Hierarchically Nested Dimensions Theory(HNDT) V3: The Triadic Emergence of Spacetime, Mass, and Energy

Notes: This is Version 3 (V3) of the Hierarchically Nested Dimensions Theory (HNDT), building upon the conceptual framework of V1 and V2. V3 provides a complete mathematical formalization of the theory. The core postulate is a generative hierarchy of dimensions: D₀ < D₁ < D₂ < D₃ < D₄ where denotes dimensional subordination — lower dimensions are more fundamental, contained within higher dimensions, capable of upward penetration, while higher dimensions can only project downward. A continuous parameter 0, 1 (the manifestation degree) governs how properties manifest in lower dimensions. From these postulates, the theory derives seven foundational quantum phenomena (superposition, wave‑particle duality, Heisenberg uncertainty, entanglement, tunneling, measurement collapse, and spin‑statistics), corrects the Schwarzschild gravitational potential with hierarchical terms, and predicts a characteristic ² suppression in the CMB power spectrum at multipoles <30, consistent with the low‑ deficit reported by Planck 2018. Two falsifiable predictions are presented: a correction to quantum decoherence times (testable with superconducting qubits) and the CMB suppression (testable by LiteBIRD and CMB‑S4). HNDT offers a logically parsimonious, mathematically consistent, and empirically testable alternative to geometric interpretations of dimensions, providing a new pathway toward unifying quantum physics and gravity. This version (V3) includes all mathematical derivations, equations, numerical simulation roadmaps, and detailed comparisons with established physics. The earlier qualitative frameworks (V1 and V2) are fully superseded by this complete formalization.