How did Judaism, Samaritans, Christians, and Muslims split from one shared family tree?
Research question: How and when did Judaism, Samaritanism, Christianity and Islam split from a shared Abrahamic root, and what did each keep or change?
The verified facts only partly answer this. They show that Genesis presents the everlasting covenant as established with Isaac, while Ishmael is also blessed and made a great nation with twelve princes 89. The Mishneh Torah excludes Ishmael's descendants from the line that counts, citing Genesis 21:12, and also excludes Esau's descendants unless they keep Abraham's faith and upright behavior 35. The Quran assigns Abraham and Ishmael the duty of purifying the House for worshippers 4, while the continuous story linking them to Mecca appears only in later Islamic tradition, expanded through hadith, biography, and exegesis 67. The only dating offered is narrative time in the patriarchal era with no date given, so the facts do not establish when any split occurred 810. No verified fact addresses Samaritanism or Christianity, so their part of the question is unanswered.
Sources
"The earlier surviving Hagar–Ishmael narrative places its events around Beersheba and Paran and contains no Meccan journey, Zamzam, Kaaba, or Arabian pilgrimage."Did Abraham and Ishmael build the Kaaba? - On Its Own Terms
"He lived in the wilderness of Paran, and his mother got a wife for him from the land of Egypt."Did Abraham and Ishmael build the Kaaba? - On Its Own Terms
"The descendants of Ishmael are excluded as implied by Genesis 21:12: 'It is through Isaac, that your offspring will be called.'"Mishneh Torah, Kings and Wars 10:7 [Mishneh Torah, trans. by Eliyahu Touger. Jerusalem, Moznaim Pub. c1986-c2007]
"And We imposed a duty upon Abraham and Ishmael, (saying): Purify My house for those who go around and those who meditate therein and those who bow down and prostrate themselves."Did Abraham and Ishmael build the Kaaba? - On Its Own Terms
"Esau's descendants are also excluded, for Isaac told Jacob Genesis 28:4: 'May God grant Abraham's blessing to you and your descendants,' implying that only he is the true offspring of Abraham who maintains his faith and his upright behavior."Mishneh Torah, Kings and Wars 10:7 [Mishneh Torah, trans. by Eliyahu Touger. Jerusalem, Moznaim Pub. c1986-c2007]
"The continuous story first appears in later Islamic tradition, and it is that supplied narrative on which the sanctuary’s Abrahamic authority rests."Did Abraham and Ishmael build the Kaaba? - On Its Own Terms
"Hadith, biography, and exegesis turn the Quran’s allusions into the familiar continuous story."Did Abraham and Ishmael build the Kaaba? - On Its Own Terms
"But My covenant will I establish with Isaac, whom Sarah shall bear unto thee at this set time in the next year."Genesis 17:25-27 [Hebrew Bible (JPS 1917 English, Sefaria)]
"And as for Ishmael, I have heard thee; behold, I have blessed him, and will make him fruitful, and will multiply him exceedingly; twelve princes shall he beget, and I will make him a great nation."Genesis 17:25-27 [Hebrew Bible (JPS 1917 English, Sefaria)]
"And Ishmael his son was thirteen years old, when he was circumcised in the flesh of his foreskin."Genesis 17:25-27 [Hebrew Bible (JPS 1917 English, Sefaria)]