Independent verification in 10 languages

verification/ re-implements the core AB-cloud protocol in ten programming languages with an identical output contract:

C++ · Fortran · Go · Haskell · JavaScript · Julia · MATLAB · Python · R · Rust

Why

A single-implementation result can always be questioned as an implementation artefact. Ten independent implementations, each reading the same ζ-zero data and printing the same statistics, remove that objection.

The three referee objections (answered in-repo)

1. "Is it just the Hofstadter butterfly?" — the pure Hofstadter Hamiltonian (V30) does not reproduce the ζ-spacings; the vortex phases are essential.
2. "Is it just Poisson noise?" — the correlation hole test: R₂ of the cloud is closer to GUE (d = 0.140) than to Poisson (d = 0.227).
3. "Is the agreement cherry-picked?" — the permutation test with Z = 14.10 (r_resid = 0.9963 vs null 0.001 ± 0.071).

ζ-zero datasets

verification/data/ — 13,661 / 50,000 / 500,000 / 2,000,000 zeros (compiled from Odlyzko's public tables; provenance notes in the folder).

Running

cd verification/python
python3 ab_cloud_verify.py --zeros ../data/zeta_zeros_50000.txt

Each language folder contains its own README with build/run instructions.