Hierarchically Nested Dimensions Theory (HNDT): A Foundational Axiomatic Framework for the Structure of Existence (V8)

Version 8 (V8) – Extended Axiomatic Core with Dual Parameters *Supersedes Version 7 (DOI: 10.5281/zenodo.19918121). The five‑axiom ontological core of HNDT remains unchanged.* Major changes in V8: Second fundamental parameter: Ziran value θ Introduced discrete θ (alongside continuous λ) to govern the mode of D₂ coupling, distinguishing physical categories (mass, energy, space, temperature). Stability analysis: 2³ = 8 combinatorial modes, of which four are dynamically stable, corresponding to the four anchoring pairs of D₃. The remaining four are transient/virtual. Refined Axiom 3 (λ and θ) λ is a dimensionless ontological order parameter controlling degree of manifestation. Removed all numerical λ thresholds (e.g., 0.2‑0.8) – replaced with qualitative descriptions of intermediate, high, and low λ regimes. Expanded Axiom 4: scale validity of anchoring pairs The four anchoring pairs represent a mid‑λ effective ontology, valid for the macro‑scale, observer‑accessible regime of D₃. Added forward reference to Section 6.4 on scale‑induced phase transitions. New conceptual subsection in Section 5 “Hongdao Gradient and the Unified Nesting of Scales” explains how a single λ replaces the three disconnected frameworks (Newtonian, relativistic, quantum), producing nested physical regimes. Unified observer‑related terminology Replaced bio‑centric terms (“carbon‑based”, “life‑compatible”, “conscious observers”) with neutral expressions: “observer‑accessible regime”, “observers operating at high λ”. Theoretical stratification clarified Explicitly distinguished axiomatic core from phenomenological layer (λ Langevin equation, tanh² CMB form, decoherence timescale) and placeholders, protecting the core from empirical adjustments. Empirical predictions unchanged from V7 CMB low‑ℓ suppression, black hole shadow enlargement, decoherence lower bound τ ∝ 1/(m d²). Numerical values in the decoherence table are order‑of‑magnitude illustrations. Open Research Interfaces restructured Added Section 6.4 “Scale Dependence and Anchoring Transitions” for extreme‑λ phase transitions (high λ: gravitation → spacetime geometry; low λ: force sectors → nuclear interactions). Version metadata updated Publication date: May 2026. Version 7 is the immediate predecessor. All core axioms (1–5) remain unchanged from V7; only their exposition and contextualization have been extended.