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

A nuanced understanding of how nodes handle timestamps when coming back online reveals a strategic approach to accepting the most-work chain's timestamps, recognizing potential discrepancies in their internal clocks. This acknowledgment of "clock error" underscores the importance of nodes maintaining an accurate sense of current UTC time, ideally within a margin of +/- 5 seconds. The proposal that nodes could recalibrate their clocks based on the median error of past block arrivals introduces a method to enhance timestamp accuracy, albeit with reservations about its impact on the decentralized nature of blockchain networks. Furthermore, the imaginative suggestion of using telescopes for clock calibration highlights the lengths to which the system might go to prevent attackers from exploiting time-based vulnerabilities.

The issue of time synchronization extends into the realm of block propagation and the detection of stale blocks, shedding light on the challenges faced by the network in ensuring fairness and efficiency. The identification of a hashrate-weighted propagation delay points to the nuanced dynamics of network performance, raising questions about the potential for larger pools to engage in strategic behaviors that could undermine the equitable distribution of rewards. This exploration into the timing of block propagation emphasizes the critical role of technological infrastructure, such as Fibre-like networks, in minimizing delays and optimizing the overall health of the blockchain ecosystem.

Moreover, the conversation around Fibre miners and the potential for a 0.03% excess profit for those with superior connectivity solutions illustrates the subtle advantages that can influence mining outcomes. The analysis delves into the specifics of block release timings and the consequential disparities in reward distribution among miners, highlighting the delicate balance between technological advancement and fair play in the mining sector. The focus on empirical data and mathematical modeling to understand these dynamics further enriches the dialogue on ensuring fairness and integrity within the blockchain space.

Addressing the broader implications of timestamp accuracy and the prevention of selfish mining strategies, the discussion transitions to policy and technological considerations. By establishing a "timeout" period for blocks with timestamps falling outside an acceptable range, the system can mitigate the risks associated with inaccurate or manipulated timestamps. This mechanism not only serves as a deterrent against selfish mining but also reinforces the value of precise timekeeping in maintaining the blockchain's operational integrity. The emphasis on proof of work as a means to resolve discrepancies highlights the ongoing efforts to refine consensus mechanisms, ensuring they robustly support the network's foundational principles.

Lastly, the discourse on achieving secure consensus pivots towards the need for a more substantial majority than the traditional 51% threshold, advocating for a 66.67% majority to account for various operational contingencies. This perspective underscores the complexities involved in digital message signing, timestamp accuracy, and the synchronization of clocks, pointing out the gaps in current models like Bitcoin's. By critiquing and proposing adjustments to the handling of timestamps and consensus-related messages, the dialogue fosters a deeper appreciation for the technical and strategic nuances underpinning blockchain security and reliability.