Counterexample CE-A-DSTYLE-001
What it falsifies
The D exchange-to-geometry mechanism transfers to the A criterion: a move whose first-order I_q^{-2} Mahalanobis margin is positive (row strictly closer to the destination centroid in the I^{-2} metric) must not decrease the exact A objective -tr(I_q^{-1}).
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/6 | -1/6 | -4 | 2 | 2 |
| 2 | 1/6 | -13/6 | -4 | 1 | 1 |
| 3 | 1/6 | -7/6 | 4 | 1 | 0 |
| 4 | 1/6 | 5/6 | 3 | 2 | 2 |
| 5 | 1/6 | 17/6 | 1 | 0 | 0 |
| 6 | 1/6 | -1/6 | 0 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | -8.1 |
| Labels after | -12.096 |
How it was verified
Method: exact_formula.
Integer scores centered exactly, uniform weights, all arithmetic in Fraction. The move labeled by moved_row -> destination_cell has strictly positive first-order I^{-2} margin (the D-style geometric screening says 'must improve') yet the exact A objective -tr(I^{-1}) strictly decreases (trace of the inverse increases). The D theorem's coincidence does not survive replacing log det by -tr inverse.
Claims that cite it
Recorded 28 August 2026. The fixture as JSON.