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

In the realm of blockchain and cryptocurrency, the synchronization of node operation times poses a significant challenge, particularly when considering the balance between nodes continuously operating and those catching up from inactivity. To address this issue, a policy has been discussed where nodes initially set their "tip" header to the highest common block among peers, adjusting it to the most work-intensive header only when its timestamp aligns closely with current time. This approach aims to ensure consistency and fairness across all nodes, regardless of their operational status.

Furthermore, the problem of maintaining accurate system time is exacerbated by the vulnerability of conventional time-keeping methods like NTP (Network Time Protocol) and GPS to jamming and corruption. It's suggested that miners and pools, who have a vested interest in producing blocks with accurate timestamps, could invest in their own stratum 1 NTP servers, which offer long holdover times to counteract these vulnerabilities. By potentially using new block timestamps as inputs for an automatic system clock correction algorithm, it might be possible to mitigate discrepancies. However, this correction mechanism would need to be designed carefully to avoid adjustments in cases where there are competing chains with similar work but differing timestamps.

An analysis of block receipt times versus their timestamps highlighted the varying degrees of future or past-dated blocks within a specific sample, showing a range from blocks being over 120 seconds in the future to some being significantly delayed. These statistics underline the necessity for improvements within the mining ecosystem to reduce timing discrepancies before implementing a widespread strategy relying on block timestamps for system time correction.

This discussion emphasizes the complexity of achieving time synchronization across a decentralized network of nodes, pointing out both strategic and technical challenges that must be addressed. The potential solutions involve a mix of policy implementation and technological innovation, aiming to enhance the integrity and reliability of blockchain operations.