Whether 3-byte patterns prefer icosahedral directions.
Projects each triple of consecutive bytes onto the 30 roots of H3 — the vertices of an icosidodecahedron. These roots split into 6 axis-aligned vectors (permutations of (1,0,0)) and 24 "golden" vectors involving the golden ratio (even permutations of (1/2, phi/2, 1/2phi)). H3 is the symmetry group of the icosahedron, featuring 5-fold rotational symmetry that no crystallographic lattice can achieve. The geometry asks whether the data's 3-byte structure has any preference for these non-crystallographic directions.
Nearest-neighbor enrichment: how much more likely are consecutive windows to share a root than expected by chance. Measures temporal locality in root space. Evolved via ShinkaEvolve.
Autocorrelation of the root assignment sequence. High for smooth signals where 3-byte windows change gradually; low for noise and chaos.
| Source | Origin | Value |
|---|---|---|
| Thue-Morse | symbolic-dynamics | 5.8534 |
| Padovan Word | symbolic-dynamics | 4.8273 |
| Kolakoski Sequence | symbolic-dynamics | 4.4933 |
| ··· | ||
| Sine Wave | signal-synthesis | 0.0000 |
| Sawtooth Wave | signal-synthesis | 0.0000 |
| Period-Doubled Wave | signal-synthesis | 0.0000 |
| Source | Origin | Value |
|---|---|---|
| Thue-Morse | symbolic-dynamics | 0.6408 |
| Fibonacci Tight-Binding | random-matrix-quantum | 0.4179 |
| Padovan Word | symbolic-dynamics | 0.4059 |
| ··· | ||
| Tidal Gauge (SF) | geophysical | 0.0000 |
| Collatz Trajectory | number-theory | 0.0000 |
| Lorenz Attractor | continuous-flows | 0.0000 |
H3 is the only geometry in the framework probing 5-fold icosahedral symmetry at the 3-byte scale, between G2 (pairs) and D4/H4 (quadruples). The evolved metrics (nn_enrichment, temporal_coherence) shift focus from static root statistics to temporal dynamics in root space — how the signal's trajectory through the 30 icosahedral directions evolves over time.