Riemann Zeta Zeros
number_theory · 36 views
number_theory
What It Is
Unfolded nearest-neighbour spacings of the first 100,000 Riemann zeta nontrivial zeros (Odlyzko) --- Montgomery-Odlyzko: GUE-distributed (quadratic level repulsion), the canonical real-data exemplar of random-matrix statistics
Interpretation
Standard analysis sees: anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Chladni:modal_nodal_cascade (+2.6z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.64
asymmetry0.74
occupancy0.60
short-range corr0.10
long-range memory0.06
spectral colour1.00
periodicity0.22
complexity0.82
time-irreversibility0.40
volatility clustering0.38
multifractality0.13
dimensionality0.83
nonstationarity0.13
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Chladni:modal_nodal_cascade | +2.6z | bank-miss 2.6σ |
Boltzmann:frustration | +2.6z | bank-miss 1.4σ |
Composition
dtypefloat64
range[0.02875, 2.745]
unique values16384 / 16384
mean ± std1 ± 0.403
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Riemann_Zeta_Zeros.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Riemann_Zeta_Zeros.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Riemann_Zeta_Zeros.png)
Inflation (Substitution) > barcode
/d_curve/Riemann_Zeta_Zeros.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/Riemann_Zeta_Zeros.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/Riemann_Zeta_Zeros.png)
Ulam Spiral (Sacks) > default
/default/Riemann_Zeta_Zeros.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| GUE Spacings | 2.58 | cross-domain |
| GOE Spacings | 2.66 | cross-domain |
| Blue Noise | 3.38 | cross-domain |
Which Geometries Light Up
Boltzmann › Boltzmann:frustration | rank 4/298 | 1.0000 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_entropy | rank 5/298 | 3.2614 |
Gottwald-Melbourne › Gottwald-Melbourne:k_statistic | rank 4/298 | 0.9984 |
Inflation (Substitution) › Inflation (Substitution):acf_geometric | rank 2/298 | 0.9071 |
Level Statistics › Level Statistics:wd_classification | rank 1/298 | 0.2779 |
Spectral Analysis › Spectral Analysis:spectral_slope | rank 1/298 | 2.0000 |
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