Poisson Spacings
random-matrix-quantum · 37 views
random-matrix-quantumspectral-RMT
What It Is
Uncorrelated Poisson spacings P(s)=exp(-s) --- integrable quantum systems, no level repulsion
Interpretation
Standard analysis sees: heavy-tailed; right-skewed; aperiodic / broadband; high-complexity (noise-like). The atlas finds no named structure, but the source is distinctively extreme on Level Statistics:wd_classification (-2.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.85
asymmetry0.91
occupancy0.35
short-range corr0.30
long-range memory0.35
spectral colour0.72
periodicity0.06
complexity0.99
time-irreversibility0.55
volatility clustering0.30
multifractality0.36
dimensionality0.59
nonstationarity0.37
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Level Statistics:wd_classification | -2.2z | bank-miss 1.1σ |
Composition
dtypefloat64
range[0.0001026, 9.231]
unique values16384 / 16384
mean ± std0.991 ± 0.995
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/Poisson_Spacings.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Poisson_Spacings.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Poisson_Spacings.png)
Inflation (Substitution) > barcode
/d_curve/Poisson_Spacings.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/Poisson_Spacings.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/Poisson_Spacings.png)
Ulam Spiral (Sacks) > default
/default/Poisson_Spacings.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Geometric Waiting Times | 1.93 | cross-origin |
| Zipf Distribution | 2.40 | cross-origin |
| Prime Gaps | 2.62 | cross-origin |
Which Geometries Light Up
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 3/307 | 0.9993 |
Nonstationarity › Nonstationarity:trajectory_dim | rank 3/307 | 0.8197 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 305/307 | 0.0003 |
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