Counterexample CE-DS-GLOBAL-GEOMETRY-002
What it falsifies
A finite globally optimal profiled Ds partition assigns each row to its nearest cell under its own efficient-score semimetric.
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/8 | 29/8 | -15/4 | 0 | 0 |
| 2 | 1/8 | -43/8 | 9/4 | 1 | 1 |
| 3 | 1/8 | -11/8 | 1/4 | 2 | 2 |
| 4 | 1/8 | -43/8 | -3/4 | 1 | 1 |
| 5 | 1/8 | 13/8 | -7/4 | 2 | 2 |
| 6 | 1/8 | 29/8 | 13/4 | 0 | 0 |
| 7 | 1/8 | 13/8 | 17/4 | 0 | 0 |
| 8 | 1/8 | 13/8 | -15/4 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 10.650520833333333 |
| Labels after | 10.650520833333333 |
How it was verified
Method: exhaustive.
All 966 canonical partitions ranked by the exact Schur-complement objective in Fraction arithmetic; unique global optimum violates its own efficient-semimetric nearest-cell rule at row 6 by exactly 8/195. Independent second witness for the same claim as CE-DS-GLOBAL-GEOMETRY-001 (different instance; do not conflate). Regression: tests/test_research_claims.py::test_global_profiled_ds_partition_can_violate_its_own_metric_rule.
Claims that cite it
Recorded 28 August 2026. The fixture as JSON.