Thanks for posting! From RFC 3325, the definition of a P-Asserted-Identity header is the following.
The P-Asserted-Identity header field is used among trusted SIP
entities (typically intermediaries) to carry the identity of the user
sending a SIP message as it was verified by authentication.
The softswitch and SBCs can choose how to use this information. It may be used within a trusted domain to validate the sender of the SIP message. This is sometimes needed when the From header is set to "anonymous". In other cases, this header is actually used as the caller ID.
The Diversion header is defined in RFC 5806.
The Diversion header allows implementation of feature logic based on from whom the call was diverted.
Therefore, we typically see or use the Diversion header whenever a call is being forwarded to a new destination not specified in the original request. If the Adtran unit were to just change the Request URI to the new destination, the call will often be rejected by the softswitch. Generally this is because the From header contains the original caller ID, and the softswitch does not associate this caller ID with this customer site. In other words, it appears to be a spoofed caller ID. The Diversion header allows us to specify that the call was diverted by a known number for this customer, which the softswitch can utilize to validate the call.