Riemann Hypothesis Research Log

STATUS: RIEMANN HYPOTHESIS OPEN.

B PROGRAM: CONTINUE. L7 complete. L8 not started.

The Riemann Hypothesis says that every nontrivial zero of the zeta function has real part \(1/2\). This AI-assisted log follows attempts at an analytic proof and the subsequent investigation of whether a fixed arithmetic RH sentence is provable in, or independent of, ZFC. No new proof of RH, its negation, either side of unprovability, or full independence has been obtained.

Curated by @ykbballer91. The original record begins on 2026-09-29; first publication was on 2026-09-30.

Where the work stands

B is the researcher's chosen program to investigate the ZFC independence of fixed RH. Independence means that neither a statement nor its negation can be proved from the specified axioms. Both consistency obligations remain OPEN: 2 → 2. This neither establishes independence as promising nor measures RH completion.

L7 restricts the integers under consideration to those with no gaps in their prime support, while controlling precision and proof cost when returning to the original finite comparison. Transferring proofs does not establish their absence. No new independence consequence follows.

Read the current state · Latest update: 2026-10-09

The earlier finite-Weil route is HOLD. Capture CAP and strict parity PAR on one sequence remain OPEN, 2 → 2, in an account separate from B. This does not prove that route impossible. Cycles 6–17, CORE-S, and the joint transfer remain dated results.

Explore the record

• Guide — the question, notation, and evidence labels.
• Timeline — what was tried, what survived, and why the question changed.
• Roadmap — current B and the analytic route on hold.
• Sources — public evidence and the boundaries of edited summaries.

L0–L7 research originals remain privately preserved; this release publishes selected editorial summaries. Complete new proofs, internal audits, and code are not published. These summaries are not the full evidence needed for third-party reproduction of every claim. The paired guides, historical public articles, and earlier evidence each retain their stated scope.