Counterexample CE-DS-TILT-DUAL-GAP-001
What it falsifies
The scalar-interest tilt-dual bracket is always exact: min_beta max_z between(S_psi-beta S_lambda; z) equals the exact global profiled-Ds value. FALSE: two explicit tilt quadratics give a rational lower certificate strictly above the exhaustive global optimum.
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/4 | -11/2 | 39/8 | 0 | 0 |
| 2 | 1/4 | 3/2 | -65/8 | 0 | 1 |
| 3 | 1/4 | 7/2 | 31/8 | 1 | 2 |
| 4 | 1/4 | 9/2 | -49/8 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 2925/296 |
| Labels after | 116805/11816 |
How it was verified
Method: exact rational exhaustive enumeration plus convex-mixture lower certificate.
All arithmetic is fractions.Fraction. The certificate does not need the generally algebraic exact minimizer of the full quadratic envelope.
Claims that cite it
- Publication-grade audit of the DS19 tilt-DP certificate complexAUDIT-DS-PRACTICAL-CERTIFIED-SOLVER
- Profiled compile verdict is selected by an observable certificate stateDS-PROFILED-COMPILE-CERTIFICATE
- Scalar-POI tilt-DP gives a valid two-sided certificate with an exact saddle closure gateDS-TILT-DUAL-CERTIFICATE
- The scalar-POI tilt dual can have an order-one strong-duality gapDS-TILT-DUAL-STRONG-DUALITY-FAILS
- Best practical Ds solver with theorem-backed certificateOPEN-DS-PRACTICAL-CERTIFIED-SOLVER
Recorded 1 September 2026. The fixture as JSON.