diff --git a/wizard-work/beam/toposort.py b/wizard-work/beam/toposort.py
new file mode 100644
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+++ b/wizard-work/beam/toposort.py
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+"""Topological sort with deterministic ordering and cycle-path reporting.
+
+Public API:
+    topo_sort(graph) -> TopoResult
+where graph is a mapping node -> iterable of dependencies (edges node -> dep).
+
+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).
+"""
+from __future__ import annotations
+
+from collections import defaultdict, deque
+from dataclasses import dataclass
+from typing import Any, Iterable, Mapping
+
+
+@dataclass(frozen=True)
+class TopoResult:
+    sorted: list[Any] | None
+    cycle: list[Any] | None
+
+
+def topo_sort(graph: Mapping[Any, Iterable[Any]]) -> TopoResult:
+    # Normalize: ensure every referenced node exists as a key.
+    nodes: set[Any] = set(graph.keys())
+    for deps in graph.values():
+        for d in deps:
+            nodes.add(d)
+
+    # adjacency: node -> set of dependencies
+    deps_of: dict[Any, set[Any]] = {n: set() for n in nodes}
+    for n, ds in graph.items():
+        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
+    in_deg: dict[Any, int] = {n: len(deps_of[n]) for n in nodes}
+    # reverse adjacency: dep -> dependents
+    dependents: dict[Any, list[Any]] = defaultdict(list)
+    for n in nodes:
+        for d in deps_of[n]:
+            dependents[d].append(n)
+
+    # ready set as a min-heap via sorted list (nodes sortable; if not, fall back)
+    try:
+        ready = sorted((n for n in nodes if in_deg[n] == 0), key=_key)
+    except TypeError:
+        ready = [n for n in nodes if in_deg[n] == 0]
+    out: list[Any] = []
+    # We'll use a list as a priority queue by re-sorting on pop; fine for tests.
+    while ready:
+        # pop smallest
+        ready.sort(key=_key)
+        cur = ready.pop(0)
+        out.append(cur)
+        for dep in sorted(dependents[cur], key=_key):
+            in_deg[dep] -= 1
+            if in_deg[dep] == 0:
+                ready.append(dep)
+
+    if len(out) == len(nodes):
+        return TopoResult(sorted=out, cycle=None)
+
+    # Cycle exists. Reconstruct a cycle path.
+    # Nodes not emitted are in cycles. Pick the smallest unemitted node.
+    unemitted = [n for n in nodes if n not in set(out)]
+    try:
+        start = min(unemitted)
+    except TypeError:
+        start = unemitted[0]
+
+    # Walk dependency edges among unemitted nodes to find a cycle.
+    # 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):
+        color[u] = 1
+        for v in sorted(deps_of[u], key=_key):
+            if color.get(v, 0) == 0:
+                parent[v] = u
+                r = dfs(v)
+                if r is not None:
+                    return r
+            elif color.get(v, 0) == 1:
+                # found cycle: v is ancestor of u
+                # 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
+    for s in sorted(unemitted, key=_key):
+        if color[s] == 0:
+            parent[s] = None  # type: ignore
+            r = dfs(s)
+            if r is not None:
+                res = r
+                break
+
+    # Reconstruct cycle path robustly using parent pointers from the found edge.
+    # Find the back edge (u -> v) where v is an ancestor.
+    back_u = back_v = None
+    # 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):
+        nonlocal back_u, back_v
+        color2[u] = 1
+        for v in sorted(deps_of[u], key=_key):
+            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):
+        if color2[s] == 0:
+            parent2[s] = None  # type: ignore
+            if dfs2(s):
+                break
+
+    # 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)
+    if cur == back_v:
+        path.append(back_v)
+        path.reverse()
+        # path: back_v ... back_u
+        cycle = path  # back_v -> ... -> back_u, and edge back_u -> back_v closes
+    else:
+        cycle = [back_v, back_u] if back_v is not None else unemitted[:1]
+
+    return TopoResult(sorted=None, cycle=cycle)
+
+
+def _key(x):
+    tn = type(x).__name__
+    if isinstance(x, (set, frozenset)):
+        return (1, tn, repr(x), id(x))
+    try:
+        _ = x < x
+    except Exception:
+        return (1, tn, repr(x), id(x))
+    return (0, tn, x)
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