Critical-line stage
Riemann zeta / internal alignment
Prime quotient geometry and zero-pinned localization.
\(\Re(\rho)=\tfrac12\)
Additive readout
Binary Goldbach
Structural and effective manuscripts on the Goldbach fibre.
\(A-h,\;A+h\)
Fixed-gap fibre
Twin primes
Primitive-zero transfer on \(n,n+2\).
\(x^2-1=n(n+2)\)
Stopped survivor
Mersenne primes
Stopped-survivor branch on terminal divisor traces.
\(\ell=2kq+1\)
Affine channel
Sophie Germain primes
Same-channel discrepancy on the frozen-two carrier.
\(x/2\in\mathbb P,\;x+1\in\mathbb P\)