The methodology delineates transaction processing into three distinct phases: confirmation, validation, and download, each tailored to address specific requirements and constraints without imposing unnecessary order, thus maximizing concurrent operations.

The confirmation phase is critical for ensuring transaction integrity through "confirmability" checks, which are inherently dependent on block order. This phase focuses on verifying the existence and spentness of transactions, establishing a foundation for subsequent validations that hinge on the chronological order of transactions within the blockchain.

During the validation phase, the system performs script execution and prevout queries concurrently across blocks. This phase is designed to run independently of block order, except where specifically required by validations that necessitate sequential processing. By segregating these tasks, the validation phase achieves a high degree of parallelism, leveraging the inherent concurrency capabilities of the system to expedite processing.

The download phase operates under the premise that header context is universally accessible and not bound by block context. This phase prioritizes tasks that are block-context free, allowing for simultaneous execution alongside the confirmation and validation phases. The strategic partitioning of tasks based on their dependency on block order versus those that can be executed in isolation or concurrently underscores the system's innovative approach to maximizing efficiency and throughput in blockchain transaction processing.

By carefully factoring necessary constraints to avoid imposing extraneous order, the outlined methodology significantly enhances the scalability and performance of blockchain systems. This approach not only streamlines transaction processing but also opens avenues for further optimizations in blockchain technology.