Published June 26, 2026
| Version v29
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A Corrected Suffix-Balanced Global-Minimum Certificate for Excluding Collatz m-Cycles for m ≤ 95 Expanded Version with Detailed Finite-Certificate Explanations
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Description
本文提出了一种可复现的计算机辅助证明框架,用于排除非平凡的Collatz(m)循环(其中m≤95)。该证明结合了精确有理区间运算、连分数分母证明和有限整数剩余类枚举。为了避免依赖Hercher原始证明中难以展开的块估计,本文引入了一种新的后缀平衡块方法,该方法直接控制选定连续块中每个局部最小值的贡献,并得到一个完整的自包含误差界。然后,针对m=92、m=93、m=94和m=95的情况构造了精确的剩余排除证明,结果与Simons-de Weger型上界相矛盾。所有关键常数和有限搜索均由仅使用精确整数或有理运算的配套程序进行验证,使得结果可独立复现。
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v14_m95.pdf
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