BSL Residues
number_theory · 36 views
number_theory
What It Is
BSL numerator rho(v) mod D for random gap vectors --- probes equidistribution of the Collatz cycle equation. If residues are uniform, no algebraic structure prevents cycles; zero-avoidance is then a 'near miss' phenomenon. Uses (p=10, q=19, D=465239), a verified zero-avoidance case
Interpretation
Standard analysis sees: rich, high-entropy values; aperiodic / broadband; high-complexity (noise-like); monofractal; high-dimensional / space-filling. The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.31
asymmetry0.31
occupancy0.90
short-range corr0.22
long-range memory0.37
spectral colour0.80
periodicity0.02
complexity0.89
time-irreversibility0.44
volatility clustering0.22
multifractality0.14
dimensionality0.92
nonstationarity0.30
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
dtypefloat64
range[38, 4.652e+05]
unique values13833 / 16384
mean ± std2.33e+05 ± 1.32e+05
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/BSL_Residues.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/BSL_Residues.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/BSL_Residues.png)
Inflation (Substitution) > barcode
/d_curve/BSL_Residues.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/BSL_Residues.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/BSL_Residues.png)
Ulam Spiral (Sacks) > default
/default/BSL_Residues.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| ChaCha20 | 1.68 | cross-domain |
| Wichmann-Hill | 1.75 | cross-domain |
| MT19937 (Mersenne Twister) | 1.84 | cross-domain |
Which Geometries Light Up
2-adic › 2-adic:multiscale_markov_predictability | rank 295/298 | 0.0269 |
Catch24 › Catch24:SB_MotifThree_quantile_hh | rank 2/298 | 2.1972 |
Catch24 › Catch24:SB_TransitionMatrix_3ac_sumdiagcov | rank 295/298 | 0.0000 |
Möbius-S³ › Möbius-S³:phase_profile_deviation | rank 295/298 | 0.1125 |
Spherical S² › Spherical S²:spectral_gini | rank 295/298 | 0.3237 |
Zariski › Zariski:nonsep_fraction | rank 296/298 | 0.0066 |
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