Hierarchically Nested Dimensions Theory (HNDT) (Version 1.3)

Hierarchically Nested Dimensions Theory (HNDT) – Version 1.3 Version: 1.3Publication date: July 2026Authors: Yingkui Lu (corresponding), Yifei LuDOI: [to be assigned] Abstract Summary This paper presents Version 1.3 of the Hierarchically Nested Dimensions Theory (HNDT), building upon the axiomatic core of V1.1 and the mathematical supplements of V1.2. The main new contribution is the Hongdao Conjecture—an endogenous epistemological corollary derived from the axioms—which provides a novel ontological interpretation of the century-long difficulty of Einstein's unified field program, attributing it to structural epistemic boundaries embedded in the dimensional nesting architecture rather than merely mathematical or technical limitations. Additional refinements include a formal categorical formulation of Projection Incompleteness, a four-tier Framework Structure and Status classification to aid reader evaluation, and ten structured Open Research Interfaces for future collaboration. All axioms from V1.1 and all supplements from V1.2 remain unchanged; the update is fully backward-compatible. What's New in Version 1.3 (Compared to V1.2) Hongdao Conjecture (new Section 9): Argues that any D3D3-confined unified theory covering quantum/classical/cosmological regimes faces intrinsically elevated verification and falsification barriers due to projection incompleteness—offering a structural explanation for the unified field problem. Projection Incompleteness Formalization (Section 8.4): Categorical formulation proving the non-surjectivity of D4→D3D4→D3 reverse projections, demonstrating that multiple D4D4 completions may correspond to the same D3D3 state. Framework Structure & Status (new section): A four-tier classification (Axiomatic Core / Partially Formalized / Heuristic Models / Conjectures) clarifying the maturity of each component. Open Research Interfaces (Section 10): Expanded to ten structured collaboration pathways, including λλ dynamics, dark energy, quantum measurement, and comparisons with IIT, causal set theory, and RQM. All V1.1 axioms, definitions, and scaling laws, as well as all V1.2 mathematical formalizations, remain unchanged. License Creative Commons Attribution 4.0 International (CC BY 4.0) How to Cite Yingkui Lu, & Yifei Lu. (2026). Hierarchically Nested Dimensions Theory (HNDT): A Foundational Framework for Scale-Unified Ontology in Physics (Version 1.3). Zenodo. [DOI to be inserted] Contact luyingkui2026@outlook.com Additional Notes This is a theoretical/foundational study; no empirical datasets are included. The authors welcome collaboration on further formalization, empirical testing, and development of the framework. Preprint deposited on Zenodo for rapid dissemination and community feedback. Future journal submission is intended.