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.我们将检验辐射退耦（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）处求值，并投影至宇宙视界（cosmic horizon）。通过将独立测量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（dimensionless boundary invariant）$X$。基于包含190个分离食双星（detached eclipsing-binary, DEB）成员的基准样本，我们发现恒星光球层会聚集在投影黑体相空间容量$X_0 = pi^3/15 approx 2.067$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（algebraic tautology），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要求质量与重力在辐射边界处完全抵消，最终得到一个纯粹的几何不变量。将这一与质量无关的边界归一化投影至哈勃视界（Hubble horizon），可得到暗能量密度占比（dark energy density fraction）的无参数预言：$Omega_Lambda = pi^3/45 approx 0.6890$，这与普朗克约束（Planck constraints）相符。在空间平直宇宙（spatially flat universe）的假设下，该边界容量严格要求总物质密度占比（total matter density fraction）满足$Omega_m = 1 - pi^3/45 approx 0.3110$，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到晚期宇宙离散空洞网络（void network）的转变表述为几何填充间隙（geometric packing gap），并以最优局部填充极限（接吻数$k=12$）为动机，可得到运动学映射$H_{0, ext{local}} = H_{0, ext{CMB}} (13/12) approx 73.0 ext{km/s/Mpc}$。这一几何表述仅通过纯空间边界，就从本质上解决了最棘手的宇宙学异常问题。 核心预言结果 该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，即可从本质上解决现代宇宙学中三大最顽固的异常问题： * 暗能量（$Omega_Lambda$）：将其作为投影二维视界表面容量而非三维体密度进行求值，得到$Omega_Lambda = pi^3/45 approx 0.6890$。 * 总物质（$Omega_m$）：由空间平直约束（$Omega_{ ext{tot}} = 1$）直接推导得到其互补几何余项，即$Omega_m = 1 - pi^3/45 approx 0.3110$。 * 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几何填充间隙（基于接吻数$k=12$），得到$H_{0, ext{local}} = H_{0, ext{CMB}} (13/12) approx 73.0 ext{km/s/Mpc}$。