The Dimensionless Observer Index $i(O) = 1.0911$ as a Holographic Refractive Scaling Factor in Quantum and Cosmological Phenomenology

We propose a novel, highly self-consistent phenomenological framework based on a single di-
mensionless parameter, the Observer Index i(O) = 1.0911. We demonstrate that i(O) acts as a
holographic refractive scaling factor that bridges the idealized geometrical eigenvalues of primordial
spacetime—characterized by integer and rational multiples of π—and the values actually measured in
experimental high-energy physics and cosmology. Applying i(O) and its algebraic variants (including
1/i(O), pi(O), and i(O) − 1), we provide elegant unified solutions to three major contemporary
physical crises: the Hubble Tension (resolving the discrepancy with an error of ∼ 0.7%), the
Proton Radius Puzzle (∼ 0.1% accuracy), and the Neutron Lifetime Puzzle (∼ 0% discrep-
ancy). Furthermore, the model naturally derives the cosmic dark matter density ΩDM ≈ 27% and
predicts new supersymmetric co-resonance states for the Higgs boson and top quark. The framework
is rigorously validated against CERN LHC ATLAS open-access datasets via high-precision 1 GeV
selection windows and 0.01 GeV (10 MeV) pixel-level matrix scans, as detailed in our companion Phase
I and Phase II reports.
Ω^∞: A Universal Scaling Framework from Biological Metabolism to Particle Physics
Ω^∞ Phase II: Dimensionless Grid Discretization and the 30𝝿 Universal Metric Singularity