循环群的等距五点子集上的单位作用：七类分类的轨道与不动点 refinement
Unit Actions on Homometric Five-Point Subsets of Cyclic Groups: Orbit and fixed-point refinement of the seven-family classification
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中文总结 AI 辅助
该论文证明了Erickson和Jones关于五点二进制手镯七类等距类在单位乘法（模符号）下不变的猜想，推导了单位轨道数和固定类数的公式，确定了七类的轨道大小分布及A型、F型的稳定子。
中文摘要 AI 辅助
Erickson和Jones将五点二进制手镯的非平凡等距类分为A-G七类，并猜想每一类在单位乘法（模符号）下保持不变。我们证明了该猜想，表明诱导作用对A型是对角的，对B-E型是乘法的，对F型是仿射的，对G型通过U₂₀/{±1}≅C₄正则作用。我们推导了单位轨道数和被所有单位固定的类数的闭式算术公式，确定了七类的轨道大小分布，包括A型和F型的稳定子显式描述。
英文摘要
Erickson and Jones classified the nontrivial homometry classes of five-point binary bracelets into seven families, Types A-G, and conjectured that each family is invariant under multiplication by units modulo sign. We prove this conjecture and show that the induced actions are diagonal for Type A, multiplicative for Types B-E, affine for Type F, and regular through $U_{20}/\{\pm1\}\cong C_4$ for Type G. We derive closed arithmetic formulas for the numbers of unit orbits and classes fixed by every unit, and determine the orbit-size distributions in all seven types, including explicit stabilizer descriptions for Types A and F.
