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Hexagram 31 — Guai, Breakthrough
Chronological no. 31 (binary-weight order) · King Wen no. (traditional) 43 · 夬
By Anibal Edelberto Amiot — Updated October 1, 2026
the youngest daughter
the father
The Lake rises above Heaven: the image of breakthrough. Water, carried higher than what should normally contain it, threatens to overflow — an extreme tension that calls for a clear, irreversible decision. This is the figure of resolution that can wait no longer. Thus the noble one spreads his bounty downward, never resting on virtue alone: cutting decisively must always be accompanied by generosity toward those the decision affects.
The decision that cuts clean and eliminates the superfluous. There comes a moment when hesitation itself becomes more dangerous than the sharpness of the decision. This line says true breakthrough does not consist in destroying everything, but in precisely removing what, in excess, threatened the whole.
The six lines
At the base of the earth, fullness stirs: the yang onset that carried the whole figure now yields its place.
The steadied earth reaches its limit: the solidity that upheld the structure is about to change its nature.
At the threshold between earth and man, force wavers: what acted through firmness hesitates before turning.
In the action of man, fullness meets its limit: the initiative that led the figure folds back upon itself.
At the sage's seat, fullness hollows out: the force that governed the figure from its center is about to invert.
At the summit, emptiness reaches its fullest extent and closes: the furthest opening turns toward its opposite.
Source: La Livrée d'Hermès, Anibal Amiot — chapter 7.1 (pp. 63–68). French version of this page.
For the notions used here — magic square, layer and casting, the Yi Jing — see the project lexicon.
The patterns of this hexagram
Eight 12×12 Jacquard patterns are generated from this hexagram, one for each admissible family of the system. Each has its own page: cell, tiling, recolourings and data.
Bases — YANG mutant
Bases — YANG
Pair of two — YANG + YIN mutant
Pair of two — YIN mutant + YANG mutant
Pair of two — YIN + YANG
Pair of two — YIN + YANG mutant
Triple — without YANG
Triple — without YANG mutant
Neighbouring hexagrams
30 — Da Guo, Preponderance of the Great · 32 — Bo, Splitting Apart
Hexagrams sharing a trigram
Same upper trigram (☱ Dui): 24 — Cui, Gathering Together · 25 — Sui, Following · 26 — Kun, Oppression · 27 — Dui, The Joyous · 28 — Xian, Influence · 29 — Ge, Revolution · 30 — Da Guo, Preponderance of the Great
Same lower trigram (☰ Qian): 7 — Tai, Peace · 15 — Da Zhuang, The Power of the Great · 23 — Xu, Waiting · 39 — Da Chu, The Taming Power of the Great · 47 — Da You, Possession in Great Measure · 55 — Xiao Chu, The Taming Power of the Small · 63 — Qian, The Creative
