Counterexample CE-D-COMPILE-SINGLETON-TIE-001
What it falsifies
Positive-tolerance D exchange stability alone guarantees admissible training-label disagreements under the deterministic nearest-centroid rule.
- Cell 0
- Cell 1
| Atom | Weight | Score 1 | Cell before | Cell after |
|---|---|---|---|---|
| 1 | 1 | 0 | 0 | 0 |
| 2 | 1 | 1 | 1 | 0 |
| 3 | 1 | 2 | 0 | 0 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | log(3) |
| Labels after | log(3) |
How it was verified
Method: exact_formula.
Fraction regression enumerates every admissible one-row relocation; log ratios are invariant under uniform weight scaling. Singleton prediction is inadmissible; the batch fixture retains both cells.
Claims that cite it
Recorded 11 September 2026. The fixture as JSON.