Spectral Duality Lab — DragonWorx.Bio

Reconstruction

Zeros N100

x max60

Prime Statistics

Primes to100K

Bins40

Layers

Readout

Zeros—

Primes—

r zeros—

r primes—

GUE r0.5996

Poisson r0.3863

800 zeros tabulated (mpmath, verified vs Riemann–von Mangoldt count). Primes via in-browser sieve. Prime variance uses ψ-weights (Σ log p; prime powers omitted — sub-percent effect). r primes > 0.3863: real arithmetic correlations between consecutive gaps, not an error.

Explicit Formula ψ(x) from N zeros

True ψ(x)

N-zero recon

prime powers

Level Spacing zeros vs prime gaps, unfolded

Zeta zeros

Prime gaps

GUE

Poisson

Zero Correlations two-point R₂(r)

Empirical

GUE

Poisson

Prime Variance V(h)/h in short intervals — Goldston–Montgomery

ψ-variance / h

GM: log(x̄/h)−γ−log2π

Cramér: log x̄ − 1