I apologize in advance if this has already been covered in a previous post, but I am having a devil of a time in locating anything through the search engine.

The wording on both of these cards are similar in that I assume that due to committing a card, not being part of the cost but part of the effect, can not only be done on an already commited foundation, but would keep that foundation committed respective to each cards effects. Am I correct in assuming this?

Thanks

No.

You can't commit an already committed card, you'd have to pick a different target.

Chinese Boxing's effect would keep a card committed during the ready phase even if the card had been readied beforehand and then committed again.

Program Malfunction would only keep a card committed so long as Program Malfunction stayed committed. If it's readied for any reason then the spell is broken, even if Program Malfunction is committed again.

Stamp for Cascade. To commit a foundation is defined as turning a ready foundation to the sideways/committed position. If a foundation is already committed, you cannot choose to commit it via any effect.