Counterexample CE-DS-NONCENTERED-POPULATION-CUT-UNSTABLE-001
What it falsifies
The literal labels induced by an isolated nondegenerate population Ds rule are automatically exact one-point exchange-stable on every finite sample. FALSE: on this support-minimal movable N=4 sample from the named off-(L) law, one boundary-scale relocation raises the exact profiled value by 37/14608. The population-to-empirical theorem must select finite global optima or otherwise control exact moves; it cannot identify the raw population-cut labels with a terminal state.
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/4 | -3/4 | -5/16 | 0 | 0 |
| 2 | 1/4 | -1/4 | -25/16 | 1 | 1 |
| 3 | 1/4 | 1/4 | 3/16 | 1 | 2 |
| 4 | 1/4 | 3/4 | 27/16 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 363/2656 |
| Labels after | 49/352 |
How it was verified
Method: exhaustive.
Pure fractions.Fraction recomputation; all six canonical nonempty K=3 partitions and every admissible move checked by agenticresearch/py/ds_noncentered_global_basin.py and pinned in tests/test_research_claims.py.
Claims that cite it
Recorded 31 August 2026. The fixture as JSON.