For the logistic map, all period-2ᵏ orbits appear below the accumulation point r∞≈3.570; period 5 appears only beyond it.
Sources 第十五章 旋机吸引子系统的形式化 · 命题七
External anchor Feigenbaum (1978); Sharkovskii (1964)
SGC-0016
Premises and dependents
Downstream, level 1 (claims resting on this one)
- SGC-0040 Interpretive The Feigenbaum accumulation point r∞≈3.570 can be read as a dynamical realization of the Axiom-of-Foundation boundary. logical
- SGC-0041 Interpretive Period-doubling 2ᵏ corresponds to the nested yin-yang trigram system; period 5 corresponds to the Five Phases. logical · awaiting author confirmation
Cite
Claim template
〔定理级〕Logistic 映射的倍周期 2ᵏ 轨道全部出现在累积点 r∞≈3.570 之内；周期 5 只出现在其外。——李旭彤《生之科学》（第十五章 旋机吸引子系统的形式化·命题七），问道研究所，2026。
Chinese
李旭彤：〈SGC-0016〉Logistic 映射的倍周期 2ᵏ 轨道全部出现在累积点 r∞≈3.570 之内；周期 5 只出现在其外〔定理级〕，载《生之科学》第十五章 旋机吸引子系统的形式化·命题七，问道研究所，2026。https://reresearch.org/claim/sgc-0016/
English
Li, Xutong (2026). SGC-0016 [Theorem]: For the logistic map, all period-2ᵏ orbits appear below the accumulation point r∞≈3.570; period 5 appears only beyond it. In: Science of Generation, 第十五章 旋机吸引子系统的形式化, 命题七. Reasoning Research Institute. https://reresearch.org/en/claim/sgc-0016/
BibTeX
@misc{SGC-0016,
author = {Li, Xutong},
title = {{SGC-0016}: For the logistic map, all period-2ᵏ orbits appear below the accumulation point r∞≈3.570; period 5 appears only beyond it.},
howpublished = {Science of Generation Portal},
organization = {Reasoning Research Institute},
year = {2026},
url = {https://reresearch.org/en/claim/sgc-0016/},
note = {Epistemic tier: Theorem. Source: 第十五章 旋机吸引子系统的形式化, 命题七}
}