The Relational Foundation V2

Abstract

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