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"真空灾变"是否仅是我们对Λ（宇宙学常数，cosmological constant）和H₀（哈勃常数，Hubble constant）进行参数化时所产生的几何伪影？ 本数据说明与配套Python脚本证明，物理学领域两大最显著反常现象——哈勃张力（Hubble tension）与宇宙学常数问题（cosmological constant problem）——可通过简单几何边界条件进行数值复现，无需引入新的动力学物理或自由参数。 核心发现 球堆积视角下的哈勃张力 我们证明，H₀的全局（宇宙微波背景（Cosmic Microwave Background，CMB））测量值与局域（SH0ES项目）测量值之间的偏差，对应于连续流体与离散堆积结构之间的几何差异。将三维接吻数（3D kissing-number）堆积因子(1 + 1/12)应用于普朗克2018卫星的H₀^CMB = 67.4 km/s/Mpc数据，可预测局域测量值为73.02 km/s/Mpc，与SH0ES项目的测量结果（73.04 ± 1.04）的偏差仅约0.02个标准差，匹配度极高。 作为视界不变量的宇宙学常数 我们证明，当将Λ视为边界曲率项时，表观上高达10¹²²的Λ‘精细调谐’问题将不复存在。Λ与哈勃视界面积A_H的无量纲乘积可简化为一个量级为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%，二者高度吻合。 数据内容 PDF说明文档：对Λ和H₀的几何约束进行了简洁推导与阐述。 Python脚本（`cosmic_geometry_test_suite.py`）：可复现的零参数测试套件，可基于普朗克2018与SH0ES项目的输入数据对上述几何恒等式进行验证，并输出明确的通过/不通过判定结果。