标题： 社交媒体网络中的分层同步与失真缩放：分形拓扑理论 显示英文标题

标题： Hierarchical Synchronization and Distortion Scaling in Social Media Networks: A Fractal-Like Topology Theory

摘要： 社交媒体作为信息传播主导渠道的迅速普及，加剧了对系统性信息扭曲的担忧，即内容在连续的传播层中逐渐被改变。 尽管先前的研究已经从定性角度探讨了这种扭曲，但传播拓扑结构与随机认知扰动之间的定量相互作用仍不够明确。 在本研究中，我们提出了一种新颖的分形启发式有向分层网络模型，以捕捉传播的结构模式，并引入了噪声阻碍的Hegselmann-Krause（NFHK）框架来模拟噪声下的意见动态。 分析结果得到了群论和图论的支持，揭示了噪声积累导致意见扭曲增加以及层内同步的出现。 多智能体模拟验证了这些效应，表明噪声强度影响收敛速度和弱层内聚类。 使用一个具有代表性的转发级联进行实证验证，证明了所提出的模型即使没有直接连接也能再现现实世界中的扭曲模式和同步行为。 本研究揭示了数字平台中信息扭曲的统一机制，并为公众意见治理和平台监管提供了拓扑感知的见解。 显示英文摘要

摘要： The rapid proliferation of social media as a dominant channel for information dissemination has intensified concerns over systemic information distortion, whereby content is progressively altered through successive layers of transmission. While prior studies have explored such distortion qualitatively, the quantitative interplay between propagation topology and stochastic cognitive perturbations remains insufficiently understood. In this work, we propose a novel fractal-inspired directed hierarchical network model to capture the structural patterns of propagation, and introduce a Noise-Frustrated Hegselmann-Krause (NFHK) framework to model opinion dynamics under noise. Analytical results, supported by group and graph theory, reveal that noise accumulation leads to increasing opinion distortion and the emergence of intra-layer synchronization. Multi-agent simulations confirm these effects, showing that noise intensity shapes both convergence rates and weak intra-layer clustering. Empirical validation using a representative retweet cascade demonstrates that the proposed model reproduces real-world distortion patterns and synchronization behaviors, even without direct links. This work uncovers a unified mechanism for information distortion in digital platforms and offers topology-aware insights for public opinion governance and platform regulation.