Euler-product positivity plus the functional equation does not force Re(xi'/xi) >= 0 on Re s > 1/2: the shifted product W_a(s) = zeta(s+a) zeta(s-a) at a = 1/4 carries every hypothesis in larger quantity than zeta and has zeros off its own critical line.
hunts/epp_herglotz (Record 50 of 98 in chronological sequence)
Guiding Question
Does Euler-product positivity plus the functional equation force Re ξ'/ξ ≥ 0 on Re s > 1/2?
Method & Verification
The mechanism was written in MISSION.md in a commit containing nothing else, then attacked with the explicit rival W_a at a = 1/4, measuring the functional equation, Hardy-style Z, scalar Euler product, EPP coefficients, and off-line zeros in a committed box.
Lineage & Relationships
None
Primary Sources (at pin 8fa46e134)
Editorial Notes
Status is settled, negative. Disposition maps to completed because the kill finished; the outcome is a negative result, not RH progress. No HANDBACK.json at the pin. Headline filled from RESULTS.md rather than the H1 title. The repaired mechanism needing square-root cancellation is recorded as the exact remaining step, not as a new attack.
Date Provenance
commit 601a3bea4a19cdaa7ebf66287e77dda37f4b59ec, hunts/epp_herglotz/RESULTS.md, author 2026-08-21T19:42:19-05:00