G 测量离散的张量计量收敛框架:装置无关基准 G₀ 的二维外推定义与检验 - Tensor Metrology Convergence Framework for Discrete G Measurements: Two-Parameter Extrapolated Definition and Verification of the Device-Independent Baseline G₀

中文版本说明 v13 将主文重构为独立的计量框架稿:以张量中心化与 SO(3) 分解为核心,给出两阶/二维外推与验收判据。理论推导部分已外移至伴随论文,主文仅保留接口与可执行数据要求,为实验团队保留实现与改进空间。 English Version Note v13 restructures the main text into a standalone metrology framework manuscript: centred on tensor centralisation and SO(3) decomposition, it provides two-stage / two-dimensional extrapolation and acceptance criteria. Theoretical derivations have been moved to a companion paper; the main text retains only interfaces and executable data requirements, preserving room for experimental teams to choose their own implementation and refinement approaches. 摘要 万有引力常数 G 的精密测量在过去三十余年持续出现显著离散,且离散幅度远超各实验所报告的不确定度预算。本文提出一个面向计量学的张量中心化收敛框架:把每组实验的标量报告值视为同一有效耦合张量 Kᵢⱼ 在装置几何与读出协议下的投影,并将其写成"尺度×形状"分离 Kᵢⱼ = κ₀ Qᵢⱼ。在三维特殊正交群(Special Orthogonal Group, SO(3))的不可约分解下,Qᵢⱼ 可分离为 ℓ = 0, 1, 2 三个通道;框架以迹读出 q₀(χ, f) = ⅓ tr Q(χ, f) 估计球核幅度,并以取向采样坐标 χ 与协议坐标 f(Hz)组织可审计的二维扫描。通过两阶处理与二维外推 (χ, f) → (0, 0),给出装置无关的截距 q₀,从而在给定归一参照 G_ref 时定义 G₀ = G_ref · q₀。本文强调可执行的数据接口、收敛判据与验收口径,使"收敛/不收敛"成为可证伪命题,并为测试团队保留实现细节的自主选择空间。 Abstract Precision measurements of the gravitational constant G have exhibited significant scatter over the past three decades, with discrepancies far exceeding the uncertainty budgets reported by individual experiments. This paper proposes a Tensor-Centred Convergence Framework oriented toward metrology: each experiment's scalar reported value is treated as the projection of a single effective coupling tensor Kᵢⱼ under the apparatus geometry and readout protocol, decomposed into a "scale × shape" separation Kᵢⱼ = κ₀ Qᵢⱼ. Under the irreducible decomposition of the three-dimensional Special Orthogonal Group SO(3), Qᵢⱼ separates into ℓ = 0, 1, 2 channels; the framework estimates the spherical-kernel amplitude via the trace readout q₀(χ, f) = ⅓ tr Q(χ, f), and organises an auditable two-dimensional scan in orientation-sampling coordinate χ and protocol coordinate f (Hz). Through two-stage processing and a two-dimensional extrapolation (χ, f) → (0, 0), an apparatus-independent intercept q₀ is obtained, thereby defining G₀ = G_ref · q₀ for a given normalisation reference G_ref. The paper emphasises executable data interfaces, convergence criteria, and acceptance apertures, making "convergence / non-convergence" a falsifiable proposition while preserving each testing team's autonomy over implementation details. Information: The chinese version is the original, the english version is the translated version!