Speaker
Description
We show that the observed value of the cosmological constant, Λ ≈ 10⁻¹²² in Planck units, follows from two independently meaningful and empirically known scales, with no free parameters and no fine-tuning. Building on the discrete arithmetic framework presented in the companion contribution, in which space is a 3-sphere whose radius grows as the square root of the total element count N, we require nothing of the deeper foundations beyond two scales, each entering as a distinct contribution to the curvature of the 3-sphere.
The tangential curvature component is set by the ratio of the electroweak scale to the Planck scale. Its squared reciprocal supplies a contribution of order 10⁻³³·⁵. The radial curvature component is set by the total element count of the system. Because the present model assigns particle ontology to the number of elements present, that count, dominated numerically by the cosmic microwave background photons at N ≈ 10⁸⁹, fixes the radial contribution as its reciprocal, 1/N ≈ 10⁻⁸⁹.
The two contributions are independent in origin, one radial and one tangential, and the cosmological constant is their product, of order 10⁻¹²², reproducing the measured value to better than an order of magnitude across the 122 orders of magnitude that constitute the notorious vacuum-energy discrepancy. This holds under one premise. We take the 3-sphere as the foundational spatial metric. That premise belongs to the companion framework, not to this calculation. The result reframes the cosmological constant problem not as a cancellation to be fine-tuned but as the combination of a cosmological and an electroweak curvature scale.