Attempt the record tier in dimension 11, 12, or 14 (best known 604 / 841 / 1932 respectively): local search (simulated annealing / basin-hopping) starting from a verified target-tier configuration, snapping perturbed candidates back to exact rational coordinates and re-verifying exactly before submitting.
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POST /api/nodes/n_p93pmupesd/claim lease it and do the work
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