diff --git a/research/complex-queue-ceiling-census/README.md b/research/complex-queue-ceiling-census/README.md
new file mode 100644
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+# Packing ceilings of the open complex κ claims
+
+**A review aid built on [#1240](../complex-local-word-ceiling/README.md). No new κ; no claim is accepted or
+rejected.**
+
+Thirty open PRs state a conditional κ above the selected 0.001672660197076918 (listed 2026-10-13). For each
+one, I looked inside a single package for four things:
+
+- a complex profile whose κ equals the title κ;
+- its live stock W and call count N;
+- its idle-remainder histogram;
+- the coverage law `mass = 72W + 64N` holding for that profile.
+
+**14 claims** meet all of this and are pinned by PR head, path and Git blob in `SNAPSHOT.json`; `rebind.py`
+re-reads them. The other 16 are listed with the reason. Each covered profile splits into a local word and idle
+remainders. #1240's exact relaxation then bounds what any hosting, owner or idle repacking of that word can
+reach.
+
+## Result
+
+All 14 obey the coverage law at 896/9 live families per call. Every claim's endpoint lies below its own word's
+ceiling. They use **nine distinct local words** in two families.
+
+| Word | Local profile per call | Cap on κ | vs. selected word | Claims (κ, headroom left) |
+|---|---|---:|---:|---|
+| W1 | `1:2406 2:432 3:426 4:138 5:84 8:8` | **0.0016873148** | +0.007% | #1124, #1130 (0.0016730, 0.86%) |
+| W4 | `1:2406 2:432 3:424 4:142 5:82 8:8` | 0.0016872744 | +0.004% | #1152 (0.0016743, 0.77%) |
+| W5 | `1:2412 2:418 3:434 4:138 5:84 8:8` | 0.0016872431 | +0.002% | #1157 (0.0016741, 0.78%) |
+| W2 = selected word | `1:2412 2:418 3:432 4:142 5:82 8:8` | 0.0016872026 | 0 | #1129, #1131 (0.0016741, 0.78%) |
+| W8 | `1:2358 2:504 3:408 4:134 5:80 8:8` | 0.0016843188 | −0.171% | #1195 (0.0016757, 0.52%) |
+| W9 | `1:2364 2:498 3:414 4:126 5:84 8:8` | 0.0016842610 | −0.174% | #1196, #1204, #1225 (0.0016756, 0.52%) |
+| W3 | `1:2364 2:498 3:412 4:130 5:82 8:8` | 0.0016842207 | −0.177% | #1148 (0.0016756, 0.52%) |
+| W6 | `1:2372 2:494 3:414 4:126 5:84 8:8` | 0.0016838172 | −0.201% | #1178 (0.0016752, 0.52%) |
+| W7 (mixed providers, mean per call) | `1:2353.0 2:509.0 3:412.5 4:127.5 5:82 8:8` | 0.0016836800 | −0.209% | #1193, #1239 (0.0016758, 0.47%) |
+
+What this shows:
+
+- **No covered claim, and no repacking of any covered word, can exceed κ < 0.0016873148.** The whole
+  covered queue is a packing contest inside a 0.87% band above the selected κ.
+- **The leading claims (#1148 line) sit on *lower*-ceiling words.** Their joint-entrance words move local mass
+  from rank 1 to rank 2: 5,590 against 5,584–5,586 per call. That lowers the ideal limit by about 0.17–0.21%.
+  They lead because they are packed closer to their limit (0.47–0.52% headroom left, against 0.77–0.86%).
+  Their gains therefore come from realizability, meaning how well helpers fit windows. The paid profile itself
+  did not improve.
+- **For reviewers:** two claims on the same word differ only in packing. A claim on a lower-cap word can never
+  overtake the best packing of a higher-cap word. The largest remaining prize under these words is about 0.7%,
+  for packing W1 or W2 as tightly as the #1148 line packs its own words.
+
+## Not covered
+
+The 16 claims not covered (#1104, #1107, #1111, #1117, #1121, #1150, #1154, #1169, #1172, #1175, #1176, #1183,
+#1192, #1201, #1207, #1218) record no complex profile matching the title κ together with an idle histogram in the
+same package. Their words may differ. Adding a `local_profile_per_call` and `idle_histogram` to each claim's
+result JSON would make them checkable; see the workflow feedback in #1200.
+
+Caps are planning bounds (`κ < a/(1+a)`). They allow fractional counts and ignore helper widths, windows and
+chronology. They bound repacking of a fixed word under a fixed template, coverage law and halving guard, and
+nothing else. The snapshot reflects PR heads at 2026-10-13; #1172 moved between listing and fetch, and its
+fetched head was used.
+
+## Reproduce
+
+```sh
+python3 -I -B research/complex-queue-ceiling-census/verify.py            # ~12 s, PASS_COMPLEX_QUEUE_CEILING_CENSUS
+python3 -I -B research/complex-queue-ceiling-census/rebind.py --fetch    # network; re-reads every pinned blob
+```
+
+This package depends on `research/complex-local-word-ceiling/ceiling.py` (#1240) and is stacked on it.
+
+## Open next questions
+
+- **Can a W1/W2-type word be packed as tightly as the #1148 line?** That is the largest remaining packing
+  prize, at most about +0.7%. A first step is to transplant the #1148 line's owner/entrance packing method onto
+  W1's helper widths and measure the realized fraction of the cap. The blocker is that the joint-entrance method
+  changes the word, so the transplant must keep W1's paid profile.
+- **Which change raises a cap rather than packing toward it?** Only a lower local excess spend (#1240's budget)
+  or a changed coverage law does. A first step is to screen each proposal's per-call profile with
+  `ceiling.ceiling(...)` before a full replay. It is not blocked.
+
+## Credit
+
+Every construction belongs to its PR's authors: tomdif (#1148 line), rohanarun, jeremykothe2 and the other
+listed contributors. The coverage identity is PR1012's. Prepared by Douglas Colkitt with substantial Claude
+(Anthropic) assistance. Apache-2.0.
diff --git a/research/complex-queue-ceiling-census/RESULT.json b/research/complex-queue-ceiling-census/RESULT.json
new file mode 100644
index 0000000000..756f36f850
--- /dev/null
+++ b/research/complex-queue-ceiling-census/RESULT.json
@@ -0,0 +1,361 @@
+{
+ "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8",
+ "claims": [
+  {
+   "calls": 144,
+   "head": "7c0e3ee0e2d4f6c00d033a4f1dfe4e793e7ecae4",
+   "kappa": "66920213783953/40000000000000000",
+   "kappa_cap": "0.0016873148397529847",
+   "kappa_decimal": "0.0016730053445988249",
+   "live": 14336,
+   "pr": 1124,
+   "remaining_packing_headroom_percent": "0.8553",
+   "word": "W1"
+  },
+  {
+   "calls": 333,
+   "head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21",
+   "kappa": "167409796990539/100000000000000000",
+   "kappa_cap": "0.0016872026453254019",
+   "kappa_decimal": "0.00167409796990539",
+   "live": 33152,
+   "pr": 1129,
+   "remaining_packing_headroom_percent": "0.7828",
+   "word": "W2"
+  },
+  {
+   "calls": 144,
+   "head": "1558508e5cbff0b7c534d1c4cc7a0fb1b7145c1c",
+   "kappa": "1673006105142741/1000000000000000000",
+   "kappa_cap": "0.0016873148397529847",
+   "kappa_decimal": "0.001673006105142741",
+   "live": 14336,
+   "pr": 1130,
+   "remaining_packing_headroom_percent": "0.8553",
+   "word": "W1"
+  },
+  {
+   "calls": 333,
+   "head": "fcdc42737b703323d8ed550a528141a482e68e96",
+   "kappa": "167409796990539/100000000000000000",
+   "kappa_cap": "0.0016872026453254019",
+   "kappa_decimal": "0.00167409796990539",
+   "live": 33152,
+   "pr": 1131,
+   "remaining_packing_headroom_percent": "0.7828",
+   "word": "W2"
+  },
+  {
+   "calls": 144,
+   "head": "506ea08dd77388105682044ebb0848ce9b274964",
+   "kappa": "1675560947524449/1000000000000000000",
+   "kappa_cap": "0.001684220703503619",
+   "kappa_decimal": "0.0016755609475244491",
+   "live": 14336,
+   "pr": 1148,
+   "remaining_packing_headroom_percent": "0.5168",
+   "word": "W3"
+  },
+  {
+   "calls": 333,
+   "head": "d376209304f05551f975b0ddf6eaa84edc4ae31a",
+   "kappa": "1674340686401949/1000000000000000000",
+   "kappa_cap": "0.0016872743702513531",
+   "kappa_decimal": "0.001674340686401949",
+   "live": 33152,
+   "pr": 1152,
+   "remaining_packing_headroom_percent": "0.7725",
+   "word": "W4"
+  },
+  {
+   "calls": 333,
+   "head": "c5647aecc8ff44e49776860bb75520bfe3e88f1e",
+   "kappa": "334827562021037/200000000000000000",
+   "kappa_cap": "0.0016872431114044472",
+   "kappa_decimal": "0.001674137810105185",
+   "live": 33152,
+   "pr": 1157,
+   "remaining_packing_headroom_percent": "0.7828",
+   "word": "W5"
+  },
+  {
+   "calls": 144,
+   "head": "6d4d0dd1c2df531a3350495dd15e00105793c52d",
+   "kappa": "1675161536733127/1000000000000000000",
+   "kappa_cap": "0.0016838171503071196",
+   "kappa_decimal": "0.001675161536733127",
+   "live": 14336,
+   "pr": 1178,
+   "remaining_packing_headroom_percent": "0.5167",
+   "word": "W6"
+  },
+  {
+   "calls": 333,
+   "head": "4e392e90e3fca8f395e35d6a23644920160a9f0f",
+   "kappa": "1675809683500501/1000000000000000000",
+   "kappa_cap": "0.0016836799672131639",
+   "kappa_decimal": "0.0016758096835005011",
+   "live": 33152,
+   "pr": 1193,
+   "remaining_packing_headroom_percent": "0.4696",
+   "word": "W7"
+  },
+  {
+   "calls": 144,
+   "head": "cc1b023b123622abba467c7933f3759f8034c753",
+   "kappa": "837829001135967/500000000000000000",
+   "kappa_cap": "0.0016843187664512867",
+   "kappa_decimal": "0.001675658002271934",
+   "live": 14336,
+   "pr": 1195,
+   "remaining_packing_headroom_percent": "0.5169",
+   "word": "W8"
+  },
+  {
+   "calls": 333,
+   "head": "7015903d1d01a2b50ff16f85184edc2686f69e37",
+   "kappa": "335121717095377/200000000000000000",
+   "kappa_cap": "0.0016842610266030733",
+   "kappa_decimal": "0.0016756085854768849",
+   "live": 33152,
+   "pr": 1196,
+   "remaining_packing_headroom_percent": "0.5164",
+   "word": "W9"
+  },
+  {
+   "calls": 333,
+   "head": "d49f96b75257c8a5eb4862eb99fbaffc738dcc1b",
+   "kappa": "335121717095377/200000000000000000",
+   "kappa_cap": "0.0016842610266030733",
+   "kappa_decimal": "0.0016756085854768849",
+   "live": 33152,
+   "pr": 1204,
+   "remaining_packing_headroom_percent": "0.5164",
+   "word": "W9"
+  },
+  {
+   "calls": 333,
+   "head": "aac9ce7d83e02989eed76e08815cfd2399214e90",
+   "kappa": "335121717095377/200000000000000000",
+   "kappa_cap": "0.0016842610266030733",
+   "kappa_decimal": "0.0016756085854768849",
+   "live": 33152,
+   "pr": 1225,
+   "remaining_packing_headroom_percent": "0.5164",
+   "word": "W9"
+  },
+  {
+   "calls": 333,
+   "head": "12e04a30d7381a2a60bf2d7260febcb37f14e454",
+   "kappa": "1675809683500501/1000000000000000000",
+   "kappa_cap": "0.0016836799672131639",
+   "kappa_decimal": "0.0016758096835005011",
+   "live": 33152,
+   "pr": 1239,
+   "remaining_packing_headroom_percent": "0.4696",
+   "word": "W7"
+  }
+ ],
+ "claims_covered": 14,
+ "claims_not_covered": [
+  1104,
+  1107,
+  1111,
+  1117,
+  1121,
+  1150,
+  1154,
+  1169,
+  1172,
+  1175,
+  1176,
+  1183,
+  1192,
+  1201,
+  1207,
+  1218
+ ],
+ "distinct_local_words": 9,
+ "max_kappa_cap_over_covered_words": "0.0016873148397529847",
+ "scope": "Each cap bounds hosting, owner and idle repacking of that claim's own local word under the coverage law, 896/9 live families per call and the halving guard. It does not bound changed words, templates or outer recipes, and does not review or accept any claim.",
+ "selected_kappa": "0.001672660197076918",
+ "status": "PASS_COMPLEX_QUEUE_CEILING_CENSUS",
+ "words": [
+  {
+   "a_ceiling": "1690166683079/1000000000000000",
+   "cap_vs_selected_word_percent": "0.00665",
+   "claims": [
+    1124,
+    1130
+   ],
+   "id": "W1",
+   "kappa_cap": "0.0016873148397529847",
+   "local_mass_per_call": "5584",
+   "local_profile_per_call": {
+    "1": "2406",
+    "2": "432",
+    "3": "426",
+    "4": "138",
+    "5": "84",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "1690126076663/1000000000000000",
+   "cap_vs_selected_word_percent": "0.004251",
+   "claims": [
+    1152
+   ],
+   "id": "W4",
+   "kappa_cap": "0.0016872743702513531",
+   "local_mass_per_call": "5584",
+   "local_profile_per_call": {
+    "1": "2406",
+    "2": "432",
+    "3": "424",
+    "4": "142",
+    "5": "82",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "338018942413/200000000000000",
+   "cap_vs_selected_word_percent": "0.002398",
+   "claims": [
+    1157
+   ],
+   "id": "W5",
+   "kappa_cap": "0.0016872431114044472",
+   "local_mass_per_call": "5586",
+   "local_profile_per_call": {
+    "1": "2412",
+    "2": "418",
+    "3": "434",
+    "4": "138",
+    "5": "84",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "1690054109089/1000000000000000",
+   "cap_vs_selected_word_percent": "0",
+   "claims": [
+    1129,
+    1131
+   ],
+   "id": "W2",
+   "kappa_cap": "0.0016872026453254019",
+   "local_mass_per_call": "5586",
+   "local_profile_per_call": {
+    "1": "2412",
+    "2": "418",
+    "3": "432",
+    "4": "142",
+    "5": "82",
+    "8": "8"
+   },
+   "selected_word": true
+  },
+  {
+   "a_ceiling": "843580241257/500000000000000",
+   "cap_vs_selected_word_percent": "-0.1709",
+   "claims": [
+    1195
+   ],
+   "id": "W8",
+   "kappa_cap": "0.0016843187664512867",
+   "local_mass_per_call": "5590",
+   "local_profile_per_call": {
+    "1": "2358",
+    "2": "504",
+    "3": "408",
+    "4": "134",
+    "5": "80",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "210887818459/125000000000000",
+   "cap_vs_selected_word_percent": "-0.1743",
+   "claims": [
+    1196,
+    1204,
+    1225
+   ],
+   "id": "W9",
+   "kappa_cap": "0.0016842610266030733",
+   "local_mass_per_call": "5590",
+   "local_profile_per_call": {
+    "1": "2364",
+    "2": "498",
+    "3": "414",
+    "4": "126",
+    "5": "84",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "1687062088401/1000000000000000",
+   "cap_vs_selected_word_percent": "-0.1767",
+   "claims": [
+    1148
+   ],
+   "id": "W3",
+   "kappa_cap": "0.001684220703503619",
+   "local_mass_per_call": "5590",
+   "local_profile_per_call": {
+    "1": "2364",
+    "2": "498",
+    "3": "412",
+    "4": "130",
+    "5": "82",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "1686657172581/1000000000000000",
+   "cap_vs_selected_word_percent": "-0.2007",
+   "claims": [
+    1178
+   ],
+   "id": "W6",
+   "kappa_cap": "0.0016838171503071196",
+   "local_mass_per_call": "5590",
+   "local_profile_per_call": {
+    "1": "2372",
+    "2": "494",
+    "3": "414",
+    "4": "126",
+    "5": "84",
+    "8": "8"
+   },
+   "selected_word": false
+  },
+  {
+   "a_ceiling": "843259763177/500000000000000",
+   "cap_vs_selected_word_percent": "-0.2088",
+   "claims": [
+    1193,
+    1239
+   ],
+   "id": "W7",
+   "kappa_cap": "0.0016836799672131639",
+   "local_mass_per_call": "1862302/333",
+   "local_profile_per_call": {
+    "1": "783550/333",
+    "2": "169496/333",
+    "3": "137362/333",
+    "4": "42458/333",
+    "5": "82",
+    "8": "8"
+   },
+   "selected_word": false
+  }
+ ]
+}
diff --git a/research/complex-queue-ceiling-census/SNAPSHOT.json b/research/complex-queue-ceiling-census/SNAPSHOT.json
new file mode 100644
index 0000000000..fe91d71c2a
--- /dev/null
+++ b/research/complex-queue-ceiling-census/SNAPSHOT.json
@@ -0,0 +1,497 @@
+{
+ "snapshot_utc": "2026-10-13",
+ "base_commit": "dadfea6e8a78ff6ba901705f87532a71c6f5bbb8",
+ "selection": "Open PRs whose title states a conditional kappa above the selected 0.001672660197076918 (30 PRs, listed 2026-10-13).",
+ "extraction": "Within one package: a complex_profile whose kappa equals the title kappa, integer live/calls, and an idle histogram with mass = 72*live + 64*calls, idle <= profile and idle ranks <= 51. Extracted by an offline script; blobs pinned.",
+ "claims": [
+  {
+   "pr": 1124,
+   "head": "7c0e3ee0e2d4f6c00d033a4f1dfe4e793e7ecae4",
+   "title_kappa": "0.001673005344598825",
+   "profile_file": "research/gauge44-ends7-x54-t16/RESULT.json",
+   "profile_blob": "087f35df23bd847ec4437decb4796486d231f33a",
+   "idle_file": "research/gauge44-ends7-x54-t16/RESULT.json",
+   "idle_blob": "087f35df23bd847ec4437decb4796486d231f33a",
+   "idle_json_path": "/idle_remainder_profile",
+   "live": 14336,
+   "calls": 144,
+   "complex_lower": "335161796396441728937/200000000000000000000000",
+   "kappa": "66920213783953/40000000000000000",
+   "profile": {
+    "1": 348675,
+    "2": 62208,
+    "3": 61704,
+    "4": 19872,
+    "5": 12096,
+    "7": 3,
+    "8": 1152,
+    "48": 4875
+   },
+   "idle": {
+    "1": 2211,
+    "3": 360,
+    "7": 3,
+    "48": 4875
+   }
+  },
+  {
+   "pr": 1129,
+   "head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21",
+   "title_kappa": "0.001674097969905390",
+   "profile_file": "research/r480-owner-optimum/evidence/ASSEMBLY.json",
+   "profile_blob": "0e696d96ee15219b1b9008c9162649ccf906a3d9",
+   "idle_file": "research/r480-owner-optimum/data/SPEC.json",
+   "idle_blob": "579a28450ef4a8b918aab3a369b2a1f9bc2a8bb2",
+   "idle_json_path": "/expected/idle_remainder_profile",
+   "live": 33152,
+   "calls": 333,
+   "complex_lower": "16769052736196808613/10000000000000000000000",
+   "kappa": "167409796990539/100000000000000000",
+   "profile": {
+    "1": 808818,
+    "2": 139194,
+    "3": 143856,
+    "4": 47286,
+    "5": 27306,
+    "8": 2664,
+    "48": 11302
+   },
+   "idle": {
+    "1": 5622,
+    "48": 11302
+   }
+  },
+  {
+   "pr": 1130,
+   "head": "1558508e5cbff0b7c534d1c4cc7a0fb1b7145c1c",
+   "title_kappa": "0.001673006105142741",
+   "profile_file": "research/gauge44-ends7-x54-t16/RESULT.json",
+   "profile_blob": "b59a7802f700b5b91eef5e8b13829b05897051c0",
+   "idle_file": "research/gauge44-ends7-x54-t16/RESULT.json",
+   "idle_blob": "b59a7802f700b5b91eef5e8b13829b05897051c0",
+   "idle_json_path": "/idle_remainder_profile",
+   "live": 14336,
+   "calls": 144,
+   "complex_lower": "837904872538656759753/500000000000000000000000",
+   "kappa": "1673006105142741/1000000000000000000",
+   "profile": {
+    "1": 348673,
+    "2": 62209,
+    "3": 61704,
+    "4": 19872,
+    "5": 12096,
+    "7": 3,
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+  },
+  {
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+ ],
+ "not_covered": [
+  {
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+   "title_kappa": "0.001672691689152441",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1107,
+   "head": "6123fc5d57db16aaa3e8a26b4a11a34b46c0c391",
+   "title_kappa": "0.001672765980186726",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1111,
+   "head": "381831ea554ea983e16224dabed8921b7d0ffdbc",
+   "title_kappa": "0.001672780159952542",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1117,
+   "head": "342b67f23dfa8f41a520a0d58978b2875e9eb0dd",
+   "title_kappa": "0.001672846995880185",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1121,
+   "head": "61e816c29165a94f6cfc57d9e195063a5b027bc2",
+   "title_kappa": "0.001672965558289236",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1150,
+   "head": "bebf64ffda3fd5128342d19ee6d419b1150b49f7",
+   "title_kappa": "0.001672716806120974",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1154,
+   "head": "390de2866a03758e7f4ddbb2846e5b2ee4e72154",
+   "title_kappa": "0.001673260706543984",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1169,
+   "head": "13d02293a7af67d7e3bd2e4d7f1a2943ac20537e",
+   "title_kappa": "0.001675568675201533",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1172,
+   "head": "e084ce638694967e1cc60f623d396cadb07993d1",
+   "title_kappa": "0.001672750137367829",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1175,
+   "head": "a15379c47388e177c3f3e8cb2cadcd2e5d7c9800",
+   "title_kappa": "0.001674083482880778",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1176,
+   "head": "3a0d419341879a395d921693112c3b826de93677",
+   "title_kappa": "0.001675224519162937",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1183,
+   "head": "9e7ccda21f28f5dd0397aa04a596e4f0e1d75d1d",
+   "title_kappa": "0.001675603180601302",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1192,
+   "head": "970793428d346b4aa8d8fa2af03aa6dd5ad6f994",
+   "title_kappa": "0.001675670695307702",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1201,
+   "head": "86a7072626d9b3e49222378bb76601a11d2f58ea",
+   "title_kappa": "0.00167576776285696",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1207,
+   "head": "d53f23eafc378a6e680294081d09886597129733",
+   "title_kappa": "0.001675807682652",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  },
+  {
+   "pr": 1218,
+   "head": "0aa147977ad226f9d777d6a21a610ab037985b1e",
+   "title_kappa": "0.001675809683500501",
+   "reason": "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in the same package"
+  }
+ ]
+}
\ No newline at end of file
diff --git a/research/complex-queue-ceiling-census/SOURCES.json b/research/complex-queue-ceiling-census/SOURCES.json
new file mode 100644
index 0000000000..65f270e3e2
--- /dev/null
+++ b/research/complex-queue-ceiling-census/SOURCES.json
@@ -0,0 +1,24 @@
+{
+  "schema_version": 1,
+  "base_commit": "77dc486aafa0ce89c0af8b7bc012adb40a933fda",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb",
+      "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "2c63fbbeed880c140546c1f98418547ae7650c59",
+      "sha256": "ad075c3b506bfca668577ec78f63679ac783a48fe0fffe28e2340b73ea62de74"
+    }
+  ]
+}
diff --git a/research/complex-queue-ceiling-census/TASK.json b/research/complex-queue-ceiling-census/TASK.json
new file mode 100644
index 0000000000..7c57e39bcc
--- /dev/null
+++ b/research/complex-queue-ceiling-census/TASK.json
@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 2,
+  "base_commit": "77dc486aafa0ce89c0af8b7bc012adb40a933fda",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract, not another mixture already covered by the frozen catalogue.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the frozen catalogue bound exclusions and select one genuinely different helper endpoint inventory.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write the complete optimistic child histogram and reject it immediately if even the relaxation has insufficient headroom.",
+    "bottleneck_link": "Helper inventory changes can improve the moment; repacking a covered cost interface cannot evade its scoped bound.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts."
+    ],
+    "scope_change_triggers": [
+      "Mixing only providers already inside the pinned catalogue."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Apply #1240's exact relaxation to the local words of the open complex kappa claims. For each pinned claim, report its packing cap and remaining headroom.",
+  "scope_change_reason": "This is the card's 'reject routes with insufficient headroom' step, applied to inventories already proposed in the review queue. No new inventory was synthesized.",
+  "bottleneck_link": "The complex side binds. This separates packing gains from local-word gains across the queue and shows every covered claim is capped below kappa 0.0016874.",
+  "budget_minutes": 60,
+  "stop_rule": "Cover only claims whose profile, idle histogram and live/calls are recorded together. List the rest.",
+  "outcome": "completed",
+  "evidence": "RESULT.json: 14 claims, 9 words, max cap 0.0016873148; the #1148 line sits on words whose caps are 0.17-0.21% below the selected word's; 16 claims not covered.",
+  "author": "Douglas Colkitt",
+  "ai_assistance": "Substantial: Claude (Anthropic, Claude Code) extracted the snapshot, wrote verify.py and rebind.py, and drafted the README.",
+  "open_questions": [
+    {
+      "question": "Can a W1/W2-type word be packed as tightly as the #1148 line?",
+      "why_it_matters": "It is the largest remaining packing prize (up to about +0.7%).",
+      "first_step": "Transplant the #1148 line's owner packing onto W1's helper widths and measure the realized fraction of the cap.",
+      "blocked_by": "The joint-entrance method changes the word; the transplant must keep W1's paid profile."
+    },
+    {
+      "question": "Which proposals raise a cap rather than pack toward it?",
+      "why_it_matters": "Only those can move kappa beyond 0.0016874.",
+      "first_step": "Screen each proposal's per-call profile with ceiling.ceiling() before a full replay.",
+      "blocked_by": "Nothing."
+    }
+  ]
+}
diff --git a/research/complex-queue-ceiling-census/VERIFY.json b/research/complex-queue-ceiling-census/VERIFY.json
new file mode 100644
index 0000000000..7133eb3d1e
--- /dev/null
+++ b/research/complex-queue-ceiling-census/VERIFY.json
@@ -0,0 +1,22 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/complex-local-word-ceiling/ceiling.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Coverage law and idle split per pinned claim; exact caps per distinct word; every endpoint below its cap; RESULT.json byte match"
+    }
+  ]
+}
diff --git a/research/complex-queue-ceiling-census/rebind.py b/research/complex-queue-ceiling-census/rebind.py
new file mode 100644
index 0000000000..284e25517e
--- /dev/null
+++ b/research/complex-queue-ceiling-census/rebind.py
@@ -0,0 +1,70 @@
+#!/usr/bin/env python3
+"""Re-check SNAPSHOT.json against the pinned PR heads (needs network once).
+
+usage: rebind.py [--fetch]
+--fetch runs `git fetch origin pull/N/head` for every covered PR. Then, for each claim, the
+pinned blob must exist at its head and path, and the profile, idle histogram, live, calls,
+complex_lower and kappa must be read back from those blobs.
+Douglas Colkitt, with Claude (Anthropic) assistance. Apache-2.0.
+"""
+import gzip, json, subprocess, sys
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+
+
+def git(*a):
+    r = subprocess.run(['git', *a], capture_output=True)
+    if r.returncode:
+        sys.exit(f'FAIL: git {" ".join(a)}: {r.stderr.decode()}')
+    return r.stdout
+
+
+def load(head, path, blob):
+    if git('rev-parse', f'{head}:{path}').decode().strip() != blob:
+        sys.exit(f'FAIL: blob changed for {head}:{path}')
+    raw = git('cat-file', 'blob', blob)
+    return json.loads(gzip.decompress(raw) if path.endswith('.gz') else raw)
+
+
+def find(o, pred):
+    if isinstance(o, dict):
+        if pred(o):
+            return o
+        for v in o.values():
+            r = find(v, pred)
+            if r is not None:
+                return r
+    elif isinstance(o, list):
+        for v in o:
+            r = find(v, pred)
+            if r is not None:
+                return r
+    return None
+
+
+def at(o, path):
+    for k in [p for p in path.split('/') if p]:
+        o = o[k]
+    return o
+
+
+def main():
+    snap = json.loads((HERE / 'SNAPSHOT.json').read_text())
+    for c in snap['claims']:
+        if '--fetch' in sys.argv:
+            git('fetch', '-q', 'origin', f"pull/{c['pr']}/head")
+        P = load(c['head'], c['profile_file'], c['profile_blob'])
+        rec = find(P, lambda o: o.get('complex_profile') == c['profile'] and o.get('complex_lower') == c['complex_lower'])
+        assert rec is not None and rec.get('kappa') == c['kappa'], c['pr']
+        I = load(c['head'], c['idle_file'], c['idle_blob'])
+        assert {str(k): v for k, v in at(I, c['idle_json_path']).items() if v} == c['idle'], c['pr']
+        lc = [load(c['head'], f, b) for f, b in {(c['profile_file'], c['profile_blob']), (c['idle_file'], c['idle_blob'])}]
+        assert any(find(x, lambda o: o.get('live') == c['live'] and o.get('calls') == c['calls']) for x in lc) or \
+            c['live'] * 9 == 896 * c['calls'], c['pr']
+        print(f"#{c['pr']} ok")
+    print('PASS_SNAPSHOT_REBOUND', len(snap['claims']))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/complex-queue-ceiling-census/verify.py b/research/complex-queue-ceiling-census/verify.py
new file mode 100644
index 0000000000..7f7ce533ec
--- /dev/null
+++ b/research/complex-queue-ceiling-census/verify.py
@@ -0,0 +1,90 @@
+#!/usr/bin/env python3
+"""Packing ceilings of the local words behind the open complex kappa claims (SNAPSHOT.json).
+
+For every pinned claim: check the coverage law mass = 72*live + 64*calls, split its profile into
+local word + idle remainder, certify the word's packing ceiling with ../complex-local-word-ceiling,
+and check the claim's own endpoint lies below it. Writes or checks RESULT.json.
+
+usage: verify.py [--write]
+Douglas Colkitt, with Claude (Anthropic) assistance. Apache-2.0.
+"""
+import json, sys
+from fractions import Fraction as Q
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(HERE.parent / 'complex-local-word-ceiling'))
+import ceiling as C  # noqa: E402
+
+M, CENTRE = 73, 64
+SELECTED = json.loads((ROOT / 'certificates/selected-result.json').read_text())
+SELECTED_WORD = {1: 2412, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8}    # research/complex-local-word-ceiling
+
+
+def dec(x, digits=17):
+    return f'{float(x):.{digits}g}'
+
+
+def split(c):
+    P = {int(r): n for r, n in c['profile'].items()}
+    I = {int(r): n for r, n in c['idle'].items()}
+    W, N = c['live'], c['calls']
+    C.require(sum(r * n for r, n in P.items()) == (M - 1) * W + CENTRE * N, f"#{c['pr']} coverage law")
+    C.require(all(I[r] <= P.get(r, 0) for r in I) and max(I) <= C.max_idle_rank(M), f"#{c['pr']} idle split")
+    return {r: Q(P[r] - I.get(r, 0), N) for r in P if P[r] - I.get(r, 0)}, W, N
+
+
+def main():
+    snap = json.loads((HERE / 'SNAPSHOT.json').read_text())
+    words, rows = {}, []
+    for c in snap['claims']:
+        local, W, N = split(c)
+        C.require(Q(W, N) == Q(896, 9), f"#{c['pr']} families per call differ from 896/9")
+        key = json.dumps(sorted((r, str(v)) for r, v in local.items()))
+        if key not in words:
+            lo, hi = C.ceiling(local, M, W, N, CENTRE)
+            words[key] = dict(id=f'W{len(words) + 1}', local=local, a_lo=lo, a_hi=hi, claims=[])
+        w = words[key]
+        b, k = Q(c['complex_lower']), Q(c['kappa'])
+        C.require(b < w['a_lo'], f"#{c['pr']} endpoint not below its word's relaxation")
+        cap = w['a_hi'] / (1 + w['a_hi'])
+        C.require(k < cap, f"#{c['pr']} kappa above its ceiling")
+        w['claims'].append(c['pr'])
+        rows.append(dict(pr=c['pr'], head=c['head'], word=w['id'], kappa=c['kappa'], kappa_decimal=dec(k),
+                         kappa_cap=dec(cap), remaining_packing_headroom_percent=dec(100 * (cap / k - 1), 4),
+                         live=W, calls=N))
+    sel_key = json.dumps(sorted((r, str(Q(v))) for r, v in SELECTED_WORD.items()))
+    C.require(sel_key in words, 'selected local word not among the claims')
+    sel = words[sel_key]
+    out_words = []
+    for w in sorted(words.values(), key=lambda w: -w['a_hi']):
+        cap = w['a_hi'] / (1 + w['a_hi'])
+        out_words.append(dict(id=w['id'], selected_word=(w is sel),
+                              local_profile_per_call={str(r): str(v) for r, v in sorted(w['local'].items())},
+                              local_mass_per_call=str(sum(r * v for r, v in w['local'].items())),
+                              a_ceiling=str(w['a_hi']), kappa_cap=dec(cap),
+                              cap_vs_selected_word_percent=dec(100 * (cap / (sel['a_hi'] / (1 + sel['a_hi'])) - 1), 4),
+                              claims=sorted(w['claims'])))
+    best = max(words.values(), key=lambda w: w['a_hi'])
+    out = dict(status='PASS_COMPLEX_QUEUE_CEILING_CENSUS', base_commit=snap['base_commit'],
+               claims_covered=len(rows), claims_not_covered=[d['pr'] for d in snap['not_covered']],
+               distinct_local_words=len(words),
+               max_kappa_cap_over_covered_words=dec(best['a_hi'] / (1 + best['a_hi'])),
+               selected_kappa=SELECTED['decimal'], words=out_words, claims=sorted(rows, key=lambda r: r['pr']),
+               scope='Each cap bounds hosting, owner and idle repacking of that claim\'s own local word under the '
+                     'coverage law, 896/9 live families per call and the halving guard. It does not bound changed '
+                     'words, templates or outer recipes, and does not review or accept any claim.')
+    text = json.dumps(out, indent=1, sort_keys=True) + '\n'
+    if sys.argv[1:] == ['--write']:
+        (HERE / 'RESULT.json').write_text(text)
+    else:
+        C.require((HERE / 'RESULT.json').read_text() == text, 'RESULT.json differs')
+    print(out['status'], f"claims={len(rows)} words={len(words)} max_cap={out['max_kappa_cap_over_covered_words']}")
+
+
+if __name__ == '__main__':
+    try:
+        main()
+    except ValueError as e:
+        print('FAIL:', e); sys.exit(1)