Canonical Benchmark Problems
Clay Millennium Problems, Langlands Program, and the GRH/Grand-GRH spectral-arithmetic hierarchy.
Canonical benchmark problems
This cluster collects nine externally socially stabilised mathematical challenges retained as canonical benchmarks for the τ framework: the seven Clay Millennium Problems, the Langlands Program, and the Grand-GRH spectral-arithmetic hierarchy.
| Challenge | ID | External | τ Response |
|---|---|---|---|
| Riemann Hypothesis | CB-RIEMANN | externally open | structurally constrained |
| Poincaré Conjecture | CB-POINCARE | externally solved | external recovery checkpoint |
| P versus NP | CB-PVSNP | externally open | structurally constrained |
| Navier–Stokes Existence and Smoothness | CB-NAVIER-STOKES | externally open | structurally constrained |
| Yang–Mills Existence and Mass Gap | CB-YANG-MILLS | externally open | structurally constrained |
| Hodge Conjecture | CB-HODGE | externally open | structurally constrained |
| Birch and Swinnerton-Dyer Conjecture | CB-BSD | externally open | structurally constrained |
| Langlands Program | CB-LANGLANDS | programmatic | structurally constrained |
| Grand GRH and the Spectral-Arithmetic Hierarchy | CB-GRAND-GRH | externally open | structurally constrained (τ-native) |
What this family does not claim
- It does not claim τ has solved any Clay problem.
- The Poincaré conjecture is treated as an external recovery checkpoint — externally solved by Perelman, retained to test τ’s representation of the relevant 3-manifold and Ricci-flow concepts.
- Cross-domain links from Navier–Stokes and Yang–Mills to the Physics SCL will be wired in Wave 6 once Physics items ship.
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