Goldbach r(2n)

What It Is

Goldbach r(2n) --- number of unordered representations of 2n as p+q with both p,q prime. Highly erratic (Hardy-Littlewood: mean ~2*C_2*S(n)*2n/log^2(2n)) with strong primorial bias (r(2n) jumps when 2n is divisible by many small primes). Distinct mechanism from Divisor Count d(n): additive prime structure vs multiplicative divisor structure

Interpretation

Standard analysis sees: anti-correlated (alternating); blue spectrum (high-frequency power); strongly periodic; homoskedastic; monofractal. The atlas additionally detects Nonstationarity:adf_pvalue. It sits beside Stern-Brocot Walk in the atlas (standard-bank rank 127) — a neighbor conventional features miss.

Composition

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

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Open in Atlas →

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