Counterexample CE-DS-MATRIX-TILT-NONQUASICONVEX-001
What it falsifies
For d_psi > 1, the outer matrix-tilt ceiling B -> max_z log det V_z(B) is convex or at least quasiconvex merely because every V_z is matrix-convex and log det is monotone.
| Atom | Weight | Score 1 | Score 2 | Score 3 | Score 4 | Cell before | Cell after |
|---|---|---|---|---|---|---|---|
| 1 | 1/8 | 2 | 0 | 0 | 0 | 0 | 0 |
| 2 | 1/8 | -2 | 0 | 0 | 0 | 1 | 1 |
| 3 | 1/8 | 0 | 2 | 0 | 0 | 2 | 2 |
| 4 | 1/8 | 0 | -2 | 0 | 0 | 3 | 3 |
| 5 | 1/8 | 0 | 0 | 2 | 0 | 4 | 4 |
| 6 | 1/8 | 0 | 0 | -2 | 0 | 5 | 5 |
| 7 | 1/8 | 0 | 0 | 0 | 2 | 6 | 6 |
| 8 | 1/8 | 0 | 0 | 0 | -2 | 7 | 7 |
The fixture lives in 4 score dimensions, so its atoms are listed rather than drawn.
How it was verified
Method: exact_formula.
The rows are centered and their uncentered second moment is I_4. Completion of squares gives V(B)=I_2+BB^T. Exact determinant comparison 25>17 violates the midpoint sublevel condition for quasiconvexity; quasiconvexity failure also disproves convexity.
Claims that cite it
- Publication-grade audit of the DS19 tilt-DP certificate complexAUDIT-DS-PRACTICAL-CERTIFIED-SOLVER
- The multivariate-POI matrix-tilt outer ceiling need not be quasiconvexDS-MATRIX-TILT-NONQUASICONVEX
- Profiled compile verdict is selected by an observable certificate stateDS-PROFILED-COMPILE-CERTIFICATE
- Best practical Ds solver with theorem-backed certificateOPEN-DS-PRACTICAL-CERTIFIED-SOLVER
Recorded 1 September 2026. The fixture as JSON.