Final answer:
The best solution for a secure and efficient transaction system with verifiable message integrity is an open distributed transaction ledger with a proof of work mechanism, aligning with blockchain technology.
Step-by-step explanation:
The identifying a system solution that will satisfy various requirements including reduced transaction time, increased security and message integrity, and improved cryptographic security, in an environment with a broad user base and asynchronous transactions. Considering the given options, the best solution that meets all of the architect's objectives is D. An open distributed transaction ledger that requires proof of work to append entries. This option aligns well with the demand for decreased transaction times, bolstered security, and verifiable message integrity.
Such a system, often associated with blockchain technology, provides a decentralized method where transactions are securely recorded in a sequence of blocks that are linked and secured using cryptography. Each block typically contains a cryptographic hash of the previous block, a timestamp, and transaction data, ensuring message integrity and security. The proof of work aspect makes it computationally expensive to alter any aspect of the ledger, thus ensuring enhanced cryptographic security and public accountability.