A Finite Quantum Origin for Vacuum Energy, Newton's Constant, and the Cosmic Matter Fraction

THE PRESENT LIMITATION Modern physics describes laboratory and cosmic observations with exceptional precision. However, several central physical quantities still enter through separate empirical routes. The electromagnetic coupling is determined through precision atomic and quantum-electrodynamic measurements. Newton’s constant G is obtained from gravitational experiments. The vacuum scale and the cosmic matter fraction are inferred from cosmological observations within a chosen model. The Standard Model and General Relativity do not derive these numerical values from a single shared microscopic structure. In particular, the extreme smallness of the observed vacuum energy remains the cosmological-constant problem. WHAT MITTERMEIER ATTRACTOR THEORY CHANGES Mittermeier Attractor Theory (MAT) reverses this explanatory order. It begins with a finite, dimensionless quantum cell whose arithmetic structure, topology, and internal response are fixed. These data generate a small dimensionless quantity, δₛ. This quantity is not fitted to gravitational or cosmological observations. It is calculated before the gravitational, atomic, and cosmological sectors are evaluated. The same δₛ produces three distinct physical responses. In the vacuum sector, it selects a unique, nonzero vacuum scale through an exact renormalization-group closure condition. In the atomic sector, it determines the hierarchy between the electron and Planck scales. Standard Rydberg spectroscopy then supplies the SI length reference required to calculate the Planck length lP and Newton’s constant G. In the cosmological sector, δₛ generates two fixed projections of the cosmic matter fraction. No measured value of G, the Planck length, the Hubble constant, the Planck matter fraction, or the DESI matter fraction is used to generate these outputs. FROM THE FINITE CELL TO COSMOLOGY The connection between the finite quantum cell and cosmology is established by a finite-to-continuum projection. The cell first determines δₛ. Renormalization-group closure then selects the dimensionless vacuum value Λ₀*. The Rydberg–Planck bridge independently supplies the Planck length lP. Together, these quantities determine the physical cosmological constant through Λₚhys = Λ₀* / lP². On a spatially flat Friedmann–Lemaître–Robertson–Walker background, a fixed two-sheet baseline and a bounded matter–vacuum gate project the same δₛ into two matter-fraction observables, Ωₘ, P and Ωₘ, D. SCIENTIFIC SIGNIFICANCE Within this architecture, the vacuum scale, the strength of gravity, and the cosmological matter projections are no longer treated as independent empirical numbers. They arise as different responses to one upstream finite-cell datum. A modification of the cell therefore changes all three sectors simultaneously. The sectors cannot be retuned independently. This creates cross-checks extending across more than one hundred orders of magnitude and gives the framework a direct failure criterion: an upstream modification cannot repair one observable without also changing the others. Within the declared MAT architecture, the vacuum catastrophe is converted into a finite boundary-value problem. The resulting vacuum energy is not zero. The construction instead produces a very small positive vacuum scale of the observed order. The same calculation also reaches atomic gravity and the cosmological matter sector. The central result is therefore a linked prediction structure: one finite quantum origin generates correlated outputs for dark energy, Newton’s constant G, and the cosmic matter content. WHY THE STARTING CELL IS NOT AN ARBITRARY NUMERICAL CHOICE The cell is anchored in a cubic number field of discriminant −23. Its real root is the plastic constant, the smallest Pisot number. Its complex embedding is associated with the invariant trace field of the Weeks manifold, the closed orientable hyperbolic three-manifold of minimum volume. The Weeks geometry is rigid and therefore possesses no continuous shape parameter. Its topology supplies twenty-five torsion sectors. Within the MAT construction, finite Heisenberg–Weil quantization organizes these sectors into a five-state quantum register. The simultaneous arithmetic and geometric minimality restricts the available freedom before any physical observable is calculated.