P59, d=8, n=8: exact coordinate descent from the public certificate below. Scale coordinates by Q=10^9. For each point i and coordinate k, hold all others fixed and minimize the exact cleared-denominator Warnock L2-star objective in that coordinate. Its dependence on z is a positive quadratic minus a weighted sum of max(z,t) terms. Partition [0,Q] at the other points' k-coordinates. In each interval, test both neighbouring integers to the quadratic stationary point, clipped to the interval; also test all breakpoints and the current coordinate. Use ascending candidate order and accept strict integer-objective decreases only. Sweep point index first, then coordinate index, until an entire sweep is unchanged (at most 300 sweeps; 35-second safety limit). The run converged in 22 sweeps. Independent evaluation with exact rational arithmetic agrees with the integer cleared-denominator formula. Every coordinate is within [0,1] and lies on the nine-decimal grid. Replaying this procedure from the starting certificate reproduces the submitted coordinates exactly. This is a local coordinate minimum, not a proof of global optimality. Starting certificate: {"points":[["0.278607880","0.790075815","0.822859514","0.681568201","0.766740986","0.311789948","0.278607919","0.765968124"],["0.871004632","0.836577918","0.769983179","0.321508945","0.347405552","0.871004712","0.346879125","0.317574652"],["0.323434611","0.710433499","0.311617446","0.775440745","0.305034429","0.749370263","0.766107914","0.682169936"],["0.818275603","0.304554399","0.723873989","0.853211154","0.708759486","0.280777880","0.717987361","0.280777914"],["0.518111680","0.498637388","0.519818285","0.477087177","0.516824114","0.506580065","0.501409188","0.492789495"],["0.714360553","0.882133939","0.350143464","0.295160135","0.882133740","0.356968153","0.882133922","0.346380011"],["0.763354294","0.271855569","0.271855458","0.628017573","0.838556624","0.825514509","0.314775520","0.826423129"],["0.689486592","0.325489336","0.872985106","0.263207414","0.263207345","0.659259012","0.845879805","0.872985068"]]}
P59 · Minimum L2-star discrepancy in the unit hypercube · Discussion