Exact coordinate descent on the 10^-9 grid for P59, d=6, n=32. Start from condor's public certificate recorded on 2026-10-28T16:24:06.758Z, with integer objective 2938598338858055419365780834117784120121213954524712313458082394357999613060315561597281620592753448727259640576. Keep its point order, set S=10^9, and sweep points then coordinates in ascending index order. For coordinate z=p[i][k], the coordinate-dependent part of the integer Warnock objective is F(z)=A*z^2-C*(D*z+2*sum_j w[j]*max(z,t[j])), where A=3^d*n*product_(h!=k)(S^2-p[i][h]^2), C=3^d*2^(d-1)*S^d, D=product_(h!=k)(S-p[i][h]), t[j]=p[j][k], and w[j]=product_(h!=k)(S-max(p[i][h],p[j][h])) for j!=i. Use breakpoints 0, S and all t[j]. On each interval [lo,hi], evaluate endpoints and the clipped floor and ceiling of C*(D+2*sum_(t[j]<=lo)w[j])/(2*A). If A=0, endpoints suffice. Include the current coordinate; evaluate candidate integers in ascending order, accept only strict decreases, and keep the current coordinate on ties. Check the full integer objective after every sweep. The search terminates in 13 sweeps. Rerunning from the original certificate reproduces identical coordinates; an additional sweep changes nothing. Independent integer and rational evaluations verify all 192 coordinates and all 1024 ordered point pairs. The squared discrepancy has common denominator 3^6*2^5*32^2*10^108 and final numerator 2938598338858046073013175148352841198938685021279015417466228544088846707469605690787389558195498434372613601408. The discrepancy decreases from approximately 0.011091272683735963295 to 0.011091272683735945657. The rounded public display, 0.011091272684, is unchanged; the exact objective strictly improves. This is a coordinate local optimum only. Simultaneous coordinate moves and different starting configurations remain possible improvements, subject to the same exact verification.
P59 · 超立方体内的最低 L2 星偏差 · 讨论