张量计量收敛与内禀球核标尺 q₀:候选引力常数基准 G₀ 的闭环互证框架 - Tensor-Metrology Convergence and Intrinsic Spherical-Kernel Gauge q₀: A Closed-Loop Verification Framework for the Candidate Gravitational Constant Baseline G₀

Abstract: 本文面向引力常数 G 百年来“测量值不收敛”的历史痛点,提出了一个介观尺度的引力作用机制,建构了一个由“模型侧(介观结构涨落)”与“计量侧(张量收敛)”闭环互证的统一框架。在模型侧,以热力学第二定律(Second Law of Thermodynamics, SLT)为第一性约束,在介观体胞层级引入结构涨落的两层级联动:原子尺度载波加速度幅度 w₀ 与介观包络协同加速度幅度 W₀,并定义内禀无量纲比值 q₀ ≡ W₀/w₀ ,认为 q₀ 就是决定引力常数 G₀ 的体系的“球核标尺”。在计量侧,我们把两体耦合在该尺度上的线性响应核(结构涨落自由能的二阶变分所给出的海森矩阵(Hessian matrix))记为有效耦合张量 Kᵢⱼ;装置与协议差异决定了我们对 Kᵢⱼ 的实验读出方式,并表现为无量纲形状张量 Qᵢⱼ 的取向依赖、非互易与协议粗粒化等偏差。通过“尺度 × 形状分离” Kᵢⱼ = k₀Qᵢⱼ,并对 Kᵢⱼ 作特殊正交群(Special Orthogonal Group, SO(3))不可约分解(自然分解为 ℓ = 0 球核标量、ℓ = 1 反对称分量与 ℓ = 2 对称无迹偏张量),我们把取向采样、协议粗粒化与非互易等装置/协议相关效应视为主要进入 ℓ = 1, 2 的读出污染。在外参 (χ, f) 的二维极限外推 (χ, f) → (0, 0) 下,这些非标量分量应在极限中系统性消退,从而留下唯一的 ℓ = 0 球核标量候选 G₀ = k₀q₀ 作为装置无关基准。以这个装置无关新基准形成了本文的归一化新方法。关于 G₀ 的推导细节置于附录,以保持主文叙事的紧凑和可读性。Abstract: Addressing the century-old problem that measured values of the gravitational constant G have failed to converge, this paper proposes a mesoscopic-scale mechanism for gravitational interaction and constructs a unified framework in which a model side (mesoscopic structural fluctuations) and a metrology side (tensor convergence) form a closed, mutually verifying loop. On the model side, taking the Second Law of Thermodynamics (SLT) as a first-principles constraint, we introduce a two-tier cascade of structural fluctuations at the mesoscopic unit-cell level: an atomic-scale carrier acceleration amplitude w₀ and a mesoscopic envelope cooperative acceleration amplitude W₀. We define the intrinsic dimensionless ratio q₀ ≡ W₀/w₀ and identify q₀ as the spherical-nucleus gauge of the system that determines the gravitational constant G₀. On the metrology side, we denote the linear-response kernel of the two-body coupling at this scale—the Hessian matrix given by the second-order variation of the structural-fluctuation free energy—as the effective coupling tensor Kᵢⱼ. Differences in apparatus and protocol determine how Kᵢⱼ is experimentally read out, manifesting as orientation dependence of the dimensionless shape tensor Qᵢⱼ, non-reciprocity, and protocol coarse-graining biases. Through a "scale × shape" separation Kᵢⱼ = k₀Qᵢⱼ and an irreducible decomposition of Kᵢⱼ under the special orthogonal group SO(3)—which naturally splits into an ℓ = 0 spherical-nucleus scalar, an ℓ = 1 antisymmetric component, and an ℓ = 2 symmetric traceless deviatoric tensor—we treat orientation sampling, protocol coarse-graining, and non-reciprocity as apparatus/protocol-dependent effects that enter primarily into the ℓ = 1, 2 sectors as readout contamination. Under a two-dimensional limit extrapolation of the external parameters (χ, f) → (0, 0), these non-scalar components should systematically vanish, leaving the unique ℓ = 0 spherical-nucleus scalar candidate G₀ = k₀q₀ as the apparatus-independent reference value. This apparatus-independent reference forms the basis of the new normalization method proposed in this paper. Detailed derivations of G₀ are placed in the appendices to maintain the compactness and readability of the main text.Additional information: The original is the chinese text, the english version was translated using AI.Context: 本文基于 https://zenodo.org/records/18697711 与 https://zenodo.org/records/18700509 合并而成。 This paper is a combined paper based on https://zenodo.org/records/18697711 and https://zenodo.org/records/18700509