diff --git a/internal/engine/dependency_order.go b/internal/engine/dependency_order.go
new file mode 100644
index 0000000..5d0b631
--- /dev/null
+++ b/internal/engine/dependency_order.go
@@ -0,0 +1,200 @@
+package engine
+
+import (
+	"container/heap"
+	"sort"
+)
+
+// dependencyKey is an immutable tuple used to order dependency-graph nodes.
+// Callers provide unique keys and valid edge endpoints.
+type dependencyKey []string
+
+// dependencyEdge points from a prerequisite to the node that depends on it.
+type dependencyEdge struct {
+	prerequisite int
+	dependent    int
+}
+
+type dependencyReadyHeap struct {
+	nodes []int
+	keys  []dependencyKey
+}
+
+func (h dependencyReadyHeap) Len() int { return len(h.nodes) }
+
+func (h dependencyReadyHeap) Less(i, j int) bool {
+	return dependencyKeyLess(h.keys[h.nodes[i]], h.keys[h.nodes[j]])
+}
+
+func (h dependencyReadyHeap) Swap(i, j int) {
+	h.nodes[i], h.nodes[j] = h.nodes[j], h.nodes[i]
+}
+
+func (h *dependencyReadyHeap) Push(value any) {
+	h.nodes = append(h.nodes, value.(int))
+}
+
+func (h *dependencyReadyHeap) Pop() any {
+	last := len(h.nodes) - 1
+	node := h.nodes[last]
+	h.nodes = h.nodes[:last]
+	return node
+}
+
+// dependencyKeyLess compares tuple components bytewise, with a shorter tuple
+// sorting first when all of its components match the corresponding prefix.
+func dependencyKeyLess(left, right dependencyKey) bool {
+	for i := 0; i < len(left) && i < len(right); i++ {
+		if left[i] != right[i] {
+			return left[i] < right[i]
+		}
+	}
+	return len(left) < len(right)
+}
+
+// scheduleDependencies applies Kahn's algorithm, always selecting the
+// smallest currently-ready key. Duplicate edges count only once. If scheduling
+// stalls, an explicit depth-first traversal of the residual graph returns an
+// actual directed cycle, rotated to its smallest key and closed by repeating
+// its first node; blocked non-cycle dependents are excluded.
+//
+// Nodes are visited by precomputed key rank, which also makes each adjacency
+// list deterministic without sorting edges. The work is O(E + V log V), with
+// O(V + E) additional memory, apart from key copying and tuple comparisons.
+func scheduleDependencies(keys []dependencyKey, edges []dependencyEdge) (order, cycle []int) {
+	ownedKeys := make([]dependencyKey, len(keys))
+	for i, key := range keys {
+		ownedKeys[i] = append(dependencyKey(nil), key...)
+	}
+
+	nodeOrder := make([]int, len(ownedKeys))
+	for i := range nodeOrder {
+		nodeOrder[i] = i
+	}
+	sort.Slice(nodeOrder, func(i, j int) bool {
+		return dependencyKeyLess(ownedKeys[nodeOrder[i]], ownedKeys[nodeOrder[j]])
+	})
+
+	incoming := make([][]int, len(ownedKeys))
+	for _, edge := range edges {
+		incoming[edge.dependent] = append(incoming[edge.dependent], edge.prerequisite)
+	}
+
+	outgoing := make([][]int, len(ownedKeys))
+	indegree := make([]int, len(ownedKeys))
+	for _, dependent := range nodeOrder {
+		seen := make(map[int]struct{}, len(incoming[dependent]))
+		for _, prerequisite := range incoming[dependent] {
+			if _, duplicate := seen[prerequisite]; duplicate {
+				continue
+			}
+			seen[prerequisite] = struct{}{}
+			indegree[dependent]++
+			// Dependents are visited by key rank, so each outgoing list is
+			// already ordered by key.
+			outgoing[prerequisite] = append(outgoing[prerequisite], dependent)
+		}
+	}
+
+	ready := dependencyReadyHeap{keys: ownedKeys}
+	for _, node := range nodeOrder {
+		if indegree[node] == 0 {
+			ready.nodes = append(ready.nodes, node)
+		}
+	}
+	heap.Init(&ready)
+
+	order = make([]int, 0, len(ownedKeys))
+	for ready.Len() != 0 {
+		node := heap.Pop(&ready).(int)
+		order = append(order, node)
+		for _, dependent := range outgoing[node] {
+			indegree[dependent]--
+			if indegree[dependent] == 0 {
+				heap.Push(&ready, dependent)
+			}
+		}
+	}
+	if len(order) == len(ownedKeys) {
+		return order, nil
+	}
+	return nil, dependencyCycle(ownedKeys, nodeOrder, outgoing, indegree)
+}
+
+type dependencyDFSFrame struct {
+	node int
+	next int
+}
+
+// dependencyCycle searches the residual graph iteratively to avoid recursion
+// depth depending on input size.
+func dependencyCycle(keys []dependencyKey, nodeOrder []int, outgoing [][]int, indegree []int) []int {
+	const (
+		unvisited = uint8(0)
+		active    = uint8(1)
+		finished  = uint8(2)
+	)
+
+	state := make([]uint8, len(keys))
+	position := make([]int, len(keys))
+	for i := range position {
+		position[i] = -1
+	}
+	path := make([]int, 0, len(keys))
+	frames := make([]dependencyDFSFrame, 0, len(keys))
+
+	for _, root := range nodeOrder {
+		if indegree[root] == 0 || state[root] != unvisited {
+			continue
+		}
+		state[root] = active
+		position[root] = len(path)
+		path = append(path, root)
+		frames = append(frames, dependencyDFSFrame{node: root})
+
+		for len(frames) != 0 {
+			frame := &frames[len(frames)-1]
+			if frame.next == len(outgoing[frame.node]) {
+				state[frame.node] = finished
+				position[frame.node] = -1
+				path = path[:len(path)-1]
+				frames = frames[:len(frames)-1]
+				continue
+			}
+
+			next := outgoing[frame.node][frame.next]
+			frame.next++
+			if indegree[next] == 0 {
+				continue
+			}
+			switch state[next] {
+			case unvisited:
+				state[next] = active
+				position[next] = len(path)
+				path = append(path, next)
+				frames = append(frames, dependencyDFSFrame{node: next})
+			case active:
+				return canonicalDependencyCycle(keys, path[position[next]:])
+			}
+		}
+	}
+
+	// A stalled Kahn traversal always leaves a cycle in the residual graph.
+	return nil
+}
+
+func canonicalDependencyCycle(keys []dependencyKey, path []int) []int {
+	start := 0
+	for i := 1; i < len(path); i++ {
+		if dependencyKeyLess(keys[path[i]], keys[path[start]]) {
+			start = i
+		}
+	}
+
+	cycle := make([]int, len(path)+1)
+	for i := range path {
+		cycle[i] = path[(start+i)%len(path)]
+	}
+	cycle[len(path)] = cycle[0]
+	return cycle
+}
diff --git a/internal/engine/dependency_order_test.go b/internal/engine/dependency_order_test.go
new file mode 100644
index 0000000..990c961
--- /dev/null
+++ b/internal/engine/dependency_order_test.go
@@ -0,0 +1,215 @@
+package engine
+
+import (
+	"reflect"
+	"testing"
+)
+
+func TestScheduleDependenciesOrdersReadyNodes(t *testing.T) {
+	tests := []struct {
+		name  string
+		keys  []string
+		edges [][2]string
+		want  []string
+	}{
+		{
+			name: "independent branches",
+			keys: []string{"branch-c", "branch-a", "branch-b"},
+			want: []string{"branch-a", "branch-b", "branch-c"},
+		},
+		{
+			name: "unequal chains",
+			keys: []string{"chain-d", "chain-c", "chain-b", "chain-a"},
+			edges: [][2]string{
+				{"chain-a", "chain-b"},
+				{"chain-b", "chain-c"},
+				{"chain-c", "chain-d"},
+			},
+			want: []string{"chain-a", "chain-b", "chain-c", "chain-d"},
+		},
+		{
+			name: "multiple dependencies",
+			keys: []string{"application", "right", "base", "left"},
+			edges: [][2]string{
+				{"base", "left"}, {"base", "right"},
+				{"left", "application"}, {"right", "application"},
+			},
+			want: []string{"base", "left", "right", "application"},
+		},
+		{
+			name: "shared dependency at equal depths",
+			keys: []string{"sink", "right", "root", "left"},
+			edges: [][2]string{
+				{"root", "left"}, {"root", "right"},
+				{"left", "sink"}, {"right", "sink"},
+			},
+			want: []string{"root", "left", "right", "sink"},
+		},
+		{
+			name: "shared dependency at unequal depths",
+			keys: []string{"sink", "deep", "side", "middle", "root"},
+			edges: [][2]string{
+				{"root", "middle"}, {"middle", "deep"}, {"root", "side"},
+				{"deep", "sink"}, {"side", "sink"},
+			},
+			want: []string{"root", "middle", "deep", "side", "sink"},
+		},
+		{
+			name:  "newly ready small key precedes older large key",
+			keys:  []string{"z-ready", "a-new", "b-ready"},
+			edges: [][2]string{{"b-ready", "a-new"}},
+			want:  []string{"b-ready", "a-new", "z-ready"},
+		},
+		{
+			name: "duplicate edges count once",
+			keys: []string{"dependent", "prerequisite"},
+			edges: [][2]string{
+				{"prerequisite", "dependent"},
+				{"prerequisite", "dependent"},
+			},
+			want: []string{"prerequisite", "dependent"},
+		},
+	}
+
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			keys, edges, indexes := dependencyGraph(test.keys, test.edges)
+			order, cycle := scheduleDependencies(keys, edges)
+			if len(cycle) != 0 {
+				t.Fatalf("unexpected cycle: %v", dependencyNames(cycle, indexes))
+			}
+			if got := dependencyNames(order, indexes); !reflect.DeepEqual(got, test.want) {
+				t.Fatalf("schedule = %v, want %v", got, test.want)
+			}
+		})
+	}
+}
+
+func TestScheduleDependenciesUsesTupleKeys(t *testing.T) {
+	keys := []dependencyKey{
+		{"a", "z"},
+		{"a"},
+		{"a", "aa"},
+		{"A"},
+	}
+	order, cycle := scheduleDependencies(keys, nil)
+	if len(cycle) != 0 {
+		t.Fatalf("unexpected cycle: %v", cycle)
+	}
+	want := []int{3, 1, 2, 0}
+	if !reflect.DeepEqual(order, want) {
+		t.Fatalf("schedule = %v, want %v", order, want)
+	}
+}
+
+func TestScheduleDependenciesReportsActualCanonicalCycles(t *testing.T) {
+	tests := []struct {
+		name  string
+		keys  []string
+		edges [][2]string
+		want  []string
+	}{
+		{
+			name:  "self cycle",
+			keys:  []string{"self"},
+			edges: [][2]string{{"self", "self"}},
+			want:  []string{"self", "self"},
+		},
+		{
+			name: "multi-node cycle excludes blocked dependent",
+			keys: []string{"blocked", "cycle-b", "cycle-a"},
+			edges: [][2]string{
+				{"cycle-a", "cycle-b"},
+				{"cycle-b", "cycle-a"},
+				{"cycle-b", "blocked"},
+			},
+			want: []string{"cycle-a", "cycle-b", "cycle-a"},
+		},
+	}
+
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			keys, edges, indexes := dependencyGraph(test.keys, test.edges)
+			order, cycle := scheduleDependencies(keys, edges)
+			if len(order) != 0 {
+				t.Fatalf("unexpected schedule: %v", dependencyNames(order, indexes))
+			}
+			if got := dependencyNames(cycle, indexes); !reflect.DeepEqual(got, test.want) {
+				t.Fatalf("cycle = %v, want %v", got, test.want)
+			}
+		})
+	}
+}
+
+func TestScheduleDependenciesIsStableAcrossInsertionPermutations(t *testing.T) {
+	edges := [][2]string{
+		{"base", "left"}, {"base", "right"},
+		{"left", "sink"}, {"right", "sink"},
+	}
+	permutations := [][]string{
+		{"sink", "right", "base", "left"},
+		{"left", "base", "sink", "right"},
+		{"right", "left", "base", "sink"},
+	}
+	for i, permutation := range permutations {
+		keys, permutedEdges, indexes := dependencyGraph(permutation, edges)
+		if i%2 != 0 {
+			reverseDependencyEdges(permutedEdges)
+		}
+		order, cycle := scheduleDependencies(keys, permutedEdges)
+		if len(cycle) != 0 {
+			t.Fatalf("permutation %d returned cycle %v", i, dependencyNames(cycle, indexes))
+		}
+		if got, want := dependencyNames(order, indexes), []string{"base", "left", "right", "sink"}; !reflect.DeepEqual(got, want) {
+			t.Fatalf("permutation %d schedule = %v, want %v", i, got, want)
+		}
+	}
+
+	cycleEdges := [][2]string{{"b", "a"}, {"a", "b"}, {"b", "blocked"}}
+	cyclePermutations := [][]string{{"blocked", "b", "a"}, {"a", "blocked", "b"}, {"b", "a", "blocked"}}
+	for i, permutation := range cyclePermutations {
+		keys, permutedEdges, indexes := dependencyGraph(permutation, cycleEdges)
+		if i%2 != 0 {
+			reverseDependencyEdges(permutedEdges)
+		}
+		order, cycle := scheduleDependencies(keys, permutedEdges)
+		if len(order) != 0 {
+			t.Fatalf("cycle permutation %d returned schedule %v", i, dependencyNames(order, indexes))
+		}
+		if got, want := dependencyNames(cycle, indexes), []string{"a", "b", "a"}; !reflect.DeepEqual(got, want) {
+			t.Fatalf("cycle permutation %d returned %v, want %v", i, got, want)
+		}
+	}
+}
+
+func dependencyGraph(nodeNames []string, namedEdges [][2]string) ([]dependencyKey, []dependencyEdge, map[int]string) {
+	keys := make([]dependencyKey, len(nodeNames))
+	indexes := make(map[string]int, len(nodeNames))
+	for i, name := range nodeNames {
+		keys[i] = dependencyKey{name}
+		indexes[name] = i
+	}
+	edges := make([]dependencyEdge, len(namedEdges))
+	for i, edge := range namedEdges {
+		edges[i] = dependencyEdge{prerequisite: indexes[edge[0]], dependent: indexes[edge[1]]}
+	}
+	byIndex := make(map[int]string, len(nodeNames))
+	for name, index := range indexes {
+		byIndex[index] = name
+	}
+	return keys, edges, byIndex
+}
+
+func dependencyNames(nodes []int, names map[int]string) []string {
+	result := make([]string, len(nodes))
+	for i, node := range nodes {
+		result[i] = names[node]
+	}
+	return result
+}
+
+func reverseDependencyEdges(edges []dependencyEdge) {
+	for i, j := 0, len(edges)-1; i < j; i, j = i+1, j-1 {
+		edges[i], edges[j] = edges[j], edges[i]
+	}
+}