A Closed-Form Derivation of the Cosmological Constant Incorporating an Observation Map and the Origin of the Hubble Tension: \\ A Test Based on the Spacetime-Safety Equation

Preprint. This paper incorporates observation explicitly into a closed-form derivation of an effective cosmological constant Λ_eff, and organizes the Hubble tension (method-dependent differences in inferred H0) as a consequence of observation-map structure. Observation is defined as a set-valued mappingE : (ρψ, ΔL, ρI) → P(Ω),and realized vs. unrealized phases are classified by whether O(t) := E(ρψ, ΔL, ρI) is non-empty or empty (∅), avoiding numerical identity encodings. An expansion rate is derived from the volume-update rule V_{n+1} = (1+α) V_n, giving H = (1/(3Δt)) ln(1+α). Using the spacetime-safety coupling ln(1+α) = ε/π as an input, we obtain H = ε/(3πΔt) and identify Λ_eff := 3H^2/c^2 in closed form: Λ_eff = ε^2/(3π^2 c^2 Δt^2). To connect with data, we define a countable estimator complexity L(D) = N_zp + N_corr + N_hyper and test the linear predictive model H0(D) = H_ref + m(L(D) − L_ref) by weighted least squares across seven representative methods, finding a strong linear dependence consistent with the proposed organization of the Hubble tension. Related (DOI only)10.5281/zenodo.18169180 | 10.5281/zenodo.18297667 | 10.5281/zenodo.18169038 | 10.5281/zenodo.18158453 | 10.5281/zenodo.18160701 | 10.5281/zenodo.18160918 | 10.5281/zenodo.18160477