Here is an argument that proposes that part of the Didache is in fact the Apostolic Decree from the Jerusalem Council (!)
The 'Apostolic Decree' commonly describes the letter reputedly composed by James and the Jerusalem apostles in c. AD 49 and sent to Gentile converts in Antioch, Syria and Cilicia. The meeting that gave rise to this document (described in Acts 15.1-22) discussed the question of whether circumcision should be required of Gentiles wishing to convert to the (Jewish) Jesus movement. Luke's record of this 'decree' (Acts 15:23-29) emphasises that the requirements laid on these Gentile converts did not include circumcision.
Paul, in Galatians 2.1-10, appears to refer to the same meeting. Crucially, however, Paul omits mention of any 'decree'. This is surprising if Luke's account is accurate, since an appeal to the apostles' authoritative ruling should have silenced Paul's critics; those demanding the circumcision of Gentile converts. Scholars have generally explained this anomoly by suggesting that, although a Jerusalem meeting took place, no 'decree' was ever issued. Rather, Luke came across some rules for Gentile admission without circumcision, devised elsewhere, and imported them into his account of the Jerusalem meeting to give them added authority.
Another option, not previously considered, is that the Jerusalem meeting did produce a decree but that its contents were sufficiently ambiguous to support both pro- and anti-circumcision interpretations. This would explain Luke's reading of events as well as Paul's unwillingness to quote a document whose contents might have been turned to opposite effect. [...]
