ScoreQuant

Counterexample CE-DS-NONCENTERED-SINGULAR-DESTINATION-001

What it falsifies

An exact global optimum over regular (nonsingular-nuisance) finite labelings is one-point exchange-stable under ANY feasibility convention, so DS18.2's finite stability step needs no convention. FALSE off the null set: on this support-minimal N=4 table from the named off-(L) law, both exact global regular optima reach the single nuisance-singular labeling by one admissible relocation whose DS11 pseudo-inverse value exceeds the regular optimum by exactly 1/96. The in-bin (DS9) convention -- singular destinations are infeasible -- is therefore load-bearing and must be named. This does not refute DS18, whose law makes such tables null.

CE-DS-NONCENTERED-SINGULAR-DESTINATION-001: labels before, 4 atoms in 3 cells-1-0.50000.5001-1-0.50000.500score 1score 2
Labels before
CE-DS-NONCENTERED-SINGULAR-DESTINATION-001: labels after / optimum, 4 atoms in 3 cells-1-0.50000.5001-1-0.50000.500score 1score 2
Labels after / optimum
  • Cell 0
  • Cell 1
  • Cell 2

Objective

The criterion value at each labelling, exactly as the fixture certifies it.

LabellingObjective
Labels before1/12
Labels after3/32

How it was verified

Method: exhaustive.

Pure fractions.Fraction recomputation from the (X, Z) construction through the law; all six canonical K=3 partitions and every admissible relocation from both global regular optima checked by agenticresearch/py/audit_ds_noncentered_global_basin_transfer.py boundary and pinned in tests/test_research_claims.py.

Claims that cite it

Recorded 31 August 2026. The fixture as JSON.