Counterexample CE-DS-GLOBAL-GEOMETRY-001
What it falsifies
Every finite globally optimal Ds assignment is self-consistent under its own first-order efficient-score/common-semimetric nearest-cell rule.
This is the fixture behind DS-GLOBAL-NONGEOMETRIC: an exact eight-row, two-score-dimension, three-cell example, enumerated exhaustively, whose unique global profiled optimum violates its own first-order rule by margins of 2862/3239 and 618/3239. Calling compile_quantizer() on a result fitted under ProfiledDOptimality is refused, citing this fixture, because a profiled result has no canonical rule to compile into; the remedy is to fit a reusable rule directly with fit_quantizer rather than convert a fixed-sample partition into one.
- Cell 0
- Cell 1
- Cell 2
| Atom | Weight | Score 1 | Score 2 | Cell before | Cell after |
|---|---|---|---|---|---|
| 1 | 1/8 | 1/2 | 7/8 | 0 | 0 |
| 2 | 1/8 | -1/2 | 55/8 | 0 | 0 |
| 3 | 1/8 | -11/2 | 39/8 | 1 | 1 |
| 4 | 1/8 | 3/2 | -65/8 | 0 | 0 |
| 5 | 1/8 | -7/2 | 47/8 | 0 | 0 |
| 6 | 1/8 | -1/2 | -65/8 | 1 | 1 |
| 7 | 1/8 | 7/2 | 31/8 | 2 | 2 |
| 8 | 1/8 | 9/2 | -49/8 | 2 | 2 |
How it was verified
Method: exact rational exhaustive enumeration.
Canonical fixture selected from the newest 26 Aug 2026 score-space manuscript. An independent older v5 fixture also exists and should be retained in archive, but not conflated with this one.
Claims that cite it
What the library refuses
- Trigger
compile_quantizer()on a result fitted underProfiledDOptimality- Reason
a global profiled optimum can violate its own first-order rule, so profiled labels have no canonical extension
- Remedy
Fit a reusable rule directly with
fit_quantizerinstead of converting a fixed-sample partition
Recorded 26 August 2026. The fixture as JSON.