Consistency of Structure Expression and Symbolic Constraint: A Cross-Domain Empirical Study of Software Code and Genomic Data

Abstract

This paper tests a statistical hypothesis about interacting multi-systems: when two persistently interacting systems express the same structure state consistently, that structure produces a more concentrated symbol distribution within either single system — in short, "a structure expressed consistently by two systems is a more constraining structure". The test is performed in two mutually independent domains. First, software code: four open-source code libraries (Flask, Requests, Click, NumPy, together with C/C++/Java counterparts) are treated as systems; syntactic structures of programs (e.g. conditional expressions, function definitions) as structure states; and the symbols that follow a structure (identifiers, syntactic tokens) as symbols. The consistency with which two libraries express the same structure state is measured by the anchoring fidelity A=1−JS/ln⁡2A=1−JS/ln2, where JSJS is the Jensen–Shannon divergence between the two libraries' symbol distributions (larger AA means higher consistency); the constraining power of a structure is measured by the conditional entropy HH of its symbol distribution (smaller HH means stronger constraint on subsequent symbols). The hypothesis H1 takes the testable form ρ(A,H)<0ρ(A,H)<0 (consistency is positively associated with constraining power). Second, genomics: the 65,423 human enhancers of the FANTOM5 database are treated as structures, and their activity bins across 1,827 biological samples as symbols; H1 is tested with the same pair of quantities. Main results: among 10 code-library pairs, 9 satisfy H1 (consistency and conditional entropy are significantly negatively correlated, ρ(A,H)=−0.45ρ(A,H)=−0.45 to −1.00−1.00), and the conclusion is robust under finite-sample corrections (subsets with N≥20/N≥50); in genomics, the "two-system" design based on biologically distinct sample clusters gives ρ(A,H)=−0.59ρ(A,H)=−0.59 to −0.60−0.60 (p≈0p≈0, n=59,379n=59,379) — the effect has the same sign and a similar magnitude in both domains. The paper also tests the theoretical corollary of "time-direction tilt": the angle between the two systems' per-structure symbol-change directions (time-direction vectors) should shrink as the consistency AA grows (ρ(A,∣θ∣)<0ρ(A,∣θ∣)<0); this corollary holds with a consistent sign on the software-code and genomic data, and is unstable on low-support C-language structures. Three methodological corrections are recorded faithfully: the column-mapping error of the original DNA script, the falsification of the original claim "random pairs lack this coupling", and the withdrawal of a first-order bias-correction formula. Keywords: multi-system interaction; structure consistency; conditional entropy; Jensen–Shannon divergence; finite-sample correction; software code; genomic enhancers 本文检验一个关于多系统相互作用的统计假说:当两个持续交互的系统对同一结构状态的表达彼此一致时,该结构在单系统内产生的符号分布更加集中——简言之,"被两个系统一致表达的结构,是更有约束力的结构"。 检验在两个彼此独立的领域进行。第一,软件代码:将四个开源代码库(Flask、Requests、Click、NumPy 及其 C/C++/Java 对照库)视为系统,将程序中的语法结构(如条件表达式、函数定义)视为结构状态,将结构后续出现的符号(标识符、语法标记)视为符号;两库对同一结构状态的一致程度用锚定保真度 A=1−JS/ln⁡2A=1−JS/ln2 度量(JSJS 为两库符号分布之间的 Jensen–Shannon 散度,AA 越大表示两库越一致),结构的约束力用符号分布的条件熵 HH 度量(HH 越小表示该结构对后续符号的约束越强)。假说 H1 的检验形式为 ρ(A,H)<0ρ(A,H)<0(一致性与约束力正相关)。第二,基因组:将 FANTOM5 数据库的 65,423 个人类增强子视为结构,将其跨 1,827 个生物样本的活性分档视为符号,用同一组量检验 H1。 主要结果:在 10 个代码库配对中,9 个满足 H1(一致性与条件熵显著负相关,ρ(A,H)=−0.45∼−1.00ρ(A,H)=−0.45∼−1.00),且结论在有限样本校正(N≥20/N≥50 子集)下稳健;在基因组中,按生物学样本群划分的"两系统"设计给出 ρ(A,H)=−0.59∼−0.60ρ(A,H)=−0.59∼−0.60(p≈0p≈0,n=59,379n=59,379)——两个领域的效应方向与量级一致。本文还检验了理论的推论"时间方向倾斜":一个结构在两个系统内各自的符号变化方向(时间方向向量)之间的夹角应随一致性 A 增大而收缩(ρ(A,∣θ∣)<0ρ(A,∣θ∣)<0);该推论在软件代码与基因组数据上方向一致地成立,而在低样本支撑的 C 语言结构上不稳定。文中如实记录了三处方法学修正:初版 DNA 脚本的列映射错误、初版"随机配对无耦合"结论被证伪、一阶偏置校正公式被撤回。 关键词:多系统交互;结构一致性;条件熵;Jensen–Shannon 散度;有限样本校正;软件代码;基因组增强子