The influences of the lines
How much each line weighs in a property
Choose a property and see how much each line weighs in the verdict; compare the total with the Walsh spectral sum.
Every property of a hexagram (satisfying a rule, falling into a family) is a Boolean function of 6 variables. The influence of line k is the probability that flipping that line changes the verdict: how decisive it is. Choose a property from the site itself and look at the split.
influence = fraction of the 64 hexagrams where flipping that line changes the verdict
The total influence (the sum of the six) coincides exactly with the weighted spectral sum of Walsh (each coefficient squared, weighted by its number of lines): the theorem of the analysis of Boolean functions that links this experiment with Fourier over the cube. For yang parity, flipping any line always changes the parity, so all six have influence 1: a maximally sensitive function.
A curiosity, not a theorem: for the no-two-adjacent-yin rule, the lines that weigh most are 2 (the inside) and 5 (the ruler), exactly the two the tradition singles out as central. It is a suggestive resonance; the mathematics only says they are the interior lines, with two neighbours each.
For the no-two-adjacent-yin rule, the influences by line are 10, 22, 18, 18, 22, 10 out of 64 (largest at lines 2 and 5); for yang parity, the influence of every line is exactly 1.
verificar_influenciasThe total influence of a property coincides with the weighted spectral sum of Walsh (the sum of popcount(w) times the coefficient squared): the theorem that links this experiment with Fourier over the cube.
verificar_influenciasThe types of claim and the full bibliography (APA) are in Foundations.