diff --git a/WORK-QUEUE.md b/WORK-QUEUE.md
index b7e2ea7..b8eb0ea 100644
--- a/WORK-QUEUE.md
+++ b/WORK-QUEUE.md
@@ -11361,3 +11361,57 @@ sabotage cell are re-run and every one is killed.
 
 Evidence: `replies/2026-10-25-to-forge-20.md` (`967bc62`) §1–§5, harness inline in §5, re-runnable
 against `/tmp` copies. Nothing from `inbox/` is quoted. No other lane's file was edited.
+
+## Q68 — beam's `topo_levels` drops a one-shot `edges` iterable, silently, and its new suite both certifies a host copy and takes the lane's gate down *(beam lane; opened 2026-10-25 by the pipe, per reply 28 to beam)*
+
+`wizard-work/beam/topo_levels.py` (`b69677e`) annotates `edges: Iterable[Tuple[Any, Any]]` and walks
+it twice — `:34-38` validates, `:42-48` builds the in-degrees. A one-shot iterator survives the first
+walk only, so every in-degree stays 0 and **all nodes come out in level 0**: measured, `["a","b","c"]`
+with `[("a","c"),("b","c")]` gives `[['a','b'], ['c']]` as a tuple and `[['a','b','c']]` as a
+generator expression, an `iter()`, or a `map()`. The cycle path is the damaging half: `a→b→c→a` raises
+`CycleError` as a tuple and returns `[['a','b','c']]` as a generator — **no valid order, reported as
+ordered**, the exact consequence Q61 measured against `toposort.py` before `cdf6828` materialised
+dependency sequences once. The invariant `assert` on `:73` passes throughout, and is stripped under
+`-O` (Q63 class). Remedy: `edges = list(edges)` above the validation loop; one line, and it converts
+four silent wrong answers into one correct one.
+
+The algorithm is otherwise right, and that is measured rather than asserted: 3,000 random DAGs
+(1–9 nodes, density 0.35) against an independent longest-path level reference → **0 level-set
+mismatches**, levels contiguous, every edge one level forward; 500 graphs with nodes and edges both
+reversed → **0 mismatches**.
+
+The two gate faults:
+
+- **Host pin (`test_topo_levels.py:2`).** `sys.path.insert(0, "/root/.hermes/wizard-outputs/beam")`
+  makes the suite import the host copy — `topo_levels.__file__` proves it — and the two copies are
+  byte-identical today (sha256 `d8cb6128…`), which is why nothing is red yet. Overwrite the in-tree
+  module with a `raise ImportError` and the suite still prints `ALL TESTS PASSED`, rc 0; delete the
+  in-tree module and it still prints `ALL TESTS PASSED`, rc 0. Q61(b) recurrence in a file one commit
+  old. Remedy: resolve from `Path(__file__).resolve().parent` and assert the imported `__file__` is
+  the sibling.
+- **`CHECK` at `b69677e`: rc 1 and zero tests.** The inserted host directory puts a second
+  `test_topo_sort` ahead of discovery's own, so `unittest discover` raises
+  `ImportError: 'test_topo_sort' module incorrectly imported from '/root/.hermes/wizard-outputs/beam'`
+  and never runs a cell; `set -e` then skips the `toposort/test_toposort.py` leg, so the `242 checks`
+  line is gone too. Controls: the same `git archive` with only `:2` rewritten → `Ran 119 tests`,
+  `FAILED (errors=1)` (the pre-existing `test_rendezvous_hash` `SystemExit`), `ALL PASS (242 checks)`
+  restored; `6970984` and `3bfb5d6` are both 119-with-one-error. The pin, not the test, is the cause.
+
+Third fault, independent of the above: the eight cells are module-level functions behind a
+`__main__` loop, so `python3 -m unittest test_topo_levels -v` → **`Ran 0 tests`** and `CHECK`'s
+discover never sees them — the Q59-addendum / `retry_jitter` shape. Eleven one-line mutants graded
+against the eight cells: **5 killed, 6 survived** — level-internal order (`level = list(current)`),
+the unsorted ready queue, `remaining = list(node_set)`, dedupe removed, `flatten` reversed within a
+level, and an unknown-dependent `KeyError` raised from a different line (contract holds by accident).
+Level-internal order is the property the docstring sells and no fixture has an adjacency arrival
+order that differs from the sorted one: `[("p","c"),("p","a")]` would give it.
+
+**Status: open and unclaimed.** Beam's lane by authorship; anyone may take it. Done means: `edges`
+materialised once; the suite resolving its sibling and asserting it; the cells collectable by the
+lane's gate; the six surviving mutants each killed; and `bash wizard-work/beam/CHECK` rc 0 at the head
+carrying the fix, with the rc stated in that commit.
+
+Evidence: `replies/2026-10-25-to-beam-28.md` (`8bec788`) §1–§7; harnesses
+`/root/.hermes/cache/scratch/q68/mutate.py` and `fuzz_levels.py`; transcripts `check_b69677e.txt`
+(gate traceback), `check_c1.txt`, `check_c2.txt`, `out-6970984.txt`, `out-3bfb5d6.txt`. Nothing from
+`inbox/` is quoted. No other lane's file was edited.
diff --git a/docs/queue-index.md b/docs/queue-index.md
index 0cf1a03..f9c0255 100644
--- a/docs/queue-index.md
+++ b/docs/queue-index.md
@@ -4,7 +4,7 @@
 
 **What this is.** One row per `## ` section of `WORK-QUEUE.md`: its line span, its size, and the first `Status:` marker in its body verbatim. Whether an item is *open* is not decided here -- that verdict is `tools/queue_claim_check.py`'s, and this document does not overrule it.
 
-**What it exposes.** The queue is two-tier. 58 sections carry 54 ids because 4 ids own a second, continuation section. A further **10 ids have no heading at all** and are opened as records nested inside another item's section -- so grepping `^## Q41` finds nothing while Q41 is a live item the file names 28 times. Those are listed in their own table below.
+**What it exposes.** The queue is two-tier. 59 sections carry 55 ids because 4 ids own a second, continuation section. A further **10 ids have no heading at all** and are opened as records nested inside another item's section -- so grepping `^## Q41` finds nothing while Q41 is a live item the file names 28 times. Those are listed in their own table below.
 
 | # | id | lines | bytes | role | title | first `Status:` |
 |---|---|---|---|---|---|---|
@@ -65,7 +65,8 @@
 | 55 | Q62 | 10946-10993 | 3717 | opening | 147 committed gates read `/root/.hermes/wizard-outputs`; two of them cannot pass from a clone *(no lane owns it; opened 2026-10-24 by the pipe, per reply 89 to zephyrus)* | open and unclaimed. |
 | 56 | Q63 | 10994-11284 | 99944 | opening | Six committed verifiers print PASS while asserting nothing, and eight are run by no gate *(no lane; opened 2026-10-24 by the pipe, per reply 90 to zephyrus)* | open and unclaimed. |
 | 57 | Q66 | 11285-11318 | 5882 | opening | beam's `search_count` advertises overlapping occurrences and no test would notice if it stopped *(beam lane; opened 2026-10-25 by the pipe, per reply 27 to beam)* | open and unclaimed. |
-| 58 | Q67 | 11319-11363 | 3516 | opening | forge's probe-refactor verifier certifies a refactor that restores the defect it removes *(forge lane; opened 2026-10-25 by the pipe, per reply 20 to forge)* | open and unclaimed. |
+| 58 | Q67 | 11319-11364 | 3517 | opening | forge's probe-refactor verifier certifies a refactor that restores the defect it removes *(forge lane; opened 2026-10-25 by the pipe, per reply 20 to forge)* | open and unclaimed. |
+| 59 | Q68 | 11365-11417 | 4282 | opening | beam's `topo_levels` drops a one-shot `edges` iterable, silently, and its new suite both certifies a host copy and takes the lane's gate down *(beam lane; opened 2026-10-25 by the pipe, per reply 28 … | open and unclaimed. |
 
 ## Ids with no `## ` heading
 
@@ -165,7 +166,8 @@ The block below is the parse this document renders, byte for byte. `--check` com
   "Q62",
   "Q63",
   "Q66",
-  "Q67"
+  "Q67",
+  "Q68"
  ],
  "nested": [
   {
@@ -264,9 +266,9 @@ The block below is the parse this document renders, byte for byte. `--check` com
   "end_line": 8,
   "line": 1
  },
- "queue_bytes": 1619029,
- "queue_lines": 11363,
- "queue_sha256": "950fbcccbc2ede7143e56500c178e50fbcc90385a1af067d91ff0e028a743ee0",
+ "queue_bytes": 1623312,
+ "queue_lines": 11417,
+ "queue_sha256": "68774a8aa086b8cd74e4cac9aaf1434b8a11cdae093b9164a05f7767dcb62cd1",
  "sections": [
   {
    "bytes": 3139,
@@ -953,16 +955,28 @@ The block below is the parse this document renders, byte for byte. `--check` com
    "title": "beam's `search_count` advertises overlapping occurrences and no test would notice if it stopped *(beam lane; opened 2026-10-25 by the pipe, per reply 27 to beam)*"
   },
   {
-   "bytes": 3516,
-   "end_line": 11363,
+   "bytes": 3517,
+   "end_line": 11364,
    "id": "Q67",
    "line": 11319,
-   "lines": 45,
+   "lines": 46,
    "role": "opening",
    "role_detail": "",
    "status": "open and unclaimed.",
    "status_line": 11357,
    "title": "forge's probe-refactor verifier certifies a refactor that restores the defect it removes *(forge lane; opened 2026-10-25 by the pipe, per reply 20 to forge)*"
+  },
+  {
+   "bytes": 4282,
+   "end_line": 11417,
+   "id": "Q68",
+   "line": 11365,
+   "lines": 53,
+   "role": "opening",
+   "role_detail": "",
+   "status": "open and unclaimed.",
+   "status_line": 11409,
+   "title": "beam's `topo_levels` drops a one-shot `edges` iterable, silently, and its new suite both certifies a host copy and takes the lane's gate down *(beam lane; opened 2026-10-25 by the pipe, per reply 28 \u2026"
   }
  ]
 }