Balance Constants, Majority Cycles, and the Gold Partition Conjecture through Fourteen Elements

We determine exact balance and linear-extension-majority data for all 1,338,193,159,771 unlabeled posets on fourteen elements. The least balance constant above 1/3 is 37/106. The least among posets that are not nontrivial ordinal sums is 254/725, confirming Peczarski's broken-rung prediction at order 14. Exactly 128 classes attain balance 1/3, all in the ordinal-sum family proved in the paper. The longest simple cycle in the linear-extension-majority digraph has length 8 and occurs in exactly 30 classes. A separate exhaustive pass over the same isomorphism classes verifies Peczarski's Gold Partition Conjecture through fourteen elements, with zero unresolved classes, and therefore verifies the 1/3–2/3 Conjecture through order 14. Both computations use exact arithmetic and deterministic modulus shards. Release 2.0.0 contains the sixteen-page manuscript, exact public source and tests, compact aggregate reports, and the complete accepted shard archives for both order-14 computations. The data archives include checksum manifests, build/run provenance, exact production sources, and retained witnesses. Source repository: https://github.com/agupta/gold-partition-conjecture