Riemann Hypothesis
CB-RIEMANN
canonical benchmark
canonical benchmarks
External: externally open
τ response: structurally constrained
All non-trivial zeros of the Riemann zeta function lie on the critical line Re(s)=1/2.
Current τ response
See the paired Riemann Hypothesis — Challenge Response on the Results lane for the program's current response status, registry evidence, verification route, and external-review boundary.
Current status: structurally constrained.
Challenge statement
All non-trivial zeros of the Riemann zeta function lie on the critical line Re(s)=1/2.
Why this challenge is in the ledger
Foundational arithmetic-spectral test for any framework claiming to address number theory and prime distribution. The τ-zeta extension provides an internal spectral object whose relationship to classical ζ requires explicit bridge work.
τ-facing burden
Show how τ-zeta connects to or constrains classical zeta-function structure; clarify whether τ provides a new route, a re-description, or a structural analogue.
First reviewer questions
- Does τ-zeta give nontrivial information about classical RH?
- Is the τ-zeta object a genuine spectral analogue or only a categorical analogy?
- How does τ-zeta interact with the explicit formula and zero-density estimates?
Source anchors
Source anchors are background references, not endorsements of Panta Rhei claims.