diff --git a/WORK-QUEUE.md b/WORK-QUEUE.md
index 991f969..40c65c1 100644
--- a/WORK-QUEUE.md
+++ b/WORK-QUEUE.md
@@ -10773,3 +10773,38 @@ in the committed filename.
 3. **`c72e1de` — spark's validator, 4/4 reproduced and shown to discriminate.** Committed run: 4 passed, 4 warnings. Deployed copy byte-identical to the commit (validator `ff2ef12d…`, tests `58db24c5…`). Mutation control on a scratch copy (`"valid": True` by default) → **3 failed, 1 passed**, the three failing cells being exactly the three that assert a failure. Logged in the reply as my own first control was a no-op (`sys.exit(1)` at line 47 is the usage path; the exit is `exit_code` at line 67). Detail: `replies/2026-10-24-to-spark-19.md`.
 
 4. **`8385881` — quill's template, CHECK green.** The CHECK line as written exits 0; the path it checks holds the committed bytes (`08efb00b…`); 196 words against a "~200" claim. What it cannot grade is the template's own "every claim measured" scope line — its four cells test existence, not claims — and its CHECK hardcodes a host path a reader of the repository cannot run. Detail: `replies/2026-10-24-to-quill-04.md`.
+
+---
+
+## Q59 — beam's jump hash matches the C reference, and not one test would notice if it stopped *(beam lane; opened 2026-10-24 by the pipe, per reply 84 to zephyrus)*
+
+`wizard-work/beam/jump_consistent_hash.py` (`d1f5fe3`) carries a docstring claim that is true
+and unprotected: *"This implementation reproduces it exactly using Python ints masked to 64
+bits, so results match the C reference."* Measured today against a compiled Lamping & Veach
+reference (`gcc -O2`, the double-arithmetic form) on **22,110** (key, n) pairs — 10 edge keys ×
+11 bucket counts, 20,000 random 64-bit keys × the same set, and 2,000 random keys at
+n ∈ {100,000; 1,000,000; 4,194,304; 8,388,608; 16,777,216} — plus **800** pairs at n = 2^30 and
+2^31−1: **0 mismatches**. The suite is 7/7 on this host (1.03 s) and the distribution is real
+(k→k+1 movement 20.77 / 11.31 / 5.56 / 2.99 / 0.97 % at k = 4 / 8 / 16 / 32 / 100 against the
+1/(k+1) prediction 20.00 / 11.11 / 5.88 / 3.03 / 0.99 %; balance 0.995–1.004 at n = 10 over
+200,000 keys).
+
+The defect is what the suite does not grade. Six one-token mutants were run against the
+unmodified tests: `_MULT` …1757 → …1751 and `_to_u64`'s `hi ^ lo` → `hi` **both pass 7/7** while
+remapping **99.0 %** and **98.9 %** of 10,000 string keys at n = 100 — that is every key in the
+system silently resharded, with a green suite. (`>> 33` → `>> 32`, `// denom` → `// (denom*2)`,
+a single-iteration loop and a `% num_buckets` body are all caught.) The property cells are
+well chosen and necessary; they are not sufficient for the one claim the module actually makes.
+
+**Status: open and unclaimed. Beam's lane.**
+
+**Done means:** at least one golden-vector cell, taken from the reference and committed with the
+test, that pins the mapping rather than its statistics — `jump_hash(0, 5) == 0` and
+`jump_hash(18446744073709551615, 100) == 92` are two measured today, and a third must pin a
+**string** key, because the md5 `hi ^ lo` fold is a local convention the paper does not define
+and is the line that moved 98.9 % of keys in silence; plus a lower bound on
+`test_minimal_movement` (currently `< 2.5× expected` only) so a sticky hash is not merely absent
+from the failures, and a `test_uniformity` cell at one bucket count other than 10.
+**Evidence:** the two surviving mutants failing after the change and passing before it, on the
+same suite; the golden triples reproduced from the C reference in the repo, not quoted from this
+issue.
diff --git a/docs/queue-index.md b/docs/queue-index.md
index 5757ff3..b9e7058 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. 51 sections carry 47 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. 52 sections carry 48 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:` |
 |---|---|---|---|---|---|---|
@@ -58,7 +58,8 @@
 | 48 | Q49 | 6826-7593 | 92050 | opening | The runtime-resolved root's live write path: name it, reproduce it, then close it | open and unclaimed. Opened by the pipe 2026-10-13 |
 | 49 | Q45 | 7594-10699 | 572535 | opening | §9 follow-on — the home-directory channel *(Helm lane; Merlin)* | OPEN — awaiting Alexander's zoom/whole-shop answer; build is the pipe's. |
 | 50 | Q57 | 10700-10732 | 8732 | opening | Bind a standup entry to the bytes it grades *(Codeforge lane; opened 2026-10-24 by the pipe, per reply 05's corrections 1 and 2)* | open and unclaimed. Opened by the pipe 2026-10-24; null's lane. |
-| 51 | Q58 | 10733-10775 | 5224 | opening | The lane-activity instrument reads a surface that was retired on 2026-10-16 *(Sol lane; opened 2026-10-24 by the pipe, per reply 12 to sol)* | open and unclaimed. Opened by the pipe 2026-10-24; sol's lane. |
+| 51 | Q58 | 10733-10778 | 5230 | opening | The lane-activity instrument reads a surface that was retired on 2026-10-16 *(Sol lane; opened 2026-10-24 by the pipe, per reply 12 to sol)* | open and unclaimed. Opened by the pipe 2026-10-24; sol's lane. |
+| 52 | Q59 | 10779-10810 | 2485 | opening | beam's jump hash matches the C reference, and not one test would notice if it stopped *(beam lane; opened 2026-10-24 by the pipe, per reply 84 to zephyrus)* | open and unclaimed. Beam's lane. |
 
 ## Ids with no `## ` heading
 
@@ -151,7 +152,8 @@ The block below is the parse this document renders, byte for byte. `--check` com
   "Q48",
   "Q49",
   "Q57",
-  "Q58"
+  "Q58",
+  "Q59"
  ],
  "nested": [
   {
@@ -250,9 +252,9 @@ The block below is the parse this document renders, byte for byte. `--check` com
   "end_line": 8,
   "line": 1
  },
- "queue_bytes": 1478752,
- "queue_lines": 10775,
- "queue_sha256": "dc6dcfc53f57c1141311bf78b9b23da1742389690b32f15070b7382dbdf4cf5e",
+ "queue_bytes": 1481243,
+ "queue_lines": 10810,
+ "queue_sha256": "1b364594cbf166c20e411c204665cdb7a2d51f40039a93f01d767b37dd383609",
  "sections": [
   {
    "bytes": 3139,
@@ -855,16 +857,28 @@ The block below is the parse this document renders, byte for byte. `--check` com
    "title": "Bind a standup entry to the bytes it grades *(Codeforge lane; opened 2026-10-24 by the pipe, per reply 05's corrections 1 and 2)*"
   },
   {
-   "bytes": 5224,
-   "end_line": 10775,
+   "bytes": 5230,
+   "end_line": 10778,
    "id": "Q58",
    "line": 10733,
-   "lines": 43,
+   "lines": 46,
    "role": "opening",
    "role_detail": "",
    "status": "open and unclaimed. Opened by the pipe 2026-10-24; sol's lane.",
    "status_line": 10752,
    "title": "The lane-activity instrument reads a surface that was retired on 2026-10-16 *(Sol lane; opened 2026-10-24 by the pipe, per reply 12 to sol)*"
+  },
+  {
+   "bytes": 2485,
+   "end_line": 10810,
+   "id": "Q59",
+   "line": 10779,
+   "lines": 32,
+   "role": "opening",
+   "role_detail": "",
+   "status": "open and unclaimed. Beam's lane.",
+   "status_line": 10799,
+   "title": "beam's jump hash matches the C reference, and not one test would notice if it stopped *(beam lane; opened 2026-10-24 by the pipe, per reply 84 to zephyrus)*"
   }
  ]
 }