Bombieri–Ghosh's prime sieve in the critical strip: exact velocities of the Davenport–Heilbronn zeros, and which way the pairs move

Bombieri and Ghosh (2011) describe the zeros of the Davenport–Heilbronn function in the half-plane σ > 1: removing the Euler factor of a prime p ≡ 2, 3 (mod 5) from both of its components moves those zeros left, while removing a prime ≡ 1, 4 (mod 5) changes nothing. We apply the same sieve, with a parameter u that runs from the full Euler factor to its removal, to the certified off-line pairs of the census below t = 20,000. A two-line formula gives the exact velocity of any simple zero: log p · dρ/du is the prime's share of the phase derivative at the zero (proved, and checked against Arb root tracking); primes ≡ 1, 4 (mod 5) are inert in the strip to all orders (proved). A sign law for which way the two members of a pair move was registered before computing and is scored in the note, together with how it weakens with the prime and what happens when the factor of 2 is removed completely. At an off-line pair the small defective primes are aligned, and the sieve translates the pair leftward rather than closing it. Written jointly with Claude, an AI system made by Anthropic, which carried out much of the computation, the derivations and the drafting; the human author is responsible for the content. Not peer reviewed. The package contains the PDF, its LaTeX source, and the scripts, registered predictions and result files it cites.