{
  "handle": "DAG",
  "data_schema": {
    "type": "object",
    "required": [
      "nodes",
      "edges",
      "root_id"
    ],
    "properties": {
      "nodes": {
        "type": "array",
        "description": "List of task nodes"
      },
      "edges": {
        "type": "array",
        "description": "Dependency arrows (Task A -> Task B)"
      },
      "root_id": {
        "type": "string",
        "description": "Entry point(s) for execution"
      }
    }
  },
  "mechanism": "A directed acyclic graph {{topology}} that allows branching ({{parallelize}}) and merging, but forbids cycles. It models complex dependency chains where tasks can run concurrently but must respect precedence.",
  "gloss": "Directed acyclic dependency graph",
  "_meta": {
    "ring": 2,
    "tier": 1,
    "supersedes": [
      "sema:DAG#mh:SHA-256:ed37a1e0310857feba371491e4652f9a142905af341adbc67e6386c5b3c1672f",
      "sema:DAG#mh:SHA-256:ed81568cef305d3f4f39c7ef157bfc4c74ef721c8ad1e9001a2d11793ce936df",
      "sema:DAG#mh:SHA-256:cb54c9360f063d839412e33158dc205c02af684d85132f6a982caba17274f253"
    ],
    "path": [
      "Infrastructure",
      "Data Structures"
    ]
  },
  "invariants": [
    "Acyclic: no path leads from a node back to itself.",
    "Edges are directed.",
    "Rooted: exactly one node has no predecessor, named by `root_id`.",
    "Nodes with no directed path between them may run concurrently."
  ],
  "sema_id": "sema:DAG#mh:SHA-256:ed5b6bdbe8d785f1dceb6cc1c7020d9c2340be7b507a3678da2da58211e455aa",
  "sema_ref": "DAG#ed5b",
  "sema_stub": "ed5b",
  "failure_modes": [
    "Cycle on insert: an added edge closes a loop, which the acyclicity invariant forbids and which must be detected at insertion rather than at traversal.",
    "False precedence: an edge asserts a dependency that does not exist, serialising work that could have run concurrently."
  ],
  "dependencies": {
    "references": {
      "parallelize": "sema:Parallelize#mh:SHA-256:c1c795defd6f4f9cab2823cf832ae91f5f0651bef082108bb494047d91be04a1",
      "topology": "sema:Topology#mh:SHA-256:58ad1ff07863b0fbf1250185232c48d8815752e4ce4f32a971166a56be297467"
    }
  },
  "sema_layer": "Infrastructure",
  "sema_category": "Data Structures",
  "used_by": {
    "composes_with": {
      "GraphOfThought": "sema:GraphOfThought#mh:SHA-256:aff044b7909bc26511c42ece0cf090bd4d1f82431a5728e94fedcd2ad9733160"
    }
  }
}