Mister-Meeseeks · Oct 14, 2026 · Oct 14, 2026
diff --git a/research/complex-queue-ceiling-uncovered/README.md b/research/complex-queue-ceiling-uncovered/README.md
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+# Screening the queue-ceiling census's uncovered sixteen
+
+**Review aid built on [CrocSwap/integer-mult-bounds#1240](../complex-local-word-ceiling/README.md) and
+[CrocSwap/integer-mult-bounds#1264](../complex-queue-ceiling-census/README.md). No new kappa; no claim is accepted or
+rejected.** Prepared by Aaron Wang / navinor, with help from opencode. Apache-2.0.
+
+The queue-ceiling census screened 14 of the 30 open complex kappa claims and listed 16 as not
+covered: "no profile whose kappa equals the title kappa, with live/calls and an idle histogram in
+the same package". This package screens all 16 at their snapshot-pinned heads. The reason the
+census could not see their data is naming, not absence: the same four inputs are recorded under
+`global_profile`/`profile`, `idle_profile`, `complete_invocations`, inside an `expected` block,
+or (for CrocSwap/integer-mult-bounds#1175) README prose. With those aliases and the census's own `live*9 == 896*calls` rule,
+every one of the 16 has all four inputs, and each recorded profile satisfies the coverage law
+`mass = 72*live + 64*calls` exactly.
+
+## Result
+
+**30 of 30 census-listed claims are now screened. No newly screened word raises a cap.**
+The 16 claims sit on 11 distinct per-call local words (7 new against the census's nine). The
+highest cap among them is **0.0016872744** (word N1, identical to census W4), **+0.004%** over the
+selected word's cap 0.0016872026 and *below* the census's best cap 0.0016873148 (W1). So the whole
+covered queue remains a packing contest inside the +0.87% band above the selected kappa
+0.001672660197076918; extending coverage to the 16 did not surface a word that raises the limit.
+
+| Word | Local profile per call | κ cap | vs selected word | Claims |
+|---|---|---:|---:|---|
+| N1 = census W4 | `1:2406 2:432 3:424 4:142 5:82 8:8` | **0.0016872744** | +0.004% | CrocSwap/integer-mult-bounds#1104, CrocSwap/integer-mult-bounds#1107, CrocSwap/integer-mult-bounds#1117, CrocSwap/integer-mult-bounds#1121, CrocSwap/integer-mult-bounds#1150, CrocSwap/integer-mult-bounds#1172 |
+| N5 = census W2 = selected | `1:2412 2:418 3:432 4:142 5:82 8:8` | 0.0016872026 | 0 | CrocSwap/integer-mult-bounds#1175 |
+| N2 (new) | `1:43307/18 2:7633/18 3:15661/36 4:5003/36 5:82 8:8` | 0.0016863769 | −0.049% | CrocSwap/integer-mult-bounds#1111 |
+| N3 (new) | `1:42949/18 2:8135/18 3:15623/36 4:4753/36 5:82 8:8` | 0.0016845577 | −0.157% | CrocSwap/integer-mult-bounds#1154 |
+| N4 = census W3 | `1:2364 2:498 3:412 4:130 5:82 8:8` | 0.0016842207 | −0.177% | CrocSwap/integer-mult-bounds#1169 |
+| N7 (new) | `1:262220/111 2:55462/111 3:45824/111 4:14338/111 5:82 8:8` | 0.0016839954 | −0.190% | CrocSwap/integer-mult-bounds#1183 |
+| N10 (new) | `1:261194/111 2:56488/111 3:45782/111 4:14158/111 5:82 8:8` | 0.0016836930 | −0.208% | CrocSwap/integer-mult-bounds#1207 |
+| N11 = census W7 | `1:783550/333 2:169496/333 3:137362/333 4:42458/333 5:82 8:8` | 0.0016836800 | −0.209% | CrocSwap/integer-mult-bounds#1218 |
+| N9 (new) | `1:261194/111 2:56488/111 3:45560/111 4:14602/111 5:80 8:8` | 0.0016836527 | −0.210% | CrocSwap/integer-mult-bounds#1201 |
+| N8 (new) | `1:261860/111 2:55822/111 3:46004/111 4:14158/111 5:82 8:8` | 0.0016835547 | −0.216% | CrocSwap/integer-mult-bounds#1192 |
+| N6 (new) | `1:42607/18 2:8981/18 3:14921/36 4:4591/36 5:82 8:8` | 0.0016831053 | −0.243% | CrocSwap/integer-mult-bounds#1176 |
+
+Every claim's recorded endpoint lies below its own word's relaxation (the exact `ceiling()`
+bracket), and every recorded kappa lies below its cap, as for the census's 14. Fractional counts
+are exact reduced rationals: the per-call split divides by the call count (144 or 333).
+
+Two per-claim notes:
+
+- **CrocSwap/integer-mult-bounds#1175 is the selected word with a new idle packing.** Its recorded global profile splits into
+  the selected local word exactly (`1:2412 2:418 3:432 4:142 5:82 8:8`, 72 calls on 7,168 live),
+  with idle remainder `{1:1214, 2:1, 32:1, 48:2443}`. Its recorded kappa 0.001674083482880778
+  sits 0.78% below the W2 cap (the selected record's own endpoint sits 0.87% below it). This is
+  the "pack a selected-type word tightly" route from the CrocSwap/integer-mult-bounds#1166 handoff, already pursued there.
+- **CrocSwap/integer-mult-bounds#1175's PR title kappa 0.001675338871723469 differs from every kappa its package records**
+  (the package's headline is 0.001674083482880778). The screen uses the recorded value and flags
+  the mismatch; which profile the title value belongs to is the authors' to say.
+
+## Method
+
+Per claim, the four census inputs are read from the claim's own package at its pinned head and
+blob: the global paid profile, the idle-remainder histogram, live stock W and call count N
+(`complete_invocations` or the `live*9 == 896*calls` rule). Accepted aliases are recorded per row
+in [SNAPSHOT.json](SNAPSHOT.json); `rebind.py` re-reads the pinned blobs and checks the recorded
+values. [verify.py](verify.py) then repeats the census's checks with `../complex-local-word-ceiling/ceiling.py`:
+the coverage law, the idle split (idle ≤ profile, idle ranks ≤ 51), 896/9 live families per call,
+the per-word exact packing ceiling, the claim's endpoint below its word's relaxation, and the
+recorded kappa below its cap. Five rejection controls mutate the snapshot (coverage law, idle
+split, families per call, endpoint above relaxation, title mismatch) and must fail.
+
+## Reproduce
+
+Standard library only, from the repository root (about 9 s):
+
+```sh
+python3 -I -B research/complex-queue-ceiling-uncovered/verify.py
+python3 -I -B research/complex-queue-ceiling-uncovered/rebind.py --fetch   # network; re-reads pinned PR blobs
+```
+
+Expected final lines: `PASS_COMPLEX_QUEUE_CEILING_UNCOVERED claims=16 words=11 new=7 max_cap=0.0016872743702513531 controls=5`
+and `PASS_SNAPSHOT_REBOUND_UNCOVERED 16`.
+
+## Scope and limits
+
+- Caps are planning bounds (`κ < a/(1+a)`) for hosting, owner and idle repacking of each claim's
+  own recorded word under the coverage law, 896/9 live families per call and the halving guard.
+  They ignore helper widths, windows and chronology, and do not bound changed words, templates or
+  outer recipes.
+- The screen reads what each package records. It does not re-derive any profile from a circuit,
+  re-run any claim's replay, or validate helper placement; a recorded profile could in principle
+  disagree with its own construction. Two heads (CrocSwap/integer-mult-bounds#1172, CrocSwap/integer-mult-bounds#1175) moved since the census listing;
+  the pinned heads are current at snapshot time (2026-10-14).
+- Structured-input claims in these packages often carry the status "pending native and strict
+  admission"; nothing here strengthens those statuses.
+- No new kappa, no accepted or rejected claim, and no selected-record change.
+
+## Open next questions
+
+- **Which proposal raises a cap rather than packing toward it?** Now that all 30 census-listed
+  claims are screened inside the +0.87% band, the next cap-raising candidate must come from a
+  changed local excess spend or a changed coverage law. First step: screen each new proposal's
+  per-call profile with `ceiling.ceiling()` before a full replay. Blocker: none.
+- **Should claims record `local_profile_per_call` and `idle_histogram` in their result JSONs?**
+  This screen needed alias names and, for CrocSwap/integer-mult-bounds#1175, prose parsing; CrocSwap/integer-mult-bounds#1175's title kappa also
+  disagrees with its package. First step: adopt the census's field names (or the CrocSwap/integer-mult-bounds#1200 request's)
+  in each claim's result JSON. Blocker: the claim authors own those files.
+
+## Credit
+
+Every construction belongs to its claim's authors: G. V. Chudnovsky (CrocSwap/integer-mult-bounds#1175), tomdif and the
+CrocSwap/integer-mult-bounds#1148-line authors (CrocSwap/integer-mult-bounds#1169 lineage), jeremykothe2 (CrocSwap/integer-mult-bounds#1183/#1192/#1201/#1207/#1218 lineages), and
+the authors of CrocSwap/integer-mult-bounds#1104/#1107/#1111/#1117/#1121/#1150/#1154/#1172/#1176 as cited in their packages.
+The coverage identity is CrocSwap/integer-mult-bounds#1012's; the ceiling model and the queue-census method are Douglas
+Colkitt's ([CrocSwap/integer-mult-bounds#1240](https://github.com/CrocSwap/integer-mult-bounds/pull/1240),
+[CrocSwap/integer-mult-bounds#1264](https://github.com/CrocSwap/integer-mult-bounds/pull/1264)). This package was prepared by
+Aaron Wang / navinor, with help from opencode.