Pre-registered Test of Ω_Λ = π³/45 Against Forthcoming DESI and Euclid Data

This note fixes, before the DESI DR3, Euclid DR1 and Simons Observatory/CMB-S4 cosmology releases, the numerical predictions of the present-horizon boundary closure Λ₀R²_H,0 = π³/15 and the criteria under which they are considered falsified.

Predictions: Ω_Λ,0 = π³/45 = 0.689028; Ω_m,0 = 0.31088 (flat, after radiation); w = −1 at all epochs; Ω_Λ/(1−Ω_K) = π³/45. Closure II, tested separately: Ω_c/Ω_b = 2π − 1 = 5.283185.

Exclusion criteria: BAO+CMB flat-ΛCDM Ω_m more than 3σ from 0.31088, or a departure from w = −1 at ≥5σ in any single BAO+CMB+SN combination (≥3σ across all SN samples).

Status at registration (known results, not blind tests): Planck 2018 alone 0.6σ; DESI DR2 BAO alone 1.6σ; DESI DR2 BAO + CMB 2.3σ. The closure value lies between the CMB and BAO determinations, which DESI reports to be in 2.3σ mutual tension within ΛCDM.

This record will not be revised; any change will appear as a new, separately dated record.