Stable Noise
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Symmetric α-stable (Lévy) noise, α=1.8 --- IID infinite-variance heavy tails with no temporal structure. Antithetic-symmetrized (±-mirrored magnitudes, then shuffled) so in-sample skew, mean, and time-irreversibility are exactly zero. A heavy-tail contrast control: it isolates tail-weight from burst asymmetry, so a 'heavy-tailed and time-irreversible' source pairing can be tested against 'heavy-tailed but time-reversible'.
Interpretation
Standard analysis sees: heavy-tailed; aperiodic / broadband; high-complexity (noise-like). The atlas finds no named structure, but the source is distinctively extreme on SL(2,ℝ) (Thurston):parabolic_fraction (+7.2z) — beyond what the standard bank predicts for it. It sits beside S&P 500 Returns in the atlas (standard-bank rank 38) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.98
asymmetry0.43
occupancy0.21
short-range corr0.34
long-range memory0.42
spectral colour0.71
periodicity0.08
complexity0.91
time-irreversibility0.43
volatility clustering0.22
multifractality0.54
dimensionality0.76
nonstationarity0.79
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
SL(2,ℝ) (Thurston):parabolic_fraction | +7.2z | bank-miss 1.4σ |
Fisher Information:geodesic_velocity | +3.6z | bank-miss 1.9σ |
Zariski:nonsep_fraction | +3.4z | bank-miss 2.1σ |
Symplectic:recurrence_rate | +2.9z | bank-miss 2.0σ |
Fractal (Mandelbrot):interior_fraction | +2.5z | bank-miss 1.8σ |
Composition
dtypefloat64
range[-139.2, 139.2]
unique values16384 / 16384
mean ± std-8.67e-19 ± 2.69
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Stable_Noise.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Stable_Noise.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Stable_Noise.png)
Inflation (Substitution) > barcode
/d_curve/Stable_Noise.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Stable_Noise.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Stable_Noise.png)
Ulam Spiral (Sacks) > default
/default/Stable_Noise.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Student-t Noise | 2.24 | |
| BTC Returns | 3.06 | cross-origin |
| S&P 500 Returns | 3.66 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:DN_Spread_Std | rank 305/306 | 0.0174 |
Cayley › Cayley:spectral_gap | rank 4/306 | 0.0299 |
Fisher Information › Fisher Information:geodesic_velocity | rank 2/306 | 1.8629 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):interior_fraction | rank 1/306 | 0.9980 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):mean_hyperbolic_radius | rank 306/306 | 0.0625 |
Klein Bottle › Klein Bottle:wht_spectral_kurtosis | rank 302/306 | 1.3834 |
Mostow Rigidity › Mostow Rigidity:distance_rigidity | rank 302/306 | 0.2896 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):parabolic_fraction | rank 1/306 | 0.9148 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_burstiness | rank 303/306 | 0.0060 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_spectral_radius | rank 303/306 | 1.0190 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):cocycle_growth_rate | rank 305/306 | 0.0079 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):hyperbolic_fraction | rank 305/306 | 0.0065 |
Sol (Thurston) › Sol (Thurston):path_length | rank 306/306 | 320.1348 |
Spherical S² › Spherical S²:concentration | rank 5/306 | 0.9927 |
Symplectic › Symplectic:recurrence_rate | rank 5/306 | 0.9684 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 5/306 | 0.9927 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):hapax_ratio | rank 3/306 | 0.3345 |
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