact thermodynamic law with zero free parameters (ΔBIC = 1,508 over Gaussian); the constitutive coupling signature is confirmed in solar coronal plasma with a 1.21× active/quiet R_ID ratio (N = 444,889 pixels, p ≈ 0); and a closure-proximity correction field yields 19.5% LOOCV improvement in nuclear binding at 77σ from null, with a mechanistic shell-closure gradient (doubly magic 58%, singly magic 31%, non-magic 10%) that pinpoints the structural origin. The nuclear result is measured against a minimal four-term SEMF with no shell or pairing corrections: the closure field is the sole non-additive element. A Regime C constitutive law, mc² = α_C·E_conf·ln(N_raw/N_phys), yields the nucleon mass to 0.03% (938.6 vs 938.9 MeV), the proton spin fraction ΔΣ = 0.321 (measured 0.28–0.33; testable at EIC), the Madelung orbital filling rule (19/19 orbitals), and all seven nuclear magic numbers — all with zero adjustable parameters. The nucleon mass, quark spin fraction, and cosmological visible matter fraction are three ratios of the same N_raw = 3 × 8 × 27 = 648 information partition — they are not fitted independently; and the LIGO merger-efficiency floor α_C is exactly linked to the proton spin fraction ΔΣ and visible-matter fraction f_vis by the algebraic corollary α_C = (ΔΣ − f_vis)/(2(1 − ΔΣ − f_vis)), so these quantities are mutually determined faces of the single confinement partition. The Boundary-Addressability Principle derives the Planck/QCD hierarchy from N_raw = 648 alone: ln(E_P/E_conf) = 2 ln(N_colour)/α_C + log₂(N_f) − log₂(N_raw)·α_C⁴ = 45.8798, yielding G to 0.016% from CODATA with zero free parameters and no G as input — a derivation of Newton’s constant from the confinement information partition, now axiomatically complete: the quartic correction −log₂(648)·α𝐶⁴ is closed by the Bandwidth Saturation Axiom (Axiom 7, Appendix Q), the seventh foundational element of TRF. The LIGO merger efficiency floor is derived as a cross-regime theorem: α_C = ln(N_spin/N_F)/(2 ln(N_colour)) = 0.148798, residual 1.79×10⁻⁶. Applied to the de Sitter horizon, the Coin recovers ρ_Coin = ρ_critical algebraically without QFT vacuum-energy additivity; the 648 partition fixes a 17.0% flavour-visibility fraction within confined matter; its cosmological projection to the visible-matter abundance is a zero-parameter structural extension, consistent with Planck’s 15.8% value and independently supported by the electromagnetically weighted quark momentum fraction ≈ 17–19% from global PDF fits. The fine-structure constant is derived to 0.004% accuracy (1/α = 137.031 vs CODATA 137.036) via the Relational Closure Principle: the photon IS the relational encounter (ds² = 0) and cannot occupy a free state in its own information budget, so its self-occupancy fraction f_F/N_gauge corrects the bare EM information cost. This is a conditional one-loop derivation; the sole remaining closure is the formal derivation of the partition factor Z = 1 + f_F/N_gauge from the Coin entropy bookkeeping. A matrix of falsifiable predictions defines the conditions under which the framework would be disconfirmed. The Koide formula K = (m_e + m_μ + m_τ)/(√m_e + √m_μ + √m_τ)² = 2/3 is derived as a structural theorem of TRF’s Z₃ generation symmetry (Appendix P, Sections P.12–P.13): the Flavour Equipartition Principle fixes r = √2 in the Z₃ parameterisation, and the Lepton Encounter Principle — lepton mass is the square of the irreversible relational projection onto the vacuum reference — closes the derivation with zero free parameters entering the ratio. The lepton mass ratios are recovered to m_μ/m_e = 206.875 (0.052%) and m_τ/m_μ = 16.8173 (0.0016%); the 0.0006% empirical departure from exact K = 2/3 is the expected O(x⁴) correction in the Coin entropy expansion — a prediction, not a discrepancy. The absolute lepton mass scale and the 1.68% m_e offset remain open and are orthogonal to the ratio derivation. Keywords: Relational Ontology, Quantum Decoherence, Consciousness, Ontological Resolution, Thermodynamic Irreversibility, Hard Problem of Consciousness, Integration-Dissipation Ratio, Relational Tensor, Thermodynamic Coin, Quantum Darwinism, Pixel Tax, Causal Discovery, Bayesian Model Comparison, Dual Formal Verification, EEG Validation, Solar Coronal Validation, Cross-Domain Invariance, Onsager Uniformity, Master Constitutive Law, Nucleon Mass, Proton Spin Crisis, QCD Bag Constant, Cosmological Constant, Nuclear Magic Numbers, Yang-Mills Mass Gap, Regime C, Madelung Rule, Atomic Ionisation Energies, Nuclear Magic Numbers Derivation, Iterative Relational Actualisation, Pauli Exclusion, Dark Matter Prediction, EM-Weighted Momentum Fraction
We argue that quantum randomness is a logical necessity arising from the nature of intrinsically relational properties—properties lacking definite states outside specific contexts of causal interaction. This motivates Relational Actualism (RAQM), an ontological framework classifying physical properties as invariant, classical, or intrinsically relational. RAQMgrounds wave function actualization in physical interaction rather than observer-relative facts. The actualization criterion is physically grounded and mathematically precise: an interaction constitutes an actualization event when it produces an irreversible increase in the entanglement entropy of the system with its asymptotic environment, generating a robust, redundant causal record. In weakly coupled QFT, a sufficient condition is the exchange of a real, on-shell excitation (pμ pμ = m2c2). This criterion is basis-independent, nonperturbative, and requires no new fundamental constants. To reconcile a globally consistent wave function with special relativity, the Tomonaga-Schwinger equation establishes a foliation-independent global update mechanism. We derive a consistency condition demonstrating that RAQM’s actualization map preserves identical observable statistics at spacelike-separated points regardless of hypersurface choice—a derived result, not a postulate—strictly forbidding superluminal signaling via algebraic microcausality. The no-signaling result applies rigorously to the non-selective (outcome-averaged) actualization map; conditioned branches are treated explicitly. Three specific, discriminating empirical predictions are stated: a finite actualization propagation velocity bounded by the Lieb-Robinson speed, an environment-dependent transition duration scaling as ℏ/ΔEenv, and a sharp reversibility threshold at the actualization criterion. RAQM is distinguished from Relational Quantum Mechanics (which relativizes facts), dynamical collapse models (which ground collapse in stochastic gravitational thresholds rather than causal interaction), decoherence-only models (which leave the outcome problem open), and Everettian Many-Worlds (which denies definite events). Classical behavior emerges dynamically when continuous actualization events eliminate all unconstrained degrees of freedom. The companion papers RAGC and RACI extend these results to gravity, cosmology, and biological complexity; RAHC [Sandeman, 2026e] extends the framework further to the emergence of agentic intelligence, formalizing the recursive coarse-graining hierarchy that generates successive levels of causal closure from the microscopic DAG; key theorems in those papers have been formally verified in Lean 4/Mathlib. A second Lean 4 file (RA_AQFT_Proofs_v10.lean) formalises the finite-dimensional AQFT proof program and proves the frame-independence and Rindler stationarity theorems; see the note on formal verification in the companion paper RAGC [Sandeman, 2026b].
Relational Actualism (RA) is a foundational framework in which on-shell actualization events — irreversible physical interactions satisfying ΔS(ρ‖σ₀) > 0 that write permanent vertices into a growing causal Directed Acyclic Graph — are taken as the primitive constituents of physical reality. From this single ontological commitment, with no new fields or free parameters, the framework derives the results of Papers 1–3 and unifies quantum mechanics, general relativity, and emergent complexity under one algorithm. The Engine of Becoming is a five-step Covariant Stochastic Graph Rewriting System. Step 1 identifies the causal frontier ∂G. Step 2 assigns quantum amplitudes to all possible extensions via Sorkin's foliation-independent quantum measure. Step 3 filters candidates by the entropy criterion ΔS > 0 — a Lorentz scalar, formally verified as frame-independent in Lean 4. Step 4 selects actualizing events with probability given by the quantum measure, yielding the Born rule without postulate. Step 5 recomputes the effective metric from the actualization density λ(x) via Gᵤᵥ = 8πG(Tᵤᵥ^(A) + Θᵤᵥ^(λ)), where Θᵤᵥ^(λ) = ξ[∇ᵤ∇ᵥ(ln λ) − gᵤᵥ□(ln λ)]. Quantum mechanics is the Level-2 (slowly varying λ) limit. General relativity is the Level-3 (dense graph) limit. The Einstein equations with Λ = 0 are the unique macroscopic output, established by the Local Ledger Condition (Lean-verified), the BDG action as the unique discrete Lorentz-invariant action in d = 4 (Glaser 2014), and Lovelock's uniqueness theorem. Time in RA is not a background parameter. Time is the process of the causal DAG growing. Proper time along a worldline is the count of actualization events τ = N_act/λ₀. The arrow of time is not derived from entropy gradients: it is encoded in the directed edges of the DAG, which are irreversible by construction. Ontic randomness at Step 4 is irreducible: the outcome of an actualization event is not determined by any prior fact in V. This is not epistemic uncertainty but the universe's genuine openness. The framework generates an emergent complexity hierarchy through iterated Step-5 coarse-graining. Biological assembly corresponds directly to actualization events (each JOIN operation in Assembly Theory is an exothermic on-shell energy transfer, confirmed by B3LYP/6-311+G* DFT across all five primary biological bond types). The Causal Firewall is the μ = 1 Erdős-Rényi percolation transition: the same critical actualization density governs QCD confinement–deconfinement, flat galactic rotation curves, fault-tolerance thresholds in quantum error correction, and the onset of stable biological complexity. Biosignatures should correlate with thermodynamic environments sustaining μ ≥ 1. The complete falsifiable prediction set of the program comprises 18 specific predictions spanning particle physics, quantum optics, cosmology, quantum computing, and astrobiology, all tabulated here. Hard walls are stated with precision: Bianchi compatibility, amplitude locality (discrete intrinsic proof), continuum limit convergence, and the covariant □(ln λ) extension. Collaboration targets are identified for each.
What physical process underlies the transition between unconscious and conscious brain states? Indicators such as the Perturbational Complexity Index (PCI) can track consciousness level with clinical reliability, yet the mechanism that generates conscious experience remains unspecified. We develop a framework—the Boundary Process Hypothesis (BPH)—built on a single empirically risky conjecture: we hypothesize that consciousness may be the quantum-to-classical decoherence transition as experienced from the inside. On this view, what we call ‘experience’ is the dynamical process through which quantum coherence is irreversibly lost and effective classicality takes hold—the decoherence/einselection process described by Zurek (2003). The hard problem of consciousness and the measurement problem of quantum mechanics, on this reading, may be structurally related aspects of a single physical process—a testable conjecture, not a settled conclusion. We position BPH relative to Integrated Information Theory, Orchestrated Objective Reduction, and recent work on quantum-classical hybrid agency, then derive one primary and two secondary falsifiable predictions: (P1, primary) putative decoherence-related proxy variables (spectral entropy and excess noise ratio from NV-diamond magnetometry) should improve out-of-sample prediction of PCI scores beyond a strong classical baseline under pharmacological modulation; (P2, exploratory) experienced meditators may show detectable proxy differences versus controls after strong confound control; (P3, secondary) graded anesthetic depth should map onto systematically changing proxy profiles. We outline a staged experimental program beginning with a near-term in vitro pilot. Falsification is explicit: if the proxy-augmented model fails to improve consciousness-level prediction over the classical-only baseline by at least ΔR² ≥ 0.05 across two independent datasets, the empirical core of BPH is disconfirmed.
We construct a mathematically rigorous framework for an algorithmic theory of reality (ATR), deriving emergent spacetime and gravity from purely informational, pre-geometric axioms. Operating within a finite-dimensional Hilbert space with no assumed spacetime structure, we formalize the observer as a context-dependent, attention-parameterized POVM acting on a sub-state of a timeless global pure state. The Born rule is derived (not assumed) from Gleason's theorem and its POVM extension [Busch 2003]. Time emerges via the Page-Wootters mechanism, while the observer's selective measurement strategy is shown to be thermodynamically optimal under the Bennett-Landauer erasure limit. Equipping the observer's attention parameter space with the Quantum Fisher Information Metric (QFIM), we obtain an emergent Riemannian geometry bridged to Lorentzian signature via an analytically justified Wick rotation, whose causal structure is shown to be uniquely determined by the Lieb-Robinson bound of the underlying dynamics. By demonstrating that the observer's local Lindblad dynamics exhibit a strictly positive spectral gap (via the Frigerio-Verri irreducibility criterion), we derive the entanglement area law from exponential correlation decay and recover Newton's constant G as an emergent parameter. Einstein's field equations follow as thermodynamic consistency conditions across attention horizons — with no conjectural input for the form of the equations. The preferred factorization (tensor product structure) problem is resolved in principle via thermodynamic Darwinism: only factorizations that group spatially correlated degrees of freedom sustain long-lived observers. The framework offers natural resolutions for black hole singularities and the ER=EPR correspondence, and yields quantitative, falsifiable predictions — including a sub-tick correlation plateau in superconducting qubits, shown by explicit Hamiltonian simulation to be detectable at 199𝜎significancewithcurrenttechnology.Version3Update(April2026)§3.2:Explicitdefinitionsaddedforobserverclockparameters(\nu_\alpha$, Δtα). §9.3: Upgraded Prediction 9.4 to a rigorous first-principles Hamiltonian simulation. Falsification: Ruled out stroboscopic aliasing via an off-resonant control simulation. Proofs: Hardened the structural derivations linking the spectral gap to the Einstein Field Equations.