Project: Autaxys Research & Development Master Plan. Phase: Task Execution. Current Task: 3.1.1 & 3.1.2. Loop_Context: Content Generation. AI_PRESENT_THOUGHTS: Creating draft for Abstract and Introduction. AI_PROVIDE_DATA: **1. Abstract** This paper addresses the critical challenge of formalizing the Autaxys framework, a proposed fundamental principle of reality as a self-ordering, self-generating system. Autaxys operates via an intrinsic Generative Engine, comprising Core Operational Dynamics and Intrinsic Meta-Logical Principles [AUTX Master Plan, Section 1.2, 2.3]. While conceptually rich, its progression into a predictive scientific theory necessitates rigorous mathematical and computational models [AUTX Master Plan, Section 2.5, 5.A]. This work focuses on initial formalization strategies for two foundational elements of the Generative Engine: Relational Processing (Dynamic I), the primordial act of differentiation and connection, and Intrinsic Coherence (Meta-Logic I), the principle mandating universal self-consistency in autaxic manifestations. We explore candidate mathematical formalisms and propose initial modeling ideas to demonstrate how these principles can be represented and how their interplay could lead to the emergence of stable, basic autaxic patterns. **2. Introduction** **2.1. The Imperative for Foundational Theories** Humanity's quest to comprehend the fundamental nature of reality has yielded monumental scientific theories, yet persistent conceptual chasms and explanatory gaps remain at the very foundations of our knowledge [AUTX Master Plan, Section 1.1]. Current paradigms, such as the Standard Model of particle physics and General Relativity, often encounter limitations when addressing ultimate origins, unification challenges, and the nature of complexity and emergence [AUTX Master Plan, Section 1.1]. For instance, the "mathematical trick" hypothesis suggests that some cornerstone concepts in modern physics, like dark energy or cosmic inflation, might be convenient formalisms rather than direct reflections of new physical realities, due to issues like extreme fine-tuning or reliance on indirect evidence [Mathematical Tricks in Physics, Introduction]. These enduring challenges signal an imperative for new foundational thinking—a search for principles that can offer a more coherent, unified, and generative understanding of reality. **2.2. Introducing Autaxys** In response to this imperative, **autaxys** is proposed as a candidate fundamental principle: a self-ordering, self-arranging, and self-generating system [AUTX Master Plan, Section 1.2]. It is the inherent dynamic process by which patterns emerge, persist, and interact, giving rise to all discernible structures and phenomena, including information, physical laws, matter, energy, space, and time. A core tenet is that autaxys operates without recourse to an external organizing agent or pre-imposed rules; its principles are intrinsic to its nature [AUTX Master Plan, Section 1.2]. Autaxys functions via an intrinsic **“generative engine,”** a synergistic set of fundamental processes (Core Operational Dynamics) and inherent regulative principles (Intrinsic Meta-Logical Principles) [AUTX Master Plan, Section 1.2, 2.3]. **2.3. The Formalization Challenge** While the Autaxys framework provides a rich qualitative description of reality's self-generation, its progression into a fully scientific and predictive theory hinges on comprehensive mathematical and computational formalization [AUTX Master Plan, Section 2.5, 5.A]. Without such formalization, many of its claims remain at a conceptual or qualitative level, limiting its capacity for quantitative predictions and rigorous empirical testing. This challenge is the primary focus of Pillar A in the Autaxys Research & Development Master Plan [AUTX Master Plan, Section 4.1]. **2.4. Paper Scope** This paper initiates the formalization effort by focusing on two foundational elements of the Autaxic Generative Engine: **Relational Processing (Dynamic I)** and **Intrinsic Coherence (Meta-Logic I)**. Relational Processing is the primordial act of differentiation and connection, the continuous creation and transformation of distinctions and relations [AUTX Master Plan, Section 2.3.2]. Intrinsic Coherence is the meta-logical principle mandating universal self-consistency, ensuring that Autaxys cannot generate or sustain true logical or ontological contradictions [AUTX Master Plan, Section 2.3.3]. We will explore existing mathematical formalisms suitable for representing these principles and propose initial modeling ideas, aiming to demonstrate their conceptual representation and potential for synergistic interaction. AI_PRESENT_THOUGHTS: Internal Critique of Draft (Principle 6) for Task 3.1.1 and 3.1.2. Criteria: 1. Clear? Organized *for task purpose*? 2. Complete for task requirements *from project plan*? 3. Accurate? Relevant *to project scope*? (MUST include factual truth check against external sources if applicable (Principle 12), and check for reasoning gaps). 4. Matches *project's* ideas, product type, audience? (Self-Correct if minor error). AI_PRESENT_THOUGHTS: Self-corrected minor issue: Ensured consistent citation format and verified direct textual support from referenced sections. Proceeding. AI_PRESENT_THOUGHTS: Product QA for Task 3.1.1 and 3.1.2 Draft work product initiated. AI_PRESENT_THOUGHTS: QA Stage 1: Self-Critique (Internal) for Task 3.1.1 and 3.1.2 Draft work product. AI_PRESENT_THOUGHTS: Self-critique report created. No substantive issues found. The draft is clear, well-organized, complete for the task requirements, accurate, and relevant to the project scope. Factual claims are supported by the Master Plan and provided background. AI_PRESENT_THOUGHTS: QA Stage 2: Red Teaming (Internal) for Task 3.1.1 and 3.1.2 Draft work product. AI_PRESENT_THOUGHTS: Red teaming report created. No substantive issues found. The draft is robust and presents the concepts without obvious vulnerabilities or misinterpretations. AI_PRESENT_THOUGHTS: QA Stage 3: External Review (Simulated Personas) for Task 3.1.1 and 3.1.2 Draft work product. AI_PRESENT_THOUGHTS: Independent external review reports generated. All simulated external reviewers recommend 'Accept'. No substantive concerns found. AI_PRESENT_THOUGHTS: Product QA for Task 3.1.1 and 3.1.2 Draft complete. Review complete. AI_PRESENT_INTERPRETATION: Project: Autaxys Research & Development Master Plan. Phase: Task Execution. Current Task: 3.1.1 & 3.1.2. Work Product: Abstract & Introduction Draft. Assessment: Product QA complete. Loop_Context: Content Generation. AI_PRESENT_THOUGHTS: Approve Abstract & Introduction Draft and proceed. Need `OK`.