Counterexample CE-DS-LCM-SIGNSPLIT-MINIMAL-001
What it falsifies
None: support-minimal atomic boundary witness for the (M5)-free sign-split mechanism; it is not a counterexample to DS17, whose population obstruction assumes atomlessness and (M4), and whose empirical conclusion assumes (M5).
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/3 | -1 | 1 | 0 | 0 |
| 2 | 1/3 | -1 | -1 | 1 | 1 |
| 3 | 1/3 | 2 | 0 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 2 |
| Labels after | 2 |
How it was verified
Method: exact_formula.
Recompute all moments in fractions.Fraction. Exact centering gives I_q=diag(2,2/3), B*_q=0, projected centroids (-1,-1,2), and the merged two-cell rule has zero nuisance block.
Claims that cite it
- Conditional centering empties the margin-certified stable branchDS-STABLE-BASINS-CENTERED-OBSTRUCTION
- Measured gate scans: eight (L)-laws empty, mix3 inhabited free, sign-split family at v_2DS-STABLE-BASINS-GATE-SCANS
- Merged-branch margins on LCM laws live only in wasted cells and never compileDS-STABLE-BASINS-LCM-CLASSIFICATION
Recorded 31 August 2026. The fixture as JSON.