The Decoupling Mechanism as a Boundary Condition: Geometric Resolution to the Dark Sector and Hubble Tensions

We test whether radiative decoupling surfaces admit a scale-independent geometric normalization that can be evaluated at stellar photospheres and projected to the cosmic horizon. By coupling independently measured radiative observables with Newtonian surface gravity, we define a dimensionless boundary invariant, X. Using a benchmark sample of 190 detached eclipsing-binary (DEB) components, we find that stellar photospheres cluster near the projected blackbody phase-space capacity X₀ = π³/15 ≈ 2.067. While evaluating this invariant using standard macroscopic relations yields an algebraic tautology, this strict circularity mathematically demonstrates that standard physical laws inherently force mass and gravity to perfectly cancel at the radiative boundary, leaving a pure geometric invariant. Projecting this identical, mass-independent boundary normalization to the Hubble horizon yields a parameter-free prediction for the dark energy density fraction, Ω_Λ = π³/45 ≈ 0.6890, consistent with Planck constraints. Assuming a spatially flat universe, this boundary capacity strictly mandates a total matter density fraction of Ω_m = 1 - π³/45 ≈ 0.3110, seamlessly matching empirical consensus without fine-tuning. Finally, expressing the transition from a continuous early-universe fluid to a discrete late-universe void network as a geometric packing gap, motivated by the optimal local packing limit (k=12), yields a kinematic mapping H₀_local = H₀_CMB(13/12) ≈ 73.0 km/s/Mpc. This geometric formulation natively resolves the most persistent cosmological anomalies through pure spatial boundaries. Key Predictive Results This framework introduces a parameter-free, purely geometric formulation that natively resolves three of the most persistent anomalies in modern cosmology without the need for unobserved parameters or fine-tuning: * Dark Energy (Ω_Λ): Evaluated as a projected 2D horizon surface capacity rather than a 3D bulk volume density, yielding Ω_Λ = π³/45 ≈ 0.6890. * Total Matter (Ω_m): Derived directly from the spatial flatness constraint (Ω_tot = 1) as the complementary geometric remainder, yielding Ω_m = 1 - π³/45 ≈ 0.3110. * The Hubble Tension (H₀): Modeled as a kinematic offset reflecting the mandatory geometric packing gap between a continuous early-universe fluid and a discrete late-universe void network (based on the kissing number k=12), yielding H₀_local = H₀_CMB(13/12) ≈ 73.0 km/s/Mpc.我们检验辐射退耦（radiative decoupling）曲面是否存在与尺度无关的几何归一化方式，该方式可在恒星光球层（stellar photospheres）处计算，并投影至宇宙视界。通过将独立测得的辐射可观测量与牛顿表面重力（Newtonian surface gravity）相结合，我们定义了一个无量纲边界不变量X。利用包含190个分离食双星（detached eclipsing-binary, DEB）子星的基准样本，我们发现恒星光球层聚类于投影黑体相空间容量X₀=π³/15≈2.067附近。 尽管利用标准宏观关系计算该不变量会得到代数重言式，但这种严格的循环论证在数学上证明：标准物理定律本质上会使质量与重力在辐射边界处完全抵消，仅留下纯粹的几何不变量。将这一与质量无关的相同边界归一化投影至哈勃视界（Hubble horizon），可得到暗能量密度分数（dark energy density fraction）Ω_Λ=π³/45≈0.6890的无参数预言，与普朗克（Planck）观测约束结果一致。 在假设宇宙空间平直的前提下，该边界容量严格限定总物质密度分数（matter density fraction）为Ω_m=1−π³/45≈0.3110，无需精细调参即可与经验共识完美契合。最后，将早期宇宙连续流体（continuous early-universe fluid）向晚期宇宙离散空洞网络（discrete late-universe void network）的转变表述为几何填充间隙（geometric packing gap），受最优局部填充极限（k=12）启发，可得到运动学映射（kinematic mapping）H₀_local=H₀_CMB(13/12)≈73.0 km/s/Mpc。这一几何表述仅通过空间边界就自然解决了最持久的宇宙学反常问题。 关键预言结果 本框架提出了一种无参数、纯几何的表述方式，无需引入未观测参数或精细调参，即可自然解决现代宇宙学中三大最持久的反常问题： * 暗能量（Dark Energy）：将其作为投影二维视界表面容量而非三维体密度进行评估，得到Ω_Λ=π³/45≈0.6890。 * 总物质（Total Matter）：由空间平直约束（Ω_tot=1）直接推导为互补的几何余项，得到Ω_m=1−π³/45≈0.3110。 * 哈勃张力（Hubble Tension）：将其建模为运动学偏移，反映早期宇宙连续流体与晚期宇宙离散空洞网络之间的强制性几何填充间隙（基于接吻数k=12），得到H₀_local=H₀_CMB(13/12)≈73.0 km/s/Mpc。