Stellar Boundary Invariant Resolves Λ and H₀ Tensions

Are the “Crisis in Cosmology” and the “Vacuum Catastrophe” simply geometric artifacts of how we parametrize Λ and H₀? This data note and accompanying Python script demonstrate that two of the largest anomalies in physics—the Hubble tension and the cosmological constant problem—can be numerically reproduced as simple geometric boundary conditions, without introducing new dynamical physics or free parameters. Key findings Hubble tension via sphere packing We show that the discrepancy between global (CMB) and local (SH0ES) measurements of H₀ corresponds to the geometric difference between a continuous fluid and a discrete packed structure. Applying the 3D kissing‑number packing factor (1 + 1/12) to the Planck 2018 value H₀ᴄᴍʙ = 67.4 km/s/Mpc predicts a local value of 73.02 km/s/Mpc, matching the SH0ES measurement (73.04 ± 1.04) at the level of about 0.02 standard deviations. Cosmological constant as a horizon invariant We show that the apparent 10¹²² “fine‑tuning” of Λ disappears when Λ is treated as a boundary curvature term. The dimensionless product of Λ and the Hubble‑horizon area A_H reduces to an algebraic identity of order unity (~25.8), consistent with the geometric phase‑space factor 4π(π³/15) ≈ 25.98 to within about 0.7%. Content PDF note: concise derivation and statement of the geometric constraints on Λ and H₀. Python script (`cosmic_geometry_test_suite.py`): a reproducible, zero‑parameter test suite that evaluates these geometric identities against Planck 2018 and SH0ES inputs and reports explicit PASS/FAIL criteria.