Where does the 33.33% threshold for selfish mining come from?

The discussion revolves around the implementation of a novel approach to handling block timestamps in blockchain technology, specifically aiming to mitigate the issue of selfish mining. The proposal suggests that if a block's timestamp is within a reasonable margin of error—defined as +/- 5 seconds, plus an additional 2 seconds allowed for propagation delay—then it would not be possible for miners to engage profitably in selfish mining practices. This is because blocks that do not meet these timing criteria would be subjected to a "timeout" period of one block time. This timeout serves as an opportunity for Proof of Work (PoW) to potentially override any issues caused by network partitions.

Furthermore, the proposal outlines a mechanism to prioritize blocks based on their timestamp accuracy. Blocks with timestamps deemed "reasonable" under this system would be given precedence. Specifically, when such a block is encountered, its full data would be requested and re-announced immediately, even if it represents the same amount of work as the current tip of the blockchain. Moreover, if the current tip has an "unreasonable" timestamp and a newly discovered block has an equal amount of work but a "reasonable" timestamp, the protocol would switch to favor the new block. The criteria for a "reasonable" timestamp are technically defined as abs(now() - header.nTime) < 10s and either the block having more work than the current tip or its timestamp being within 10 seconds of the system's time when the current tip was received.

This approach aims to enhance the integrity and fairness of the blockchain by ensuring that miners cannot gain an undue advantage through manipulative practices such as selfish mining. It emphasizes the importance of accurate and honest timestamping of blocks and proposes a practical solution to enforce this behavior within the network.