The spectral fingerprint of the orderings
The personality of each ordering, in three spectra
Choose an ordering and compare its fingerprint: the Walsh energy bars, the dominant DFT harmonic and the Haar scale.
The family tree measures the kinship between orderings by inversions. This is its other face: the personality of each one, by spectrum. With a common yardstick for all five (position → binary value, centred), we extract three signatures: the energy of Walsh by order of line interaction, the dominant harmonic of the DFT and the scale of the dominant Haar wave.
Declared convention: this signal (the value placed at each position) is different from the one in Fourier over the cube and in the ring (position → King Wen number). There the structure of the book's content is measured; here the same yardstick is needed to compare the five orderings, so the signal is the value itself placed at each position.
DFT spectrum (magnitude by harmonic k = 1 to 32)
Jing Fang is the anti-linear one. 0% of linear energy and 74.5% in interactions of 4 lines: the loner of the brotherhood also has the strangest signature, and now one can see why its path sounds different.
King Wen resonates at k = 16 (period 4), at the same scale as the groups of 4 that Chan (2026) detects by another route: two independent methods pointing to the same scale.
Fu Xi and Gray calibrate the system. Fu Xi is a pure tone (100% linear, a single harmonic) and Gray almost linear (75% of order 1): the yardsticks against which the personality of the rest is read.
The spectral signature of the five orderings (common signal position -> binary value, centred, different from the King Wen signal of Fourier over the cube): Fu Xi is a pure tone (100% of the Walsh energy in order 1) and Gray almost linear (75% order 1, 25% order 2), the calibration rods; Jing Fang is the anti-linear one, with zero order-1 energy and 74.5% in four-line interactions, the strangest signature, consistent with being the loner of the brotherhood.
verificar_firmasThe dominant DFT harmonic of King Wen is k = 16 (period 4), in resonance with the groups of four hexagrams that Chan (2026) detects by another route: two independent methods pointing to the same scale. The dominant harmonics of the five orderings are 1, 1, 24, 16 and 7; the dominant Haar waves have widths 64, 64, 4, 4 and 32.
verificar_firmas · source: Chan, 2026The types of claim and the full bibliography (APA) are in Foundations.