Universal emergence of the mathematical continuum from the prime lattice at Planck information depth

The ratio of the k-th prime to its primorial converges to 22 fundamental irrational constants — including π, ϕ, e, ln 2, γ, multiple zeta values, Catalan’s G, Khinchin’s K, both Feigenbaum constants δ and α (governing the Mandelbrot set), and Liouville’s constant — with 31–52 correct decimal digits precisely when k ≈ 80. This depth marks the primorial first carrying ∼ 1030 bits, matching the Planck-scale information content of the observable universe. A universal scaling law k ≈ ⌈4.784D + 0.8⌉ predicts the resonance depth to within ±2. The phenomenon, first predicted by Pisano within the ADEC (Autopoietic Dynamic Entropic Clock) model, is fully verified here using the BNUT (Benjamin Non-local Unified Theory) research platform and is reproducible with 12 lines of open-source code.