How constrained the data's 8-byte structure is relative to the densest sphere packing in 8 dimensions.
Takes each group of 8 consecutive bytes, normalizes them, and finds the closest of the 240 root vectors of E8. These roots come in two families: 112 "integer" roots (pairs of coordinate axes) and 128 "half-integer" roots (all coordinates ±1/2 with even sign parity). The geometry also snaps each 8-byte window to the nearest actual E8 lattice point via parity correction, measuring the residual distance. Data with algebraic constraints concentrates on a few roots; unconstrained data spreads evenly across all 240.
Variation in root alignment quality across windows, capturing how consistently the data's 8-byte structure matches E8 directions. High for signals with a mix of aligned and unaligned windows.
Rate at which consecutive windows switch between integer and half-integer root cosets. Measures temporal dynamics of parity structure. Evolved via ShinkaEvolve.
Fraction of the 240 E8 roots actually used. High diversity means the data explores the full root system; low means it's confined to a subspace.
Shannon entropy of root usage, normalized by maximum. Uniform distributions across 240 roots score high; periodic orbits score near 0.
| Source | Domain | Value |
|---|---|---|
| Logistic r=3.68 (Banded Chaos) | chaos | 0.4574 |
| Square Wave | waveform | 0.3659 |
| Pulse-Width Modulation | waveform | 0.2736 |
| ··· | ||
| Sine Map (Feigenbaum) | chaos | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
| Logistic Edge-of-Chaos | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| ECG Fusion | medical | 8.6584 |
| Neural Net (Pruned 90%) | binary | 8.4853 |
| ECG Supraventr. | medical | 8.3756 |
| ··· | ||
| Logistic r=3.5 (Period-4) | chaos | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
| Sine Map (Feigenbaum) | chaos | 0.0000 |
E8 Lattice is the highest-dimensional root system geometry in the framework (window size 8), complementing G2 (2), H3 (3), D4 and H4 (4). Its 240-root system is the densest lattice sphere packing in 8D, and the coset_transition metric captures temporal structure in how the data moves between the integer and half-integer sublattices — a signature that lower-dimensional root systems cannot detect.