Hierarchically Nested Dimensions Theory (HNDT): A Foundational Axiomatic Framework for the Structure of Existence (Version 9)

Version 9 (V9) – Extended Axiomatic Core with Heuristic Empirical Interfaces *Supersedes Version 8 (DOI: 10.5281/zenodo.20021423). The five‑axiom ontological core remains unchanged.* Major changes in V9: Three‑layer stratification – Formal separation of (i) axiomatic core, (ii) heuristic empirical conjectures (CMB, decoherence, black hole shadow), (iii) open interfaces. Projection incompleteness – New epistemological corollary: any D3D3-based theory cannot uniquely reconstruct D4D4. Redefines physics as anomaly detection rather than a closed “theory of everything”. Three essential properties of D3D3 – Ontological consistency (λ), manifested diversity (θ), directional uncertainty. Completes HNDT as an ontological metatheory. Anchoring drift – Upgraded from open question to Corollary 3.1: same θ mode manifests differently across λ regimes, unifying quantum, terrestrial, and cosmological scales. θ fully formalised – Group structure Z2×Z2×Z2Z2×Z2×Z2 with complete mapping of 8 modes: 4 stable (anchoring pairs) and 4 transient. λ mathematical refinement – Confinement by diverging potential (soft wall) replaces heuristic “absorbing boundary”; “order parameter” explicitly analogical. Observational threshold λc – Introduced to break circularity between high λ and observation; non‑observational (λ<λc) vs. observational (λ≥λc) regimes. Dual‑pole stability – Presented as Heuristic Conjecture A (not a corollary), with clear statement of required extra assumptions. Terminological D0D0 as formalizability (not Platonic); D4D4 as transcendent closure; Adjacent Support clarified as ontological dependence; two layers of D4D4 knowledge (structural vs. constitutive). Conceptual comparison restored – Table 2 expanded to include Whitehead’s process philosophy, with citations to French (2014) and Whitehead (1929). Falsifiability criteria – Lakatosian three‑layer structure (axiomatic core / phenomenological scalings / quantitative placeholders) with explicit degeneration condition. References streamlined – Retained 7 core cited references; removed uncited general textbooks to avoid “zombie references”. Version metadata – Date: May 2026. Supersedes V8. Core axioms (1–5) unchanged from V8.