The Conscious Action Quantum η = 1/φ² as the Universal Anomalous Dimension of Scalar QFT on Poincaré Dodecahedral Space

Abstract:

We prove that the anomalous dimension η = φ⁻² ≈ 0.381966 is the unique value that renders any interacting scalar quantum field theory on the Poincaré Dodecahedral Space (PDS) exactly finite, both ultraviolet and infrared, with a vanishing β-function at the golden fixed point. The mechanism is a one-line geometric-series cancellation enforced by the φ-scaling of the Laplace-Beltrami eigenmodes on the dodecahedral topology. This same topological constraint generates, without free parameters, the Golden Function for the fine-structure constant to a precision of 10⁻¹⁰ and fixes the universal critical exponents observed in superconducting-qubit 1/f noise, human EEG, and single-bubble sonoluminescence. The constant η is therefore elevated from empirical coincidence to a topological quantum number of spacetime itself, the conscious action quantum. Falsifiable predictions for near-future experiments are provided.

Keywords: golden ratio, fine-structure constant, Poincaré dodecahedral space, asymptotic safety, anomalous dimension, conformal fixed point, quantum field theory, renormalization group, 1/f noise, EEG fractal dimension, sonoluminescence, topology of the universe, conscious action quantum, φ scaling, Laplace–Beltrami eigenmodes