diff --git a/wizard-work/beam/test_topo_beam.py b/wizard-work/beam/test_topo_beam.py
new file mode 100644
index 0000000..f8d54d1
--- /dev/null
+++ b/wizard-work/beam/test_topo_beam.py
@@ -0,0 +1,41 @@
+import sys
+sys.path.insert(0, "/root/.hermes/wizard-outputs/beam")
+from topo import topo_sort, has_cycle, CycleError
+
+def test_empty():
+    assert topo_sort([]) == []
+
+def test_single():
+    assert topo_sort([("a", [])]) == ["a"]
+
+def test_linear():
+    assert topo_sort([("b", ["a"]), ("c", ["b"])]) == ["a", "b", "c"]
+
+def test_diamond():
+    r = topo_sort([("d", ["b", "c"]), ("b", ["a"]), ("c", ["a"])])
+    assert r[0] == "a" and r[-1] == "d"
+    assert r.index("b") < r.index("c")
+
+def test_stability():
+    assert topo_sort([("x", []), ("y", []), ("z", [])]) == ["x", "y", "z"]
+
+def test_cycle():
+    try:
+        topo_sort([("a", ["b"]), ("b", ["a"])])
+        assert False
+    except CycleError as e:
+        assert set(e.remaining) == {"a", "b"}
+
+def test_self_loop():
+    assert has_cycle([("a", ["a"])])
+
+def test_no_cycle():
+    assert not has_cycle([("a", []), ("b", ["a"])])
+
+def test_dup_preds():
+    assert topo_sort([("b", ["a", "a"])]) == ["a", "b"]
+
+if __name__ == "__main__":
+    for name in [n for n in globals() if n.startswith("test_")]:
+        globals()[name]()
+    print("ALL TESTS PASSED")
diff --git a/wizard-work/beam/topo.py b/wizard-work/beam/topo.py
new file mode 100644
index 0000000..16c7f71
--- /dev/null
+++ b/wizard-work/beam/topo.py
@@ -0,0 +1,71 @@
+"""Deterministic topological sort (Kahn's algorithm) with cycle detection.
+
+Nodes are arbitrary hashable values. Input is an iterable of (node, predecessors)
+pairs where predecessors are the nodes that must come before node. Ordering
+among independent nodes is stable by input order of first appearance (earliest
+discovered zero-indegree / ready node wins).
+
+Returns a list of nodes in topological order. Raises CycleError if the graph
+contains a cycle, listing the remaining (unsorted) nodes.
+"""
+from __future__ import annotations
+
+import heapq
+from collections import OrderedDict
+
+
+class CycleError(Exception):
+    def __init__(self, remaining):
+        self.remaining = tuple(remaining)
+        super().__init__("cycle detected among: %r" % (self.remaining,))
+
+
+def topo_sort(edges):
+    order = OrderedDict()   # node -> discovery index
+    preds = {}
+    succs = {}
+    indeg = {}
+
+    idx = 0
+    def discover(n):
+        nonlocal idx
+        if n not in order:
+            order[n] = idx
+            idx += 1
+            preds[n] = set()
+            succs[n] = []
+            indeg[n] = 0
+
+    for node, predecessors in edges:
+        discover(node)
+        for p in predecessors:
+            discover(p)
+            if p not in preds[node]:
+                preds[node].add(p)
+                succs[p].append(node)
+                indeg[node] += 1
+
+    # Kahn with a min-heap keyed by discovery index for global stability.
+    heap = [(order[n], n) for n in order if indeg[n] == 0]
+    heapq.heapify(heap)
+    result = []
+    while heap:
+        _, n = heapq.heappop(heap)
+        result.append(n)
+        for s in succs[n]:
+            indeg[s] -= 1
+            if indeg[s] == 0:
+                heapq.heappush(heap, (order[s], s))
+
+    if len(result) != len(order):
+        remaining = [n for n in order if n not in set(result)]
+        raise CycleError(remaining)
+    return result
+
+
+def has_cycle(edges):
+    try:
+        topo_sort(edges)
+        return False
+    except CycleError:
+        return True