Hierarchically Nested Dimensions Theory (HNDT): A Foundational Axiomatic Framework for the Structure of Existence (Version 1.1)

Title:Hierarchically Nested Dimensions Theory (HNDT): A Foundational Axiomatic Framework for the Structure of Existence (Version 1.1) Version: 1.1Publication date: May 2026Authors: Yingkui Lu (corresponding), Yifei Lu DOI: (Zenodo will assign a DOI automatically upon publishing; you may also reserve one in advance.) Abstract summary:This paper presents a unified axiomatic ontological framework, HNDT, which posits a strict hierarchical nesting of five dimensions (D₀ to D₄), from a primordial logical‑mathematical substrate to a holographically complete informational domain. Key advances in this version include the unification of manifestation degree, integrative efficacy, generalized observational value, and phase‑space scarcity into a single parameter λ (Hongdao value) linked to Boltzmann brain statistics, as well as heuristic testable predictions for CMB low‑ℓ suppression, decoherence scaling, and black hole shadow enlargement. What’s new in version 1.1 (compared to earlier versions): Unified four aspects of λ into one numerical measure, with explicit connection to phase‑space probability (P ∝ e−Cλ). Added a three‑layer Lakatosian structure (axiomatic core, phenomenological scaling, quantitative estimates) with clear falsification criteria. Introduced hierarchical coupling coefficients γ_k = 2−k(k−1)/2 as a heuristic scaling law. Provided heuristic numerical estimates for CMB (ℓ_c ≈ 30), decoherence (τ ∝ 1/md²), and M87* black hole shadow (10–30% enlargement). Added supplementary discussions: anchoring drift, hierarchical classification of integrative carriers (abiotic, biotic, carbon‑based, technological), endogenous temporal perception, projection incompleteness epistemological corollary. Expanded open research interfaces (7 directions) and limitations section. Licence:Creative Commons Attribution 4.0 International (CC BY 4.0) – recommended for open access sharing. How to cite:Yingkui Lu, & Yifei Lu. (2026). Hierarchically Nested Dimensions Theory (HNDT): A Foundational Axiomatic Framework for the Structure of Existence (Version 1.1). Zenodo. [DOI will be inserted after publication] Contact:luyingkui2026@outlook.com Additional notes: This work is a theoretical/foundational study. No empirical datasets are included. The authors welcome collaboration on formalization, empirical testing, and further development. Preprint deposited on Zenodo for rapid dissemination and community feedback; intended future journal submission (e.g., International Journal of Theoretical Physics or similar).