AI 中文总结
研究将黄金分割猜想的验证从至多11个元素扩展到14个元素，通过序理想格上的精确整数递归计算，证明1/3 - 2/3猜想在14阶成立，给出完整分片存档等，扩展了该猜想的验证范围。
AI 中文摘要
2006年，佩恰尔斯基验证了元素个数至多为11的偏序集的黄金分割猜想。我们将这一详尽边界扩展到了14个元素。在14阶时，排除唯一链，其余1,338,193,159,770个同构类中的每一个都获得了佩恰尔斯基的一个证明。特别地，1/3 - 2/3猜想在14阶成立，比之前完整的互秩概率普查多了一阶。计算使用了序理想格上的精确整数递归，并分为4,096个确定性分片。论文还附带了完整的分片存档、源代码和独立的小阶检查。
英文摘要
We determine the exact extremal balance data of all 1,338,193,159,771 unlabeled posets on fourteen elements. The least balance constant exceeding $1/3$ is $37/106$. The least over posets that are not nontrivial ordinal sums is $254/725$, attained by a ladder with broken rungs; this confirms a conjecture of Peczarski at order 14, while orders 12 and 13 reproduce De Loof, De Baets, and De Meyer. No balance constant lies in the gap above $1/3$ that Peczarski conjectures to be empty. Exactly 128 classes attain $1/3$, and every one is an ordinal sum of singletons and copies of the three-element poset with one relation, a family whose non-chain members are counted by $a(n)-1$, where $a(n)=a(n-1)+a(n-3)$. In the linear-extension-majority digraph the longest simple cycle has length 8, against 7 at order 13, and exactly 30 classes attain it; of the thirteen such classes whose witnesses the census retains, nine have a cycle spectrum containing no odd cycle at all. A second exhaustive pass over the same classes verifies Peczarski's Gold Partition Conjecture through fourteen elements, extending his order-11 frontier and implying in particular that the $1/3$-$2/3$ Conjecture holds through order 14. All arithmetic is exact and every extremal witness is recomputed by an independent program.
Comments16 pages, 3 figures. Version 2 adds an exhaustive order-14 balance and linear-extension-majority census, including extremal balance constants, the equality locus, and cycle spectra; the Gold Partition result is unchanged. Code, data, and archived computational artifacts: https://doi.org/10.5281/zenodo.21696940
