Euler-Mascheroni γ Digits
number_theory · 36 views
number_theory
What It Is
Base-256 digits of γ = lim(Hₙ − ln n)'s fractional part. Even irrationality is an open question. Atlas-novelty here would be a striking empirical hint about γ's structure.
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.29
asymmetry0.30
occupancy0.98
short-range corr0.21
long-range memory0.28
spectral colour0.75
periodicity0.12
complexity0.95
time-irreversibility0.37
volatility clustering0.27
multifractality0.21
dimensionality0.97
nonstationarity0.31
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypeuint8
range[0, 255]
unique values256 / 16384
mean ± std128 ± 74.2
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/Euler-Mascheroni_γ_Digits.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Euler-Mascheroni_γ_Digits.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Euler-Mascheroni_γ_Digits.png)
Inflation (Substitution) > barcode
/d_curve/Euler-Mascheroni_γ_Digits.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/Euler-Mascheroni_γ_Digits.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/Euler-Mascheroni_γ_Digits.png)
Ulam Spiral (Sacks) > default
/default/Euler-Mascheroni_γ_Digits.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| AES Encrypted | 1.76 | cross-domain |
| MINSTD (Park-Miller) | 1.81 | cross-domain |
| Catalan G Digits | 1.84 |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:filling_ratio | rank 2/298 | 0.9830 |
Cantor Set › Cantor Set:jump_entropy | rank 296/298 | 0.0553 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 2/298 | 0.9993 |
Klein Bottle › Klein Bottle:wht_spectral_kurtosis | rank 294/298 | 1.3838 |
Nonstationarity › Nonstationarity:dynamic_coupling | rank 295/298 | 1.0699 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 297/298 | 0.0003 |
Predictability › Predictability:sample_entropy | rank 5/298 | 2.2123 |
Zariski › Zariski:nonsep_fraction | rank 295/298 | 0.0066 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):bigram_predictability | rank 298/298 | 0.0099 |
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