Riemann and zeta in PT reading

Presenting the PT reading of Riemann as a research programme without overselling a closed proof.

Plain

The idea

The Riemann Hypothesis is about hidden order in the prime numbers. PT cares because primes are precisely sieve survivors.

The PT question becomes: is the critical line $1/2$ the spectral trace of the same persistence threshold that appears elsewhere in the theory?

Euler product

Standard

Standard reading

The monograph contains a Riemann programme: reformulating the question through Čencov monotonicity, DPI, spectral operators, and sieve-related decompositions.

The page must stay clear: it should not announce a standard proof of RH. It should expose the PT dictionary, partial results, and remaining obstructions.

Takeaways

The page should be attractive but careful.
The $1/2$ threshold links sieve, spectrum, and persistence.
The status is research programme, not public closed theorem.

Technical

Technical formulation

The Riemann chapters explore a route where the spectral condition $\lambda\ge s^2=1/4$ would be equivalent to RH under specific PT hypotheses.

The public strength is the coherence of the $1/2$ threshold; the open point is complete assembly without excessive auxiliary hypotheses.

Monograph: Riemann part, ch21_RH_cencov_dpi, ch37_RH_bifurcation, ch37b_RH_proofs.

Formulas

$\Re(s)=\frac12$

$\lambda\ge s^2=\frac14$

$\zeta(s)=0\Rightarrow \Re(s)=\frac12\quad\text{(RH, not claimed closed here)}$

public code

Code and scripts

The links below point to public resources or planned GitHub repositories. No local working path is exposed to the reader.

GitHub

Igrekess/PT_Riemann

GitHub repository to publish before this can become a download link.

GitHub

Igrekess/PT_NT

GitHub repository to publish before this can become a download link.