beam: Q61 -- materialise each dependency iterable once, resolve the module locally, drop the dead first pass

topo_sort read graph.values() twice, so a dependency delivered as a generator,
map, filter or reverse iterator was exhausted by the first walk and the node
kept an empty dependency set. The result was a successful call with a wrong
order -- and, measured, a 3-cycle delivered as generators reported as a
successful order with cycle=None.

Every dependency sequence is now materialised exactly once, up front; every
later pass reads that copy, so double-consumption is structurally impossible.
Removed the unreachable first DFS pass in the cycle path (ruff F841 start/path/
res) leaving one find_back_edge; the self-loop case is explicit.

test_toposort.py resolved the module from /root/.hermes/wizard-outputs/beam,
a host path ahead of the test's own directory: a module that refuses to import
beside it left the suite green. It now resolves from Path(__file__).parent and
asserts the imported file's identity. 242 checks: 9 graph shapes x 7 delivery
forms, cycles in all 7, plus a guard that the duplicate toposort/ copy has not
drifted.

Falsified both ways: the suite fails on blob 4da0d8e and on the one-token
mutation tuple(ds) -> ds. CHECK rc 0 (85 unittests OK), verify.py 8/8.

wizard-work/beam/test_toposort.py

@@ -1,46 +1,171 @@
+"""Tests for toposort.topo_sort.
+
+Runs two ways, both from this directory only:
+    python3 test_toposort.py
+    python3 -m unittest discover -p 'test_*.py'
+
+Assertions execute at import (the convention this file already used), so a
+failure surfaces under `unittest discover` as an import error rather than a
+silent pass.
+
+Q61 / 2026-10-24: the module is resolved from THIS file's directory and from
+nowhere else. The previous `sys.path.insert(0, '/root/.hermes/wizard-outputs/beam')`
+measured a host copy rather than the committed bytes, so the gate could pass
+while the repository's blob was broken. `MODULE_PATH` is asserted below.
+"""
+import pathlib
 import sys
-sys.path.insert(0, '/root/.hermes/wizard-outputs/beam')
+
+HERE = pathlib.Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE))
+
+import toposort as toposort_module
 from toposort import topo_sort
 
-def check(graph, expected_order=None):
+# The module under test must be the committed file next to this test.
-    r = topo_sort(graph)
+MODULE_PATH = pathlib.Path(toposort_module.__file__).resolve()
-    if expected_order is not None:
+assert MODULE_PATH == (HERE / "toposort.py"), (MODULE_PATH, HERE)
-        assert r.cycle is None, (graph, r)
+
-        assert r.sorted == expected_order, (graph, r.sorted, expected_order)
+_checks = 0
-    return r
+
+
+def eq(got, expected, what):
+    global _checks
+    _checks += 1
+    assert got == expected, f"{what}: got {got!r}, expected {expected!r}"
+
+
+def ok(cond, what):
+    global _checks
+    _checks += 1
+    assert cond, what
+
+
+def order_of(spec, take):
+    """Build a graph from `spec`, passing every dependency sequence through `take`."""
+    return {n: (() if ds is None else take(ds)) for n, ds in spec.items()}
+
+
+def check_valid(result, spec, what):
+    """result must be a valid topological order of `spec` (deps before dependents)."""
+    global _checks
+    _checks += 1
+    assert result.cycle is None, f"{what}: unexpected cycle {result.cycle!r}"
+    order = result.sorted
+    assert order is not None, f"{what}: sorted is None with no cycle"
+    nodes = set(spec)
+    for ds in spec.values():
+        nodes.update(ds or ())
+    assert sorted(order) == sorted(nodes), f"{what}: not a permutation: {order!r}"
+    pos = {n: i for i, n in enumerate(order)}
+    for node, ds in spec.items():
+        for dep in (ds or ()):
+            assert pos[dep] < pos[node], f"{what}: {dep!r} after {node!r} in {order!r}"
+
+
+def check_cycle(result, spec, what):
+    """result.cycle must be a real cycle: consecutive edges exist, last -> first."""
+    global _checks
+    _checks += 1
+    assert result.sorted is None, f"{what}: expected no order, got {result.sorted!r}"
+    cyc = result.cycle
+    assert cyc, f"{what}: empty cycle"
+    for i, u in enumerate(cyc):
+        v = cyc[(i + 1) % len(cyc)]
+        assert v in (spec.get(u) or ()), f"{what}: no edge {u!r}->{v!r} in {cyc!r}"
+
+
+# ---------------------------------------------------------------- baseline cases
+r = topo_sort({'a': ['b'], 'b': []})
+eq(r.sorted, ['b', 'a'], "simple")
+eq(r.cycle, None, "simple cycle")
+
+eq(topo_sort({'a': [], 'b': []}).sorted, ['a', 'b'], "disconnected")
+eq(topo_sort({}).sorted, [], "empty")
+
+DIAMOND = {'a': ['b', 'c'], 'b': ['d'], 'c': ['d'], 'd': []}
+d = topo_sort(DIAMOND)
+eq(d.cycle, None, "diamond cycle")
+check_valid(d, DIAMOND, "diamond")
+
+two = topo_sort({'a': ['b'], 'b': ['a']})
+eq(two.sorted, None, "2-cycle sorted")
+check_cycle(two, {'a': ['b'], 'b': ['a']}, "2-cycle")
+
+eq(topo_sort({'a': ['a']}).cycle, ['a'], "self loop")
+eq(topo_sort({'a': ['b']}).sorted, ['b', 'a'], "successor only")
+
+# ------------------------------------------------- Q61(a): iterator dependencies
+# Specs are written with plain tuples; `take` decides how each dependency
+# sequence is delivered. Every delivery form must produce the SAME order, and
+# that order must be valid -- not merely equal to a wrong reference.
+SPECS = {
+    "single":     {'a': ('b',), 'b': ()},
+    "chain3":     {'c': ('b',), 'b': ('d',), 'd': ()},
+    "chain6":     {'f': ('e',), 'e': ('d',), 'd': ('c',), 'c': ('b',), 'b': ('a',), 'a': ()},
+    "diamond":    DIAMOND,
+    "fork":       {'root': ('l', 'r'), 'l': (), 'r': ()},
+    "join":       {'a': ('x',), 'b': ('x',), 'c': ('a', 'b'), 'x': ()},
+    "multi":      {'a': ('b',), 'b': (), 'c': ('d',), 'd': (), 'e': ()},
+    "missingdep": {'a': ('z',)},
+    "empty":      {},
+}
+
+TAKERS = {
+    "tuple":         tuple,
+    "list":          list,
+    "generator":     lambda ds: (d for d in ds),
+    "map_object":    lambda ds: map(str, ds),
+    "filter":        lambda ds: filter(lambda d: True, ds),
+    "reversed_iter": lambda ds: reversed(list(ds)),
+    "set":           set,
+}
+
+for name, spec in SPECS.items():
+    reference = topo_sort(order_of(spec, tuple))
+    check_valid(reference, spec, f"{name}/tuple")
+    for tname, take in TAKERS.items():
+        result = topo_sort(order_of(spec, take))
+        eq(result.cycle, None, f"{name}/{tname} cycle")
+        eq(result.sorted, reference.sorted, f"{name}/{tname} order")
+        check_valid(result, spec, f"{name}/{tname}")
+
+# The exact repro from Q61: a two-node graph where the generator was exhausted
+# by the first pass and the result was a silent, wrong 'success'.
+gen = topo_sort({'a': iter(['b']), 'b': []})
+eq(gen.sorted, ['b', 'a'], "Q61 repro: generator dependency")
+
+# Cycles must survive iterator delivery too -- and still be reported as cycles.
+CYCLES = {
+    "self":  {'a': ('a',)},
+    "two":   {'a': ('b',), 'b': ('a',)},
+    "three": {'a': ('b',), 'b': ('c',), 'c': ('a',)},
+    "tail":  {'head': ('a',), 'a': ('b',), 'b': ('a',)},
+}
+for name, spec in CYCLES.items():
+    for tname, take in TAKERS.items():
+        check_cycle(topo_sort(order_of(spec, take)), spec, f"{name}/{tname}")
+
+eq(topo_sort({'a': iter(['a'])}).cycle, ['a'], "self loop as iterator")
+
+# ------------------------------------------------------- determinism / stability
+for _ in range(3):
+    eq(topo_sort(order_of(SPECS["join"], list)).sorted,
+       topo_sort(order_of(SPECS["join"], tuple)).sorted, "repeat determinism")
+
+# ------------------------------------------- Q61(b) sibling copy drift guard
+# wizard-work/beam carries a second, historically byte-identical copy at
+# toposort/toposort.py. Two copies of a fixed bug is how it comes back; assert
+# they agree rather than trusting that they do.
+SIBLING = HERE / "toposort" / "toposort.py"
+if SIBLING.exists():
+    ok(SIBLING.read_bytes() == (HERE / "toposort.py").read_bytes(),
+       f"sibling copy differs from toposort.py: {SIBLING}")
+
 
-# DAG simple
-check({'a': ['b'], 'b': []}, ['b','a'])
-# disconnected
-check({'a': [], 'b': []}, ['a','b'])
-# empty
-check({}, [])
-# diamond
-check({'a':['b','c'],'b':['d'],'c':['d'],'d':[]}, ['d','b','c','a'] if False else None) or True
-r = topo_sort({'a':['b','c'],'b':['d'],'c':['d'],'d':[]})
-assert r.cycle is None
-# verify validity
-pos = {n:i for i,n in enumerate(r.sorted)}
-for n,deps in {'a':['b','c'],'b':['d'],'c':['d'],'d':[]}.items():
-    for d in deps:
-        assert pos[d] < pos[n]
-# cycle
-r = topo_sort({'a':['b'],'b':['a']})
-assert r.sorted is None
-assert r.cycle is not None
-# cycle is valid: each consecutive edge exists and last->first
-g={'a':['b'],'b':['a']}
-cyc=r.cycle
-for i in range(len(cyc)):
-    u=cyc[i]; v=cyc[(i+1)%len(cyc)]
-    assert v in g.get(u,[]), (u,v,cyc)
-# self loop
-r = topo_sort({'a':['a']})
-assert r.sorted is None and r.cycle == ['a']
-# node only as successor
-r = topo_sort({'a':['b']})
-assert r.sorted == ['b','a']
 def test_all():
-    pass
+    """Kept so pytest/unittest see a callable; module-level asserts already ran."""
+    return _checks
 
-print("ALL PASS")
+
+print(f"ALL PASS ({_checks} checks)")

wizard-work/beam/toposort.py

@@ -8,10 +8,17 @@ A node's dependencies must appear before it in the output. Ties broken by
 node's natural ordering (so results are deterministic). If a cycle exists,
 result.sorted is None and result.cycle is a list of nodes forming the cycle
 (in dependency order, last -> first closing the loop).
+
+The declared contract is `Iterable`, not "re-iterable": a dependency set may
+arrive as a generator, a map object, a filter, or any other one-shot iterator.
+Every dependency sequence is therefore materialised exactly once, up front, and
+all later passes read that single materialised copy. Iterating `graph.values()`
+twice would silently exhaust a generator, leaving the node with an empty
+dependency set, in-degree 0 and a wrong-but-successful ordering.
 """
 from __future__ import annotations
 
-from collections import defaultdict, deque
+from collections import defaultdict
 from dataclasses import dataclass
 from typing import Any, Iterable, Mapping
 
@@ -23,25 +30,21 @@ class TopoResult:
 
 
 def topo_sort(graph: Mapping[Any, Iterable[Any]]) -> TopoResult:
-    # Normalize: ensure every referenced node exists as a key.
+    # Materialise each dependency iterable once. `None` means "no dependencies".
-    nodes: set[Any] = set(graph.keys())
+    # This is the only place any dependency sequence is consumed.
-    for deps in graph.values():
+    deps_src: dict[Any, tuple[Any, ...]] = {
-        if deps is None:
+        n: () if ds is None else tuple(ds) for n, ds in graph.items()
-            continue
+    }
-        for d in deps:
-            nodes.add(d)
 
-    # adjacency: node -> set of dependencies
+    # Normalise: every referenced node exists as a key, even if it has no entry.
+    nodes: set[Any] = set(graph.keys())
+    for ds in deps_src.values():
+        nodes.update(ds)
+
+    # adjacency: node -> set of dependencies (a self-dependency is a 1-cycle)
     deps_of: dict[Any, set[Any]] = {n: set() for n in nodes}
-    for n, ds in graph.items():
+    for n, ds in deps_src.items():
-        if ds is None:
+        deps_of[n].update(ds)
-            ds = []
-        for d in ds:
-            if d == n:
-                # self-loop is a cycle of length 1
-                deps_of[n].add(d)
-            else:
-                deps_of[n].add(d)
 
     # Kahn's algorithm with a sorted ready queue for determinism.
     # in-degree = number of unprocessed dependencies
@@ -72,105 +75,62 @@ def topo_sort(graph: Mapping[Any, Iterable[Any]]) -> TopoResult:
     if len(out) == len(nodes):
         return TopoResult(sorted=out, cycle=None)
 
-    # Cycle exists. Reconstruct a cycle path.
+    # A cycle exists. Everything Kahn could not emit is in a cycle or reaches
-    # Nodes not emitted are in cycles. Pick the smallest unemitted node.
+    # one, so a DFS restricted to those nodes is guaranteed to find a back edge.
-    unemitted = [n for n in nodes if n not in set(out)]
+    emitted = set(out)
-    try:
+    unemitted = [n for n in nodes if n not in emitted]
-        start = min(unemitted)
-    except TypeError:
-        start = unemitted[0]
 
-    # Walk dependency edges among unemitted nodes to find a cycle.
+    color: dict[Any, int] = {n: 0 for n in nodes}  # 0 unvisited, 1 visiting, 2 done
-    # Use DFS with color marking.
-    color: dict[Any, int] = {n: 0 for n in nodes}  # 0 unvisited,1 visiting,2 done
     parent: dict[Any, Any] = {}
 
-    def dfs(u):
+    def find_back_edge(u: Any) -> tuple[Any, Any] | None:
+        """DFS from u; return the (node, ancestor) back edge that closes a cycle."""
         color[u] = 1
         for v in sorted(deps_of[u], key=_key):
-            if color.get(v, 0) == 0:
+            state = color.get(v, 0)
+            if state == 0:
                 parent[v] = u
-                r = dfs(v)
+                found = find_back_edge(v)
-                if r is not None:
+                if found is not None:
-                    return r
+                    return found
-            elif color.get(v, 0) == 1:
+            elif state == 1:
-                # found cycle: v is ancestor of u
+                return (u, v)
-                # reconstruct v -> ... -> u -> v
-                cycle_nodes = [v]
-                cur = u
-                while cur != v and cur is not None:
-                    cycle_nodes.append(cur)
-                    cur = parent.get(cur)
-                    if cur is None:
-                        break
-                cycle_nodes.reverse()
-                # ensure v at front already; make path v...u
-                # cycle_nodes currently [v, ..., u]? Let's rebuild cleanly.
-                path = [v]
-                cur = u
-                chain = [u]
-                while cur != v and cur is not None:
-                    cur = parent.get(cur)
-                    if cur is not None and cur != v:
-                        chain.append(cur)
-                chain.reverse()
-                # chain now from v's child ... u? Reconstruct differently below.
-                return ("FOUND", v, u)
         color[u] = 2
         return None
 
-    res = None
+    back: tuple[Any, Any] | None = None
     for s in sorted(unemitted, key=_key):
-        if color[s] == 0:
+        if color.get(s, 0) == 0:
-            parent[s] = None  # type: ignore
+            parent[s] = None
-            r = dfs(s)
+            back = find_back_edge(s)
-            if r is not None:
+            if back is not None:
-                res = r
                 break
 
-    # Reconstruct cycle path robustly using parent pointers from the found edge.
+    if back is None:
-    # Find the back edge (u -> v) where v is an ancestor.
+        # Unreachable for a real cycle; never report a silent success instead.
-    back_u = back_v = None
+        return TopoResult(sorted=None, cycle=list(unemitted[:1]))
-    # Re-run a focused search to capture back edge.
-    color2: dict[Any, int] = {n: 0 for n in nodes}
-    parent2: dict[Any, Any] = {}
 
-    def dfs2(u):
+    back_u, back_v = back
-        nonlocal back_u, back_v
+    if back_u == back_v:
-        color2[u] = 1
+        # self-loop: a cycle of length 1
-        for v in sorted(deps_of[u], key=_key):
+        return TopoResult(sorted=None, cycle=[back_v])
-            if color2.get(v, 0) == 0:
-                parent2[v] = u
-                r = dfs2(v)
-                if r:
-                    return r
-            elif color2.get(v, 0) == 1:
-                back_u, back_v = u, v
-                return True
-        color2[u] = 2
-        return False
 
-    for s in sorted(unemitted, key=_key):
+    # back_u depends on back_v, and parent[x] = y means "y depends on x", so
-        if color2[s] == 0:
+    # walking parents from back_u reaches back_v. Reversed, that walk is the
-            parent2[s] = None  # type: ignore
+    # cycle in dependency order: every node is followed by one of its own deps,
-            if dfs2(s):
+    # and the last node depends on the first, closing the loop.
-                break
+    path: list[Any] = [back_u]
-
+    cur = parent.get(back_u)
-    # Build path from back_v to back_u via parent2, then close.
-    path = []
-    cur = back_u
     while cur is not None and cur != back_v:
         path.append(cur)
-        cur = parent2.get(cur)
+        cur = parent.get(cur)
-    if cur == back_v:
+    if cur != back_v:
-        path.append(back_v)
+        # Parent chain broken (should not happen); degrade to a live node
-        path.reverse()
+        # rather than inventing an edge that does not exist.
-        # path: back_v ... back_u
+        return TopoResult(sorted=None, cycle=list(unemitted[:1]))
-        cycle = path  # back_v -> ... -> back_u, and edge back_u -> back_v closes
+    path.append(back_v)
-    else:
+    path.reverse()
-        cycle = [back_v, back_u] if back_v is not None else unemitted[:1]
+    return TopoResult(sorted=None, cycle=path)
-
-    return TopoResult(sorted=None, cycle=cycle)
 
 
 class _Sortable:

wizard-work/beam/toposort/toposort.py

@@ -8,10 +8,17 @@ A node's dependencies must appear before it in the output. Ties broken by
 node's natural ordering (so results are deterministic). If a cycle exists,
 result.sorted is None and result.cycle is a list of nodes forming the cycle
 (in dependency order, last -> first closing the loop).
+
+The declared contract is `Iterable`, not "re-iterable": a dependency set may
+arrive as a generator, a map object, a filter, or any other one-shot iterator.
+Every dependency sequence is therefore materialised exactly once, up front, and
+all later passes read that single materialised copy. Iterating `graph.values()`
+twice would silently exhaust a generator, leaving the node with an empty
+dependency set, in-degree 0 and a wrong-but-successful ordering.
 """
 from __future__ import annotations
 
-from collections import defaultdict, deque
+from collections import defaultdict
 from dataclasses import dataclass
 from typing import Any, Iterable, Mapping
 
@@ -23,25 +30,21 @@ class TopoResult:
 
 
 def topo_sort(graph: Mapping[Any, Iterable[Any]]) -> TopoResult:
-    # Normalize: ensure every referenced node exists as a key.
+    # Materialise each dependency iterable once. `None` means "no dependencies".
-    nodes: set[Any] = set(graph.keys())
+    # This is the only place any dependency sequence is consumed.
-    for deps in graph.values():
+    deps_src: dict[Any, tuple[Any, ...]] = {
-        if deps is None:
+        n: () if ds is None else tuple(ds) for n, ds in graph.items()
-            continue
+    }
-        for d in deps:
-            nodes.add(d)
 
-    # adjacency: node -> set of dependencies
+    # Normalise: every referenced node exists as a key, even if it has no entry.
+    nodes: set[Any] = set(graph.keys())
+    for ds in deps_src.values():
+        nodes.update(ds)
+
+    # adjacency: node -> set of dependencies (a self-dependency is a 1-cycle)
     deps_of: dict[Any, set[Any]] = {n: set() for n in nodes}
-    for n, ds in graph.items():
+    for n, ds in deps_src.items():
-        if ds is None:
+        deps_of[n].update(ds)
-            ds = []
-        for d in ds:
-            if d == n:
-                # self-loop is a cycle of length 1
-                deps_of[n].add(d)
-            else:
-                deps_of[n].add(d)
 
     # Kahn's algorithm with a sorted ready queue for determinism.
     # in-degree = number of unprocessed dependencies
@@ -72,105 +75,62 @@ def topo_sort(graph: Mapping[Any, Iterable[Any]]) -> TopoResult:
     if len(out) == len(nodes):
         return TopoResult(sorted=out, cycle=None)
 
-    # Cycle exists. Reconstruct a cycle path.
+    # A cycle exists. Everything Kahn could not emit is in a cycle or reaches
-    # Nodes not emitted are in cycles. Pick the smallest unemitted node.
+    # one, so a DFS restricted to those nodes is guaranteed to find a back edge.
-    unemitted = [n for n in nodes if n not in set(out)]
+    emitted = set(out)
-    try:
+    unemitted = [n for n in nodes if n not in emitted]
-        start = min(unemitted)
-    except TypeError:
-        start = unemitted[0]
 
-    # Walk dependency edges among unemitted nodes to find a cycle.
+    color: dict[Any, int] = {n: 0 for n in nodes}  # 0 unvisited, 1 visiting, 2 done
-    # Use DFS with color marking.
-    color: dict[Any, int] = {n: 0 for n in nodes}  # 0 unvisited,1 visiting,2 done
     parent: dict[Any, Any] = {}
 
-    def dfs(u):
+    def find_back_edge(u: Any) -> tuple[Any, Any] | None:
+        """DFS from u; return the (node, ancestor) back edge that closes a cycle."""
         color[u] = 1
         for v in sorted(deps_of[u], key=_key):
-            if color.get(v, 0) == 0:
+            state = color.get(v, 0)
+            if state == 0:
                 parent[v] = u
-                r = dfs(v)
+                found = find_back_edge(v)
-                if r is not None:
+                if found is not None:
-                    return r
+                    return found
-            elif color.get(v, 0) == 1:
+            elif state == 1:
-                # found cycle: v is ancestor of u
+                return (u, v)
-                # reconstruct v -> ... -> u -> v
-                cycle_nodes = [v]
-                cur = u
-                while cur != v and cur is not None:
-                    cycle_nodes.append(cur)
-                    cur = parent.get(cur)
-                    if cur is None:
-                        break
-                cycle_nodes.reverse()
-                # ensure v at front already; make path v...u
-                # cycle_nodes currently [v, ..., u]? Let's rebuild cleanly.
-                path = [v]
-                cur = u
-                chain = [u]
-                while cur != v and cur is not None:
-                    cur = parent.get(cur)
-                    if cur is not None and cur != v:
-                        chain.append(cur)
-                chain.reverse()
-                # chain now from v's child ... u? Reconstruct differently below.
-                return ("FOUND", v, u)
         color[u] = 2
         return None
 
-    res = None
+    back: tuple[Any, Any] | None = None
     for s in sorted(unemitted, key=_key):
-        if color[s] == 0:
+        if color.get(s, 0) == 0:
-            parent[s] = None  # type: ignore
+            parent[s] = None
-            r = dfs(s)
+            back = find_back_edge(s)
-            if r is not None:
+            if back is not None:
-                res = r
                 break
 
-    # Reconstruct cycle path robustly using parent pointers from the found edge.
+    if back is None:
-    # Find the back edge (u -> v) where v is an ancestor.
+        # Unreachable for a real cycle; never report a silent success instead.
-    back_u = back_v = None
+        return TopoResult(sorted=None, cycle=list(unemitted[:1]))
-    # Re-run a focused search to capture back edge.
-    color2: dict[Any, int] = {n: 0 for n in nodes}
-    parent2: dict[Any, Any] = {}
 
-    def dfs2(u):
+    back_u, back_v = back
-        nonlocal back_u, back_v
+    if back_u == back_v:
-        color2[u] = 1
+        # self-loop: a cycle of length 1
-        for v in sorted(deps_of[u], key=_key):
+        return TopoResult(sorted=None, cycle=[back_v])
-            if color2.get(v, 0) == 0:
-                parent2[v] = u
-                r = dfs2(v)
-                if r:
-                    return r
-            elif color2.get(v, 0) == 1:
-                back_u, back_v = u, v
-                return True
-        color2[u] = 2
-        return False
 
-    for s in sorted(unemitted, key=_key):
+    # back_u depends on back_v, and parent[x] = y means "y depends on x", so
-        if color2[s] == 0:
+    # walking parents from back_u reaches back_v. Reversed, that walk is the
-            parent2[s] = None  # type: ignore
+    # cycle in dependency order: every node is followed by one of its own deps,
-            if dfs2(s):
+    # and the last node depends on the first, closing the loop.
-                break
+    path: list[Any] = [back_u]
-
+    cur = parent.get(back_u)
-    # Build path from back_v to back_u via parent2, then close.
-    path = []
-    cur = back_u
     while cur is not None and cur != back_v:
         path.append(cur)
-        cur = parent2.get(cur)
+        cur = parent.get(cur)
-    if cur == back_v:
+    if cur != back_v:
-        path.append(back_v)
+        # Parent chain broken (should not happen); degrade to a live node
-        path.reverse()
+        # rather than inventing an edge that does not exist.
-        # path: back_v ... back_u
+        return TopoResult(sorted=None, cycle=list(unemitted[:1]))
-        cycle = path  # back_v -> ... -> back_u, and edge back_u -> back_v closes
+    path.append(back_v)
-    else:
+    path.reverse()
-        cycle = [back_v, back_u] if back_v is not None else unemitted[:1]
+    return TopoResult(sorted=None, cycle=path)
-
-    return TopoResult(sorted=None, cycle=cycle)
 
 
 class _Sortable: