While using Open Transaction as a Decentralized Exchange, how can one guarantee sanctity of the trade carried out by the parties? Lets assume Alice holds 100 shares of Twitter and wants to sell those shares on Open Transactions. Bob decides to purchase those shares. They decide the terms of the transaction, price etc and sign a smart contract. The transaction gets completed. Bob pays Alice for the shares either in dollars or bitcoins etc and alice transfers the 100 twitter shares to Bob. 

How does one preserve sanctity of this transaction because, Alice can repudiate this transaction at a later date. On a parallel Centralized Stock Exchange the ownership of these 100 shares will still be attributed to Alice and she will continue to get dividends etc as an owner.
This is more of a legal than a technical question. All Bob needs to do is to have Alice provably transfer her shares. For example, Bob could demand that Alice associates her smart contract keys with her real identity through some means such as key signatures. That way, they can put their dispute before traditional court. Then the transaction is left to the judgement of a judge.

In future cryptocurrency systems, to solve this problem, and to not rely on subjective law, we envision share ownership to also be verified on the blockchain. Colored coins and turing-complete blockchains allow shares to really be owned by their respective owner. When decentralized anonymous organizations develop, blockchain ownership of shares will also directly and self-enforcibly give the cryptographic right to voting and dividends.