Hello,

Article: https://medium.com/@shunsai.takahashi/proof-of-approval-a-better-blockchain-consensus-protocol-b19a55dc331b
Paper: https://github.com/Takanium/doc/blob/master/research/proof-of-approval.pdf (Updated June 9, 2018)

The previous version of this paper was discussed here https://bitcointalk.org/index.php?topic=3125137.0. This version builds upon the previous version and (to my understanding) fixes flaws that were pointed out. It achieves:

• Defense against attacks known as Costless Simulation, History or Long Range - much stronger than Weak Subjectivity https://blog.ethereum.org/2014/11/25/proof-stake-learned-love-weak-subjectivity/.
• Defense against Nothing at Stake attack.
• As before, does not consume physical resources.
• As before, achieves near instant finality.
• Updated reward system that rewards approvers.
• Updated creator selection (previous version didn't have any) to reduce number of proposed blocks in a slot and prevent network from being bogged down.
• Added attacks defense discussion.
• Added glossary for easier reading.

This article explains how Proof-of-Approval defends against History or Costless Simulation attack https://medium.com/@shunsai.takahashi/weak-subjectivity-not-required-fb1c467bc5ad .
Looking forward to your feedback.

Regards,
Shunsai