de Bruijn–Newman Equivalence

A visual exploration of how a fixed sech² transport Λ(T,H) and the de Bruijn–Newman heat-flow H(λ,z) both probe the critical line.

Λ(T,H) Sech² Kernel Base
de Bruijn–Newman Heat-Flow Probe (H(λ,z))
Zero Location (γ)
📄 Zenodo: RH Singularity Proof Paper 💻 GitHub: Computational Repository

Continuous Tracking CM Gas Flow

Visual Calogero-Moser approximation of ζ zero repulsion under λ-deformation. Simulating stabilized Dyson log-gas dynamics with exact global far-field forces.

Effective λ Proxy: 0.000
Local Rigidity Δt: SCANNING
Interaction Topology: Global (N×N)
Density Drift: STABILIZED
Stabilized CM ODE
dt_k/dλ = 2 ∑_{j≠k} (t_k-t_j) / ((t_k-t_j)²+ε²) λ_eff(H) = (π² H²) / 6
Global integral system maintaining spectral rigidity. Replaces DBN analytic PDE for stable visualization.
CURRENT HEIGHT T: 0.00
ACTIVE ZERO γ: 14.13
Classical de Bruijn–Newman
H(λ,z) = ∫_ℝ Φ(t) e^{λ t²} e^{i z t} dt ∂H/∂λ = ∂²H/∂z²
Analytic heat-flow evolution in λ.
Λ(T,H) Sech² Functional
Λ(T,H) = ∫ |Z(T+u)|² g_H(u) / ∫ g_H(u) g_H(u) = sech²(u/H)
Transport analogue inspired by DBN.