The integration of zkStark technology with aggregated IPA has been proposed as a viable solution for application circuits and recursive verifiers. This combination aims to achieve a proof size of approximately 6~7 KB and reduce verification time to around one second for each OP_ZKP transaction. Such improvements are critical for maintaining swift and secure transactions within the blockchain ecosystem.

To address potential scalability issues and ensure inclusivity among miners with varying computational capacities, a threshold value T has been introduced. This limit restricts the number of OP_ZKP transactions within any given bitcoin block to a maximum that can be feasibly verified by smaller miners, such as those using Raspberry Pi 4 devices. Implementing batched verification for aggregated IPA (aIPA) plays a central role in this strategy, enabling efficient verification processes even when transaction volumes approach the set threshold.

Furthermore, to circumvent the constraints imposed by batched verification methods when the count surpasses threshold T, a novel approach utilizing block proofs has been suggested. In scenarios exceeding the transaction limit within a block, a recursive verification method could be employed to verify all OP_ZKP transactions collectively, thereby generating a new proof for miner verification. This approach allows for the reconsideration of zkStark technology, promising rapid verification times and manageable proof sizes without being hindered by batched verification limitations.

For ongoing collaboration and feedback, a live document has been made available on GitHub at https://github.com/opzkp/tea-horse, inviting comments and suggestions from the community to further refine these implementations.