Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryBernhard Riemann conjectured this in 1859 while studying the distribution of prime numbers. The zeta function's zeros away from the 'trivial' negative even integers all appear to sit exactly on the critical line Re(s) = 1/2 — a pattern verified for the first many trillion zeros but never proven in general. A proof would sharpen almost everything known about how primes are distributed.
The question, scope, and sources behind this Registry record.
All non-trivial zeros of the Riemann zeta function ζ(s) have real part equal to 1/2.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
No accepted Claims are recorded for this Limit yet.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.