发表机构
Universitat Oberta de Catalunya (UOC); Universidad Internacional de La Rioja (UNIR)（加泰罗尼亚开放大学; 拉里奥哈国际大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为KRATOS识别-可比性诊断工具提供完整数学规范，推导其界、分解和零行为，揭示复合排序对小群体和重尾分布的敏感性，并附数值验证。
AI 中文摘要
KRATOS是一种群结构文献计量诊断工具，用于比较固定有限分析群体宇宙中文档分布（参与度）与引文权重分布（识别度）。本文给出其完整数学规范，并推导出控制其解释的属性。除各组件的界和等式条件外，我们证明：识别对齐分数仅通过组平均引文率与语料库均值的比率依赖于引文数据；参与-识别因子的组成上限是到均匀参考的总变差距离的仿射函数；该因子本身满足基于此上限和参与加权识别分数的弗雷歇型界。我们建立了复合指数的精确对数分解、主识别分数与互反对称识别分数之间的排序、不变性属性，以及全局和分层置换零假设下识别比率的闭式一阶和二阶矩。这些结果解释了为何复合排序可能对小群体、重尾引文分布和元数据重新分配敏感。所有结果均通过附带的脚本进行数值验证。该规范仅涉及测量结构；它不定义认知变化或正义的度量。
英文摘要
KRATOS is a group-structured bibliometric diagnostic that compares the distribution of documents (participation) with the distribution of citation weight (recognition) over a fixed, finite universe of analytical groups. This note gives its complete mathematical specification and derives the properties that govern its interpretation. Beyond bounds and equality conditions for each component, we show that the recognition-alignment score depends on citation data only through ratios of group mean citation rates to the corpus mean; that the composition ceiling of the participation--recognition factor is an affine function of the total variation distance to the uniform reference; and that the factor itself satisfies Fréchet-type bounds in terms of this ceiling and a participation-weighted recognition score. We establish an exact logarithmic decomposition of the composite index, an ordering between the primary and a reciprocal-symmetric recognition score, invariance properties, and closed-form first and second moments of the recognition ratios under global and stratified permutation nulls. These results explain why composite orderings can be sensitive to small groups, heavy-tailed citation distributions and metadata reassignment. All results are verified numerically with an accompanying script. The specification concerns measurement structure only; it does not define a measure of epistemic change or justice.
Comments10 pages
