Quantum Geometrodynamics (QGD): On the Geometric Origin of the Universe

This paper develops Quantum Geometrodynamics (QGD), a unified theoretical framework wherein all observable physics — including quantum mechanics, gravity, and gauge interactions — emerges as geometric and topological necessities of a four-dimensional spatial manifold ℳ₄. The central result is that all four axioms of QGD emerge as necessary consequences of a single structure: the quaternionic (ℍ) nature of the primordial vacuum. The Skolem–Noether theorem mandates that the ℍ-preserving subgroup within SO(4) ≅ SU(2)L × SU(2)R/ℤ₂ is the diagonal SU(2)diag, implying isoclinic rotation and hence self-dual geometry. This reduces QGD's foundation to the definition of "nothingness" — the minimal possible starting point. The framework yields four operational axioms: A1: Self-Dual Gravitational Instanton with BPS condition M = ℓ = a; A2: Kinematic time emergence via dw = c dt; A3: Quantum mechanics from Hopf fibration topology of S³; A4: Standard Model Higgs field as the scalar sector. From these, we derive: action quantization, the Born rule, spin-statistics, the Schrödinger equation, Einstein's equations, the scaling law ℓ(t) = ct, and BPS thermodynamic stability. The cosmological "dark sector" receives geometric reinterpretation: Dark Energy as vacuum strain energy (w = −1/3), predicting ΩΛ = 2/3; Dark Matter as cosmic background acceleration a₀ = cH₀/(2π), predicting ΩDM = 1/π. The prediction ρtotal(z) ∝ (1+z)² resolves the JWST early galaxy problem and Hubble tension. This document contains the full unified treatment. The individual topics are also available as separate focused papers (Papers 0–VI) in this record series. Keywords: quantum geometrodynamics, quaternionic vacuum, emergent spacetime, dark energy, dark matter, MOND, Tri-Unity, gauge theory, Hopf fibration, S³ topology, cosmological constant problem, Hubble tension