AI 中文总结
研究递归卷曲细丝，将螺旋化表述为迭代映射，通过边缘约当模式和螺距无序确定相关特性，精确有限级速率区分情况，经三维梁计算验证响应与收敛。
AI 中文摘要
重复卷曲产生细丝层次结构。我们将螺旋化表述为作用于任意杆柔顺性的迭代映射，而非使一种规定结构均匀化。一个边缘约当模式产生外半径平方反比刚度类，而螺距无序在放大和屏蔽的伸长 - 扭转响应之间创建一个李雅普诺夫阈值。一个精确的有限级速率在三级区分代表性的放大和屏蔽情况；直接三维梁计算通过四级验证响应并通过五级验证收敛。
英文摘要
Repeated coiling creates a filament hierarchy. We formulate helicalization as an iterated map acting on an arbitrary rod compliance, rather than homogenizing one prescribed construction. A marginal Jordan mode yields an outer-radius inverse-square stiffness class, while pitch disorder creates a Lyapunov threshold between amplified and screened extension--twist response. An exact finite-level rate distinguishes representative amplified and screened cases by level three; direct three-dimensional beam calculations validate the response through level four and convergence through level five.
Comments6 pages, 3 figures; 10-page Supplemental Material included as an ancillary file
