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

A crucial aspect discussed is the shift in miner rewards from block subsidies to transaction fees, which alters the incentives for miners. This transition mitigates concerns regarding inflation caused by miners advancing time to lower difficulty, as previously, exploiting the difficulty algorithm could substantially increase a miner's share of the total Bitcoin issuance. However, with fees replacing subsidies, the impact of such manipulations shifts towards affecting transaction space and, consequently, revenue based on market dynamics. The Forward Blocks presentation at Scaling Bitcoin 2018 provides an in-depth analysis of these dynamics, highlighting the nuanced effects of miner behavior on the blockchain ecosystem.

Accurate timestamping emerges as a foundational requirement for maintaining blockchain integrity, influencing various operations from preventing selfish mining to regulating coin release schedules. Nodes employ sophisticated methods to synchronize time without depending on a singular source like GPS or NTP, thus avoiding centralization. The proposal of using astronomical observations for time calibration underscores the lengths to which the system goes to preserve decentralization and security against attackers.

The discussion extends into how nodes manage operational times, especially when rejoining the network, ensuring consistency across all participating nodes. This involves setting initial headers to reflect the most work-intensive chain that aligns with current time, a policy aimed at maintaining fairness. The vulnerability of conventional time-keeping methods to tampering necessitates innovative solutions, such as miners investing in stratum 1 NTP servers, to produce blocks with accurate timestamps, thereby enhancing the ecosystem's resilience against timing discrepancies.

Furthermore, the examination of network latency's effect on stale blocks introduces a critical evaluation of network performance and its implications for blockchain fairness. By proposing a recharacterization of network efficiency and investigating the occurrence rate of stale blocks, the analysis sheds light on potential strategic behaviors like intentional block withholding. This exploration emphasizes the importance of equitable network participation and the challenges in achieving optimal performance amidst varying propagation delays.

The concept of Fibre miners leveraging superior connectivity to gain a marginal profit advantage illustrates the subtle complexities of mining dynamics. This scenario not only highlights the technological disparities within the mining community but also raises questions about the broader implications of such advantages on network fairness and reward distribution. The detailed scrutiny into the delay introduced by Fibre miners in releasing blocks to non-Fibre counterparts reveals a nuanced understanding of mining strategies and their impacts on the blockchain ecosystem.

In addressing the safeguarding of blockchain integrity, the discussion revolves around the handling of block timestamps and the prevention of selfish mining through stringent timestamp regulations. This approach prioritizes accuracy and honesty in timestamping, proposing practical solutions to enforce fair play among miners. The emphasis on precise timing measures seeks to deter manipulative practices, thereby contributing to the overall robustness and trustworthiness of the blockchain network.

The narrative further delves into the prerequisites for secure consensus in distributed systems, highlighting the inadequacy of a simple majority for genuine security. It points out the essential conditions for a reliable consensus mechanism, including synchronized honest clocks and the digital signing of messages. The analysis critiques Bitcoin's approach to these conditions, suggesting improvements to enhance security and mitigate vulnerabilities inherent in less stringent consensus models.

Lastly, the mathematical exploration of selfish mining offers a thorough investigation into its profitability and impact on network fairness. By analyzing state transitions and profitability thresholds, the research provides valuable insights into the conditions under which selfish mining becomes advantageous. This meticulous examination, supported by theoretical calculations and simulations, underscores the significance of hashrate distribution and block propagation in assessing blockchain protocols' susceptibility to strategic exploitation.