Resolving the Cosmological Constant Problem via Dual-Scale Geometric Holography

The most severe discrepancy in modern theoretical physics is the vacuum catastrophe—a staggering 10¹²⁰ order-of-magnitude gap between the vacuum zero-point energy density calculated by classical quantum field theory and the dark energy density observed astronomically. Based on a dimensionless dual-geometric model a(x) = 1/x² - x², this paper reveals that this discrepancy is not a naturalness problem requiring fine-tuning, but rather an exact algebraic identity that holds inevitably under dual geometric scales: ρcrit/ρP = 3/8π(lₚ/LH)². Through holographic projection from the microscopic quantum scale onto the macroscopic Hubble boundary, the vacuum zero-point energy is suppressed and diluted by the maximum number of states on the holographic screen N ≈ 10¹²⁰, naturally decaying to the observed value. This geometric mechanism not only resolves the 10¹²⁰ divergence catastrophe, but also derives a tracking response wherein the dark energy density dynamically decays with cosmic expansion (ρvac ∝ 1/LH²), aligning seamlessly with recent observational results from leading surveys like DESI.