(2) Establish: hakiym means confirm or establish and is preceded by the direct article "the".

This entire chain of words in the Hebrew is signified repeatedly with the sign of the direct object. In Hebrew with the direct articles bold and enlarged for emphasis. ... L'maan hakiym-ot'cha hayom ...The dash character is called a maquef and is used within construct chains to indicate that if one of the words in the chain is direct, the entire chain of words is direct. In normal usage only one of the words uses the sign of the direct object. In this case, both words contain signs of direct object and therefore the entire chain receives extra emphasis of the direct indicator. Additionally, hayom "the day" places the emphasis on now, causing it to be translated "this day".

The sign of the direct object, alef tov "et" which in this case is pronounced "ot", when attached to chof sofit chametz, "cha", means emphatically and directly "YOU and no other!" Here, alef tov is tied to alif vav/holom tov, "ot" which is accusative and is often translated 'to consent' or 'agree'**. Keep in mind that alef and tov together reveal the messiah (Rev 1:8,11) so there is a special "you" attached to messiah in this context. My perception of this is that those who chose to establish themselves individually with the covenant, were established by G-d as His chosen people. Choosing to stand in agreement with this covenant is the equivalent of attaching oneself to the messiah. Baruch haShem!

G-d did not overlook anyone. Males, females, and children who were sons of Abraham were all included in this covenant. Additionally, the "strangers in the camp", i.e. not sons of Abraham who chose to stand with Israel, were chosen by G-d. This is reinforced in verse 13,14 (14,15) "Neither with you only do I make this covenant and this oath; But with him that stands here with us this day before the LORD our God, and also with him that is not here with us this day:" G-d made plans for all who would choose to be included in His covenant and He chose those of us who came later as well. Baruch haShem!