Optimistic rollups are blockchain scaling solutions that reduce main-chain computation while maintaining high security. Rollup operators execute transactions and post state commitments to the main chain, which are assumed valid unless challenged. These challenges let users dispute invalid commitments within a set period, ensuring correctness. However, if challenges can be censored, the rollup’s security and censorship resistance – a core blockchain property requiring all valid transactions to be processed – are compromised. To strengthen transaction verification, we introduce the concept of time consensus, where participants agree on an upper bound for when they received a transaction, using shared randomness and no direct communication. We design single-shot time consensus mechanisms achieving near-optimal trade-offs between success probability and overhead, along with tight lower bounds. These mechanisms yield approximate correlated equilibria approaching exactness as failure probability vanishes - though exact equilibria are impossible. We extend this to multi-shot time consensus with feedback, achieving improved trade-offs and robustness against adversarial manipulation of shared randomness.