This approach involves accepting up to a certain number, denoted as 'k', of weak blocks for the next height beyond the current chain tip (height X+1), with the condition that these blocks recognize the current chain tip as their parent. The mechanism for selecting which weak blocks to retain could involve prioritizing the initial 'k' weak blocks received and possibly replacing older blocks with newer ones based on their timestamp. This policy aims to address scenarios where divergent mining policies might lead to the creation of weak blocks with varying characteristics, such as differences in transaction selection criteria due to factors like fee rates, transaction filtering, preferential treatment of transactions through out-of-band fees, or inclusion of transactions enabled by new soft fork rules not universally supported.

The rationale behind keeping multiple weak blocks, especially those that diverge in mining policy, acknowledges the low probability of occurrence but sees potential value in retaining weak blocks at height X or X-1 if they include consensus-valid transactions that are not yet included in the mempool or newer weak blocks. This strategy could enhance the inclusivity and diversity of transactions processed on the network. However, the complexity of implementing such a system and tracking these various weak blocks might outweigh the benefits. The difficulty lies in managing the trade-offs between fostering a more inclusive transaction processing environment and the increased overhead of maintaining and cycling through multiple weak blocks, especially considering the likelihood of encountering weak blocks mined under independent policies is relatively low.