How heavy are the signal's distributional tails — the fraction of samples beyond 1.5 standard deviations?
Operates on the z-scored raw signal, deliberately bypassing the framework's default min-max normalization (which collapses extremes into [0,1] and destroys tail shape). It fills a specific third-party blind spot: the tsfresh::ratio_beyond_r_sigma feature, which the atlas plus catch24 together reconstruct at only R² = −0.85 — the largest single gap of any standard feature in the 2026-05-25 reverse-orthogonality sweep.
Fraction of samples farther than 1.5σ from the mean. High for heavy-tailed or multimodal distributions (Pell Word 0.29, DNA Chimp 0.24, Codon Usage 0.23); near 0 for tightly-concentrated or tiny-amplitude signals (LIGO 0.00). The threshold k = 1.5 is deliberate: k ∈ {0.5, 2.5, 3, 4} all prove redundant with Spherical S²:concentration or Catch24:DN_Spread_Std, while k = 1.5 survives both strict and iterative dedup.
| Source | Origin | Value |
|---|---|---|
| Pell Word | symbolic-dynamics | 0.2929 |
| Golden-Mean β-Shift | symbolic-dynamics | 0.2763 |
| Langton's Ant | symbolic-dynamics | 0.2472 |
| ··· | ||
| Logistic Chaos | iterated-maps | 0.0000 |
| Thue-Morse | symbolic-dynamics | 0.0000 |
| Collatz Cycle Word | number-theory | 0.0000 |
The only atlas lens that reads marginal tail-heaviness directly. It separates heavy-tailed and multimodal sources from Gaussian-like ones, independent of any temporal structure.