The residuary heirs (asabah) and their order

Agreed. After the fixed shares are paid, the remainder goes to the asabah — the male-line relatives — on the rule “give the fixed shares to those entitled to them; whatever is left goes to the nearest male”. The classes run in this order: (1) descendants — the son, then the son’s son however far down; (2) ascendants — the father, then the grandfather; (3) the deceased’s brothers and their sons; (4) paternal uncles and their sons. Within a class the nearer excludes the remoter, and at the same degree the full-blood relative excludes the half-blood: a full brother excludes a consanguine brother, whose sons in turn come before an uncle. Ibn Rushd introduces each of these steps with “the jurists agreed”. Ibn Qudama adds the composition rule and states it as beyond disagreement: four male heirs — a son, a son’s son, a full brother and a consanguine brother — pull their sisters into the residue with them and divide two-to-one, while the remaining agnates (a brother’s sons, uncles, their sons) take the residue alone, their sisters taking nothing. A sister also becomes a residuary alongside a daughter, which all four schools accept; the dissent on that point is Ibn ‘Abbas’s and Dawud al-Zahiri’s, not any school’s. We checked this; the four do not differ on the order itself.

Shared evidence: Sahih al-Bukhari 6732 — “give the fixed shares to those entitled to them; what is left goes to the nearest male” (also Sahih Muslim 1615) · Surah an-Nisa 4:11 — the children’s residue and the two-to-one division within it · Surah an-Nisa 4:176 — the brothers’ and sisters’ residue in kalalah.

Not covered by this finding: where the grandfather stands when the deceased’s brothers survive — whether he shuts them out as a father would, or shares with them — which the sources record as a real dispute and which we have not yet established school by school — not yet researched school by school. Treat that as open and ask a scholar of your school.