Counterexample CE-DS-STABLE-MARGIN-RETAINING-001
What it falsifies
One-point exchange stability forces the DS15 degeneracy on conditionally centered laws: every exchange-stable feasible profiled-Ds labeling is near the efficient-score interval supremum with a collapsing binned nuisance block, so the DS14 margin triple can never hold at a stable state. FALSE: this exactly centered N=8 sample from the centered06 grid law carries a non-global exchange-stable labeling whose nuisance block, conditioning bound, cell masses, and projected-centroid separation are all macroscopic, at a 7.7% relative price below the exact scalar interval optimum v_K. Exchange stability does not preclude the margins; it prices them (DS16).
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/8 | -3617/4096 | -2901/4096 | 0 | 0 |
| 2 | 1/8 | 3747/4096 | -3453/20480 | 1 | 1 |
| 3 | 1/8 | 1623/4096 | -7361/20480 | 1 | 1 |
| 4 | 1/8 | -4785/4096 | -23913/20480 | 0 | 0 |
| 5 | 1/8 | 819/4096 | 22627/20480 | 2 | 2 |
| 6 | 1/8 | 2791/4096 | 29519/20480 | 2 | 2 |
| 7 | 1/8 | 631/4096 | -797/4096 | 1 | 1 |
| 8 | 1/8 | -1209/4096 | 1071/20480 | 2 | 2 |
Objective
The criterion value at each labelling, exactly as the fixture certifies it.
| Labelling | Objective |
|---|---|
| Labels before | 3416482747129/14376887844864 |
| Labels after | 3416482747129/14376887844864 |
Consequences
margin-retaining exchange-stable states exist at a Theta(1) information price: the DS14 bridge's hypothesis set is inhabited by non-global stable states, so a margin-certified compile path is not vacuous at finite N
the witness nuisance block (~0.523) exceeds the global optimum's (~0.131) fourfold: the optimizer's value ranking is anti-aligned with the conditioning margin, the DS16 price mechanism in exact form
How it was verified
Method: exhaustive.
exact rational arithmetic throughout; stability certified by enumerating all admissible one-point moves with the exact rank-two profiled ratio; regression test tests/test_research_claims.py::test_ds16_exchange_stable_state_can_retain_macroscopic_margins; independent scan py/ds_stable_margins.py census (N=8..14)
Claims that cite it
Recorded 30 August 2026. The fixture as JSON.