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Domain 08 · Riemann Hypothesis

Campaign ID: RH-001
Mathematical status: open conjecture
Programme state: WP00 promoted; WP01 and WP02 implemented, merged, and CI-passed but not formally promoted
Governance: ADR-0009; ADR-0010

Canonical challenge

Every nontrivial zero of the meromorphically continued Riemann zeta function should have real part 1/2, with zeros counted using the campaign's fixed multiplicity and range conventions.

The target is the classical Riemann Hypothesis. Generalized variants, simplicity, Lindelöf, density-one results, pair correlation, random-matrix evidence, finite verification, and incomplete spectral proposals are separate statements.

Programme posture

RH-WP00 fixes the zeta, completed-function, xi, Xi, and Hardy Z normalizations; pole and zero taxonomy; symmetry and multiplicity conventions; exact core equivalences; source-bound arithmetic criteria; spectral obligations; false-proof seeds; theorem spine; proof debt; and certification boundary.

PR #90 implemented and merged the two authorized successor packages:

  • RH-WP01 — an executable eliminative false-proof atlas;
  • RH-WP02 — a source-normalized theorem, criterion, computation, evidence, and barrier ledger.

Their deterministic replay and integrated programme-policy workflow passed. They are not formally promoted: the governing legacy review records retain promotion_recommended: false and blocking Referee findings pending independent source-locator review and a schema-bound or explicitly superseding promotion decision.

Mechanism generation, claimed-proof promotion, unrestricted numerical search, novelty claims, and any new zero-range certification remain closed.

Canonical artifacts

Claim boundary

The programme has not proved or disproved RH, established a new zero-free region, critical-line proportion, prime-counting error estimate, equivalent criterion, Hilbert–Pólya operator, newly certified zero computation, or novelty result. Implementation, repository merge, replay, CI success, public documentation, and documentary publication are not theorem support.