Persona
The operator's instruction: go find previously unknown mathematics adjacent to the 10 August 2026 paper (More than two thirds of the zeros of the Riemann zeta function lie on the critical line), continuing from where wide_search stopped. Its HANDOFF left one pre-registered open thread (THREAD 1: "the full-data LP over marked periodic configurations") and one blocked one. This hunt works that frontier: what is the best unconditional constant the paper's kind of data can deliver, and can any known conditional refinement be made unconditional through the paper's machinery?
Concurrent sessions
More than one session has worked this directory at once. Read ACTIVE-CLAIMS.md before launching an agent, a prover submission, or a build here, and add a row for anything you start that runs longer than a few minutes. HANDOFF.md remains the serial, between-sessions record; ACTIVE-CLAIMS.md is the live one.
Scope
This hunt may write: hunts/frontier_math/ and figures/. It may add a cross-reference line to hunts/wide_search/HANDOFF.md's THREAD 1 section (that hunt's own operating state, not a repo-level verdict).
This hunt may not write: zeta/, ontology/, harness/, lean/ without explicit permission; no verdicts into repo-level README.md, ROADMAP.md or HANDOFF.md. It may not promote its own claims: anything here that looks like a theorem is a candidate with named unproven lemmas until it goes through the routes that can say yes.
Objective
Three lanes, worked in order of expected value:
- Answer THREAD 1. Formulate and solve the LP over pair-measure data (positivity + bandwidth-one evaluation + multiplicity types): does it collapse to the paper's 0.6725007, or move into (0.6725007, 0.68185)?
- Transplant audit. For each known RH-conditional refinement in the pair-correlation class (Cheer–Goldston 1993; Chirre–Gonçalves–de Laat 2020), determine exactly which inputs the paper's unconditional machinery supplies, which it does not, and whether the refinement transfers. Compute the transferred constant where it does.
- The walls, quantified. Where a transplant fails, record the mechanism at the level of a computation (not a feeling), so the next session does not re-derive it.
The standing checklist, answered in advance
- Rival. Structural claims here are about methods (optimisation values, certificate mechanisms), not about ζ being special; the paper itself records that its certificate is empty for Davenport–Heilbronn-type functions. Any claimed positivity structure that is supposed to hold for conjugate-closed multisets generally is checked numerically on a multiset with genuinely off-line points (the lab's DH configuration), where it must ALSO hold — a structural lemma failing on the rival would be a bug, and passing distinguishes nothing (it is not that kind of claim).
- Decoy / surrogate. LP and floor computations are checked against planted-wrong inputs (a mis-set kernel constant, wrong λ_k) that must break the agreement.
- Lesion. See 2; each instrument carries one.
- Precision response. Every optimisation value is re-run up a discretization ladder (grid, tolerance, bucket count) before being written down.
Vocabulary
Measured, observed, consistent with. Never the reserved word owned by zeta/rigor.py; not verified, confirmed, definitively. A "candidate theorem" here means: mechanism written down, constants computed, named gaps listed — and nothing more. Nothing in this hunt is evidence for or against RH.