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.“宇宙学危机”与“真空灾难”是否仅是我们对宇宙学常数Λ（Lambda）与哈勃常数H₀（Hubble Constant）进行参数化时产生的几何伪影？ 本数据说明文档与配套Python脚本证实，物理学中两大最显著的反常现象——哈勃张力与宇宙学常数问题——可通过简单的几何边界条件实现数值复现，无需引入新的动力学物理或自由参数。 关键发现 通过球填充阐释哈勃张力 我们证实，哈勃常数H₀的全局测量（基于宇宙微波背景（Cosmic Microwave Background，CMB））与局部测量（基于SH0ES项目）之间的偏差，对应于连续流体与离散填充结构间的几何差异。将三维接吻数填充因子(1 + 1/12)应用于普朗克2018年给出的H₀^CMB=67.4 km/s/Mpc，可预测出局部哈勃常数为73.02 km/s/Mpc，与SH0ES的测量结果（73.04 ± 1.04）仅相差约0.02倍标准差，匹配精度极高。 宇宙学常数作为视界不变量 我们证实，当将Λ视为边界曲率项时，表观上高达10^122的Λ“精细调谐”问题将不复存在。Λ与哈勃视界面积A_H的无量纲乘积可化简为一个量级为1的代数恒等式（约25.8），与几何相空间因子4π(π³/15)≈25.98的偏差仅约0.7%。 内容 PDF说明文档：包含对Λ与H₀的几何约束的简洁推导与正式阐述。 Python脚本（`cosmic_geometry_test_suite.py`）：一套可复现的零参数测试套件，可基于普朗克2018与SH0ES的输入数据验证上述几何恒等式，并输出明确的通过/失败判定标准。