The Prime Spectrum Function (PSF) is a native derivative of the Euler product, convergent in the strip. It correlates the non-trivial zeros outside the Dirichlet series and its continuations.
PSF:
Φ(s) = Σ (p = 2..P) ln(p) * [ p^(-σ) – cos(θ) ] / [ p^(σ) – 2 cos(θ) + p^(-σ) cos²(θ) ],
where θ = t · ln(p)
To preempt common strawmen:
- η(s) converges, yes — but it’s a repackaging of ζ(s), not an independent source.
- Cosine-sum heuristics are heuristic look-alikes, piggy-backing on evaluated ζ.
- This isn’t numerology: PSF is structural, Euler-derived, and convergent where ζ’s own series fails.
So the genuine question: if PSF is unique in this sense, does it reframe RH — from generator to constraint?
Video walkthrough: https://www.youtube.com/watch?v=UUgVquS8Fo0
To illustrate, here is a screenshot from the interactive app, where the Prime Spectrum Function (PSF) visibly generates the zero peaks directly from the primes — no continuation required. You can explore it yourself here: https://riemann.trigunamedia.com/psf/
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