Counterexample CE-DS-TILT-DUAL-TIE-MASK-001
What it falsifies
A deterministic tilt-DP implementation that reports an open bracket [Phi^+(z_DP), d] has exhibited a duality gap. FALSE: the bracket closes exactly (g^+ = d) but the DP-optimal set at the dual minimizer contains a non-closing labeling, which a deterministic tie policy can return.
- Cell 0
- Cell 1
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/3 | -1 | -1 | 0 | 0 |
| 2 | 1/3 | 0 | -2 | 1 | 1 |
| 3 | 1/3 | 0 | 0 | 0 | 1 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 4/27 |
| Labels after | 2/9 |
How it was verified
Method: exhaustive.
The tilted values at beta* are pairwise distinct, so this is a DP value tie, not a tilted-value tie: two contiguous labelings attain v_K(beta*) with different derivatives, and only the zero-derivative one satisfies the normal equation.
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
- Best practical Ds solver with theorem-backed certificateOPEN-DS-PRACTICAL-CERTIFIED-SOLVER
Recorded 2 September 2026. The fixture as JSON.