Results of this laboratory that, after a documented search, we have not found published elsewhere. The seal is an orthogonal marker: the experiment keeps its thematic category and the counts do not change.
The count of seals is frozen in the verification suite: a new one cannot appear without going through its process. A search that fails to find a source does not prove there is none.
Measured against binary counting, King Wen has 1013 inversions and Mawangdui and Jing Fang 1008: a tie at the exact random expectation, with line costs of 211, 141 and 93.
Search 2026-07-25: the published comparisons between the historical orderings are qualitative or visual (Yijing Dao; Cottrell; Cook 2006 as an attempt to derive King Wen); the inversion metric against binary counting, the 1013/1008/1008 tie and the table of line costs do not appear published.
Jing Fang's Eight Palaces and the cosets of the subgroup of pure hexagrams give ARI = −0.125: further apart than chance, because the eight generating masks are not a subgroup.
Search 2026-07-25: there is structural literature on Jing Fang's Eight Palaces (Mesker 2002; comparisons in Yijing Dao) but no quantitative comparison of partitions; the ARI = −0.125 between the palaces and the cosets of the subgroup of pure hexagrams does not appear published.
The Walsh transform of the King Wen sequence concentrates 77.4% of its energy in even interaction orders, against the 47.6% chance would spread: the pair rule, confirmed spectrally.
Search 2026-07-25: Walsh and the I Ching appear associated in the literature (Petoukhov 2017, in a genetic and numerological context; Schöter, algebra of hexagrams), and Chan (2026) detects the pair asymmetry in the time domain; the Walsh spectrum of the King Wen ordering and its concentration in even interaction orders, as a spectral confirmation of the pair rule, do not appear published.
Hexagrams with no two adjacent yin lines are exactly 21 = F(8); the ladder by number of lines is F(n+2) and, closing the ring, 18 = L(6) remain.
Web search of the formulation (21 = F(8) with no two consecutive yin lines, the ladder F(n+2), Lucas in the circular version, the Ji Ji / Wei Ji intersection); only numerology was found (Fibonacci offsets on the bagua, the golden ratio in King Wen); no equivalent verified formulation.
King Wen and Mawangdui resemble each other more than chance allows (759 inversions, z = −2.89), and that resemblance is a shared gradient of trigram families.
Search 2026-07-27: there is comparative research on the Mawangdui sequence against King Wen (Han Zhongmin, in Chinese), analysis of King Wen against binary (Chan 2026; iching-math with cycle type [52, 10, 2]) and qualitative comparisons (Yijing Dao), but no permutation statistics BETWEEN the historical orderings themselves; the 759 of KW-Mawangdui (z = −2.89) and the full picture of the kinship do not appear published. Search 2026-07-30 (mechanism): the existing comparative KW-Mawangdui scholarship is qualitative (Han Zhongmin; Shaughnessy, Unearthing the Changes, 2014) and the standard view denies mathematical meaning to Mawangdui (Yijing Dao, citing Rutt); the quantitative explanation of the kinship as a shared gradient of trigram families does not appear published.
No structural criterion decides which hexagram opens each pair better than a coin; the strongest signal, the doctrine of correct centers, stops at 12/16 (p = 0.038).
Search 2026-07-30: the orientation within the pairs has an independent nuclear proposal (already discussed in the experiment), the traditional narrative explanation of the Xugua, and adjacent work on the pairing (Radisic 2026) and on distances (Chan 2026), but the statistical test of orientation criteria (the full battery and the signal of the correct centers, 12/16 with its double reading) does not appear published. The doctrine of correctness that grounds it is canonical (the Stanford Encyclopedia of Philosophy calls Ji Ji the best hexagram in yin-yang correspondence, and Ji Ji opens its pair).
Four of these findings support the paper Statistical Structure of the Historical Orderings of the I Ching Hexagrams: the tie with binary counting, the kinship of the two oldest orderings and its mechanism, the question of the pair with its limit of demonstrability, and the spectral confirmation of the pair rule. Read the paper and its replication package.
The full system of claim types, sources and verifications lives in Foundations and sources.
