Not in atlas — all metrics redundant with existing geometries at |r| > 0.9.
What it measures: How uniformly the signal's growth structure fills angular space.
Maps the time series onto a logarithmic spiral in polar coordinates: each sample advances the angle by a data-dependent step (larger values rotate faster) while the radius grows exponentially. The resulting spiral path reflects multiplicative structure in the data.
How uniform are the angular step sizes along the spiral path? Computed as 1 minus the coefficient of variation of consecutive angular increments. 1.0 means all steps are the same size. Collatz Gap Lengths (0.984) scores highest: its angular increments are nearly constant in magnitude. Accelerometer sitting (0.968) and BTC Returns (0.961) are close behind — both have broad amplitude distributions that produce consistent angular steps. Collatz Parity scores 0.292 (strongly non-uniform — the binary values create only two angular step sizes). Constants score 0.0.
RMS of lag-1..5 autocorrelation of consecutive angular increments. Measures temporal memory in the rotation speed: high when the spiral's angular pacing drifts slowly, low when each step's rotation is independent of the last. fBm Persistent (1.00), Brownian Walk (0.995), Hilbert Walk (0.993), and physical slow drifts (Potomac River Flow 0.998, Seismograph ANMO 0.995) sit near 1.0 — their smooth value drift produces highly-autocorrelated angular steps. PRNGs (MINSTD 0.011, glibc LCG 0.016, XorShift32 0.017) and Human Proteome (0.017) sit near zero — their uniform random bytes give independent angular steps.
RMS of lag-1..5 autocorrelation of log-radii residuals after detrending the exponential growth envelope against cumulative angle. Captures oscillation around the expected exp(0.02 θ) spiral — persistent residuals mean the signal pulls off-envelope in coherent excursions. Rössler Attractor (0.996), Potomac River Flow (0.997), and Deep Earthquake P-wave (0.990) score near 1.0 — their slow wave-like structure leaves coherent departures from the pure spiral. PRNGs and Earthquake Depths/Intervals (~0.01) give white-noise residuals, no memory beyond the fit.
exp(-50 × std of per-window (window=512, step=256) exponential growth rates). Scores 1.0 when every window agrees on the spiral's growth exponent (uniform growth); drops toward 0 when the growth rate drifts. Period-locked logistic, Constants, and Edge-of-Chaos all score 1.000 — their byte distributions are stationary so every window produces the same growth fit. Stochastic drift sources bottom out: Potomac River Flow (0.881), fBm Persistent (0.890), Levy Flight (0.892), Exponential Chirp (0.894) — non-stationary amplitude changes the per-window growth rate.
Logarithmic Spiral is atlas-excluded as a whole because its metrics duplicate signals carried by SL(2,ℝ), Spectral Analysis, and Symplectic — the geometry lives in the framework as a diagnostic rather than an atlas discriminator. The four metrics together give a 2D summary: angular_uniformity and growth_stability reflect stationarity of the amplitude distribution, while angular_acf and radial_acf reflect temporal memory of the rotation and radial channels. PRNGs and white-noise sources sit at the low corner of both axes; slow physical drifts sit at the high corner.