o1 and o3 Backtracking for Constraint Satisfaction

When an internal reasoning branch in o1 or o3 leads to a contradiction or unviable state, the model discards the branch, backtracks to a previous decision node, and explores alternative paths. State all hard invariants upfront so the model can falsify invalid branches internally.

Design a zero-downtime shard rebalancing schedule for 12 database nodes under these hard invariants: (1) no node may exceed 75% disk IOPS during migration, (2) replica lag must remain under 100ms, and (3) no two primary shards in the same availability zone may migrate concurrently.