GUE Spacings
random-matrix-quantum · 37 views
random-matrix-quantumspectral-RMT
What It Is
Gaussian Unitary Ensemble spacings --- level repulsion P(s)~s² exp(-4s²/π), broken time-reversal symmetry
Interpretation
Standard analysis sees: anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); monofractal. The atlas finds no named structure, but the source is distinctively extreme on Boltzmann:frustration (+2.4z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.62
asymmetry0.74
occupancy0.61
short-range corr0.11
long-range memory0.11
spectral colour0.94
periodicity0.21
complexity0.83
time-irreversibility0.38
volatility clustering0.40
multifractality0.14
dimensionality0.83
nonstationarity0.36
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Boltzmann:frustration | +2.4z | bank-miss 1.5σ |
Composition
dtypefloat64
range[0.04156, 2.969]
unique values16384 / 16384
mean ± std1 ± 0.421
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/GUE_Spacings.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/GUE_Spacings.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/GUE_Spacings.png)
Inflation (Substitution) > barcode
/d_curve/GUE_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/GUE_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/GUE_Spacings.png)
Ulam Spiral (Sacks) > default
/default/GUE_Spacings.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| GOE Spacings | 1.69 | |
| Riemann Zeta Zeros | 2.53 | cross-origin |
| Blue Noise | 2.81 | cross-origin |
Which Geometries Light Up
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_entropy | rank 2/306 | 3.4236 |
Level Statistics › Level Statistics:wd_classification | rank 2/306 | 0.2746 |
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