Non-Associative Octonionic Weight Configurations as a Representational Substrate for Manifest and Non-Manifest Reality

1 Introduction 1.1 Motivation The analogy between cognitive systems and Large Language Models (LLMs) suggests thatmental representations can be modeled as dynamic weight configurations over a struc-tured space. A fundamental question in relational physics and complex systems is whethera similar mathematical architecture can describe the structure of reality itself: a neutralsubstrate the Primordial Relational Field (PRF) that localizes into manifest states throughconfigurations across fundamental conditions of existence.The Relational Ontology Framework (ROF) and Relational Coherence Theory (RCT) pro-pose that fundamental reality consists not of isolated entities but of relational dynamics[4, 5, 6]. Under this framework, the octonion algebra O provides the required mathe-matical substrate to describe the phase transition between a state of perfect coherence(the Coherent Void) and its manifest perturbations, which are perceived as matter, energy,time, and indeterminacy. 1.2 Thesis of the Work This preprint isolates two nested theses. The first is algebraic and elementary; the secondis interpretive and conjectural. (Thesis A, algebraic). A weight configuration in a non-associative octonionic alge-bra possesses an intrinsic structural degree of freedom the non-zero associator thatassociative algebras lack. If ontological friction is defined via the associator, asso-ciative algebras (R, C, H) are structurally incapable of representing the transitionbetween non-manifest and manifest regimes. (Thesis B, projective). The coherence coefficient is not a linear parameter on [0, 1]but a phase on the circle S1, so that Cn = 0 and Cn = 1 denote the same physicalstate. The Void and the quantum foam are two representations of the same point;manifestation is maximal at the antipodal point Cn = 1/2; and the theory is invari-ant under Cn 7 → 1 − Cn up to a choice of representative, the quotient S1/Z2 beingthe real projective line RP1. Thesis A is a trivial consequence of the definition of associativity and is presented onlyto fix notation and scope. Thesis B is the substantive proposal of this preprint: it is math-ematically precise, empirically testable, and not yet confirmed by existing data.