Part II: Cosmic Recursion: Extending Validated Recursive Dynamics to Cosmological Scales

Theoretical extension of validated recursive dynamics principles to cosmological scales. Reinterprets black holes as recursive saturation points, dark matter/energy as recursive field substrates, and cosmic evolution as self-modifying recursive processes. Addresses longstanding cosmological puzzles including black hole information paradox and fine-tuning problems through recursive framework.  Incorporates recent DESI DR2 observations showing dynamical dark energy preference (3.1-4.2σ), supporting recursive substrate interpretation. Presents specific testable predictions for CMB signatures, gravitational wave patterns, and cosmic web structure. Maintains rigorous falsification criteria while proposing paradigm-shifting reinterpretation of cosmic phenomena. Builds on convergent empirical validation across quantum, biological, neural, and climate systems documented in Part I. Provides theoretical foundation for mathematical framework developed in Part III. Version 1.3  License changed to CC-BY 4.0 to enable full scientific dissemination. No changes to content. Version 1.2 adds a significant addendum analyzing the July 2025 LIGO–Virgo–KAGRA detection of GW231123, an extreme black hole merger that challenges standard formation theories. The addendum presents this recent detection as a critical test of recursive dynamics, provides specific falsifiable predictions distinguishing the framework from General Relativity, and outlines empirical validation pathways. Main text unchanged. Version 1.1 Adds Part II to the Zenodo title.

Saturation Thresholds in Recursive Systems: A Universal Energy Field Framework for Modeling Across Scales

This paper introduces a cross-domain modeling framework based on saturation thresholds in recursive systems. Drawing on concepts from consciousness studies, complexity science, ecology, cosmology, and artificial intelligence, it proposes a Universal Energy Field (UEF) architecture governed by the Recursive Saturation Index (RSI) and a boundary function B(Mk), defined as the ratio of internal to external recursive stress. These formal tools describe how systems evolve, stabilize, or reorganize as recursive parameters approach critical thresholds. The paper presents ten demonstrative cases — from neural integration and biological aging to climate feedbacks and early galaxy formation — illustrating how recursive saturation drives systemic reorganization. By unifying cross-scale phenomena under a recursive saturation model, this framework offers a falsifiable, interdisciplinary lens for understanding emergence, boundary shifts, and phase transitions across both physical and cognitive domains. Version 3.2:  License changed to CC-BY 4.0 to enable full scientific dissemination.  No changes to content. Version 3.1 updates or corrects reference entries in the bibliography to ensure accuracy, compliance, and persistent identification. The following changes have been implemented: Authorship and Miscitation Corrections: Armstrong & Vijg (2022) corrected to Wang & Vijg (2022) Cabanela & Rummelt (2023) corrected to Lopez et al. (2021) Smith et al. (2023) (Eos cloud) corrected to Saxena et al. (2025) Chen et al. (2020) corrected to Hipp et al. (2019) BirdLife entry updated with accurate source information DOI and Identifier Updates: BirdLife (2024) — URL updated/corrected Huang et al. (2025) — DOI updated/corrected Kim et al. (2025) — DOI updated/corrected Luhmann (1995) — DOI updated/corrected Marwan et al. (2007) — DOI updated/corrected Michaud et al. (2023) — DOI updated/corrected Snell (2024) — DOI updated/corrected Wheeler (1990  — URL updated/corrected Xiao, M. (2024) — DOI updated/corrected No substantive changes were made to the main text or analysis. Revision Note (June 2025): This version includes typographic and layout refinements for clarity and consistency across the trilogy. Abstract formatting has been harmonized, figure placement and table rendering have been confirmed for visual continuity, and minor LaTeX adjustments (including the use of \sloppy in key sections) resolve previous overfull line warnings. No changes were made to the theoretical content or structure of the paper.

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0 Introduction‣ Statistical Field Theory by David Tong

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