The Jenkins community seems adamant that it doesn't want to follow a formal process. This effectively rules out any involvement with the Eclipse Foundation and any prospect of reconciliation with Hudson.

Now that Oracle has decided to transfer Hudson to the Eclipse Foundation there was some speculation as to whether the Jenkins fork could be persuaded to rejoin the original project.

The answer to this appears to be a resounding no.

At its most recent online meeting the question of possible reconciliation with Hudson as part of Hudson's move to Eclipse was discussed.

However, the Jenkin's community's strong desire to remain at GitHub, to not follow any formal development process, including having to follow a specific means to bring new committers on board, and to release weekly effectively prevent Jenkins from moving either to Eclipse nor to the Apache Foundation, which has also be proposed as a home for Jenkins. 

Further Information

Hudson becomes Jenkins

Oracle to let go of Hudson