Euler-Mascheroni γ Digits

number-theory · 37 views
number-theoryhigh-entropy

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; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas finds no named structure, but the source is distinctively extreme on Attractor Reconstruction:filling_ratio (+2.8z) — beyond what the standard bank predicts for it.

What standard analysis sees
tail heaviness0.20
asymmetry0.33
occupancy0.98
short-range corr0.27
long-range memory0.32
spectral colour0.80
periodicity0.16
complexity0.97
time-irreversibility0.42
volatility clustering0.32
multifractality0.14
dimensionality0.90
nonstationarity0.21
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Attractor Reconstruction:filling_ratio+2.8zbank-miss 1.1σ

Composition

dtypeuint8
range[0, 255]
unique values256 / 16384
mean ± std128 ± 74.2

Render Gallery

Atlas Position

Nearest neighborDistance
MINSTD (Park-Miller)1.75cross-origin
AES Encrypted1.76cross-origin
Catalan G Digits1.77

Open in Atlas →

Which Geometries Light Up

Attractor Reconstruction › Attractor Reconstruction:filling_ratiorank 2/3060.9830
Cantor Set › Cantor Set:jump_entropyrank 304/3060.0553
Higher-Order Statistics › Higher-Order Statistics:perm_entropyrank 2/3060.9993
Nonstationarity › Nonstationarity:dynamic_couplingrank 303/3061.0699
Ordinal Partition › Ordinal Partition:statistical_complexityrank 305/3060.0003
Predictability › Predictability:cond_entropy_k8rank 5/3062.9997
Zariski › Zariski:nonsep_fractionrank 302/3060.0066
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