The Gold Partition Conjecture Holds through Fourteen Elements

Peczarski verified the Gold Partition Conjecture for posets with at most 11 elements in 2006. We extend this exhaustive frontier to 14 elements. At order 14, the unique chain is set aside and every one of the remaining 1,338,193,159,770 isomorphism classes receives one of Peczarski's certificates. It follows, in particular, that the 1/3–2/3 Conjecture holds through order 14, one order beyond the previous complete mutual-rank-probability census. The calculation uses exact integer recurrences on the lattice of order ideals and was divided into 4,096 deterministic shards. The complete shard archive, source, and independent small-order checks accompany the paper. This record contains version 1.0.0 of the manuscript and its reproducibility artifact: the exact public source tree, the complete order-14 shard summaries, the order-10–13 regression ladder, checksum manifests, aggregate outputs, and build provenance. Source repository: https://github.com/agupta/gold-partition-conjecture