Data License:
All data and visualizations generated by this explorer may be used only with proper attribution to:
Flamandzki Harmonic Operator – millenniumchecked.org
Note: For performance reasons, only up to 10,000 primes are allowed in this demo.
Additional note: Vertical lines indicating zeta zeros are based on data of the first 10,000 non-trivial zeros of the Riemann zeta function, retrieved from LMFDB. The harmonic operator itself, when generating the signal, has no knowledge of these zeros beyond its inherent structure; the zero data is used purely for visualization reference.

🔬 Harmonic Interference Operator – RH Analysis

This interface computes the harmonic signal from primes using variable σ to detect destructive interference along the critical line ℜ(s) = 0.5.

📋 Output Summary

What "phase spread" does and doesn't show

For each detected local minimum, the tool reports the amplitude depth (σ-dependent, since σ weights each prime's contribution) and the phase spread of the underlying components at that t (computed as std(-(t·log p) mod 2π) across the primes used). Note that this phase formula does not depend on σ at all — σ only rescales amplitudes, it does not change relative phase — so phase spread cannot be used to argue that one σ shows "more genuine" interference than another. What differs between σ values is simply which t-points cross the depth threshold, since the amplitude envelope changes with σ.

These are raw computed values, not a classification of interference "type."

Ready.