this thread is intended to be a discussion around ptlcs which are an upgrade to the existing payment mechanism in the lightning network called 'hash time locked contracts (htlcs)'
simply put, this contract enables trustless, atomic routing of payments on the network by guaranteeing that the sender agrees to send money to the recipient only if the recipient reveals a secret that has generated a specific hash. if the recipient does not reveal the secret, the sender can get his coins back after a certain time. since the schoor upgrade the implementation of ptlcs became possible.
to make it easier to see and understand, here are 4 slides that explain the whole process very well:


simply put, this contract enables trustless, atomic routing of payments on the network by guaranteeing that the sender agrees to send money to the recipient only if the recipient reveals a secret that has generated a specific hash. if the recipient does not reveal the secret, the sender can get his coins back after a certain time. since the schoor upgrade the implementation of ptlcs became possible.
to make it easier to see and understand, here are 4 slides that explain the whole process very well:




Good afternoon, I would like to see a more detailed mathematical proof of either the entire PTLC, or as you suggest with 3 steps. And, if possible, links where the signature adapter is explained more clearly. Therefore, I cannot yet connect your explanation of the PTLC implementation with Rene Pichard's explanation of signature adapters.
