AB-Cloud — a phase resonator for the ζ zeros¶
The AB-cloud is a Hofstadter Hamiltonian decorated with topological vortices whose Aharonov–Bohm phases are derived from the non-trivial zeros of the Riemann zeta function. This repository is fully dedicated to that single programme: monographs, the canonical 37-test Julia suite, an independent 10-language verification stack, and a 3D lattice laboratory.
\[H\psi_n = \gamma_n \psi_n, \qquad \zeta(\tfrac12 + i\gamma_n) = 0\]
Headline numbers (all traceable to named tests)¶
| Quantity | Value | Status |
|---|---|---|
| ⟨r⟩ vs GUE 0.5992 | 0.5848 ± 0.0260 | consistent (dev −2.4 %) |
| Montgomery KS (cloud vs ζ zeros) | 0.047 (p = 0.27, N = 500) | H₀ not rejected |
| Byers–Yang flux defect | 3.5·10⁻¹⁵ | machine precision |
| Connes self-duality | 4 zero modes, C₁ = 2 | machine precision |
| Dirac dynamics | E_min ∝ 1/L, R² = 0.9997 | confirmed |
Author
Isaev Iskhak Khamzatovich · ORCID 0009-0003-7299-0701 · DOI 10.5281/zenodo.21825394
Where to go next¶
- :material-rocket-launch: Quick start — run the suite in 5 minutes
- :material-book-open-variant: Monographs — 5 editions, 131 figures
- :material-test-tube: Verification — 10 languages, 2M zeros
- :material-cube-outline: 3D laboratory — 36³ lattices with vortex lines