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The RP-Series: Structural Overview and Axiomatic Progression (RP0–RP21)

Beckford, Woodrow

Published Jan 1, 2025• 0 citations
Publisher

Abstract

This wrapper paper provides a high-level overview of the RP-series (RP0–RP21), summarizing the logical structure, motivation, and progression of the axioms. It is intended as an orientation guide for readers, clarifying how the axioms build from a minimal substrate and asymmetric relations to irreversible δ-transitions, coarse-graining, relaxation dynamics, and the emergence of classical time. The wrapper does not replace the technical content of the RP papers; it offers conceptual summaries only, and readers should consult the individual RP manuscripts for complete definitions, derivations, and formal arguments. The wrapper establishes the context and roadmap for the full Relaxation–Measurement framework.

DOI
10.6084/m9.figshare.30822527.v2

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This wrapper paper provides a high-level overview of the RP-series (RP0–RP21), summarizing the logical structure, motivation, and progression of the axioms. It is intended as an orientation guide for readers, clarifying how the axioms build from a minimal substrate and asymmetric relations to irreversible δ-transitions, coarse-graining, relaxation dynamics, and the emergence of classical time. The wrapper does not replace the technical content of the RP papers; it offers conceptual summaries only, and readers should consult the individual RP manuscripts for complete definitions, derivations, and formal arguments. The wrapper establishes the context and roadmap for the full Relaxation–Measurement framework.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article introduces the general structure, scope, and current status of the framework. The work provides an organized overview of the results developed in the first articles of the series, clarifies the overall logic of the theoretical construction, and situates the framework within a broader research program dedicated to the emergence of quantum, thermodynamic, and geometric structures from informational coherence constraints. The article does not introduce new specific physical postulates, but serves a methodological and introductory role: it defines the conceptual setting of the series, the relation between the different levels of the derivation, and the interpretative and theoretical limitations currently assumed within the framework.
This component contains a conceptual and interpretive synthesis of the Potential Substrate Geometry (PSG) and Kappa-Field Gravity (KFG) frameworks. It is intended to provide a unified narrative and ontological context for how quantum structure, gravitational behavior, and temporal ordering may emerge from a shared, non-spatiotemporal substrate. Unlike the companion technical papers, this document is not a mathematical or predictive work. Instead, it serves as an explanatory framework that clarifies how PSG and KFG relate to one another conceptually, highlighting the division between substrate-level structure (quantum domain) and macroscopic manifestation (gravitational domain). The synthesis introduces interpretive models for: the relationship between nonlocal quantum correlations and shared substrate regions, the emergence of spacetime curvature from coarse-grained patterns of manifestation, the origin of temporal order and irreversibility, and the reinterpretation of photon propagation as sequential manifestation along null structures. All interpretive claims in this component reflect the author’s perspective and are not presented as externally validated conclusions. This document is provided as a philosophical and conceptual companion to the technical formulation of PSG and KFG, and should be read as an overview and unification narrative rather than a formal physics paper. Readers seeking mathematical definitions, field equations, and testable formulations should consult the PSG and KFG components.
This article is the third and final part of a three-paper sequence developing Ontological Field Theory (OFT) as a unified framework grounding quantum mechanics in foundational ontological principles. The trilogy is structured as follows: Part I — Conceptual Necessity:Why Quantum Mechanics Is Inevitable: Ontological Continuity and the Necessity of Quantum Dynamics establishes that quantum mechanics follows necessarily from minimal requirements on coherent being, independently of specific physical postulates. Part II — Technical Realization:Derivation of the Schrödinger Equation from Ontological Field Theory provides the explicit field-theoretic derivation showing how the Schrödinger equation emerges as the non-relativistic limit of a covariant ontological field. Part III — Critical Context:Why Classical Physics Is an Approximation: Decoherence, Coarse-Graining, and the Limits of Determinism explains why classical determinism and trajectories arise only as emergent, approximate descriptions of fundamentally quantum and relational dynamics. Each article is logically self-contained, but the full argument is distributed across the three contributions. The conceptual analysis motivates the mathematics; the mathematics grounds the physics; and the critical examination situates classical intuition as a limiting case rather than a foundation. The papers are intended to be read as a coherent whole. We argue that quantum mechanics is not an arbitrary empirical framework but an inevitable consequence of minimal ontological requirements. Assuming only that being must exist necessarily, remain consistent, be relational, and admit self-reference, we show that classical deterministic physics is structurally insufficient. Quantum dynamics emerges as the unique low-energy realization of coherent ontological continuity. This work completes the ontological grounding of quantum mechanics by clarifying why it could not have been otherwise.