What does this research mean for the field?

The structure of existence can be modeled as a strict hierarchical nesting of five dimensions (D₀ to D₄), governed by a unified parameter (λ) that links phase-space probability to observable cosmological and quantum phenomena. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This framework aims to establish a foundational understanding of existence through a hierarchical dimensional model.

May 30, 2026Open Access

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

Key Points

This framework aims to establish a foundational understanding of existence through a hierarchical dimensional model.
Developed an axiomatic framework with a strict hierarchy from D₀ to D₄.
Unified aspects of manifestation, efficacy, observational value, and scarcity into the Hongdao value λ.
Introduced a three-layer structure with falsification criteria and heuristic scaling laws.
Demonstrated a link between the Hongdao value and Boltzmann brain statistics.
Provided estimates for CMB low-ℓ suppression, decoherence scaling, and M87* black hole shadow enlargement.
Expanded the framework to include limitations and future research directions.

Abstract

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 γₖ = 2^−k (k−1) /2 as a heuristic scaling law. Provided heuristic numerical estimates for CMB (ℓc ≈ 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, intended future journal submission (e. g. , International Journal of Theoretical Physics or similar).

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