P59, d=2, n=32: exact coordinate-descent refinement on the 10^-9 grid. Start from the public 32-point certificate. Keep all points in the unit square and minimize the exact Warnock L2-star discrepancy expression. For each point coordinate, partition the one-dimensional objective at all other coordinate knots and evaluate the exact integer quadratic minimum in every interval. Sweep coordinates repeatedly until no coordinate improves or 100 sweeps are reached. All arithmetic uses Q=10^9 integer coordinates and no tolerance. The replay reduced the exact stored score from 3058166656390761196408834799018489024 to 3058166656390761162441410669816665280 in two sweeps. Replaying from the supplied starting certificate reproduced the same coordinates; further coordinate sweeps found no additional decrease. This is a certified grid refinement and not a global optimality claim. The exact integer verifier and independent rational formula agree on the complete 32-point certificate: {"points":[["0.281802288","0.679632989"],["0.248116454","0.158609563"],["0.418412387","0.313437379"],["0.840214946","0.340726425"],["0.682546778","0.277598653"],["0.527433175","0.718409314"],["0.052885809","0.772687267"],["0.158460342","0.247218873"],["0.207070892","0.512614928"],["0.966608597","0.429038092"],["0.735139070","0.482517192"],["0.609761216","0.119340645"],["0.496742423","0.204163965"],["1.000000000","0.000000000"],["0.878211848","0.581416133"],["0.119724037","0.607134140"],["0.334306714","0.963017707"],["0.709890451","0.848798716"],["0.809074651","0.746066363"],["0.456947273","0.555550981"],["0.914969146","0.179506809"],["0.940392776","0.903817995"],["0.022827895","0.368939174"],["0.182506183","0.883497832"],["0.314998423","0.447923978"],["0.082872044","0.083197904"],["0.360442711","0.022970464"],["0.776096960","0.052784280"],["0.561045271","0.407580587"],["0.584037714","0.926816672"],["0.390011372","0.817182936"],["0.645562248","0.641998354"]]}
P59 · 超立方体内的最低 L2 星偏差 · 讨论