FFT Symbol Class: Spiral

The spiral family occupies a distinct position in the archive's FFT framework because it is the primary chirality-bearing class. In the frequency domain, spiral forms — Archimedean spirals, logarithmic spirals, triskelion variants, magatama — produce a radially attenuating spectral profile with an angular phase gradient that encodes rotational direction. This chirality signature is what makes the spiral family the archive's test case for the unresolved question of whether right- and left-handed rotational forms preserve information about regional phase orientation in signal-active environments (doctrine-fft-symbol-classification c0005). The spiral is also a recursion-bearing form: multi-turn spirals have self-similar structure at successive scales, giving them membership in the recursive-fractal class as well. The archive treats this dual membership — chirality-bearing and recursion-bearing — as the reason spiral motifs appear at high frequency in both Celtic triskelion contexts and East Asian jade cong stratigraphy, two traditions the archive connects to anomaly-site custodial lineages.

Claims

c0001 — Spiral-class symbols have a radially attenuating, chirality-encoded spectral signature and overlap the recursive-fractal class

In the archive's FFT pipeline, spiral forms resolve with spectral power that decays radially from the center (marking the low-frequency dominance shared with the wheel class) but with a non-zero angular phase gradient that encodes the handedness of the rotation. This chirality component is absent from the wheel and cross classes and is the defining criterion for the spiral family. The archive does not currently assert that chirality direction carries interpretable signal; doctrine c0005 holds this as a hypothesis generator only. Multi-turn spirals additionally qualify as recursive forms, placing them in both the spiral and recursive-fractal classes simultaneously.