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.
Combined structural score from root alignment, coset dynamics, and lattice closure. Evolved via ShinkaEvolve. Not yet in the atlas.
How closely the lattice-snapped points recover the original data. Evolved via ShinkaEvolve. Not yet in the atlas.
Net directional flow along E8 root graph edges over time. Evolved via ShinkaEvolve. Not yet in the atlas.
Mean curvature of the trajectory through E8 root space. Evolved via ShinkaEvolve. Not yet in the atlas.
Autocorrelation of the velocity (root-to-root distance per step) sequence. Evolved via ShinkaEvolve. Not yet in the atlas.
| Source | Domain | Value |
|---|---|---|
| Logistic r=3.68 (Banded Chaos) | chaos | 0.4491 |
| Square Wave | waveform | 0.2450 |
| Random Steps | exotic | 0.1848 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Logistic r=3.5 (Period-4) | chaos | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
| Source | Domain | Value |
|---|---|---|
| Zipf Distribution | exotic | 0.9891 |
| Beta Noise | noise | 0.9891 |
| Dice Rolls | exotic | 0.9891 |
| ··· | ||
| Constant 0xFF | noise | 0.0109 |
| Logistic r=3.5 (Period-4) | chaos | 0.0109 |
| Logistic r=3.2 (Period-2) | chaos | 0.0109 |
| Source | Domain | Value |
|---|---|---|
| Poisson Spacings | quantum | 0.9788 |
| Geometric Waiting Times | exotic | 0.9777 |
| Zipf Distribution | exotic | 0.9750 |
| ··· | ||
| Constant 0xFF | noise | -0.0000 |
| Logistic r=3.5 (Period-4) | chaos | -0.0000 |
| Logistic r=3.2 (Period-2) | chaos | -0.0000 |
| Source | Domain | Value |
|---|---|---|
| ECG Fusion | medical | 8.6584 |
| Neural Net (Pruned 90%) | binary | 8.4892 |
| ECG Supraventr. | medical | 8.3756 |
| ··· | ||
| Constant 0xFF | noise | 0.0000 |
| Logistic r=3.2 (Period-2) | chaos | 0.0000 |
| Logistic r=3.5 (Period-4) | 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.