AI 中文总结
该研究通过对SPARC数据库126个星系的计算核查，明确径向加速度关系的可识别性极限，指出数据质量、结构极限及残差定义对其解释的关键影响，避免误将伪影当作新物理。
AI 中文摘要
我们利用SPARC数据库的一个标准子集（N = 126），对径向加速度关系（Radial Acceleration Relation, RAR）的结构修正的可识别性极限进行了计算核查。我们并未提出新的动力学定律，而是确定了这类定律在数学上可恢复的观测条件。我们明确了三种对RAR解释有重大影响的方法学控制因素：其一，我们分离出观测质量最低的层级（Q = 3，平均值为-0.433 dex）的8个星系与其余118个星系（平均值为-0.040 dex）之间存在-0.39 dex的残差偏移。在束展宽（beam smearing）必须满足的5项预测中，有4项不成立：径向轮廓平台为-0.331 ± 0.028 dex，而非衰减至零，且该偏移并未随曲线的分辨率单元数量成比例变化。束展宽作为主要驱动因素的可能性较低，不过该偏移仍是一种数据质量特征，而非物理特征——SPARC中的Q = 3标志着存在严重的不对称性和强烈的非圆周运动，在此条件下，旋转曲线无法追踪平衡势。其二，我们将数据集的结构极限解耦为三个独立测量的量：无模型点散射（sigma_M0 = 0.1860 dex）、每个星系自由截距后的残差基底（sigma_M3 = 0.1058 dex），以及由前两者推导得出的可吸收预算sqrt(sigma_M0^2 - sigma_M3^2) = 0.1530 dex。最后，我们提供了一个8单元协议网格，用于协调留一法（Leave-One-Out, LOO）均方预测误差（Mean Squared Prediction Error, MSPE）比率。我们证明，必须严格遵循残差定义（中位数与均值、带符号与绝对值）和基线分母来评估已报道的结构-动力学耦合关系，避免将标记伪影误当作新的物理现象。
英文摘要
We present a computational audit of the identifiability limits for structural corrections to the Radial Acceleration Relation (RAR) using a canonical subset of the SPARC database (N = 126). Rather than proposing a new dynamical law, we establish the observational conditions under which such a law would be mathematically recoverable. We resolve three methodological controls that heavily influence RAR interpretations. First, we isolate a -0.39 dex residual offset between the eight galaxies in the lowest-quality observational tier (Q = 3, mean -0.433 dex) and the remaining 118 (mean -0.040 dex). Of five predictions that beam smearing must satisfy, four fail: the radial profile plateaus at -0.331 +/- 0.028 dex rather than decaying to zero, and the offset does not scale with the number of resolution elements across a curve. Beam smearing is disfavoured as the primary driver, though the offset remains a data-quality signature rather than a physical one -- Q = 3 in SPARC flags major asymmetries and strong non-circular motions, conditions under which a rotation curve does not trace the equilibrium potential. Second, we decouple the architectural limits of the dataset into three independently measured quantities -- the no-model point scatter (sigma_M0 = 0.1860 dex), the residual floor after free per-galaxy intercepts (sigma_M3 = 0.1058 dex), and the propagated analytic error floor -- together with the absorbable budget sqrt(sigma_M0^2 - sigma_M3^2) = 0.1530 dex derived from the first two. Finally, we provide an 8-cell protocol grid to reconcile Leave-One-Out (LOO) Mean Squared Prediction Error (MSPE) ratios. We demonstrate that reported structural-dynamical couplings must be evaluated with strict adherence to residual definitions (median vs. mean, signed vs. absolute) and baseline denominators to avoid adopting labeling artifacts as new physics.
Comments9 pages, 4 figures. Companion paper to arXiv:2608.08945. Canonical dataset (N = 126), analysis code, and QA/QC pipeline available at https://doi.org/10.5281/zenodo.21959872
