ATPEW — Unifying Space-Time, Gravity, and Quantum Mechanics through a Primordial Energy Wave (V4)

Historical Note — October 2025 Formulation This document (dated October 10, 2025) is the founding formulation of the ATPEW/PEW (Aldon Theory of Primordial Energy Waves / Primordial Energy Wave) framework. It should be read as the genesis document of the series, not as its current state. What this document establishes: This V4 introduces the core postulates of the framework: a single complex scalar field Ψ = ·e^iθ (the Mother Wave) from which spacetime, gravity, quantum entanglement, and dark energy emerge. The key results established here include: The fundamental wave equation governing amplitude  and phase velocity Č The derivation of spacetime metric from Â: g_μν = (Â/Â₀) ²·η_μν The mechanical explanation of dark energy: Λ ∝ ²ₘin, where Âₘin is the minimal amplitude of the Mother Wave in the current era — this result, confirmed against Planck 2018 data, was first established in this document Local time speed C̃ₗocal as the basis of gravitational time dilation and quantum entanglement Falsifiable predictions: C̃ₗocal variations near masses, Λ–Âₘin linkage, decoherence thresholds Relation to the formal PEW Article series (2026): This document has been substantially developed and formalised in the PEW Article series published on Zenodo in 2026. The notation, mathematical rigour, and scope have evolved significantly: V4 (this document) PEW Articles 1–11 (2026) Â, Č notation Ã, C̃₀ with Hopf torus topology R/r = φ Λ ∝ ²ₘin (qualitative) Λcosmo = 3Ω_Λ·lP⁻²·αₑm^2nH, residual 0. 11% (Article 11) Entanglement via C̃ₗocal sync Entanglement via global Hopf invariant IH (Article 1) Dark matter via C̃ₗocal perturbations Galactic rotation via vortex K₀ profiles (Article 4) General postulates κ²=25. 20, γ=0. 267 eV⁻², αₑm derived topologically (Articles 1–3) Recommended reading order: For the current rigorous formulation, readers are directed to: Article 1 (Foundations): https: //doi. org/10. 5281/zenodo. 18840061 Article 10 (Harmonic Table, ΛPEW = log_φ (1/αₑm) = 10. 2247): Zenodo, 2026 Article 11 (Cosmological Constant derivation): Zenodo, 2026 This V4 document is archived to establish priority and to document the conceptual trajectory of the PEW framework from its initial formulation to the formal series.