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new file mode 100644
index 0000000000..f41ec5f577
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new file mode 100644
index 0000000000..9328b81893
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new file mode 100644
index 0000000000..f4e283d333
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+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-assembly.tex": "ccf34a6d37c4af14bebeab15be50ab204eb1caebe546385520050ec30089441d",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-complex.tex": "1c5b638aa9b75365b8addec9c8eeee6bc5e499722901079b94c65fce033fde8a",
+  "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/verify.py": "6b444c686891b20b3a92385d025818fc86d9a6ddd2f77504d9223afaa47acd21",
+  "research/complex-k492-owner-repair/vendor/multicold/verify.py": "1a0e92f610f96a5e642310a2823b152cf573c0d1630b9c174fcc8388d1ffd2a2",
+  "research/complex-t16-rare-pattern-exchanges/SOURCE.json": "4cfd44cebfe88f4450294239fbea8feecb564338dc3027b76065227f5d19cb6f",
+  "research/complex-t16-rare-pattern-exchanges/data/OWNERS.json.gz": "87902c528dfab7d503dcf8a784260e3ab6fb7424c418a1820f7261f25be7b6bc",
+  "research/complex-t16-rare-pattern-exchanges/data/PLAN.json": "7bd786ba8e66408f02aa9ef446eaf20c1bfe981ea2e4dd1e5a929f0aa7767bc0",
+  "research/complex-t16-rare-pattern-exchanges/data/SPEC.json": "8cb51f25a5da4a29d3783853025b73ff1f452429d4fdb30c599e598bcab0e71d",
+  "research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz": "d4acf04daef85d4514f80ec5fcd2492d0c60e5d6c49fa71b3e6523f8db2dea86",
+  "research/frontier1094-idle-star-ceiling/analyze.py": "d9768cff06d5e19e75b2ccc4d03ff5bc2d93098f3192c167d3f208c802877bbc",
+  "research/pending-claims-independent-pricing/SNAPSHOT.json": "9f1a69818b64abacd96bde1809e750349ce7c79d45b77490ddcd3e213ac08613",
+  "research/pending-claims-independent-pricing/arith.py": "1b4766610223bbf5e346d7cebc036eaeaedfa2f7200c075136bd750ab26ece88",
+  "research/pending-claims-independent-pricing/sweep.py": "aeafc6a5e39817a893fa8392f4f7e767b23437e3317067075bb9d5552e3df23f",
+  "research/t16-owner-audit-seed67/SOURCES.json": "d3d71303dcd25fe84a3e026c4ad53535607ba6b288fd144736ad2a5376390396",
+  "research/t16-owner-audit-seed67/inputs/k8-seven-slot-word.json.gz": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289",
+  "research/t16-owner-audit-seed67/verify.py": "f6e27f76c9ccb87b3ce6c5e673588338a09847d22771da7b3f28579661c9404b"
+}
diff --git a/research/complex-t16-two-stage-cycles/LOCAL-PINS.json b/research/complex-t16-two-stage-cycles/LOCAL-PINS.json
new file mode 100644
index 0000000000..e0f4d31521
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/LOCAL-PINS.json
@@ -0,0 +1,12 @@
+{
+  "CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+  "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+  "CLIFFORD-REVIEW.json": "cb0e10a8b284f176526c17177e91186ce09aa3e88b4f6acc561051daa072b0d0",
+  "FULL-WORD.json.gz": "49596aa4ed4fd36cd4582fd0e8ddeb09fd80370a7d8aea1ede52a135b536d289",
+  "INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+  "LOCAL-CHECKS.json": "2b8b1891a736598010232bfb26abc31973b265a53a2009a3fcfd9138b5ecadb4",
+  "LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+  "RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+  "SCALAR-FRAME-AUDIT.json": "0e2a979aae1b948e1bee6c49c218f3ce7d7df00814b3f53b3d0866497510a28b",
+  "WRAPPER-CHECKS.json": "0ae753d6fa6e922d8b8180da602828f6cb3f444fcd124d019acee74e145c0836"
+}
diff --git a/research/complex-t16-two-stage-cycles/MANIFEST.json b/research/complex-t16-two-stage-cycles/MANIFEST.json
new file mode 100644
index 0000000000..10e3b98f6d
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/MANIFEST.json
@@ -0,0 +1,54 @@
+{
+  "CANDIDATE.json": "dc745d48fbea38d91a16814981200a491a6cad5d5fa44aedff2143b64075d180",
+  "DIFF-vs-selected.json": "0b10282683ca6d81da57dea82adb02f74c352623c54f70b7d50e34449a2dd481",
+  "INPUTS.json": "86d767a3f8a26ac199b50ddf43e4c4629771bfef1f5f3474f845c17fbbeea758",
+  "LOCAL-PINS.json": "c9e7ad3818f2a841ea0d224089ca2f975caff2d04cc12b55f072fca88df53140",
+  "PR-BODY.md": "a88c854c0a3a5e80e1379c66e1b55dccf1889d45fcbf3b7ff137d4c7bd3c377e",
+  "PROOF.md": "90e31383c5297121f3e73764c77637eaa364bccb5298bc35299f38a94433e3b5",
+  "README.md": "34a77207302bafb71c6cae392e8e719319c9dc34b4ac3bc151d13c10929472d7",
+  "SEARCH.json": "9211f5c5757a084a3cbde5310822f6e11662fa299b062764f94c201278a48321",
+  "SOURCES.json": "64156303b238bddbaaf335ef1a95f96df3d09b483ea1474bad7f3264205996af",
+  "TASK.json": "20d99eda602e41e9b3b02647c24b840da82802efff4cc0fd944b397b4e2493c5",
+  "VALIDATION.json": "659ed98c1a06e6190c125d16bbfc7353fb68b78e45baaa171eead26d4543fc3a",
+  "VERIFY.json": "7da2eb004b44233806ad1deee881c3c5c1b68d696c5382747649de060e55e349",
+  "build.py": "bd5d464a52b1808b89c84fcda01336954493d4fe8437cb8768822866da7410ad",
+  "ceiling_bound.py": "b8e22ba9ae03677b814de8d145f5a86eee21bc0d1d89642cbb41f9dabd15791b",
+  "check.py": "a7f7b3274109879ca10c7eda275bc247aae09bff1eb0a56151ae698c35bf4639",
+  "data/OWNERS.json.gz": "551fd1b3a75fa5fd67cfd8c00a6c77c2f893a5120cb0c0dd8a7699f25e9bddba",
+  "data/PLAN.json": "67173cd2e38296699e596714deb8b98e199bcb3390b49c2218887011a07f23da",
+  "data/SPEC.json": "e81f2dabf16bc4d56d427bf5bc4a06f05ce27fc6c539c3de4029cb5304ed9701",
+  "evidence/ADMISSION-CONTROLS.json": "89e1a4a9eb4fe81b4bbb966e5879ee1039b0855ba0debdbd87d4d4d11765e1ce",
+  "evidence/ASSEMBLY.json": "532f63da45d8eaa4283b594280ba6f78ac6a7d4815780cedef7193383adfa369",
+  "evidence/BIT-SUPPLIER-CONTROLS.json": "f4ee4499c80a9dd4b76baf3ac4ca9bc9bf9ee8f1a227bdc58d3c0ae673e3e9ec",
+  "evidence/CEILING.json": "b4d3f30c8b3c4f3c70c292701ac090683920796acfe8751977088e2d269d117a",
+  "evidence/CHECK.json": "65e63cf4d21d4e10a6815a353f6e68da6e36e26f868e2220e2fac38be5fc9e42",
+  "evidence/INDEPENDENT-T16.json": "4a9284a43e72d999fec681414a3bafabeb06e24a1afd1d02282108400e7e18c2",
+  "evidence/REPLAY.json": "ecb242003531b8843d2661a267e388c4d4227bec4d925cbf14801168c15b8ad4",
+  "evidence/STAGES.json": "7e980074264c8bb552fcdc804b2d582445540b45b96b2b476e6f136f4652e4c9",
+  "search/aggbound.py": "29d6d16f3eb9eafa8f59411c65d903326bc1bf9fe639ad498d5ab45c70e4904b",
+  "search/buildcand.py": "d9929e5ecfc9e9fcde3e73aa1cfe9ceba4e5032e80b808685014b1b340fa5669",
+  "search/chain.py": "35a6c3281a307a66d5106eea11184e06c15613c787d577a56e6cb19b9fa3dd23",
+  "search/chain2.py": "b302c5af818bfff29e051c38fcc84536aa9c87e720f9b96d0f6205a6d45f962f",
+  "search/compose.py": "8abd9038b1f3568c696c945d7fd0d8b51d45acbf24cd2168f0d982171cdd562c",
+  "search/glob.py": "141d87da8a8561e7d96aed1611018b290c1b87f6e346310df8df2bdd1295e305",
+  "search/glob5.py": "67ec6de30b52702871f92433f3ff6b41f8a7433dea34a2c8ebfcbadb38323ff1",
+  "search/gloop.sh": "75f25f3bed493300c55c32e0a4af115fe5b76a2791a3405d63c32c193a149e47",
+  "search/lib.py": "bd76fda0a3fe47005f898b41c563bb8ba8296a7214a0540bdcf06b22a135ff24",
+  "search/lns.py": "5f46b954dd56410d14191ea1d0ce978fb6a77c90f68d3c7c909200d47434811d",
+  "search/lns2.py": "da2bf08b53ee548a4cc8bc528df379f116d69e03ace89c7c47673ea90c973f1f",
+  "search/loop3.sh": "ccc645661ac7a9ac3d26d7114345e14f6e637d3c7f539d240a3db0f8e64bbbce",
+  "search/loopx.sh": "204ec10b4e26878bfe891001295c4089ecfbda057c8ee99a0649c36748bcd402",
+  "search/loopy.sh": "c7cfc5b9d8d2c405af17dc69464b2b19140f3e8783dcb340bd281d5cb10ce103",
+  "search/mindiff_cls1.py": "faae2f3dfe4f9ec7ae46009af4047cc4b01255188f21365fe8922a86ee01eb95",
+  "search/mindiff_cls2.py": "45a7c9a07d413250f91c47cf6e43d4fc693dfb1f1a8202527e19a7e320e75b4a",
+  "search/mindiff_lns.py": "ff0ab9b7d99279d15f9b61a2451ad63b807c0e6c23eea21a4415f1157f0749e2",
+  "search/mindiff_lns2.py": "d0d88217a7a3267d051414383df8aa40cacdc31bd28e9d48ea3357af591931a8",
+  "search/mindiff_mip.py": "903035615e6766b3141a0e68da0294a5fb081b6d83b090083f09ab8b7681d601",
+  "search/mindiff_reuse.py": "25ff607a3893fa3104546699e5087c4216a34444cba09f1278e405fc16c0cf41",
+  "search/realize.py": "2dd0142935a9b6207388dc3361a7f10144b74fce2874163ef2694d42416fcfb6",
+  "search/score.py": "98c6745585b87dac1652bedf099d39469fe328ef3e3ed850299e967d151e9ac6",
+  "search/sloop.sh": "655d26e0688623a6cb9bc2bbb16e537eb0c3fd50958fee6a9b9631b52cf89afe",
+  "search/winbound.py": "28c33856b9dcebd77ba36c84b6d1dabe66cf33cbf6b70548d16e762db6a260e6",
+  "search/winlp.py": "54882cab2463a0e866589e177cf6763c677f7ff85f67929602a5668c87afcc20",
+  "verify.py": "2d7fc69436136df8588b87639be7fc86687396b3a5ea6d705a301c5d2bf5eeb4"
+}
diff --git a/research/complex-t16-two-stage-cycles/PR-BODY.md b/research/complex-t16-two-stage-cycles/PR-BODY.md
new file mode 100644
index 0000000000..90e40f2c0c
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/PR-BODY.md
@@ -0,0 +1,163 @@
+# Record candidate: T16 owner map from class-level re-solve and guided realisation on the selected supplier (κ=0.001673614205725695), with a proved packing ceiling
+
+## Contribution
+
+This PR adds `research/complex-t16-two-stage-cycles`, a registered research
+package. It is a conditional T16 owner map on the **unchanged selected PR1094
+supplier**, with no new mechanism, plus a proved packing ceiling for that
+supplier.
+
+- **κ = 0.001673614205725695** (conservative 0.001673614202872892).
+- That is **+5.7035e-4 relative** (+9.540e-7) over the selected record
+  (0.001672660197076918) and +9.334e-7 over open PR1407
+  (0.001672680818492982). Over this PR's earlier versions it is +9.297e-7
+  (first, 0.001672684510394236), +9.113e-7 (second, 0.001672702955495933),
+  +5.600e-7 (third, 0.001673054161426948) and +2.723e-7, or +1.6271e-4
+  relative (fourth, 0.001673341928508063).
+- Idle remainders go from `{1:2276, 3:377, 7:7, 48:4866}` (selected) to
+  `{1:2392, 2:8, 3:107, 4:1, 7:5, 16:1, 48:4880}`. Rank mass 1,041,408 and
+  deficit 5,120 are unchanged. The new residual vector majorizes the selected
+  one (equal totals 237,024; `check.py` asserts the partial-sum comparison), so
+  by Karamata's inequality the complex moment strictly decreases for any
+  strictly concave per-residual weight. The value of κ comes from the pinned
+  exact engines and the strict replay.
+- **Standalone diff against the selected map:** `DIFF-vs-selected.json`
+  changes 2,537 of 69,120 rows: 2,170 helpers move to another bin and 367 rows
+  only change their slice offset. Widths, call order, windows and the local and
+  bit suppliers are unchanged. No open PR is needed.
+- The unchanged PR1087 strict replay passes all 11 stages, with controls
+  69/12/6/15. `actual_73column_sigmas` is 10011: the strict audit recomputes
+  this chart count for the realized map and `assemble.py` pins it.
+- The seed67 owner auditor passes R1–R7, X1, X2 and its 11 controls. Pricing
+  with the pinned exact engines and the PR1069 sweep agree with the replay.
+
+With the PR1240 local-word ceiling endpoint a_hi = 0.001690054109089, this map
+realises 6.560% of the complex endpoint gap (fourth version: 4.688%; third:
+2.709%; second: 0.294%; first: 0.167%; PR1407: 0.142%).
+
+It claims no packing optimum and no unconditional theorem. All PR1094
+inherited assumptions remain.
+
+## Proved packing ceiling
+
+`PROOF.md` ("A proved packing ceiling") and `ceiling_bound.py` (standard
+library, exact integer arithmetic, run by `verify.py`) prove two bounds for
+**every** legal owner map on this supplier. The proof relaxes the problem to
+plain bin packing: windows and the family rule are dropped.
+
+- The instance has 32,256 bins (capacities 8, 16, 32, 48; counts 10,752,
+  7,168, 7,168, 7,168) and 69,120 helpers (widths 4, 5, 7, 8, 9; counts
+  144 × (56, 32, 30, 122, 240)). Both are derived from the package data.
+- **At most 4,887 cap-48 bins can be empty.** Give each helper weight ⌊7w/9⌋
+  and each bin weight ⌊7c/9⌋ (6, 12, 24, 37). The helpers in a bin never weigh
+  more than the bin. The total slack is 587,776 − 406,944 = 180,832 for every
+  map, and an empty cap-48 bin uses 37 of it. This map has 4,880 empty cap-48
+  bins; the selected map has 4,866.
+- **The search surrogate `Σ f ln f` is at most 4,887 · 48 ln 48 + 17 ln 17 =
+  908,139.013.** This comes from an exact knapsack over the per-bin slack. A
+  plain LP dual gives 908,156.14. This map is at 907,271.883.
+- Solver-reported, not checked: the class-level window LP and the window + R4
+  IP reach the same optimum, so windows do not tighten the bound.
+
+This bounds the surrogate and the number of empty cap-48 bins, **not κ**. As
+an indication only, pricing the bound-attaining idle multiset
+`{1:2431, 17:1, 48:4887}` with the pinned engines gives κ 0.001674088611862992
+(9.822% of the complex endpoint gap). This replaces the earlier version's
+"≈908.1k" heuristic ceiling, which could not be reproduced.
+
+## How the map was found
+
+Inside a physical family the bins' windows never overlap. So the family rule
+reduces to at most one helper per bin per call, and bins with the same capacity
+and the same allowed calls are interchangeable. κ is close to linear in the
+surrogate `Σ f ln f` over idle fragments, which the search uses as its
+objective; only the exact engines decide acceptance.
+
+1. **Earlier versions' search.** A global class-level repack and
+   cycle/LNS loop (third version), then an evacuation LNS neighbourhood
+   (fourth version), up to κ 0.001673341928508063.
+2. **Class-level re-solve** (new, `search/winlp.py`). The window model is an
+   IP over (capacity, window) classes: pattern counts, flows of each
+   (call, width) to each class, time and width balance, and aggregate R4 cuts
+   for each family group and call. Each step re-solves it warm-started from
+   the current map. Only a random 12–24-class subset may change, drawn from
+   the classes that differ from a full-model target. Each step must gain a
+   minimum surrogate amount and pays a penalty per unit of change.
+3. **Guided realisation** (new, `search/lns2.py` mode `guide`). The neighbourhood
+   is the bins holding helpers whose class (call, width) count must drop, plus
+   the bins whose pattern count must drop. CP-SAT then maximises the surrogate
+   exactly over it, and a result is kept only if the exact κ rises.
+   `search/gloop.sh` and `search/sloop.sh` loop this. Strict-replayed
+   checkpoints: 0.001673373170972473, 0.001673393061983855,
+   0.001673535326871893 and 0.001673614205725695. The search was **stopped
+   while still improving**.
+4. **Min-diff re-assignment** at the same idle profile, hence the same κ. The
+   raw map relocates 63,109 rows against the selected map. The class-level
+   min-diff tools (`search/mindiff_cls1.py`, `mindiff_cls2.py`,
+   `mindiff_lns.py`, `mindiff_lns2.py`, `realize.py`) give 63,109 → 2,210 →
+   2,170 relocations, i.e. 2,537 changed rows of which 367 are offset-only.
+   Two stage-1 class patterns could not be realised, because several helpers of
+   one width in a bin need distinct calls. The README gives the counting
+   argument for each. Both were excluded with `BAN` and stage 1 was re-solved
+   locally. The class-level relaxation implies at least 1,548 relocations for
+   any legal map with this profile (solver-reported). The min-diff stopped at
+   its two-hour budget, so the shipped map is not proven minimal.
+
+`SEARCH.json` records the checkpoints and the commands. `lns.py`, `lns2.py`,
+the loops, `check.py` and `verify.py` compare κ as `Decimal`, because the
+native assembler can drop trailing zeros.
+
+## Earlier versions of this PR
+
+- **First version**, κ 0.001672684510394236: two-stage ejection cycles on
+  PR1407's map, a 23-row successor of PR1407, with the ancestry checked by
+  content.
+- **Second version**, κ 0.001672702955495933: a longer cycle/LNS search, then
+  a min-diff re-assignment to 70 changed rows (55 relocations) against the
+  selected map; the PR1407 ancestry check was dropped.
+- **Third version**, κ 0.001673054161426948: a global class-level repack and
+  the cycle/LNS loop, then a class-level min-diff re-assignment to 1,661
+  changed rows (1,435 relocations). Its idle profile did not majorize the
+  selected one, so it relied on the exact engines alone for the sign.
+- **Fourth version**, κ 0.001673341928508063: an evacuation LNS neighbourhood
+  in the same loop, then the class-level min-diff to 1,638 changed rows (1,415
+  relocations); its profile majorized the selected one again.
+
+This fifth version replaces the map, the diff and the search record, and adds
+the proved packing ceiling. PR1407 (pai-scaffolde) remains the starting point
+of the search line and the source of the whole-helper semantics and all-input
+argument. PR2077 (lydakis) remains the origin of the vacancy-chain idea. Their
+four literal moves still do not compose (`search/compose.py`).
+
+## Provenance
+
+- **Chooser:** this work was not drawn by `scripts/choose_research_task.py`. It
+  was self-selected as the review-and-compose task: a review of PR1407 and
+  PR2077, a test of whether they compose, and then a search on the stronger
+  map. `TASK.json` records it under the closest card, `selected-packing`, with
+  `scope_status: changed` and this reason.
+- **Base:** `0fdd7d82`. The 287 pinned inputs are listed in `INPUTS.json` and
+  `SOURCES.json`.
+- **Credit:**
+  - pai-scaffolde (PR1407): starting map of the search line, whole-helper
+    semantics and all-input argument.
+  - George Lydakis (lydakis, PR2077): the vacancy-chain idea.
+  - Rohan Arun and Jeremy Kothe: the PR1050–PR1094 line and the selected
+    supplier and map.
+  - Josie Elliston: the seed67 auditor, PR1091.
+  - Sagar Thakrar: the independent pricing sweep, PR1069.
+- **Prepared by** Philippe Van Velzen with substantial Claude Code (Claude
+  Opus 5.5) assistance. No independent human review is claimed.
+
+## Reproduce
+
+```sh
+python3 scripts/research_package.py --package research/complex-t16-two-stage-cycles --check-only
+python3.12 scripts/research_package.py --package research/complex-t16-two-stage-cycles
+```
+
+The full replay takes about 60 s and uses only the standard library. The
+search is optional and needs numpy, ortools, scipy and highspy; the README and
+`SEARCH.json` give the commands.
+
+🤖 Generated with [Claude Code](https://claude.com/claude-code)
diff --git a/research/complex-t16-two-stage-cycles/PROOF.md b/research/complex-t16-two-stage-cycles/PROOF.md
new file mode 100644
index 0000000000..b367c3c4cf
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+# Why the owner map is admissible and strictly cheaper
+
+## Domain
+
+This argument is the same as PR1407's (`research/astra-ultra-hosting-20261013/PROOF.md`
+at `d8640f5b`). Relative to the selected PR1094 map, only the physical owner,
+port and slice offset of whole helper roles change. The local gauge44 provider (480 whole helpers per call), the 144
+complete calls and their order, orientations, source events, endpoint adapters,
+global bridges and terminal corrections all stay fixed. `build.py` asserts that
+every changed row keeps `stage`, `replica`, `time`, `helper` and `width`.
+
+The bin `(o, c, p)` is owner replica `o`, idle child `c` and port `p`. Its
+capacity is the rank of `c`. Its borrowing interval is the original idle
+transition: after the owner's last source-event touch and before its idle
+deadline, with all 144 bridges included. A placement of helper `h` of call `k`
+into `(o, c, p)` is legal under four conditions:
+
+1. **Capacity.** The widths assigned to the bin fit its rank, and the slices
+   are a prefix `0..used-1`.
+2. **Window.** The call position lies strictly inside the bin's interval.
+3. **Family.** The physical family `o*F + (2*pair+side)*V + p` is used by no
+   other helper of the same call.
+4. **Integrity.** `copy = 112*o + p`, each helper appears once per call, and no
+   helper is split.
+
+The search (global class-level repack, ejection cycles, CP-SAT neighbourhood
+re-assignments including the evacuation neighbourhood, class-level re-solves
+with guided realisation, and the final min-diff re-assignment) only proposes a
+final owner table. Intermediate states
+are not executed; the controller only ever sees the final table. So it is
+enough to check the final map, and this package checks it three independent
+times:
+
+- `build.py`'s own packing checker covers 1, 3 and 4 and the window
+  membership of 2 against `PLAN.windows`.
+- The seed67 auditor (Josie Elliston, PR1091) checks R1–R7, X1 and X2 and
+  rejects its 11 mutations. `check.py` also confirms that every role lies
+  strictly inside its window and that each helper appears once per call.
+- The unchanged PR1087 strict verifier re-emits every affected chart. Its
+  controller audit, finite invoice, independent T16 replay and 69 + 12 + 6 + 15
+  rejecting controls all pass.
+
+## All-input operator argument (inherited)
+
+Inside one borrowed bin, the owner has no data touch between the interval's
+opening event and its deadline. Each complete invocation applies its declared
+data shear whatever the incoming helper values are. It also applies its
+residual Clifford operator to the borrowed axes. Distinct slices partition the
+bin's original `c` axes, and the exact Gaussian-dyadic factors commute. So at the
+deadline the assigned slices together with the unused suffix act as the
+original idle child. The owner's value is the original one whenever the
+controller reads it. This is PR1407's argument, applied to a different legal
+final assignment; it needs no new step. It inherits the common-label and
+mutable-source realization assumptions; it does not prove them anew.
+
+## Strict cost improvement
+
+The paid recursive moment depends on the profile through a sum of per-residual
+weights `H(r)` that are strictly concave in the rank `r` with `H(0) = 0`. In the
+PR1407 and PR2077 arguments, `H(r) = r^p` with `0 < p < 1`. Rank mass
+(1,041,408) and deficit (5,120) are unchanged. Against the selected PR1094 map,
+the idle remainder profile changes by
+
+```
+{1:+116, 2:+8, 3:-270, 4:+1, 7:-2, 16:+1, 48:+14}
+```
+
+selected: `{1:2276, 3:377, 7:7, 48:4866}`; this map:
+`{1:2392, 2:8, 3:107, 4:1, 7:5, 16:1, 48:4880}`. The residual totals are equal
+(237,024 on both sides). Sorted in decreasing order and padded with zeros to
+the common number of bins,
+
+```
+new: 48 x 4880, 16 x 1, 7 x 5, 4 x 1, 3 x 107, 2 x 8, 1 x 2392, 0 ...
+old: 48 x 4866,         7 x 7,        3 x 377,        1 x 2276, 0 ...
+```
+
+The partial sums of the new vector are never below those of the old one.
+They agree for the first 4,866 entries (all 48), the new vector leads from
+entry 4,867 on (by 602 after 4,880 entries; the largest lead is 636, after
+4,887 entries), and the old vector never catches up before both reach 237,024
+(after 4,880 + 1 + 5 + 1 + 107 + 8 + 2,392 = 7,394 and
+4,866 + 7 + 377 + 2,276 = 7,526 entries). So the new residual vector majorizes
+the old one, strictly. In words: 270 residuals 3 and two residuals 7 are gone,
+and their residual capacity (824) reappears as 14 more completely idle bins
+(672), one residual 16, one residual 4, eight residuals 2 (16) and 116 more
+residuals 1. `check.py` checks this mechanically: it sorts and pads both
+audited idle vectors, asserts equal totals and that every partial sum of the
+candidate vector is at least the selected one's, with strict inequality
+somewhere, and records the result as `majorization` in `CHECK.json`;
+`verify.py` requires it. By Karamata's inequality for strictly concave `H`,
+
+```
+4880 H(48) + H(16) + 5 H(7) + H(4) + 107 H(3) + 8 H(2) + 2392 H(1)
+  < 4866 H(48) + 7 H(7) + 377 H(3) + 2276 H(1)
+```
+
+(for example 36,417.5 < 36,660.1 at `p = 1/2`). The complex moment strictly
+decreases while rank mass and deficit are unchanged. (Version 3 of this package
+did not have this property and relied on the exact engines alone.)
+
+The sign argument gives the direction only. The value of κ comes from the
+pinned exact engines (moment, base-two moment, outer) and the strict replay,
+not from a hand computation. The native complex lower endpoint is
+`1676419885861434425020/10^24` (selected: `1675462676808103522925/10^24`). The
+bit lower endpoint is unchanged at `1733427039589844234749/10^24`. The complex
+supplier is binding, so κ = `1673614205725695/10^18` = 0.001673614205725695.
+With the conservative bit surcharge, κ = 0.001673614202872892. The unchanged
+strict verifier's own moment engines and outer assembly reach the same κ, and
+the PR1069 sweep independently certifies the endpoint, the deficit identity
+`W - 64N`, halving, the PR589 bit record, and that κ equals both the record and
+the title value. The search used the surrogate `Σ f ln f` over idle fragments
+only to rank candidates; only the final profile matters for κ.
+
+## A proved packing ceiling
+
+This section bounds how far owner packing on this supplier can go, in two
+quantities: the number of completely idle cap-48 bins and the search surrogate
+`E = Σ_bins g(free)` with `g(f) = f ln f` (`g(f) = 0` for `f ≤ 1`). It does
+**not** bound κ directly (see the end of the section). `ceiling_bound.py`
+checks every step with exact integer arithmetic and the standard library only;
+`verify.py` runs it.
+
+**Instance.** The bins are the 288 (owner, idle child) windows of `PLAN.json`
+times 112 ports: 32,256 bins with capacities 8, 16, 32 and 48 and counts
+10,752, 7,168, 7,168 and 7,168. The helpers are the 69,120 rows of the owner
+table (144 calls × 480), with widths 4, 5, 7, 8 and 9 and counts
+144 × (56, 32, 30, 122, 240). `ceiling_bound.py` derives both counts from the
+package data and asserts them. Total capacity minus total width is 237,024, the
+idle total of every legal map.
+
+**Relaxation.** A *packing* assigns each helper to one bin so that the widths
+in each bin sum to at most its capacity. Every legal owner map is a packing;
+windows, the family rule (R4) and call distinctness are dropped. So everything
+below holds for every legal map on this supplier.
+
+**Theorem 1 (empty cap-48 bins).** Let `a(w) = ⌊7w/9⌋`, which gives
+3, 3, 5, 6, 7 for widths 4, 5, 7, 8, 9, and `A(c) = ⌊7c/9⌋`, which gives
+6, 12, 24, 37 for capacities 8, 16, 32, 48. For every multiset of widths with
+sum at most `c`, `Σ a(w) ≤ A(c)`, because `Σ a(w) ≤ 7 Σ w / 9 ≤ 7c/9` and the
+left side is an integer. (`ceiling_bound.py` also checks all 1,163 width
+patterns.) Define the slack of a bin as `A(c) − Σ a(w)` over its helpers. It is
+non-negative, and the slacks of all bins sum to
+
+```
+Σ_bins A(c) − Σ_helpers a(w) = 587,776 − 406,944 = 180,832
+```
+
+for every packing. An empty cap-48 bin has slack 37, so
+`37 · #(empty cap-48 bins) ≤ 180,832 = 37 · 4,887 + 13`: **at most 4,887 cap-48
+bins can be empty.** The selected map has 4,866, this map 4,880.
+
+**Theorem 3 (surrogate).** A bin with slack 0 has free capacity at most 1
+(`9 A(c) ≤ 7(c − f)` gives `f ≤ (7c mod 9)/7 < 9/7`), so it contributes
+`g = 0`. Let `H(s)` be the largest `g(free)` over bins (capacity and width
+pattern) with slack `s`. Then `E ≤ Σ_bins H(s_b)` with `Σ s_b = 180,832`, so `E`
+is at most the optimum of an unbounded knapsack: choose a multiset of slacks
+summing to 180,832 and maximise the sum of `H`. The empty cap-48 bin (slack 37,
+`g(48)`) has the best ratio. Every other bin has `g(free)/slack ≤ g(44)/34`
+(a cap-48 bin holding one width-4 helper), and `g(44)/34 < g(48)/37`. Let `n`
+be the number of empty cap-48 bins.
+
+- For `n ≤ 4,874`, `E ≤ n g(48) + (g(44)/34)(180,832 − 37n)`. This is
+  increasing in `n` and at `n = 4,874` it is below `4,887 g(48) + g(17)`.
+- For `4,875 ≤ n ≤ 4,887`, an exact dynamic programme over the remaining slack
+  (at most 457) gives the best value. It is attained at `n = 4,887` with
+  remaining slack 13, which a single cap-48 bin with free 17 fills (widths
+  9 + 9 + 9 + 4: weight 24, slack 13).
+
+So **`E ≤ 4,887 g(48) + g(17) = 908,139.013`** for every legal map. All
+comparisons are exact: `exp` of a sum of `g` values is a product of integers
+`f^f`, so the checker compares integers. A float knapsack over the full slack
+range is computed as a cross-check and agrees. This map has `E = 907,271.883`
+(867.1 below the bound); the selected map has 905,526.558.
+
+**Theorem 2 (LP dual; weaker, for reference).** With `λ = (36/37) ln 48`, the
+weights `v(4) = v(5) = 4λ`, `v(7) = (20/3)λ`, `v(8) = 8λ`, `v(9) = (28/3)λ`,
+`μ(c) = cλ` for `c < 48` and `μ(48) = 48 ln 48` satisfy
+`g(free) ≤ μ(c) − Σ v(w)` for every pattern. The checker verifies this exactly
+as `f^(qf) ≤ 48^p`. Summing gives `E ≤ (8,679,936/37) ln 48 = 908,156.136`,
+17.1 above Theorem 3.
+
+**Windows and R4 do not tighten it (solver-reported).** In the search session,
+the class-level window LP and the window + aggregate-R4 IP (`search/winlp.py`)
+reached the same aggregate optimum: CP-SAT found a class-level solution with
+idle profile `{1:2431, 17:1, 48:4887}`, which attains Theorem 3. This is a
+solver result on a relaxation; it is not checked here, and a class-level
+solution need not be realisable on concrete bins.
+
+**The 2,392 one-free bins are not waste.** All of this map's residual-1 bins
+are cap-32 bins with the pattern 9 + 9 + 9 + 4. That pattern has slack 0 under
+the 7/9 weights, so these bins cost nothing in Theorem 1. The bound-attaining
+profile has 2,431 of them.
+
+**What this does and does not bound.** Theorems 1 and 3 bound the number of
+empty cap-48 bins and the surrogate `E`. They do not bound κ: κ depends on the
+whole idle profile through the exact engines, and `E` is only approximately
+linear in κ. As an indication only, pricing the bound-attaining idle multiset
+`{1:2431, 17:1, 48:4887}` with the package's pinned engines (`check.py`, recorded
+as `indicative_ceiling_price` in `CHECK.json`) gives κ 0.001674088611862992
+(complex lower endpoint 0.0016768959, 9.82% of the complex endpoint gap). This
+map is 4.744e-7 below that. Nothing here proves that no legal map prices
+higher. That would need, for example, the bound-attaining multiset to majorize
+every attainable idle vector, which is not shown.
+
+## What is not claimed
+
+There is no optimality claim: the κ search is a finite heuristic (global
+repack plus LNS, including the evacuation neighbourhood, then class-level
+re-solves with guided realisation) that was still finding gains when it was
+stopped, and the min-diff step is a finite MIP/LNS whose
+relocation count is not proven minimal over all maps with this profile. The
+majorization argument shows only that this map is strictly cheaper than the
+selected one; the packing ceiling above bounds the surrogate and the number of
+empty cap-48 bins, not κ, and it is not known to be attainable. There is no
+new supplier, interface or mechanism. There is no fresh cold rebuild of the
+native ancestry, and no unconditional theorem. All PR1094 inherited
+assumptions remain.
diff --git a/research/complex-t16-two-stage-cycles/README.md b/research/complex-t16-two-stage-cycles/README.md
new file mode 100644
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--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/README.md
@@ -0,0 +1,392 @@
+# T16 owner map from a class-level re-solve and guided realisation on the selected supplier, with a proved packing ceiling
+
+On the unchanged selected PR1094 supplier, this owner map admits conditional
+**κ = 0.001673614205725695** (conservative surcharge 0.001673614202872892).
+That is **+5.7035e-4 relative** (+9.540e-7) over the selected record
+0.001672660197076918 and +9.334e-7 over open PR1407 (0.001672680818492982).
+Against this PR's earlier versions it is +9.297e-7 over the first
+(0.001672684510394236), +9.113e-7 over the second (0.001672702955495933),
++5.600e-7 over the third (0.001673054161426948) and +2.723e-7 (+1.6271e-4
+relative) over the fourth (0.001673341928508063). The local gauge44 word, helper
+widths, 144-call order, windows, physical stock, native supplier and PR589 bit
+supplier are unchanged. The unchanged PR1087 strict replay passes.
+
+This version also adds a **proved packing ceiling** (`PROOF.md`,
+`ceiling_bound.py`): on this supplier no legal owner map can have more than
+4,887 completely idle cap-48 bins (this map: 4,880; selected: 4,866), and the
+search surrogate `Σ f ln f` is at most 908,139.013 (this map: 907,271.883).
+This bounds the surrogate, not κ.
+
+**Scope.** This is a conditional T16 packing on the same supplier, with no new
+mechanism. The map is stated and verified **only against the merged selected
+PR1094 map**: `DIFF-vs-selected.json` changes @CHG@ of its 69,120 rows
+(@REL@ helpers move to another bin; @OFF@ more rows only change their slice
+offset). It depends on no open PR. It claims no packing optimum and no
+unconditional multiplication theorem.
+
+## Versions of this PR
+
+1. κ 0.001672684510394236: two-stage ejection cycles on PR1407's map (a
+   23-row successor of PR1407).
+2. κ 0.001672702955495933: depth-8 ejection cycles alternated with CP-SAT
+   large-neighbourhood re-assignments, then a min-diff re-assignment to 70
+   changed rows against the selected map.
+3. κ 0.001673054161426948: a global class-level repack followed by the same
+   cycle/LNS loop, then a class-level min-diff re-assignment (1,661 changed
+   rows, 1,435 relocations).
+4. κ 0.001673341928508063: version 3's map continued with an evacuation LNS
+   neighbourhood (nearly empty bins re-packed), then the same min-diff
+   (1,638 changed rows, 1,415 relocations).
+5. This version, κ 0.001673614205725695: version 4's map improved by
+   class-level re-solves of a window model warm-started from the current map,
+   each realised on concrete bins by a guided CP-SAT neighbourhood, then the
+   same class-level min-diff re-assignment. The idle profile still majorizes the
+   selected one (`PROOF.md`). New: a proved packing ceiling.
+
+## Construction
+
+A bin is `(owner replica, idle child, port)`. Its capacity and borrowing window
+come from the selected PR1094 plan. A placement puts one whole helper role of
+one call into a bin. It must fit the free capacity, the call must lie strictly
+inside the bin's window, and the bin's physical family must be unused by every
+other helper in that call. No helper is split and no call is reordered.
+Helpers of the same call and width are interchangeable under these rules.
+
+### Why a global repack
+
+Version 2's loop (ejection cycles plus CP-SAT LNS) had slowed to steps of about
+1e-9 in κ. Three observations led to a global model instead:
+
+* κ is, to good accuracy, a linear function of the surrogate `Σ f ln f` over
+  the idle fragments (free capacities `f`), so the surrogate is a usable
+  objective for a global model; only the exact engines decide acceptance.
+* Inside one physical family the bins' windows never overlap. So the family
+  rule (R4) reduces to "at most one helper per bin per call", and two bins with
+  the same capacity and the same set of allowed calls (a *class*: 144 classes
+  of 224 bins each) are interchangeable.
+* The problem therefore becomes a class-level pattern/flow model: how many bins
+  of each class get each width pattern, and how many helpers of each
+  (call, width) each class hosts.
+
+### κ search (`search/`, `SEARCH.json`)
+
+Steps 1–3 are version 3's search, steps 4–5 version 4's, and steps 6–7 are
+new in this version.
+Starting from version 2's raw search output (content `a7e8f0ca…`):
+
+1. **Stage 1** (`glob.py`): CP-SAT over pattern counts and flows per class,
+   with per-(class, call) Hall constraints (a call can use at most as many bins
+   of a class as there are bins whose pattern holds the widths it needs) and
+   Gale–Ryser-style constraints for several helpers of one width in a bin
+   (they need distinct calls), maximising the surrogate. Best stage 1:
+   906,706 surrogate units (the start map had 905,605).
+2. **Stage 2** (`glob5.py`): per class and width, a max-flow from calls to
+   bins realises the stage-1 solution with distinct calls per bin. Stage 1 is a
+   relaxation, so 80 helpers stayed unplaced; they were inserted greedily where
+   they cost the least surrogate. The realised map had κ 0.001672432283943020,
+   lower than the start but with a very different profile.
+3. **Loop** (`loopx.sh`): chain2 ejection cycles alternated with CP-SAT LNS
+   plateau steps (`lns.py`, now with a worker-count setting `NW` and an `f3`
+   neighbourhood mode), keeping the best map by exact κ. Strict-replayed
+   checkpoints: κ 0.001672894024167899 and 0.001673054161426948 (version 3).
+4. **Evacuation neighbourhood** (`lns.py`, mode `evac`, size `NB`). On
+   version 3's map, many cap-48 bins held only a few small helpers. The new
+   neighbourhood picks 1–3 such stranded bins (used ≤ 20), bins with spare
+   room and full bins whose windows contain some of the stranded helpers'
+   calls, and a few empty bins; it frees all their helpers and re-packs them
+   exactly with CP-SAT. A single 102-bin solve from version 3's map emptied
+   35 cap-48 bins (+291 surrogate units, 906,247 → 906,538) and gave
+   κ 0.001673213119136600.
+5. **Loop with evacuation** (`loopy.sh`): `loopx.sh` with `evac` in the mode
+   mix. Strict-replayed checkpoints: 0.001673243717212927,
+   0.001673272876788591, 0.001673312438393585, 0.001673322090452138 and
+   0.001673341928508063 (surrogate 906,774).
+6. **Class-level re-solve** (`winlp.py`, new). The window model of the global
+   repack, as an IP over (capacity, window) classes: pattern counts per class,
+   flows of each (call, width) to each class, time and width balance, and
+   aggregate R4 cuts (for each group of classes that share physical families
+   and each call, at most one helper per family). A full solve gives a target
+   class solution. Each step then re-solves the model warm-started from the
+   current map, frees only a random subset of 12–24 classes drawn from those
+   that differ from the target (all others fixed to the current map), and
+   requires a minimum surrogate gain (`GAIN`) at a penalty per unit of change
+   (`PEN`).
+7. **Guided realisation** (`lns2.py`, mode `guide`, new). The class solution
+   of step 6 is realised on concrete bins by a CP-SAT neighbourhood made of
+   the bins holding helpers whose class (call, width) count must drop, plus
+   the bins whose pattern count must drop. CP-SAT maximises the surrogate
+   exactly over that neighbourhood, and the result is kept only if the exact κ
+   rises. `gloop.sh` repeats this toward one fixed target; `sloop.sh` loops
+   steps 6–7. Two short `loopy.sh` runs first took version 4's map to
+   0.001673344533458160 (not strict-replayed); strict-replayed checkpoints
+   from there:
+   0.001673373170972473 (`gloop.sh`), 0.001673393061983855,
+   0.001673535326871893 and 0.001673614205725695 (`sloop.sh`, two loops whose
+   best maps were synchronised; surrogate 907,271.88).
+
+The search was **stopped while still improving** (the class-level loop was
+still finding gains when it was stopped). It is a finite heuristic, not an
+optimum. The
+session's loop scripts compared κ strings in one place; `lns.py` and the loops
+now compare κ as `Decimal` (the native assembler can drop trailing zeros, e.g.
+`0.0016732131191366` for `0.001673213119136600`).
+
+**Proved ceiling.** The earlier text here reported a heuristic ceiling of
+"about 908.1k surrogate units" from `winbound.py` that could not be reproduced.
+This version replaces it with a proof (`PROOF.md`, "A proved packing ceiling";
+checked by `ceiling_bound.py`, which `verify.py` runs). The proof uses integer
+weights `a(w) = ⌊7w/9⌋` per helper and `A(c) = ⌊7c/9⌋` per bin. Every bin's
+helpers weigh at most `A(c)`, and total bin weight minus total helper weight
+is 180,832 for every map. So **at most 4,887 cap-48 bins can be empty**, and
+an exact knapsack over the per-bin slack gives **`Σ f ln f ≤ 4,887 · 48 ln 48 +
+17 ln 17 = 908,139.013`** for every legal map. This map is at 4,880 empty cap-48
+bins and 907,271.883. The bound is on the surrogate, not on κ. Pricing the
+bound-attaining idle multiset `{1:2431, 17:1, 48:4887}` with the pinned
+engines gives κ 0.001674088611862992 (`check.py`). This is only an indication
+of the remaining room (4.744e-7 above this map); it is not a κ bound.
+`winbound.py` and `aggbound.py` remain as search tools only.
+
+### Min-diff re-assignment
+
+Given the selected map A and the search output F, find a legal map with F's
+idle profile (hence F's κ) that keeps as many placements of A as possible. A
+placement is `(bin, call, width)`, since helpers of one call and width are
+interchangeable. The raw search output F relocates 63,109 rows against A
+(66,449 changed rows). This version reuses the class-level tools of versions 3
+and 4:
+
+1. `mindiff_cls1.py` (HiGHS, 1,800 s, warm-started from F): a class-level MIP
+   over pattern counts and flows, with the idle profile fixed to F's,
+   maximising the flow of A's (class, call, width) placements that stays in
+   place. It stopped at the time limit with 67,539 placements' worth of flow
+   (1,581 relocations) and 58 classes changed. The dual bound implies at least
+   1,548 relocations for any legal map with F's profile once the tie-break
+   weight (at most 0.001 per bin, 32,256 bins) is discounted. That is a
+   solver-reported bound, not an independently checked certificate.
+2. `mindiff_cls2.py` (CP-SAT pass, then HiGHS pass, per changed class)
+   realised 56 of the 58 classes. Two stage-1 class solutions could not be
+   realised, because stage 1 does not see that several helpers of one width in
+   a bin need distinct calls:
+   - Class 9 (capacity 16, calls 0–8) had the same unrealisable pattern as in
+     version 4: fourteen bins with four width-4 helpers, while only calls 5, 6
+     and 8 have more than two width-4 helpers.
+   - Class 25 (capacity 32, calls 51–112) needed five (7, 7, 9, 9) bins and
+     one (7, 8, 8, 9) bin. The class's 7s come from calls 92 (6), 98 (4) and
+     99 (1), and its only 8s from calls 92 and 102. So the (7, 8, 8, 9) bin's 7
+     is not from call 92. That leaves at most four 7-pairs with distinct calls,
+     not five.
+
+   Both patterns were forbidden with `BAN`. Stage 1 was re-solved twice with
+   `KEEP` (all other classes fixed to the previous stage-1 solution) and
+   `FREE` (the classes sharing calls with the banned one): first class 9 with
+   13 overlapping cap-16 classes (optimal at once, same 1,581), then class 25
+   with 20 overlapping cap-32 classes (optimal, 1,583). `mindiff_reuse.py`
+   kept the class results that did not change. All 58 classes were realised;
+   the merge gives 2,210 relocations.
+3. `mindiff_lns.py` (two seeds): 2,210 → 2,183. One round of
+   `mindiff_lns2.py` (two seeds, the better one kept): 2,170. It was stopped
+   at the two-hour min-diff budget. The stage-1 solve took half of that
+   budget, and the LNS was gaining only a few relocations per round.
+4. `realize.py` keeps A's helper labels and offsets where possible:
+   **2,170 relocations and 367 offset-only changes (2,537 changed rows)**,
+   against 63,109 relocations in the raw search output.
+
+This is a heuristic too. The relocation count is not proven minimal. Most of
+the gap to the class-level count (1,583) comes from realising the class
+solutions on concrete bins (stage 2 loses about 630 placements), so stage 1
+is a loose relaxation here. The diff is larger than version 4's (1,415)
+because the new profile is further from the selected one (14 more empty cap-48
+bins instead of 8, 270 fewer residuals 3 instead of 205).
+
+## Exact profile change
+
+| | idle remainder profile | κ |
+|---|---|---|
+| selected PR1094 | `{1:2276, 3:377, 7:7, 48:4866}` | 0.001672660197076918 |
+| PR1407 | `{1:2277, 3:377, 16:3, 48:4866}` | 0.001672680818492982 |
+| version 1 of this PR | `{1:2278, 3:374, 8:1, 16:3, 48:4866}` | 0.001672684510394236 |
+| version 2 of this PR | `{1:2280, 2:1, 3:363, 7:3, 16:4, 48:4866}` | 0.001672702955495933 |
+| version 3 of this PR | `{1:2346, 2:3, 3:154, 5:9, 7:36, 8:2, 16:7, 28:1, 39:1, 40:1, 41:2, 44:41, 48:4829}` | 0.001673054161426948 |
+| version 4 of this PR | `{1:2355, 2:2, 3:172, 7:3, 16:11, 48:4874}` | 0.001673341928508063 |
+| this package | `{1:2392, 2:8, 3:107, 4:1, 7:5, 16:1, 48:4880}` | 0.001673614205725695 |
+| proved bound (not a map) | at most 4,887 empty cap-48 bins; `Σ f ln f ≤ 908,139.013` | — |
+
+Compared with the selected map, the idle profile changes by
+`{1:+116, 2:+8, 3:-270, 4:+1, 7:-2, 16:+1, 48:+14}`. Fourteen more bins are
+completely idle than in the selected map (version 4: eight), 270 residuals 3
+and two residuals 7 are gone. The full paid profile is
+`{1:349720, 2:60200, 3:62315, 4:20449, 5:11808, 7:5, 8:1152, 16:1, 48:4880}`.
+Rank mass is still 1,041,408 and the deficit is still 5,120. Cross-replica
+helper roles go from 57,480 to 57,420. With equal residual totals (237,024), the
+new residual vector majorizes the selected one, so Karamata's inequality gives
+the strict decrease of the complex moment for any strictly concave
+per-residual weight. `check.py` asserts the majorization mechanically, and the
+value of κ still comes from the exact engines and the strict replay
+(`PROOF.md`).
+
+`SPEC.expected.actual_73column_sigmas` is **10011** (selected: 10002; the raw
+search output had 10564). This value is not a tuning knob. The strict audit
+counts the distinct orthogonal 73-column charts that the realized owner
+chronology uses. `assemble.py` pins that count against SPEC exactly, and an
+`understated_actual_chart_types` mutation control guards it. It depends on the
+map, so the strict verifier recomputes it on every replay.
+
+Fraction of the complex endpoint gap: with the PR1240 local-word ceiling
+endpoint a_hi = 0.001690054109089, this map realises **6.560%** of the complex
+endpoint gap (version 4: 4.688%; version 3: 2.709%; version 2: 0.294%;
+version 1: 0.167%; PR1407: 0.142%). The idle multiset that attains the proved
+surrogate bound would, if a legal map realised it, price at κ
+0.001674088611862992, or 9.822% of that gap. That number is indicative, not a
+bound (`PROOF.md`).
+
+## Reproduce
+
+Run from a complete checkout at or after base `0fdd7d82`, with Python 3.12 and
+the standard library only:
+
+```sh
+python3 scripts/research_package.py --package research/complex-t16-two-stage-cycles --check-only
+python3.12 scripts/research_package.py --package research/complex-t16-two-stage-cycles
+# or directly, keeping the work tree:
+python3.12 -I -B research/complex-t16-two-stage-cycles/verify.py --work /abs/fresh/dir
+```
+
+`verify.py` follows the PR2077 package (`research/complex-t16-vacancy-chain`):
+
+1. It checks the 287 pinned inputs (`INPUTS.json`) and the package inventory
+   (`MANIFEST.json`).
+2. `build.py` applies `DIFF-vs-selected.json` to the merged selected PR1094
+   map. It checks that only owner fields change, counts the changed and
+   relocated rows, recomputes the idle histogram with its own packing checker,
+   and regenerates `PLAN.json` and `SPEC.json` byte for byte.
+   `OWNERS.json.gz` is compared on its decoded payload.
+3. It restores the PR1087 archive (`upstream1087.tar.gz`), checks all 179
+   archived files, overlays only the three data files, and extracts the selected
+   R480 gauge44 provider from `selected-replay.tar.gz` (`LOCAL-PINS.json`). It
+   then runs the unchanged `verify_t16.py`, which covers all 11 stages and
+   69/12/6/15 rejecting controls, and requires `actual_73_axis_charts` = 10011.
+4. It runs `check.py`, an independent check adapted from the session's
+   `checkmap.py`. That check uses the seed67 owner auditor (R1–R7, X1, X2 and
+   11 controls) on both the selected and the candidate map. It also prices with
+   the pinned exact engines and runs the PR1069 sweep on the strict replay's
+   lowers. It asserts that the candidate's idle residual vector strictly
+   majorizes the selected one (equal totals, partial sums of the sorted,
+   zero-padded vectors), and `verify.py` requires that result. All κ decimals
+   are compared as `Decimal`, never as strings, because the native assembler
+   drops trailing zeros.
+   It also prices the idle multiset that attains the proved surrogate bound
+   (`indicative_ceiling_price`, indicative only).
+5. It runs `ceiling_bound.py`, the proved packing ceiling (`PROOF.md`): it
+   derives the bins and helper widths from `data/`, checks Theorems 1–3 with
+   exact integer arithmetic (standard library only, under a second), and
+   reports this map's empty cap-48 bins and surrogate against the bound.
+
+The full replay takes about 60 s and stays under 1 GB of RAM. `evidence/`
+holds the receipts of the local run.
+
+The search needs third-party packages and proves nothing; `SEARCH.json` records
+the commands and checkpoints. Solver time limits are wall clock and some seeds
+came from bash `$RANDOM`, so a rerun can land on a different map of similar
+quality. The min-diff step, from the search output F (content SHA256 in
+`SEARCH.json`), ran as follows:
+
+```sh
+S=research/complex-t16-two-stage-cycles/search; W=<work dir>; F=<search output F>
+PY="uv run -q --no-project --python 3.12"; HI="--with scipy --with highspy"
+stage2() {   # stage-1 json, cache dir, CP-SAT limit, HiGHS limit; the two halves ran in parallel
+  for h in 0/2 1/2; do
+    $PY --with ortools python -I $S/mindiff_cls2.py $S $1 $2 $3 $4 $h cp
+    $PY $HI python -I $S/mindiff_cls2.py $S $1 $2 $3 $4 $h hi
+  done; }
+$PY $HI python -I $S/mindiff_cls1.py $S $F $W/c1.json 1800 $F       # time limit: 1,581 (bound: >= 1,548)
+stage2 $W/c1.json $W/cache 60 150                                    # classes 9 and 25 not realised
+# (class 25 alone with 300 s / 900 s limits: no solution; it is infeasible, see above)
+BAN='[[9,[4,0,0,0,0]]]' KEEP=$W/c1.json FREE='[9,0,18,27,36,90,99,108,117,126,135,45,54,63]' \
+  $PY $HI python -I $S/mindiff_cls1.py $S $F $W/c1b.json 900          # optimal, 1,581
+python3 $S/mindiff_reuse.py $W/c1.json $W/c1b.json $W/cache $W/cache2  # 53 of 58 reused
+stage2 <c1b.json with "changed" restricted to [0,9,18,27]> $W/cache2 60 300   # realised
+BAN='[[9,[4,0,0,0,0]],[25,[0,0,1,2,1]]]' KEEP=$W/c1b.json \
+  FREE='[25,7,16,34,38,43,52,56,61,65,79,88,97,106,110,115,119,124,128,133,137]' \
+  $PY $HI python -I $S/mindiff_cls1.py $S $F $W/c1c.json 600          # optimal, 1,583
+python3 $S/mindiff_reuse.py $W/c1b.json $W/c1c.json $W/cache2 $W/cache3   # 55 of 58 reused
+stage2 $W/c1c.json $W/cache3 60 300                                  # classes 16, 25, 52: realised
+$PY python -I $S/mindiff_cls2.py $S $W/c1c.json $W/cache3 $W/cls.json merge   # 2,210 relocations
+$PY $HI python -I $S/mindiff_lns.py $S $F $W/cls.json $W/l1.json 40 1 300 30      # 2,183 (seed 2: 2,183)
+$PY $HI python -I $S/mindiff_lns2.py $S $W/l1.json $W/l2.json 20 12 80 60         # 2,170 (seed 11: 2,176)
+$PY python -I $S/realize.py $S $W/l2.json $W/OWNERS.json.gz
+$PY python -I $S/buildcand.py $S $W/OWNERS.json.gz $W/pkg 10011   # count read from the native audit
+```
+
+The search steps of this version ran as follows (bash `$RANDOM` seeds in
+places, wall-clock limits, and two loops whose best maps were copied between
+them by hand-run sync steps, so not replayable bit for bit; which full-model
+target file each loop used was not logged):
+
+```sh
+S=research/complex-t16-two-stage-cycles/search
+PY="uv run -q --no-project --python 3.12 --with numpy --with scipy --with ortools"
+# full class-level window + R4 model, hinted with a current map: a target class solution
+$PY python -I $S/winlp.py $S <map> ip <TL> 1 2 <target.json>
+# guided realisation toward one target (first checkpoint), then the re-solve loop
+RUN=<memory cap prefix> $S/gloop.sh <dir> <version 4 map> <target.json> 2 <seed> <iters>
+RUN=<memory cap prefix> $S/sloop.sh <dir> <best so far> <target.json> <seed> <iters>
+```
+
+Version 4's search steps (evacuation solve and `loopy.sh`) are described in
+`SEARCH.json` (`fourth_version`).
+
+## Assumptions retained
+
+The all-size compiler, common-label/mutable-source realization, whole-call
+hosting, precision/tape, exact recovery, analytic transfer and PR589 bit H1–H5
+assumptions of the selected PR1094 record remain. The native local receipts are
+reused with source binding; the ancestry is not rebuilt cold. Hosted CI and
+maintainer acceptance are separate.
+
+## Credit
+
+- **pai-scaffolde, PR1407**: the search line started from its owner map
+  (through the first version of this package), and this package reuses its
+  whole-helper neutral-path semantics and all-input argument. The final map is
+  no longer a row-for-row descendant of PR1407's map, but the line of work is
+  its.
+- **George Lydakis (lydakis), PR2077** contributed the vacancy-chain idea of
+  propagating free capacity through occupied bins, the ancestor of the
+  ejection cycles. Its four literal moves do not compose with PR1407 (all 15
+  subsets are illegal on PR1407's map; `search/compose.py`).
+- **Rohan Arun and Jeremy Kothe**: the PR1050–PR1094 owner-packing line and the
+  selected PR1094 supplier and map.
+- **Josie Elliston**: the seed67 owner auditor (PR1091), used in `check.py` and
+  in the search's legality oracle.
+- **Sagar Thakrar**: the independent pricing sweep (PR1069), used in `check.py`.
+- The strict verifier, exact engines and their predecessors keep their original
+  authors and notices, which are unchanged.
+
+Prepared by Philippe Van Velzen with substantial Claude Code (Claude Opus 5.5)
+assistance. No independent human review is claimed. New material is Apache-2.0.
+
+## Open next questions
+
+The structured versions are in `TASK.json`:
+
+- **Continue the κ search.** It stopped while still improving. The first step
+  is to rerun `search/sloop.sh` from `data/OWNERS.json.gz` toward a full
+  `winlp.py` target under a memory cap, strict-replay each new best, and rerun
+  the min-diff step on the result. The proved ceiling leaves at most seven more
+  empty cap-48 bins and 867 surrogate units.
+- **A κ ceiling for owner packing.** The proved ceiling bounds the surrogate
+  (908,139.013) and the number of empty cap-48 bins (4,887), not κ. Pricing
+  the bound-attaining idle multiset gives κ 0.001674088611862992, but that is
+  not a bound. A κ bound needs either a majorization argument (does the
+  bound-attaining multiset majorize every attainable idle vector?) or the
+  relaxation stated in the exact per-residual cost.
+- **Is the ceiling attainable?** The window + R4 class model reaches it
+  (solver-reported), but no concrete map is known with more than 4,880 empty
+  cap-48 bins.
+- **A smaller diff.** The min-diff map (2,170 relocations) is not proven
+  minimal for its profile. The solver-reported relaxation bound is 1,548, and
+  the stage-1 solution itself needs 1,583. Distinct-call (Gale–Ryser)
+  constraints in `mindiff_cls1.py` would stop stage 1 from proposing
+  unrealisable class patterns; this version needed `BAN` for two classes.
+  Stage-2 realisation that also trades placements between classes, and longer
+  `mindiff_lns2.py` runs, may shrink it.
diff --git a/research/complex-t16-two-stage-cycles/SEARCH.json b/research/complex-t16-two-stage-cycles/SEARCH.json
new file mode 100644
index 0000000000..fac77a26da
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/SEARCH.json
@@ -0,0 +1,901 @@
+{
+ "scope": "A heuristic search record. Nothing here is an optimality proof: the kappa search (global class-level repack, ejection cycles, CP-SAT LNS including the evacuation neighbourhood, class-level re-solves with guided realisation) is finite and was stopped while still improving, and the min-diff step is a finite MIP/LNS. The proved packing ceiling is in PROOF.md and ceiling_bound.py; solver results quoted here are solver-reported. Every shipped number is re-derived from data/ by verify.py (strict replay, seed67 audit, exact pricing, majorization check, ceiling check).",
+ "environment": "CPython 3.12.14 via uv (uv run -q --no-project --python 3.12 --with ...), Linux x86_64, each job in a systemd scope with MemoryMax 4-6G, at most 2 busy workers. kappa search: numpy, scipy, ortools (CP-SAT). min-diff: numpy, scipy, highspy 1.15.1 (HiGHS, 1 thread), ortools (CP-SAT, 1 worker). ortools and highspy clash when loaded in one process, so mindiff_cls2.py runs its CP-SAT and HiGHS passes separately.",
+ "lineage": {
+  "pr1407_owner_content_sha256": "008694b29e3b513c8e88367e30ab2d231ea5a0b0dd85cc1efc372f60b9fbdf4c",
+  "first_version_owner_content_sha256": "714a63d290e2f9c8e1c14c289e67ab15593bd1487e6ad592d06c65c8d6ec1d32",
+  "first_version_kappa_decimal": "0.001672684510394236",
+  "note": "Search line: PR1407's map -> first version (two-stage cycles) -> second version's raw kappa search output (content a7e8f0ca...) -> global repack and cycle/LNS loop (third version; its min-diff map d05a885e...) -> evacuation LNS and loop (fourth version; its min-diff map 54a19c57...) -> loopy.sh, class-level re-solves and guided realisation (this version) -> min-diff toward the selected PR1094 map. Neither PR1407's map nor the earlier versions are exact ancestors of data/OWNERS.json.gz; the package is verified only against the selected map.",
+  "second_version_owner_content_sha256": "1764f4310b7c91b69f0533b0b95fa0d4fba267d05d6e4e870aac2d4c310d4d4d",
+  "second_version_kappa_decimal": "0.001672702955495933",
+  "third_version_owner_content_sha256": "d05a885e8cc6a38dfbc9389e61769b4cb916ee858338e3fc3d6bcff6b877569d",
+  "third_version_kappa_decimal": "0.001673054161426948",
+  "fourth_version_owner_content_sha256": "54a19c57be93e86f8cc4a9aab5ee38f58449ae64b0a80ceea95415ba3a6574ac",
+  "fourth_version_kappa_decimal": "0.001673341928508063"
+ },
+ "kappa_search": {
+  "observations": [
+   "Version 4's loop (chain2 cycles, CP-SAT LNS with evac) was slowing down; the class-level window model of version 3 (pattern counts and flows per (capacity, window) class) still had room: a full window + aggregate-R4 IP (winlp.py) reaches surrogate 908,139 (idle {1:2431, 17:1, 48:4887}), against 906,774 for version 4's map.",
+   "A full repack to such a target destroys the current map (version 3's experience); instead each step re-solves the class model with only a small random set of classes free and a change penalty, and realises the class change locally with CP-SAT.",
+   "kappa is close to linear in the surrogate sum f ln f over idle fragments; acceptance always uses the exact engines."
+  ],
+  "start": "Version 4's shipped map data/OWNERS.json.gz (content 54a19c57be93e86f8cc4a9aab5ee38f58449ae64b0a80ceea95415ba3a6574ac, kappa 0.001673341928508063, surrogate 906,773.72).",
+  "tools": [
+   "search/winlp.py: class-level window LP (scipy/HiGHS) or IP (CP-SAT) with aggregate R4 cuts per family group and call; ip mode options HINT, FREE/SEED (only a random class subset may change), FREEFROM (draw that subset from classes that differ from a full-model target JSON), PEN (change penalty), GAIN (minimum surrogate gain).",
+   "search/lns2.py: lns.py plus mode guide (neighbourhood from a class target: bins holding helpers whose class (call, width) count must drop, bins whose pattern count must drop, up to GMUL x excess + 1 each, for a fraction GFRAC of the differing classes; CP-SAT maximises the surrogate exactly) and mode rc; kappa compared as Decimal.",
+   "search/gloop.sh: repeated lns2.py guide steps toward one fixed target.",
+   "search/sloop.sh (portable copy of the session's sloop.sh and sloop2.sh): per step, winlp.py ip with FREE = 12, 18 or 24 classes drawn from those differing from TARGET, PEN=1000, GAIN=1, 120 s, 2 workers; then lns2.py guide (GFRAC=1, GMUL=2, two solves of up to 150 s); keep the result if the exact kappa rises."
+  ],
+  "how_it_ran": "Interactively. Two short loopY.sh runs (loopy.sh) from version 4's map reached 0.001673343161879072 and then 0.001673344533458160 (not strict-replayed). Full winlp.py solves (window LP, window + R4 IP; several runs with different time limits and penalties, flags not all logged) gave class targets; one reached the idle profile {1:2431, 17:1, 48:4887}, which attains the proved surrogate bound (PROOF.md). gloop.sh toward a target from 0.001673344533458160 gave the first checkpoint; then two sloop.sh loops (sloop2.sh for the second) ran in parallel, and their best maps were copied between them by a small sync script when one was ahead. The exact target JSON and seeds of each segment were not all logged, so this phase is described, not replayable command by command. A short third loop (sloop2.sh) reached 0.001673587153654833 and was not used.",
+  "checkpoints": [
+   {
+    "via": "gloop.sh (guided realisation toward a full winlp.py target)",
+    "owner_content_sha256": "8e3121a3a651c74f90134561558d9df319653948568df2f92e29c41a207f7df4",
+    "kappa_decimal": "0.001673373170972473",
+    "idle_remainder_profile": {
+     "1": 2353,
+     "2": 1,
+     "3": 172,
+     "5": 1,
+     "7": 12,
+     "16": 1,
+     "48": 4876
+    },
+    "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10659"
+   },
+   {
+    "via": "sloop.sh",
+    "owner_content_sha256": "2d0bb524b186c8e66256c5ef9fba52994525be0006305bc5609aad8470bbda14",
+    "kappa_decimal": "0.001673393061983855",
+    "idle_remainder_profile": {
+     "1": 2356,
+     "3": 163,
+     "5": 1,
+     "7": 12,
+     "10": 1,
+     "16": 2,
+     "48": 4876
+    },
+    "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10658"
+   },
+   {
+    "via": "sloop.sh / sloop2.sh (synchronised)",
+    "owner_content_sha256": "55883d83cb65a4bac7b53a827763bfac7e7048df6a939292befed130e5d4f5b4",
+    "kappa_decimal": "0.001673535326871893",
+    "idle_remainder_profile": {
+     "1": 2378,
+     "2": 10,
+     "3": 137,
+     "7": 1,
+     "16": 1,
+     "48": 4879
+    },
+    "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10571"
+   },
+   {
+    "via": "sloop.sh / sloop2.sh (raw search output F)",
+    "owner_content_sha256": "4c4a97040016b34ab7431fd351c12c286a4b4245fa73780fe0cf48e9fe1bfc3b",
+    "kappa_decimal": "0.001673614205725695",
+    "idle_remainder_profile": {
+     "1": 2392,
+     "2": 8,
+     "3": 107,
+     "4": 1,
+     "7": 5,
+     "16": 1,
+     "48": 4880
+    },
+    "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10564",
+    "conservative_kappa_decimal": "0.001673614202872892",
+    "surrogate": 907271.88,
+    "changed_rows_vs_selected": 66449,
+    "relocated_rows_vs_selected": 63109
+   }
+  ],
+  "stopped": "Stopped at the end of the session's budget while still improving; no stall criterion was met.",
+  "tooling_bug": "The session's lns2.py compared kappa strings (k > best_k), like lns.py before version 4's fix; the shipped lns2.py compares Decimal. Every checkpoint above was re-verified by a strict replay and Decimal comparisons."
+ },
+ "packing_ceiling": {
+  "status": "Proved (PROOF.md, 'A proved packing ceiling'); checked by ceiling_bound.py with exact integer arithmetic, run by verify.py.",
+  "statement": "For every legal owner map on this supplier: at most 4,887 empty cap-48 bins (Theorem 1, weights floor(7w/9) and floor(7c/9), slack total 180,832), and sum over bins of f ln f <= 4,887 g(48) + g(17) = 908,139.013 (Theorem 3, exact knapsack over slack). The LP dual of Theorem 2 gives 908,156.136.",
+  "not_a_kappa_bound": "It bounds the surrogate and the number of empty cap-48 bins, not kappa. Pricing the bound-attaining idle multiset {1:2431, 17:1, 48:4887} with the pinned engines (check.py, indicative_ceiling_price) gives kappa 0.001674088611862992; this is indicative only.",
+  "solver_reported": "In the session, the class-level window LP and the window + R4 IP (winlp.py) reached the same aggregate optimum: a class solution with idle profile {1:2431, 17:1, 48:4887}. Solver-reported, not checked here.",
+  "this_map": {
+   "empty_cap48": 4880,
+   "surrogate": 907271.883
+  },
+  "replaces": "The previous 'surrogate_ceiling' entry (about 908.1k from winbound.py, not reproduced) is superseded; winbound.py and aggbound.py remain only as search tools.",
+  "independent_check": "The session also checked the bound with a separate float knapsack over all slack values (same 908,139.013) and an mpmath certificate of the Theorem 2 dual."
+ },
+ "min_diff": {
+  "target": "F = the raw search output (content 4c4a97040016b34ab7431fd351c12c286a4b4245fa73780fe0cf48e9fe1bfc3b; 66,449 changed rows and 63,109 relocated against the selected map A). Goal: a legal map with F's idle profile (hence F's kappa) keeping as many (bin, call, width) placements of A as possible.",
+  "stages": [
+   {
+    "step": 1,
+    "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_cls1.py research/complex-t16-two-stage-cycles/search <F> c1.json 1800 <F>",
+    "result": "Time limit: kept flow 67,539 (1,581 relocations), 58 classes changed; dual bound 67,539.865 on the kept flow. With the tie-break (at most 0.001 per bin, 32,256 bins), every legal map with F's profile has at least 1,548 relocations (solver-reported, not a checked certificate)."
+   },
+   {
+    "step": 2,
+    "argv": "for h in 0/2 1/2: mindiff_cls2.py search c1.json cache 60 150 $h cp; then hi (two halves in parallel)",
+    "result": "56 of 58 classes realised. Class 9 (capacity 16, calls 0-8): fourteen bins with four width-4 helpers each need four distinct calls, but calls other than 5, 6 and 8 have five width-4 helpers in total. Class 25 (capacity 32, calls 51-112): five (7,7,9,9) bins and one (7,8,8,9) bin; the 8s come only from calls 92 and 102, so that bin's 7 is from call 98 or 99, leaving at most four distinct-call 7-pairs for five bins. A retry of class 25 alone (CP-SAT 300 s, HiGHS 900 s) found nothing, as expected."
+   },
+   {
+    "step": 3,
+    "argv": "BAN='[[9,[4,0,0,0,0]]]' KEEP=c1.json FREE='[9,0,18,27,36,90,99,108,117,126,135,45,54,63]' mindiff_cls1.py ... c1b.json 900; mindiff_reuse.py c1.json c1b.json cache cache2; mindiff_cls2.py on c1b.json restricted to classes [0,9,18,27] (60 s / 300 s)",
+    "result": "Optimal at once, 1,581; 53 class results reused; classes 0, 9, 18 and 27 realised."
+   },
+   {
+    "step": 4,
+    "argv": "BAN='[[9,[4,0,0,0,0]],[25,[0,0,1,2,1]]]' KEEP=c1b.json FREE='[25,7,16,34,38,43,52,56,61,65,79,88,97,106,110,115,119,124,128,133,137]' mindiff_cls1.py ... c1c.json 600; mindiff_reuse.py c1b.json c1c.json cache2 cache3; stage 2 (60 s / 300 s) into cache3",
+    "result": "Optimal in 12 s, 1,583; 55 class results reused; classes 16, 25 and 52 realised."
+   },
+   {
+    "step": 5,
+    "argv": "mindiff_cls2.py search c1c.json cache3 cls.json merge",
+    "result": "2,210 relocations; idle profile equal to F."
+   },
+   {
+    "step": 6,
+    "argv": "mindiff_lns.py search <F> cls.json l1.json 40 {1,2} 300 30 (two seeds in parallel)",
+    "result": "2,183 for both seeds (converged in about 30 s); seed 1 kept."
+   },
+   {
+    "step": 7,
+    "argv": "mindiff_lns2.py search l1.json l2.json 20 {11,12} 80 60 (two seeds in parallel)",
+    "result": "2,176 (seed 11) and 2,170 (seed 12); seed 12 kept. Stopped at the two-hour min-diff budget (stage 1 alone used 30 minutes; the LNS gained only a few relocations per round)."
+   },
+   {
+    "step": 8,
+    "argv": "realize.py search l2.json OWNERS.json.gz; buildcand.py search OWNERS.json.gz pkg 10011",
+    "result": "2,537 changed rows: 2,170 relocated, 367 offset-only; idle profile and kappa equal to F; strict replay PASS (11 stages, 69/12/6/15), actual_73column_sigmas 10011 read from the native audit (the first replay with F's 10564 was rejected by assembly as expected)."
+   }
+  ],
+  "final": {
+   "owner_content_sha256": "e4896b307b00477e77005a00d2d8f53289a9fe1adf757b5a28764de9b17b9835",
+   "changed_rows_vs_selected": 2537,
+   "relocated_rows_vs_selected": 2170,
+   "offset_only_rows": 367,
+   "kappa_decimal": "0.001673614205725695",
+   "actual_73column_sigmas": 10011,
+   "cross_replica_helper_roles": 57420
+  },
+  "budget": "About 1 h 50 min of wall time with at most two single-threaded solver processes; stopped at the budget."
+ },
+ "fourth_version": {
+  "kappa_search": {
+   "observations": [
+    "On the third version's map many cap-48 bins held only a few small helpers (stranded bins). Emptying them needs their helpers to be re-packed into bins whose windows cover the same calls, which single cycles and call-set neighbourhoods rarely find.",
+    "kappa is close to linear in the surrogate sum f ln f over idle fragments; acceptance always uses the exact engines."
+   ],
+   "start": "The third version's shipped map data/OWNERS.json.gz (content d05a885e8cc6a38dfbc9389e61769b4cb916ee858338e3fc3d6bcff6b877569d, kappa 0.001673054161426948, surrogate 906,246.66).",
+   "tools": [
+    "search/lns.py mode evac (env NB, default 200): 1-3 stranded cap-48 bins (0 < used <= 20), bins with spare room (biased toward larger spare) and full bins whose allowed calls meet the stranded helpers' calls, plus 0, 2 or 5 empty bins allowing those calls; all their helpers are freed and re-packed exactly with CP-SAT (same surrogate objective and DIV plateau logic as the other modes). kappa values are now compared as Decimal.",
+    "search/loopy.sh (portable copy of the session's loopY.sh): loopx.sh with the mode mix evac, evac, time, time, f3, f3, evac, early15, time, f3."
+   ],
+   "how_it_ran": "Interactively. One evac solve from the start map (102 bins in the neighbourhood; its seed and NB were not logged) emptied 35 cap-48 bins (+291 surrogate units, 906,246.66 -> 906,537.90) and gave kappa 0.001673213119136600. A loop started at the same time from the start map reached 0.001673163328271265 in about 15 minutes and was not continued. loopY.sh was then restarted from each strict-replayed best (bash $RANDOM seeds; at most two loops at a time, each job in a MemoryMax=4G scope); the segment from 0.001673243717212927 appears (from file times) to have used a variant, loopZ.sh, whose mode mix is weighted toward time and f3 (one evac in ten); the session did not log which script each segment ran. The best map has surrogate 906,773.72. The search was stopped while still improving (gains every 10-20 minutes near the end).",
+   "checkpoints": [
+    {
+     "via": "one lns.py evac solve (102 bins) from the third version map",
+     "owner_content_sha256": "6bec6e33f8bd180be81429efb6a4d8b47fa7a20b6168d335542827f78d226e91",
+     "kappa_decimal": "0.001673213119136600",
+     "idle_remainder_profile": {
+      "1": 2353,
+      "2": 1,
+      "3": 162,
+      "5": 2,
+      "7": 25,
+      "8": 2,
+      "9": 1,
+      "16": 7,
+      "40": 1,
+      "41": 1,
+      "44": 7,
+      "48": 4864
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10622"
+    },
+    {
+     "via": "loopY.sh",
+     "owner_content_sha256": "8f80fbf8257344f63afea3e2c971a17837d6771c378687e6c80d6b391bc5cce8",
+     "kappa_decimal": "0.001673243717212927",
+     "idle_remainder_profile": {
+      "1": 2356,
+      "3": 178,
+      "7": 6,
+      "8": 2,
+      "16": 13,
+      "44": 9,
+      "48": 4864
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10681"
+    },
+    {
+     "via": "loopY.sh / loopZ.sh",
+     "owner_content_sha256": "02fadadd3940d9f4d325b27e1fe09d3fbd79dd8115439ca531c874133c8865e9",
+     "kappa_decimal": "0.001673272876788591",
+     "idle_remainder_profile": {
+      "1": 2353,
+      "2": 3,
+      "3": 174,
+      "4": 1,
+      "7": 4,
+      "8": 1,
+      "16": 13,
+      "20": 1,
+      "23": 1,
+      "44": 1,
+      "48": 4871
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10680"
+    },
+    {
+     "via": "loopY.sh / loopZ.sh",
+     "owner_content_sha256": "48b090c57c64e3f25b90508e99ea4d8b53cfc7df565baefb2ceebb9141f45a1d",
+     "kappa_decimal": "0.001673312438393585",
+     "idle_remainder_profile": {
+      "1": 2356,
+      "2": 2,
+      "3": 172,
+      "4": 1,
+      "7": 1,
+      "8": 1,
+      "16": 13,
+      "17": 1,
+      "48": 4873
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10707"
+    },
+    {
+     "via": "loopY.sh",
+     "owner_content_sha256": "ee1a9eba9a8915cd5dd0754b7415e79f644d7cf25712338de63b2efd549817ed",
+     "kappa_decimal": "0.001673322090452138",
+     "idle_remainder_profile": {
+      "1": 2356,
+      "2": 2,
+      "3": 173,
+      "7": 1,
+      "16": 13,
+      "26": 1,
+      "48": 4873
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10697"
+    },
+    {
+     "via": "loopY.sh (raw search output F)",
+     "owner_content_sha256": "467a85028f89b9108fa6ed8ac14066ceab90dd523fdce9a170e261737b8f7d7c",
+     "kappa_decimal": "0.001673341928508063",
+     "idle_remainder_profile": {
+      "1": 2355,
+      "2": 2,
+      "3": 172,
+      "7": 3,
+      "16": 11,
+      "48": 4874
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10649",
+     "conservative_kappa_decimal": "0.001673341925655596",
+     "changed_rows_vs_selected": 66211,
+     "relocated_rows_vs_selected": 62678
+    }
+   ],
+   "stopped": "Stopped at the end of the session's budget while still improving; no stall criterion was met.",
+   "tooling_bug": "The session's loops compared kappa strings in lns.py (k > best_k); the pinned assembler can drop trailing zeros (0.0016732131191366 vs 0.001673213119136600), so a string comparison can misorder. Every checkpoint above was re-verified with Decimal comparisons, and the shipped lns.py, loopx.sh/loopy.sh, check.py and verify.py compare as Decimal."
+  },
+  "min_diff": {
+   "target": "F = the raw search output (content 467a85028f89b9108fa6ed8ac14066ceab90dd523fdce9a170e261737b8f7d7c; 66,211 changed rows and 62,678 relocated against the selected map A). Goal: a legal map with F's idle profile (hence F's kappa) keeping as many (bin, call, width) placements of A as possible.",
+   "stages": [
+    {
+     "step": 1,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_cls1.py research/complex-t16-two-stage-cycles/search <F> c1.json 1800 <F>",
+     "result": "Optimal in 247 s: kept flow 68,087 (1,033 relocations) at the tie-broken optimum; dual bound 68,086.564 on the objective. The tie-break costs at most 0.001 per bin (32,256 bins), so every legal map with F's profile has at least 1,002 relocations (solver-reported, not a checked certificate). 48 classes changed."
+    },
+    {
+     "step": 2,
+     "argv": "for h in 0/2 1/2: mindiff_cls2.py search c1.json cache 60 150 $h cp; then the same with hi (separate processes; the two halves ran in parallel)",
+     "result": "All classes realised except class 9 (capacity 16, calls 0-8), proven infeasible: its stage-1 solution has eleven bins with four width-4 helpers each (four distinct calls per bin), while the class's calls other than 5, 6 and 8 have only four width-4 helpers in total."
+    },
+    {
+     "step": 3,
+     "argv": "FIX='[9]' mindiff_cls1.py ... (and FIX='[9]' with KEEP=c1.json, FREE=<other changed classes>)",
+     "result": "Infeasible: A's class 9 has six bins with residual 7 and the target profile has only three. Pinning class 9 to F's class values instead (KEEP=<c1.json with class 9 replaced by F's values, written by a session helper>, FREE=<all other classes>) was feasible but raised the stage-1 optimum to 1,456 relocations; not used."
+    },
+    {
+     "step": 4,
+     "argv": "BAN='[[9,[4,0,0,0,0]]]' uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_cls1.py research/complex-t16-two-stage-cycles/search <F> c1c.json 1200 <F>; mindiff_reuse.py c1.json c1c.json cache cache2; stage 2 into cache2",
+     "result": "Optimal in 259 s, same optimum (68,087 kept, 1,033 relocations); 47 classes changed, 5 class results reused, all realised (classes 0 and 139 at the HiGHS time limit, within 2 and 7 placements of their bounds)."
+    },
+    {
+     "step": 5,
+     "argv": "mindiff_cls2.py search c1c.json cache2 cls.json merge",
+     "result": "1,518 relocations (1,741 changed rows after realize.py); kappa and idle profile equal to F."
+    },
+    {
+     "step": 6,
+     "argv": "mindiff_lns.py search <F> cls.json l1.json 40 {1,2} 300 30 (two seeds in parallel)",
+     "result": "1,501 (seed 1) and 1,496 (seed 2); seed 2 kept. A further mindiff_lns.py run (seed 3, 800 bins, 60 s) reached 1,495 in 64 iterations and was stopped."
+    },
+    {
+     "step": 7,
+     "argv": "mindiff_lns2.py search <prev> <next> ITERS SEED 80 60, rounds: (20, 11) -> 1,478; (25, 12|13) -> 1,468|1,459; (20, 21|22) -> 1,446|1,435; (18, 31|32) -> 1,419|1,415; the better seed of each round continued",
+     "result": "1,415 relocations. Stopped at the two-hour min-diff budget while still gaining about 20 relocations per round."
+    },
+    {
+     "step": 8,
+     "argv": "realize.py search l5.json OWNERS.json.gz; buildcand.py search OWNERS.json.gz pkg 10006",
+     "result": "1,638 changed rows: 1,415 relocated, 223 offset-only; idle profile and kappa equal to F; strict replay PASS (11 stages, 69/12/6/15), actual_73column_sigmas 10006 read from the native audit (the first replay with F's 10649 was rejected by assembly as expected)."
+    }
+   ],
+   "final": {
+    "owner_content_sha256": "54a19c57be93e86f8cc4a9aab5ee38f58449ae64b0a80ceea95415ba3a6574ac",
+    "changed_rows_vs_selected": 1638,
+    "relocated_rows_vs_selected": 1415,
+    "offset_only_rows": 223,
+    "kappa_decimal": "0.001673341928508063",
+    "actual_73column_sigmas": 10006,
+    "cross_replica_helper_roles": 57419
+   },
+   "budget": "About 1 h 50 min of wall time with at most two single-threaded solver processes; stopped at the budget while the LNS polish was still improving."
+  }
+ },
+ "third_version": {
+  "kappa_search": {
+   "observations": [
+    "kappa is close to linear in the surrogate sum f ln f over idle fragments (free capacities f > 1), so the surrogate is a usable global objective; acceptance always uses the exact engines.",
+    "Inside one physical family the bins' windows never overlap, so R4 reduces to at most one helper per bin per call.",
+    "Bins with the same capacity and the same set of allowed calls (144 classes of 224 bins) are interchangeable, so the packing becomes a class-level pattern/flow model.",
+    "Version 2's loop (chain2 ejection cycles plus CP-SAT LNS) had slowed to steps of about 1e-9 in kappa."
+   ],
+   "start": "Version 2's raw kappa-search output F2 (content a7e8f0cac22527fd6f987b87c2734984add89166fd2d0306453bed99c25cee96, kappa 0.001672702955495933), not its min-diff map.",
+   "tools": [
+    "search/glob.py: stage 1, CP-SAT over pattern counts x[class, pattern] and flows y[class, call, width] with per-(class, call) Hall constraints and optional Gale-Ryser-style constraints (GR=1), maximising the scaled surrogate; options S1ONLY, HINT, FIX, FREE, FIXTO, HALL.",
+    "search/glob5.py: stage 2, per-class and per-width max-flow realisation with distinct calls per bin over 40 random width orders; unplaced helpers inserted greedily where they cost the least surrogate.",
+    "search/loopx.sh (portable copy of the session's loopX.sh): chain2.py depth 8 while it improves, else one DIV=1 lns.py plateau step on a random mode (set:0,1,2,3,4, early8, early15, time, f3, fam); keeps the best map by exact kappa (score.py).",
+    "search/lns.py: as in version 2, plus NW (CP-SAT workers per solve) and the f3 mode."
+   ],
+   "how_it_ran": "Interactively. glob.py was run several times with different time limits and options (best stage-1 objective 906,706 surrogate units; the start map had 905,605). The best stage 1 (906,706.49, CP-SAT bound 906,737.56 for that run's model, 1200 s) was realised by glob5.py; stage 2 left 80 helpers unplaced, which were inserted greedily. The realised map had kappa 0.001672432283943020, below the start, with a very different profile. loopx.sh from it (seeds from bash $RANDOM) reached 0.001672894024167899 in 43 steps; a second loopx.sh run from that map reached 0.001673054161426948. The exact flags of each glob.py run were not logged, so this phase is described, not replayable command by command.",
+   "checkpoints": [
+    {
+     "via": "glob.py stage 1 + glob5.py stage 2 (80 helpers inserted greedily)",
+     "kappa_decimal": "0.001672432283943020",
+     "strict_replay": "not run"
+    },
+    {
+     "via": "loopx.sh, step 43",
+     "owner_content_sha256": "3e94d8c68b70ca89402e1be7acbed8e19f1b3389cac4a22a39e75360211a8cfe",
+     "kappa_decimal": "0.001672894024167899",
+     "idle_remainder_profile": {
+      "1": 2340,
+      "2": 1,
+      "3": 152,
+      "7": 42,
+      "8": 2,
+      "14": 16,
+      "16": 4,
+      "30": 1,
+      "39": 13,
+      "40": 1,
+      "41": 7,
+      "44": 45,
+      "48": 4808
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10751"
+    },
+    {
+     "via": "loopx.sh from the previous checkpoint, step 22 (raw search output F3)",
+     "owner_content_sha256": "e442224808c877a2660fd7bd7e0c9fd060e454a48522b68bb124a4302e740760",
+     "kappa_decimal": "0.001673054161426948",
+     "conservative_kappa_decimal": "0.001673054158574889",
+     "idle_remainder_profile": {
+      "1": 2346,
+      "2": 3,
+      "3": 154,
+      "5": 9,
+      "7": 36,
+      "8": 2,
+      "16": 7,
+      "28": 1,
+      "39": 1,
+      "40": 1,
+      "41": 2,
+      "44": 41,
+      "48": 4829
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10614",
+     "changed_rows_vs_selected": 65902,
+     "relocated_rows_vs_selected": 61985
+    }
+   ],
+   "stopped": "Stopped at the end of the session's search budget while still improving (the last loopx.sh run found its last gain 4 minutes before it was stopped)."
+  },
+  "min_diff": {
+   "target": "F3 = the raw search output (content e442224808c877a2660fd7bd7e0c9fd060e454a48522b68bb124a4302e740760; 61,985 rows relocated against the selected map A, 8,426 of A's (bin, call, width) placements shared). Goal: a legal map with F3's idle profile (hence F3's kappa) keeping as many placements of A as possible.",
+   "dropped_routes": [
+    "Version 2's fill-fixed MIP (mindiff_mip.py fill) on F3 and on F3 with bin contents permuted inside classes by linear assignment (16,414 shared): root bounds about 45k kept placements, i.e. at least about 24k relocations within that model; stopped.",
+    "Version 2's two-fill MIP from the permuted F3: incumbent 16,558 kept after several minutes; stopped.",
+    "CP-SAT variant of the class-level stage 1 (1 worker, 150 s): no solution."
+   ],
+   "stages": [
+    {
+     "step": 1,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I search/mindiff_cls1.py search <F3> c1.json 1500 <F3>",
+     "result": "Optimal in 981 s: kept flow 68,236 (884 relocations) at the tie-broken optimum; dual bound 68,235.58 on the objective, which implies at least 853 relocations for any legal map with F3's profile (solver-reported). 51 classes changed."
+    },
+    {
+     "step": 2,
+     "argv": "for h in 0/2 1/2: mindiff_cls2.py search c1.json cache 60 150 $h cp; then the same with hi (CP-SAT with ortools, HiGHS with scipy+highspy, separate processes)",
+     "result": "Classes 4, 9, 88 and 133: no feasible realisation found (CP-SAT 60 s, HiGHS 150 s). Earlier attempts with a HiGHS-only stage 2 (90 s and 240 s limits) were superseded."
+    },
+    {
+     "step": 3,
+     "argv": "FIX='[4,9,88,133]' mindiff_cls1.py search <F3> c1b.json 330; stage 2 into cache2",
+     "result": "Time limit, kept flow 68,228 (bound 68,228.28); 48 classes changed; class 94 proven infeasible in stage 2, all others realised."
+    },
+    {
+     "step": 4,
+     "argv": "FIX='[4,9,88,133,94]' KEEP=c1b.json FREE=<changed classes of c1b.json except 94> mindiff_cls1.py search <F3> c1c.json 300; mindiff_reuse.py c1b.json c1c.json cache2 cache3; stage 2 into cache3",
+     "result": "kept flow 68,225 (bound 68,225.18); 47 classes changed, 34 class results reused, 13 re-solved, all realised."
+    },
+    {
+     "step": 5,
+     "argv": "mindiff_cls2.py search c1c.json cache3 cls.json merge; realize.py search cls.json R1440.OWNERS.json.gz",
+     "result": "1,440 relocations (1,664 changed rows); strict replay PASS with actual_73column_sigmas 10055."
+    },
+    {
+     "step": 6,
+     "argv": "mindiff_lns.py search R1440.OWNERS.json.gz cls.json lns.json 40 1 300 30",
+     "result": "1,435 relocations (one gain of 5 in 40 iterations). mindiff_lns2.py search cls.json any.json 12 11 80 60: no gain in 3 iterations, stopped."
+    },
+    {
+     "step": 7,
+     "argv": "realize.py search lns.json OWNERS.json.gz; buildcand.py search OWNERS.json.gz pkg 10055",
+     "result": "1,661 changed rows: 1,435 relocated, 226 offset-only; idle profile and kappa equal to F3; strict replay PASS, actual_73column_sigmas 10055 (read from the native audit)."
+    }
+   ],
+   "final": {
+    "owner_content_sha256": "d05a885e8cc6a38dfbc9389e61769b4cb916ee858338e3fc3d6bcff6b877569d",
+    "changed_rows_vs_selected": 1661,
+    "relocated_rows_vs_selected": 1435,
+    "offset_only_rows": 226,
+    "kappa_decimal": "0.001673054161426948",
+    "actual_73column_sigmas": 10055,
+    "cross_replica_helper_roles": 57456
+   },
+   "budget": "About 2.5 hours of wall time with at most two single-threaded solver processes; stopped when the LNS polish stalled."
+  }
+ },
+ "second_version": {
+  "kappa_search": {
+   "tools": [
+    "search/chain2.py (imports chain.py, lib.py): one- and two-stage ejection cycles, depth 8 in this phase",
+    "search/lns.py: CP-SAT large-neighbourhood re-assignment of all helpers of a set of calls (modes set:<calls>, time, early<k>, queue) or of physical families (fam); DIV=1 keeps the surrogate objective and randomly maximises relocations to move along plateaus",
+    "search/loop3.sh: alternates chain2.py until it finds nothing, then one DIV=1 lns.py step on a random mode"
+   ],
+   "objective": "Surrogate E = sum over (owner, child, port) bins of f ln f for free capacity f > 1 (CP-SAT scales it by 10^4 and rounds). Every candidate is audited with the seed67 rules and priced with the pinned exact engines; a step is kept only if the exact kappa rises (or, on a DIV plateau step, stays equal).",
+   "how_it_ran": "Interactively, in order: lns.py time/set neighbourhoods from the first version's map; lns.py set:0,1,2,3,4 with 400-900 s CP-SAT limits; chain2.py depth 8; then loop.sh, loop2.sh and loop3.sh runs (loop2.sh is loop3.sh with a different mode list; loop3.sh is shipped). Seeds partly come from bash $RANDOM, so the trajectory is not reproducible bit for bit.",
+   "checkpoints": [
+    {
+     "owner_content_sha256": "94a48bfdcdb59fb309f7c11a8e46e61e4f1e2d8fe3cdc0d6053fe04cc2f7688e",
+     "via": "lns.py (call-set neighbourhoods)",
+     "kappa_decimal": "0.001672685662094163",
+     "idle_remainder_profile": {
+      "1": 2279,
+      "2": 1,
+      "3": 371,
+      "7": 2,
+      "16": 3,
+      "48": 4866
+     },
+     "strict_replay": "not run"
+    },
+    {
+     "owner_content_sha256": "18ba2bd326387d27ff7526914a5be8c4dfe37e0278a7decd60faefbfbdab631e",
+     "via": "lns.py set:0,1,2,3,4 (CP-SAT 400 s)",
+     "kappa_decimal": "0.001672686708686457",
+     "idle_remainder_profile": {
+      "1": 2278,
+      "3": 372,
+      "7": 2,
+      "16": 3,
+      "48": 4866
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15)"
+    },
+    {
+     "owner_content_sha256": "1c76875b2d6b71322963a939796099cf3d892defe52fcc08cd3b9d87ce79c4c0",
+     "via": "chain2.py depth 8",
+     "kappa_decimal": "0.001672691961154154",
+     "strict_replay": "not run"
+    },
+    {
+     "owner_content_sha256": "464f57761a713f3cdd399cad9cf826a6e19d8dd247e227da1aee4fd69ec7ce51",
+     "via": "loop2.sh then loop3.sh (chain2 + DIV lns alternation)",
+     "kappa_decimal": "0.001672699106899519",
+     "idle_remainder_profile": {
+      "1": 2281,
+      "2": 1,
+      "3": 365,
+      "7": 2,
+      "16": 4,
+      "48": 4866
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15)"
+    },
+    {
+     "owner_content_sha256": "a7e8f0cac22527fd6f987b87c2734984add89166fd2d0306453bed99c25cee96",
+     "via": "loop3.sh logic, last run (about 45 min, +3.85e-9)",
+     "kappa_decimal": "0.001672702955495933",
+     "idle_remainder_profile": {
+      "1": 2280,
+      "2": 1,
+      "3": 363,
+      "7": 3,
+      "16": 4,
+      "48": 4866
+     },
+     "strict_replay": "PASS (11 stages, 69/12/6/15); actual_73column_sigmas 10466",
+     "changed_rows_vs_selected": 30039,
+     "relocated_rows_vs_selected": 17173
+    }
+   ],
+   "stopped": "Stopped at the end of the session's search budget while still improving; no stall criterion was met."
+  },
+  "min_diff": {
+   "target": "F = the last kappa checkpoint (content a7e8f0ca...). Goal: a legal map with exactly F's idle remainder profile (hence F's kappa) that keeps as many (bin, call, width) placements of the selected map A as possible. Helpers of one (call, width) are interchangeable under R3-R6; realize.py restores A's helper labels and offsets where possible.",
+   "stages": [
+    {
+     "step": 1,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_mip.py research/complex-t16-two-stage-cycles/search <F> fill.json fill 900 -",
+     "result": "Optimal: 67,058 of 69,120 placements of A kept, 2,062 relocations",
+     "seconds": 345
+    },
+    {
+     "step": 2,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_lns.py research/complex-t16-two-stage-cycles/search <F> fill.json lns.json 60 1 300 60",
+     "result": "182 relocations (gains in the first 6 iterations and iteration 59)",
+     "approx_seconds": 120
+    },
+    {
+     "step": 3,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_mip.py research/complex-t16-two-stage-cycles/search <F> two.json two 2400 lns.json",
+     "result": "Time limit: 69,026 kept, 94 relocations; dual bound 69,028.56 kept (>= 92 relocations within this two-fill, A-or-F-candidate model)",
+     "seconds": 2401
+    },
+    {
+     "step": 4,
+     "argv": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_lns2.py research/complex-t16-two-stage-cycles/search two.json any.json 15 11 80 90",
+     "result": "55 relocations (94 -> 84 -> 80 -> ... -> 55). Run with the session copy of this script, identical except for its docstring.",
+     "followup": "uv run -q --no-project --python 3.12 --with scipy --with highspy python -I research/complex-t16-two-stage-cycles/search/mindiff_lns2.py research/complex-t16-two-stage-cycles/search any.json any2.json 15 12 160 90: no gain in 7 iterations (2 sub-MIPs proven optimal), stopped by hand",
+     "approx_seconds": 1000
+    },
+    {
+     "step": 5,
+     "argv": "python3.12 -I research/complex-t16-two-stage-cycles/search/realize.py research/complex-t16-two-stage-cycles/search any.json OWNERS.json.gz",
+     "result": "70 changed rows: 55 relocated, 15 offset-only; idle profile and kappa equal to F"
+    },
+    {
+     "step": 6,
+     "argv": "python3.12 -I research/complex-t16-two-stage-cycles/search/buildcand.py research/complex-t16-two-stage-cycles/search OWNERS.json.gz pkg 10000",
+     "result": "data/OWNERS.json.gz, PLAN.json, SPEC.json; sigmas 10000 is the strict audit count for this map (a first replay with 10004 failed with expected 10004 got 10000)"
+    }
+   ],
+   "final": {
+    "owner_content_sha256": "1764f4310b7c91b69f0533b0b95fa0d4fba267d05d6e4e870aac2d4c310d4d4d",
+    "changed_rows_vs_selected": 70,
+    "relocated_rows_vs_selected": 55,
+    "offset_only_rows": 15,
+    "kappa_decimal": "0.001672702955495933",
+    "actual_73column_sigmas": 10000,
+    "shares_with_pr1407": "2 of the 23 (bin, call, width) placements PR1407 changes; 0 identical rows",
+    "shares_with_first_version": "4 of its 37 relocated placements; 0 identical rows"
+   },
+   "variants_tried_and_dropped": [
+    "CP-SAT on the global fill-fixed and any-fill models, 1 worker, 300 s: 14,564 and 16,051 relocations (no proof).",
+    "HiGHS on the global any-fill (profile-count) model without warm start: no incumbent in 400 s (root LP bound 69,116 kept, i.e. >= 4 relocations; weak).",
+    "LP-guided dive on the two-fill model (fix fill bits the LP sets below 0.05 or above 0.95): infeasible.",
+    "Any-fill LNS on the remaining diff region (all legal placements of the rows involved, extra sampled bins): 190 -> 179 relocations on the session's first chain; superseded by the global two-fill MIP."
+   ]
+  }
+ },
+ "first_version": {
+  "tool": "search/chain2.py (imports search/chain.py and search/lib.py)",
+  "environment": "CPython 3.12.14 + numpy (uv run -q --no-project --python 3.12 --with numpy), Linux x86_64, MemoryMax=5G scope, one worker",
+  "objective": "Relaxed surrogate E = sum over (owner, child, port) bins of f ln f for free capacity f > 1; candidate cycles found by a max-plus DP over (hand width, hand time) states, then replayed exactly with the seed67 auditor geometry and priced with the pinned exact engines. E is only a search heuristic; kappa comes from the exact engines.",
+  "runs": [
+   {
+    "name": "stage-A",
+    "argv": [
+     "search/chain2.py",
+     "search",
+     "<PR1407 data/OWNERS.json.gz>",
+     "<out>/s1",
+     "6"
+    ],
+    "start_owner_content_sha256": "008694b29e3b513c8e88367e30ab2d231ea5a0b0dd85cc1efc372f60b9fbdf4c",
+    "relaxed_zero_or_positive_first_cycles": 378494,
+    "exact_first_cycles_tried": 8785,
+    "result": "Two cycles through X=(owner 12, child 4, port 0). Cycle 1 (gain 0): free 3 of bin (0,0,103) moves to X. Cycle 2: free 3 of bin (0,0,104) joins it, X free 6. dE = 6 ln 2 = 4.158883.",
+    "moves": [
+     [
+      25184,
+      [
+       12,
+       4,
+       0
+      ],
+      [
+       6,
+       2,
+       101
+      ]
+     ],
+     [
+      13669,
+      [
+       6,
+       2,
+       101
+      ],
+      [
+       12,
+       0,
+       78
+      ]
+     ],
+     [
+      1747,
+      [
+       12,
+       0,
+       78
+      ],
+      [
+       0,
+       0,
+       103
+      ]
+     ],
+     [
+      911,
+      [
+       0,
+       0,
+       103
+      ],
+      [
+       0,
+       2,
+       45
+      ]
+     ],
+     [
+      431,
+      [
+       0,
+       2,
+       45
+      ],
+      [
+       12,
+       4,
+       0
+      ]
+     ],
+     [
+      29505,
+      [
+       12,
+       4,
+       0
+      ],
+      [
+       7,
+       0,
+       64
+      ]
+     ],
+     [
+      13666,
+      [
+       7,
+       0,
+       64
+      ],
+      [
+       12,
+       0,
+       79
+      ]
+     ],
+     [
+      1725,
+      [
+       12,
+       0,
+       79
+      ],
+      [
+       0,
+       0,
+       104
+      ]
+     ],
+     [
+      910,
+      [
+       0,
+       0,
+       104
+      ],
+      [
+       12,
+       4,
+       0
+      ]
+     ]
+    ],
+    "idle_remainder_profile": {
+     "1": 2277,
+     "3": 375,
+     "6": 1,
+     "16": 3,
+     "48": 4866
+    },
+    "kappa_decimal": "0.001672683095046622",
+    "seconds": 14
+   },
+   {
+    "name": "stage-B",
+    "argv": [
+     "search/chain2.py",
+     "search",
+     "<out>/s1.OWNERS.json.gz",
+     "<out>/s2",
+     "6"
+    ],
+    "exact_first_cycles_tried": 1,
+    "result": "One strictly improving 7-move cycle through X'=(6,0,36) that passes X=(12,4,0): free 3+3+6 in bins (0,0,105), (0,0,58), (12,4,0) become 8+1+3 in bins (0,0,58), (12,4,0), (6,0,36). dE = 2.589139.",
+    "moves": [
+     [
+      28207,
+      [
+       6,
+       0,
+       36
+      ],
+      [
+       14,
+       2,
+       12
+      ]
+     ],
+     [
+      14147,
+      [
+       14,
+       2,
+       12
+      ],
+      [
+       12,
+       0,
+       80
+      ]
+     ],
+     [
+      1724,
+      [
+       12,
+       0,
+       80
+      ],
+      [
+       0,
+       0,
+       105
+      ]
+     ],
+     [
+      909,
+      [
+       0,
+       0,
+       105
+      ],
+      [
+       0,
+       0,
+       58
+      ]
+     ],
+     [
+      1241,
+      [
+       0,
+       0,
+       58
+      ],
+      [
+       12,
+       4,
+       0
+      ]
+     ],
+     [
+      431,
+      [
+       12,
+       4,
+       0
+      ],
+      [
+       0,
+       2,
+       45
+      ]
+     ],
+     [
+      1375,
+      [
+       0,
+       2,
+       45
+      ],
+      [
+       6,
+       0,
+       36
+      ]
+     ]
+    ],
+    "idle_remainder_profile": {
+     "1": 2278,
+     "3": 374,
+     "8": 1,
+     "16": 3,
+     "48": 4866
+    },
+    "kappa_decimal": "0.001672684510394236",
+    "output_equals_data_OWNERS_content": true,
+    "seconds": 16
+   },
+   {
+    "name": "post-check-two-stage",
+    "argv": [
+     "search/chain2.py",
+     "search",
+     "data/OWNERS.json.gz",
+     "<out>/s3",
+     "6"
+    ],
+    "relaxed_zero_or_positive_first_cycles": 389658,
+    "exact_first_cycles_tried": 27567,
+    "exact_second_cycles": 12816,
+    "result": "NONE (bounded: at most 3 first cycles per X, 200 second cycles each)"
+   },
+   {
+    "name": "post-check-one-stage",
+    "argv": [
+     "search/chain.py",
+     "search",
+     "data/OWNERS.json.gz",
+     "<out>/c3",
+     "1",
+     "6"
+    ],
+    "relaxed_candidates": 2256,
+    "result": "no improving chain found at depth 6 (first 5000 candidates replayed)"
+   }
+  ],
+  "composition_with_pr2077": {
+   "argv": [
+    "search/compose.py",
+    "search",
+    "<PR1407 data/OWNERS.json.gz>",
+    "<PR2077 data/OWNERS.json.gz>"
+   ],
+   "result": "All 15 non-empty subsets of PR2077's four relocations (rows 2010, 4474, 34306, 46308) are illegal placements on PR1407's map. PR1407 already placed row 7287 into bin (11,8,103) and filled bin (13,15,14) with rows 45356 and 60126, so the capacity PR2077's moves need is not there (only PR2077's literal targets were tested); PR2077's gain and PR1407's gain are alternatives, not additive."
+  },
+  "scope": "A heuristic search record. It is not an optimum proof; the post-checks are bounded passes."
+ }
+}
diff --git a/research/complex-t16-two-stage-cycles/SOURCES.json b/research/complex-t16-two-stage-cycles/SOURCES.json
new file mode 100644
index 0000000000..63189ec2d9
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/SOURCES.json
@@ -0,0 +1,1740 @@
+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+      "usage": "input"
+    },
+    {
+      "path": "research/community-frontier1094-audit/selected-replay.tar.gz",
+      "git_blob": "c24daf067f9c543421d89ca2eeaa4eb78a57fb6f",
+      "sha256": "f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6",
+      "usage": "input"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/ASSEMBLY-CONTROLS.json",
+      "git_blob": "3dcd8c85a9e9cf09c8ab523fc3f63c43f6b5f8d3",
+      "sha256": "aca6ddbcd8049e98c2ce36108488f756b08506ca558fa94e64b811774ea96d79",
+      "usage": "input"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/ASSEMBLY.json",
+      "git_blob": "9e7e5fe86db00dab86ebd114d9c82c2310d85493",
+      "sha256": "4782793661bf92c9f8281ca7b9ae92f79573a3623af49661fc445147d455dbdb",
+      "usage": "input"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/RECEIPT.json",
+      "git_blob": "339294a048a856a515fabb9c2d3865b5077b1fdf",
+      "sha256": "dee320a71985660f1ea7715f652fda110fe172a51a1194ac433734ccdce1e14c",
+      "usage": "input"
+    },
+    {
+      "path": "research/community-k492-audit/pr622/replay/baseline558/RESULT.json",
+      "git_blob": "7d634aa4e3000a5aa6c132d5a09b99c4c42847de",
+      "sha256": "a979ea3fce856e0826a61dc7fdfebea067f5a97bf118f9f186175c686a22c717",
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+    },
+    {
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+}
diff --git a/research/complex-t16-two-stage-cycles/TASK.json b/research/complex-t16-two-stage-cycles/TASK.json
new file mode 100644
index 0000000000..47e865e929
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/TASK.json
@@ -0,0 +1,74 @@
+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 4,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md",
+      "research/complex-local-word-ceiling/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Review-and-compose of the two open T16 owner-map PRs on the selected PR1094 supplier (PR1407, PR2077), a bounded two-stage ejection-cycle search on PR1407's map (first version of this package), a longer cycle/LNS search with a min-diff re-assignment (second version), a global class-level repack (CP-SAT pattern/flow model per (capacity, window) class, max-flow realisation) followed by the cycle/LNS loop and a class-level min-diff re-assignment (third version), an evacuation LNS neighbourhood in the same loop (fourth version), and in this version class-level re-solves of a window + R4 model warm-started from the current map, each realised by a guided CP-SAT neighbourhood, followed by the class-level min-diff re-assignment toward the selected map at the same idle profile; plus a proved packing ceiling (at most 4,887 empty cap-48 bins and surrogate sum f ln f <= 908,139.013 for every legal map), stated in PROOF.md and checked by ceiling_bound.py. Widths, call order, windows and both suppliers are unchanged; only owner fields of whole helper roles change.",
+  "scope_change_reason": "Self-selected, not drawn by scripts/choose_research_task.py: the session started as a review of PR1407 and PR2077 and whether their moves compose (they do not: every PR2077 subset is illegal on PR1407's map). The closest catalogue card is selected-packing. The search started from an unmerged PR's map (PR1407), but the shipped map is stated and verified only against the merged selected PR1094 map; PR1407 is lineage and credit, not a dependency.",
+  "bottleneck_link": "Strictly decreases the complete complex moment of the binding complex supplier while preserving rank mass 1041408, deficit 5120, the local gauge44 supplier and the 144-call chronology.",
+  "budget_minutes": 420,
+  "stop_rule": "kappa search: stop when the session's search budget ended (the class-level loop was still finding gains; no stall criterion was met). Min-diff: stop at a two-hour budget (the stage-1 MIP used 30 minutes; the LNS polish was gaining only a few relocations per round), followed by the strict replay, the independent seed67 audit, pricing, the majorization check and the ceiling check at the unchanged idle profile.",
+  "outcome": "completed",
+  "evidence": "Unchanged PR1087 strict T16 replay passes all 11 stages with controls 69/12/6/15, actual_73column_sigmas 10011, kappa 0.001673614205725695 (conservative 0.001673614202872892): +5.7035e-4 relative over the selected record, +9.334e-7 over PR1407, +9.297e-7 over this package's first version (0.001672684510394236), +9.113e-7 over its second (0.001672702955495933), +5.600e-7 over its third (0.001673054161426948) and +2.723e-7 over its fourth (0.001673341928508063); 6.560% of the complex endpoint gap to the PR1240 ceiling a_hi = 0.001690054109089. The idle residual vector strictly majorizes the selected one (equal totals 237,024; checked mechanically by check.py), so the complex moment strictly decreases for any strictly concave per-residual weight. Seed67 auditor R1-R7, X1, X2 and its 11 controls pass; pinned-engine pricing and the PR1069 sweep agree. The map differs from the selected PR1094 map in 2,537 rows (2,170 relocated helpers, 367 offset-only). Proved packing ceiling (ceiling_bound.py, exact integers): every legal map has at most 4,887 empty cap-48 bins (this map 4,880) and surrogate at most 908,139.013 (this map 907,271.883); this bounds the surrogate, not kappa (the bound-attaining idle multiset prices at kappa 0.001674088611862992, indicative only). Conditional on the selected PR1094 inherited assumptions; no open-PR dependency.",
+  "author": "Philippe Van Velzen",
+  "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance: PR review, composition test, search implementation (including the global repack and the class-level re-solve loop), min-diff re-assignment, the packing-ceiling proof checker, replay and packaging. No independent human review claimed.",
+  "open_questions": [
+    {
+      "question": "How much further does the finite search go on this supplier's T16 owner packing?",
+      "why_it_matters": "The search was stopped while still improving; the class-level re-solve loop moved kappa by about 2.7e-7 over the fourth version. The proved ceiling leaves at most seven more empty cap-48 bins and 867 surrogate units.",
+      "first_step": "Rerun search/sloop.sh from data/OWNERS.json.gz toward a full winlp.py target under a memory cap, strict-replay each new best, then rerun the class-level min-diff.",
+      "blocked_by": "Compute time; each new map needs the min-diff step and a strict replay again."
+    },
+    {
+      "question": "What is the best attainable kappa from owner packing on the selected supplier's T16 windows?",
+      "why_it_matters": "The proved ceiling bounds the surrogate (908,139.013) and the number of empty cap-48 bins (4,887), not kappa. The bound-attaining idle multiset {1:2431, 17:1, 48:4887} prices at kappa 0.001674088611862992, but that is not a bound, and no concrete map is known to attain it.",
+      "first_step": "Check whether the bound-attaining idle multiset majorizes every attainable idle vector (which would make its price a kappa bound by Karamata), or state the knapsack relaxation directly in the exact per-residual cost.",
+      "blocked_by": "No kappa-level argument yet; the window + R4 class model attains the surrogate bound (solver-reported) but its solutions are not realised on concrete bins."
+    },
+    {
+      "question": "Can the diff against the selected map be made smaller at the same idle profile?",
+      "why_it_matters": "Smaller diffs are cheaper to review. The class-level relaxation implies at least 1,548 relocations (solver-reported) and its own solution needs 1,583, against 2,170 shipped.",
+      "first_step": "Add distinct-call (Gale-Ryser) constraints to search/mindiff_cls1.py so that stage 1 stops proposing unrealisable class patterns (this version needed BAN for classes 9 and 25), and continue mindiff_lns2.py rounds from the shipped map.",
+      "blocked_by": "Compute time; most of the gap comes from realising class solutions on concrete bins."
+    }
+  ]
+}
diff --git a/research/complex-t16-two-stage-cycles/VALIDATION.json b/research/complex-t16-two-stage-cycles/VALIDATION.json
new file mode 100644
index 0000000000..259590408d
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/VALIDATION.json
@@ -0,0 +1,54 @@
+{
+  "status": "LOCAL_COMPLETE_STRICT_REPLAY_PASS",
+  "date": "2026-10-15",
+  "python": "CPython 3.12.14 (uv)",
+  "platform": "Linux x86_64",
+  "registered_replay": {
+    "command": "python3.12 scripts/research_package.py --package research/complex-t16-two-stage-cycles",
+    "status": "PASS_REGISTERED_RESEARCH_PACKAGE",
+    "wall_seconds": 47,
+    "max_child_rss_mib": 417,
+    "memory_cap": "systemd scope MemoryMax=5G"
+  },
+  "metadata_check": "PASS_PACKAGE_METADATA_AND_PINS",
+  "pinned_inputs": 287,
+  "archived_predecessor_files_checked": 179,
+  "stages": 11,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15,
+    "seed67_owner": 11
+  },
+  "exact_moment_engines": 2,
+  "independent_checks": [
+    "build.py packing checker (idle profile, changed and relocated row counts)",
+    "seed67 auditor R1-R7/X1/X2",
+    "strict majorization of the selected idle residual vector (check.py, required by verify.py)",
+    "pinned-engine pricing (native + conservative), plus the indicative price of the bound-attaining idle multiset",
+    "PR1069 sweep",
+    "proved packing ceiling (ceiling_bound.py, exact integer arithmetic, required by verify.py)"
+  ],
+  "cross_checks": [
+    "The session's own pipeline (buildcand.py, strict native replay in a separate scratch tree, comparing kappa as Decimal) on data/OWNERS.json.gz: strict replay PASS (11 stages, 69/12/6/15), kappa 0.001673614205725695, idle profile equal to the raw search output; 2,537 changed rows, 2,170 relocated (realize.py); actual_73column_sigmas 10011 read from the native audit (OWNERS-AND-PROFILE.json, cross-replica roles 57,420).",
+    "The raw search output F (66,449 changed rows, 63,109 relocated) was verified separately before packaging (independent strict replay in another tree): strict replay PASS (11 stages, controls 69/12/6/15), actual_73column_sigmas 10564, seed67 audit with 11 controls, pinned-engine pricing and the PR1069 sweep; that check also confirmed that its idle profile majorizes the selected one.",
+    "search/buildcand.py with actual_73column_sigmas=10011 reproduces data/OWNERS.json.gz, data/PLAN.json and data/SPEC.json byte for byte (they were copied from its output; build.py regenerates PLAN/SPEC byte for byte from the selected map plus the DIFF).",
+    "The packing ceiling was checked three ways: ceiling_bound.py (exact integers; also run on the selected map: 4,866 empty cap-48 bins, surrogate 905,526.558), the session's mpmath LP-dual and DP certificate (dualcert.py), and an independently written float knapsack (bound_indep.py) over all 180,832 slack units (908,139.013 = 4887 g(48) + g(17))."
+  ],
+  "preparation_failures": [
+    "Second version: first strict replays of min-diff maps used the raw search's sigma count; assembly rejected them. SPEC now always pins the count read from the native audit (fourth version: 10649 rejected, 10006 read from the audit; this version: 10564 rejected, 10011 read from the audit).",
+    "Second version: check.py compared the conservative kappa as a string; it now compares decimals.",
+    "Third version: classes 4, 9, 88, 133 and 94 of the first class-level stage 1 could not be realised and were fixed to the selected map.",
+    "Fourth version: class 9 of stage 1 was proven unrealisable (four width-4 helpers per bin need four distinct calls); fixing it to the selected map made stage 1 infeasible, so the pattern was banned with the new BAN option of mindiff_cls1.py instead.",
+    "Fourth version: the session's search loop compared kappa strings in lns.py; the pinned assembler can drop trailing zeros. lns.py, check.py and verify.py now compare kappa as Decimal; every checkpoint was re-verified with Decimal comparisons.",
+    "ortools and highspy cannot be imported into one process (clashing HiGHS symbols), so mindiff_cls2.py runs its CP-SAT and HiGHS passes separately.",
+    "This version: the first strict replay of the min-diff map pinned the raw search's sigma count (10564) and was rejected by assembly as expected; 10011 was read from the audit.",
+    "This version: stage 1 of the min-diff proposed unrealisable class patterns in classes 9 and 25 (several helpers of one width in a bin need distinct calls); both were banned and stage 1 re-solved locally with KEEP/FREE.",
+    "This version: the session's lns2.py compared kappa strings like the old lns.py; the shipped lns2.py compares Decimal and every checkpoint was strict-replayed."
+  ],
+  "reused_native_ancestry": true,
+  "cold_ancestry_rebuilt": false,
+  "hosted_ci": "not yet observed",
+  "maintainer_acceptance": "not claimed"
+}
diff --git a/research/complex-t16-two-stage-cycles/VERIFY.json b/research/complex-t16-two-stage-cycles/VERIFY.json
new file mode 100644
index 0000000000..bf7c4b59df
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/VERIFY.json
@@ -0,0 +1,307 @@
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+  "requirements": [],
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/docs/PUBLIC-PINS.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/engines/base_two_moment.py",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/audit_coset_paths.cpp",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/optional-audit/coset-path-input.txt",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/response/WEIGHTED-COSET-SELECTION.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/response/build_weighted_coset.py",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/verify.py",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/EXPECTED.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/EXPECTED558.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/LICENSE",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/MANIFEST.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/NOTICE.md",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/engines/moment.py",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/evidence/PR552-packaged314.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/evidence/PR552-regression-final.json",
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+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/evidence/PR558-packaged311.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/evidence/PR558-packaged314.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR543-EXPECTED.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR552-EXACT-ASSEMBLY.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR552-EXPECTED.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR552-INVOICE.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR552-OWNERS.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR558-BASELINE-ASSEMBLY.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR558-EXPECTED.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR558-INVOICE.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR558-OWNERS.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/PR558-RESULT.json",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/inputs/UPSTREAM-LINEAGE.md",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/general-clifford-frames.tex",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-assembly.tex",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-bit.tex",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/notes/three-stage-cover-complex.tex",
+    "research/complex-k492-owner-repair/vendor/multicold/vendor/pr559/verify.py",
+    "research/complex-k492-owner-repair/vendor/multicold/verify.py",
+    "research/complex-t16-rare-pattern-exchanges/SOURCE.json",
+    "research/complex-t16-rare-pattern-exchanges/data/OWNERS.json.gz",
+    "research/complex-t16-rare-pattern-exchanges/data/PLAN.json",
+    "research/complex-t16-rare-pattern-exchanges/data/SPEC.json",
+    "research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz",
+    "research/frontier1094-idle-star-ceiling/analyze.py",
+    "research/pending-claims-independent-pricing/SNAPSHOT.json",
+    "research/pending-claims-independent-pricing/arith.py",
+    "research/pending-claims-independent-pricing/sweep.py",
+    "research/t16-owner-audit-seed67/SOURCES.json",
+    "research/t16-owner-audit-seed67/inputs/k8-seven-slot-word.json.gz",
+    "research/t16-owner-audit-seed67/verify.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Selected PR1094 map + DIFF-vs-selected.json reproduce OWNERS content and PLAN/SPEC bytes, with the changed/relocated row counts and the expected idle profile checked by an independent packing checker; unchanged PR1087 strict T16 replay (11 stages, 69/12/6/15 rejecting controls, both exact moment engines, strict outer assembly, recomputed actual_73column_sigmas); independent seed67 owner audit (R1-R7, X1, X2, 11 controls), strict majorization of the selected idle residual vector, pinned-engine pricing and PR1069 sweep; kappa decimals compared as Decimal; proved packing ceiling (ceiling_bound.py: at most 4,887 empty cap-48 bins, surrogate <= 908,139.013, exact integer checks)."
+    }
+  ]
+}
diff --git a/research/complex-t16-two-stage-cycles/build.py b/research/complex-t16-two-stage-cycles/build.py
new file mode 100644
index 0000000000..9b958e9026
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/build.py
@@ -0,0 +1,116 @@
+"""Reproduce the candidate owner map, PLAN and SPEC without running a packing search.
+
+The map is the selected PR1094 owner table plus the row replacements in
+DIFF-vs-selected.json. Only owner fields change; the replacements are the
+output of the search recorded in SEARCH.json (a global class-level repack,
+ejection cycles and CP-SAT LNS, including an evacuation neighbourhood, and
+class-level re-solves with guided realisation, for kappa, then a class-level
+min-diff re-assignment toward the selected map at the same idle profile). The derivation needs no other PR.
+"""
+from collections import Counter, defaultdict
+from pathlib import Path
+import gzip
+import hashlib
+import json
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+
+P = Path(__file__).resolve().parent
+BASE = 'research/complex-t16-rare-pattern-exchanges'
+FIXED = ('stage', 'replica', 'time', 'helper', 'width')
+OWNER = ('owner_replica', 'child', 'port', 'copy', 'family', 'offset')
+CHANGED_ROWS = 2537
+RELOCATED_ROWS = 2170
+SELECTED_IDLE = Counter({1: 2276, 3: 377, 7: 7, 48: 4866})
+CANDIDATE_IDLE = Counter({1: 2392, 2: 8, 3: 107, 4: 1, 7: 5, 16: 1, 48: 4880})
+
+
+def canonical(x):
+    return json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+
+
+def digest(b):
+    return hashlib.sha256(b).hexdigest()
+
+
+def idle(roles, plan):
+    """Exact integral packing check, independent of the search code and the strict verifier."""
+    bins = defaultdict(set)
+    families = defaultdict(set)
+    for r in roles:
+        call = (r['stage'], r['replica'])
+        assert r['family'] not in families[call]
+        families[call].add(r['family'])
+        assert r['copy'] == 112*r['owner_replica']+r['port']
+        cap, window = plan['windows'][f"{r['owner_replica']},{r['child']}"]
+        assert r['time'] in window and r['offset'] >= 0 and r['offset']+r['width'] <= cap
+        key = (r['owner_replica'], r['child'], r['port'])
+        cells = set(range(r['offset'], r['offset']+r['width']))
+        assert not bins[key] & cells
+        bins[key].update(cells)
+    result = Counter()
+    for key, (cap, _) in plan['windows'].items():
+        owner, child = map(int, key.split(','))
+        for port in range(112):
+            used = bins[owner, child, port]
+            assert used == set(range(len(used)))
+            if len(used) < cap:
+                result[cap-len(used)] += 1
+    return result
+
+
+def derive(main):
+    baseline = main/BASE
+    old = json.loads(gzip.decompress((baseline/'data/OWNERS.json.gz').read_bytes()))
+    plan = json.loads((baseline/'data/PLAN.json').read_text())
+    spec = json.loads((baseline/'data/SPEC.json').read_text())
+    rows = [r.copy() for r in old]
+    diff = json.loads((P/'DIFF-vs-selected.json').read_text())
+    assert len(diff) == CHANGED_ROWS and len({d['index'] for d in diff}) == CHANGED_ROWS
+    for d in diff:
+        i = d['index']
+        assert rows[i] == d['before'] and set(d['after']) == set(d['before']) and d['after'] != d['before']
+        assert all(rows[i][k] == d['after'][k] for k in FIXED)
+        rows[i] = d['after'].copy()
+    key = lambda r: (r['owner_replica'], r['child'], r['port'])
+    assert sum(key(a) != key(b) for a, b in zip(old, rows)) == RELOCATED_ROWS
+
+    before, after = idle(old, plan), idle(rows, plan)
+    assert before == SELECTED_IDLE
+    assert after == CANDIDATE_IDLE
+    assert sum(r*n for r, n in before.items()) == sum(r*n for r, n in after.items())
+    profile = Counter({int(k): v for k, v in plan['profile'].items()})
+    profile.subtract(before)
+    profile.update(after)
+    profile = +profile
+    assert sum(r*n for r, n in profile.items()) == 1041408
+    # Container bytes are immutable inputs. Regeneration checks the full payload,
+    # then binds PLAN/SPEC to this committed container, independent of zlib version.
+    container = (P/'data/OWNERS.json.gz').read_bytes()
+    assert json.loads(gzip.decompress(container)) == rows
+    profile = {str(k): v for k, v in sorted(profile.items())}
+    plan.update(profile=profile, assignment_sha256=digest(container), assignment_content_sha256=digest(canonical(rows)))
+    plan['replica_lift']['owners_file_sha256'] = digest(container)
+    plan_bytes = (json.dumps(plan, indent=2)+'\n').encode()
+    target = json.loads((P/'CANDIDATE.json').read_text())
+    spec['data'] = dict(owners_sha256=digest(container), plan_sha256=digest(plan_bytes))
+    spec['expected'].update(target['expected_updates'])
+    assert spec['expected']['global_profile'] == profile
+    assert spec['expected']['idle_remainder_profile'] == {str(k): v for k, v in sorted(after.items())}
+    assert spec['expected']['idle_remainders'] == sum(after.values())
+    assert spec['expected']['cross_replica_helper_roles'] == sum(r['replica'] != r['owner_replica'] for r in rows)
+    return container, plan_bytes, (json.dumps(spec, indent=2)+'\n').encode()
+
+
+if __name__ == '__main__':
+    import argparse
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, default=P.parents[1])
+    ap.add_argument('--out', type=Path, required=True)
+    args = ap.parse_args()
+    blobs = derive(args.main.resolve())
+    args.out.mkdir(parents=True, exist_ok=False)
+    for name, blob in zip(('OWNERS.json.gz', 'PLAN.json', 'SPEC.json'), blobs):
+        (args.out/name).write_bytes(blob)
+    print('PASS_T16_OWNER_MAP_DATA_RECONSTRUCTION')
diff --git a/research/complex-t16-two-stage-cycles/ceiling_bound.py b/research/complex-t16-two-stage-cycles/ceiling_bound.py
new file mode 100644
index 0000000000..dafb8c087c
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/ceiling_bound.py
@@ -0,0 +1,233 @@
+"""Proved packing ceiling for the T16 owner bins of the selected PR1094 supplier (PROOF.md, "A proved packing ceiling").
+
+Standard library only; every decisive comparison is exact (integers and Fractions). Logarithms enter only through
+E = sum over bins of g(free), g(f) = f ln f (0 for f <= 1), and every comparison of sums of g values is done on
+exp(.) = products of f**f, i.e. on integers. Decimal (correctly rounded ln) is used only to print values.
+
+Inputs, derived from the package data (no hard-coded instance beyond cross-check assertions):
+  bins     = every (owner, child) key of data/PLAN.json "windows" times 112 ports, capacity = the window's rank;
+  helpers  = the widths of the 69,120 rows of data/OWNERS.json.gz (the same multiset as the selected map).
+
+Theorem 1 (integer weights a(w) = floor(7w/9), A(c) = floor(7c/9)): every multiset of widths with sum <= c has
+  sum a <= A(c) (sum a <= 7 sum w / 9 <= 7c/9 and sum a is an integer; also checked over all 1,163 patterns). Summing over bins: 37 * (#empty cap-48 bins) <= sum_bins A - sum_helpers a = 180,832,
+  so at most 4,887 cap-48 bins are empty in ANY legal map (windows and the family rule are ignored: relaxation).
+Theorem 2 (LP dual): lambda = (36/37) ln 48, v_w and mu_c below are dual-feasible for every pattern, so
+  E <= sum_c B_c mu_c - sum_w N_w v_w (exact multiple of ln 48).
+Theorem 3 (sharp surrogate bound): with the slack s = A(c) - sum a of each bin, g(free) <= H(s) := max g over
+  patterns with slack s, and the slacks sum to 180,832; an exact knapsack argument gives
+  E <= 4887 g(48) + g(17).
+This bounds the surrogate E and the number of empty cap-48 bins, not kappa."""
+from collections import Counter
+from decimal import Decimal, getcontext
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import gzip
+import json
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+P = Path(__file__).resolve().parent
+W = (4, 5, 7, 8, 9)
+a = {w: 7*w//9 for w in W}
+
+
+def A(c):
+    return 7*c//9
+
+
+def patterns(c):
+    out = []
+    def rec(i, rem, cur):
+        if i == len(W):
+            out.append(tuple(cur))
+            return
+        for k in range(rem//W[i]+1):
+            rec(i+1, rem-k*W[i], cur+[k])
+    rec(0, c, [])
+    return out
+
+
+def expg(f):
+    """exp(g(f)) as an integer: f**f for f > 1, else 1."""
+    return f**f if f > 1 else 1
+
+
+def run(data, out_path):
+    plan = json.loads((data/'PLAN.json').read_text())
+    roles = json.loads(gzip.decompress((data/'OWNERS.json.gz').read_bytes()))
+    ports = 112
+    B = Counter()
+    for key, (cap, _) in plan['windows'].items():
+        B[cap] += ports
+    N = Counter(r['width'] for r in roles)
+    # Cross-check the derived instance against the numbers stated in PROOF.md.
+    assert dict(B) == {8: 10752, 16: 7168, 32: 7168, 48: 7168}, B
+    assert dict(N) == {w: 144*k for w, k in zip(W, (56, 32, 30, 122, 240))}, N
+    caps = sorted(B)
+    idle_total = sum(c*n for c, n in B.items()) - sum(w*n for w, n in N.items())
+    assert idle_total == 237024
+
+    # Theorem 1.
+    assert a == {4: 3, 5: 3, 7: 5, 8: 6, 9: 7} and [A(c) for c in caps] == [6, 12, 24, 37]
+    pats = {c: patterns(c) for c in caps}
+    npat = sum(len(p) for p in pats.values())
+    assert npat == 1163, npat
+    for c in caps:
+        for p in pats[c]:
+            assert sum(a[w]*k for w, k in zip(W, p)) <= A(c), (c, p)
+    T = sum(A(c)*n for c, n in B.items()) - sum(a[w]*n for w, n in N.items())
+    weight_bins, weight_helpers = sum(A(c)*n for c, n in B.items()), sum(a[w]*n for w, n in N.items())
+    assert (weight_bins, weight_helpers, T) == (587776, 406944, 180832)
+    nmax = T//37
+    assert nmax == 4887
+
+    # Theorem 2: LP dual, all values exact multiples of ln 48 (Fractions); the pattern check compares
+    # q*f*ln f <= p*ln 48 as f**(q*f) <= 48**p on integers.
+    lam = Q(36, 37)   # lambda / ln 48
+    v = {4: 4*lam, 5: 4*lam, 7: Q(20, 3)*lam, 8: 8*lam, 9: Q(28, 3)*lam}
+    mu = {8: 8*lam, 16: 16*lam, 32: 32*lam, 48: Q(48)}
+    tight = []
+    for c in caps:
+        for p in pats[c]:
+            f = c - sum(w*k for w, k in zip(W, p))
+            alpha = mu[c] - sum(v[w]*k for w, k in zip(W, p))   # reduced cost = alpha ln 48 - g(f)
+            assert alpha >= 0
+            if f > 1:
+                lhs, rhs = f**(alpha.denominator*f), 48**alpha.numerator
+                assert lhs <= rhs, (c, p)
+                if lhs == rhs:
+                    tight.append((c, p, f))
+            elif alpha == 0:
+                tight.append((c, p, f))
+    beta = sum(B[c]*mu[c] for c in caps) - sum(N[w]*v[w] for w in W)   # E <= beta ln 48
+
+    # Theorem 3: H(s) = max g over (cap, pattern) with slack s (compared as integers f**f).
+    best = {}
+    for c in caps:
+        for p in pats[c]:
+            f = c - sum(w*k for w, k in zip(W, p))
+            s = A(c) - sum(a[w]*k for w, k in zip(W, p))
+            if s == 0:
+                assert f <= 1, (c, p)   # zero-slack bins have g = 0, e.g. cap 32 with (9, 9, 9, 4)
+                continue
+            if s not in best or expg(f) > expg(best[s][0]):
+                best[s] = (f, c, p)
+    assert best[37][0] == 48 and best[37][1] == 48   # only the empty cap-48 bin has slack 37 and g(48)
+    # rho = max H(s)/s over all items except the empty cap-48 bin; compare f**(f*s') vs f'**(f'*s) on integers.
+    other = []   # (slack, free) items available to bins that are not empty cap-48 bins
+    for c in caps:
+        for p in pats[c]:
+            if c == 48 and sum(p) == 0:
+                continue
+            f = c - sum(w*k for w, k in zip(W, p))
+            s = A(c) - sum(a[w]*k for w, k in zip(W, p))
+            if s:
+                other.append((s, f))
+    Hn = {}
+    for s, f in other:
+        if s not in Hn or expg(f) > expg(Hn[s]):
+            Hn[s] = f
+    rs, rf = next(iter(Hn.items()))
+    for s, f in Hn.items():   # exact argmax of g(f)/s: g(f)/s > g(rf)/rs  <=>  f**(f*rs) > rf**(rf*s)
+        if expg(f)**rs > expg(rf)**s:
+            rs, rf = s, f
+    # rho < g(48)/37 strictly: rf**(rf*37) < 48**(48*rs)
+    assert expg(rf)**37 < expg(48)**rs
+    # Exact knapsack on the small range: Pk[S] = max over multisets of `other` items with slack sum exactly S of
+    # prod f**f (= exp of the best sum of g), None if S is not attainable.
+    K = 12
+    SM = T - 37*(nmax-K)
+    Pk = [1] + [None]*SM
+    for S in range(1, SM+1):
+        cand = None
+        for s, f in Hn.items():
+            if s <= S and Pk[S-s] is not None:
+                x = Pk[S-s]*expg(f)
+                if cand is None or x > cand:
+                    cand = x
+        Pk[S] = cand
+    # For n = nmax-K .. nmax empty cap-48 bins, E <= n g(48) + log Pk[T-37n]; compare relative to n0 = nmax-K.
+    n0 = nmax-K
+    scores = {}
+    for n in range(n0, nmax+1):
+        S = T-37*n
+        if Pk[S] is not None:
+            scores[n] = expg(48)**(n-n0)*Pk[S]
+    nbest = max(scores, key=lambda n: scores[n])
+    assert nbest == nmax and Pk[T-37*nmax] == expg(17), (nbest, Pk[T-37*nmax])
+    # For n < n0: E <= n g(48) + rho (T - 37 n) <= (n0-1) g(48) + rho (T - 37 (n0-1)) (increasing in n, as
+    # g(48) > 37 rho). Show that this is below nmax g(48) + g(17):
+    #   rho * R < (nmax-n0+1) g(48) + g(17), R = T - 37 (n0-1)
+    #   <=> rf**(rf*R) < (48**(48*(K+1)) * 17**17)**rs.
+    R = T-37*(n0-1)
+    assert expg(rf)**R < (expg(48)**(K+1)*expg(17))**rs
+    # The (float) full knapsack over all T as a cross-check of the structure (not part of the proof).
+    import math
+    gf = lambda f: f*math.log(f) if f > 1 else 0.0
+    items = [(s, gf(f)) for s, (f, _, _) in best.items()]
+    dp = [0.0]+[-1e300]*T
+    for t in range(1, T+1):
+        m = -1e300
+        for s, x in items:
+            if s <= t:
+                y = dp[t-s]+x
+                if y > m:
+                    m = y
+        dp[t] = m
+    getcontext().prec = 40
+    ln = lambda n: Decimal(n).ln()
+    g48 = 48*ln(48)
+    E3 = nmax*g48 + 17*ln(17)
+    E2 = Decimal(beta.numerator)/Decimal(beta.denominator)*ln(48)
+    assert abs(Decimal(dp[T]) - E3) < Decimal('1e-6')*E3
+
+    # The package's own map, for reference: its empty cap-48 bins, slack distribution and E.
+    used = Counter()
+    content = {}
+    for r in roles:
+        k = (r['owner_replica'], r['child'], r['port'])
+        used[k] += r['width']
+        content.setdefault(k, Counter())[r['width']] += 1
+    cap_of = {}
+    for key, (cap, _) in plan['windows'].items():
+        o, c = map(int, key.split(','))
+        for p in range(ports):
+            cap_of[o, c, p] = cap
+    n48 = sum(1 for k, c in cap_of.items() if c == 48 and used[k] == 0)
+    E = sum(gf(c-used[k]) for k, c in cap_of.items())
+    slack = Counter()
+    for k, c in cap_of.items():
+        s = A(c) - sum(a[w]*n for w, n in content.get(k, Counter()).items())
+        assert s >= 0
+        slack[c, c-used[k], s] += 1
+    assert sum(s*n for (_, _, s), n in slack.items()) == T and n48 <= nmax
+    one_free = Counter()
+    for (c, f, s), n in slack.items():
+        if f == 1:
+            one_free[c, s] += n
+    out = dict(
+        bins=dict(sorted(B.items())), helpers=dict(sorted(N.items())), idle_total=idle_total, patterns=npat,
+        theorem1=dict(a=a, A={c: A(c) for c in caps}, bin_weight=weight_bins, helper_weight=weight_helpers,
+                      slack_total=T, max_empty_cap48=nmax),
+        theorem2=dict(lambda_over_ln48=str(lam), bound_over_ln48=str(beta), bound_decimal=str(E2.quantize(Decimal('0.001'))),
+                      tight_patterns=[[c, list(p), f] for c, p, f in tight]),
+        theorem3=dict(rho_item=dict(slack=rs, free=rf), bound='4887 g(48) + g(17)', bound_decimal=str(E3.quantize(Decimal('0.001'))),
+                      float_full_knapsack=round(dp[T], 3)),
+        this_map=dict(empty_cap48=n48, E=round(E, 3), surrogate_gap=round(float(E3)-E, 3),
+                      one_free_bins_by_cap_and_slack={f'{c},{s}': n for (c, s), n in sorted(one_free.items())}),
+    )
+    assert E < float(E3)
+    if out_path:
+        out_path.write_text(json.dumps(out, indent=1)+'\n')
+    print('PASS_PACKING_CEILING', 'empty_cap48<=', nmax, 'E<=', out['theorem3']['bound_decimal'],
+          'LP', out['theorem2']['bound_decimal'], 'map', n48, out['this_map']['E'])
+    return out
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--data', type=Path, default=P/'data')
+    ap.add_argument('--out', type=Path)
+    args = ap.parse_args()
+    run(args.data, args.out)
diff --git a/research/complex-t16-two-stage-cycles/check.py b/research/complex-t16-two-stage-cycles/check.py
new file mode 100644
index 0000000000..4651e0f89f
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/check.py
@@ -0,0 +1,177 @@
+"""Independent owner-map and pricing check (adapted from the search session's checkmap.py).
+
+Imports no code from this package's search or from the strict PR1087 verifier.
+It uses three merged, separately authored checkers on the candidate data:
+  * the seed67 owner auditor (research/t16-owner-audit-seed67, Josie Elliston,
+    PR1091): rules R1-R7, X1, X2 and its 11 rejecting mutation controls;
+  * the pinned exact moment/base-two/outer engines through
+    research/frontier1094-idle-star-ceiling/analyze.py (pricing both suppliers,
+    native and conservative surcharge);
+  * the PR1069 independent pricing sweep (research/pending-claims-independent-pricing,
+    Sagar Thakrar), fed with the strict replay's own complex/bit lowers.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import argparse
+import gzip
+import hashlib
+import importlib.util
+import json
+from decimal import Decimal
+import sys
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+P = Path(__file__).resolve().parent
+SELECTED_KAPPA = '0.001672660197076918'
+INDICATIVE_CEILING_KAPPA = '0.001674088611862992'
+
+
+def load(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    mod = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(mod)
+    return mod
+
+
+def read(p):
+    p = Path(p)
+    b = p.read_bytes()
+    return json.loads(gzip.decompress(b) if p.suffix == '.gz' else b)
+
+
+def run(main, replay, out_path):
+    a = load('owners', main/'research/t16-owner-audit-seed67/verify.py')
+    pins = read(main/'research/t16-owner-audit-seed67/SOURCES.json')['inputs']
+    assert hashlib.sha256((main/a.TEMPLATE).read_bytes()).hexdigest() == pins['template_sha256']
+    assert hashlib.sha256((main/a.PHASES).read_bytes()).hexdigest() == pins['data_phases_sha256']
+    assert hashlib.sha256(gzip.decompress(a.WORD.read_bytes())).hexdigest() == pins['word_content_sha256']
+    word = read(a.WORD)
+    geo = a.geometry(read(main/a.TEMPLATE), read(main/a.PHASES))
+    widths = a.word_widths(word)
+    local = a.as_profile(word['report']['local_profile'])
+    sel = main/'research/complex-t16-rare-pattern-exchanges/data'
+    selplan, selroles = read(sel/'PLAN.json'), read(sel/'OWNERS.json.gz')
+    span, callpos = a.windows(geo, [tuple(x) for x in selplan['order']])
+
+    def idle_of(roles):
+        used = Counter()
+        for z in roles:
+            used[z['owner_replica'], z['child'], z['port']] += z['width']
+        idle = Counter()
+        for (o, c) in span:
+            for p in range(a.V):
+                f = geo['rank'][c] - used[o, c, p]
+                if f:
+                    idle[f] += 1
+        return idle
+
+    def audit(roles, plan):
+        idle = idle_of(roles)
+        r = a.audit(geo, widths, local, roles, plan, idle, 16)
+        r['controls'] = len(a.controls(geo, widths, local, roles, plan, idle, 16))
+        return r
+
+    st = load('idlestar', main/'research/frontier1094-idle-star-ceiling/analyze.py')
+    st.ROOT = main
+    st.ENGINE_ROOT = main/'research/complex-k492-owner-repair/vendor/multicold/engines'
+    engines = tuple(st.load_engine(n) for n in ('moment', 'base_two_moment', 'outer'))
+    baseline = json.loads((main/'research/community-frontier1094-audit/ASSEMBLY.json').read_text())
+
+    def price(profile, bad=False):
+        return st.price(Counter({int(k): v for k, v in profile.items()}), bad, baseline, engines)
+
+    roles = read(P/'data/OWNERS.json.gz')
+    plan, spec = read(P/'data/PLAN.json'), read(P/'data/SPEC.json')
+    assert plan['order'] == selplan['order'] and plan['windows'] == selplan['windows']
+    assert a.as_profile(spec['providers']['gauge44']['expected_profile']) == local
+    assert Counter(widths) == a.as_profile(spec['providers']['gauge44']['inventory'])
+    out = dict(spec_idle=spec['expected']['idle_remainder_profile'])
+    old, new = audit(selroles, selplan), audit(roles, plan)
+    assert new['profile'] == a.as_profile(plan['profile'])
+    assert new['idle'] == {int(k): v for k, v in out['spec_idle'].items()}
+    assert old['controls'] == new['controls'] == 11
+    for tag, r in (('selected', old), ('candidate', new)):
+        out[tag] = {k: r[k] for k in ('idle', 'profile', 'rank_mass', 'deficit', 'controls', 'cross_replica_roles')}
+    diff = [i for i, (x, y) in enumerate(zip(selroles, roles)) if x != y]
+    key = lambda z: (z['owner_replica'], z['child'], z['port'])
+    moved = [i for i in diff if key(selroles[i]) != key(roles[i])]
+    for i in diff:
+        assert all(selroles[i][k] == roles[i][k] for k in ('stage', 'replica', 'time', 'helper', 'width'))
+    out.update(changed_rows=len(diff), relocated_rows=moved, offset_only_rows=len(diff)-len(moved))
+    assert len(roles) == len(selroles)
+    out['all_strictly_inside'] = all(span[z['owner_replica'], z['child']][0] < callpos[z['stage'], z['replica']]
+                                     < span[z['owner_replica'], z['child']][1] for z in roles)
+    per = Counter((z['stage'], z['replica'], z['helper']) for z in roles)
+    out['helper_once_per_call'] = set(per.values()) == {1} and len(per) == 144*len(widths)
+    assert out['all_strictly_inside'] and out['helper_once_per_call']
+
+    # Majorization of the idle residual vectors (sorted descending, padded with zeros to the
+    # common bin count): equal totals, and every partial sum of the candidate vector is at
+    # least the selected one's, strictly somewhere. Karamata then gives a strict decrease of
+    # sum H(r) for every strictly concave H (PROOF.md); the exact engines below give the value.
+    nbins = len(span)*a.V
+    def residuals(idle):
+        v = sorted((r for r, n in idle.items() for _ in range(n)), reverse=True)
+        assert len(v) <= nbins
+        return v+[0]*(nbins-len(v))
+    vn, vo = residuals(new['idle']), residuals(old['idle'])
+    assert sum(vn) == sum(vo)
+    sn = so = 0
+    dominated, strict = True, False
+    for x, y in zip(vn, vo):
+        sn += x
+        so += y
+        dominated &= sn >= so
+        strict |= sn > so
+    assert dominated and strict, 'candidate idle vector does not strictly majorize the selected one'
+    out['majorization'] = dict(residual_total=sum(vn), bins=nbins, candidate_majorizes_selected=True, strict=True)
+
+    ps, pn, pc = price(old['profile']), price(new['profile']), price(new['profile'], True)
+    out.update(price_selected=ps, price_new=pn, price_new_conservative=pc)
+    assert Decimal(ps['kappa_decimal']) == Decimal(SELECTED_KAPPA)
+    assert pn['kappa'] == spec['expected']['kappa'] and pn['endpoint'] == spec['expected']['complex_lower']
+    # Compare kappa decimals as Decimal, never as strings: the native assembler drops trailing zeros.
+    assert Decimal(pc['kappa_decimal']) == Decimal(spec['expected']['conservative_kappa_decimal'])
+    out['rel_gain'] = str((Q(pn['kappa'])-Q(ps['kappa']))/Q(ps['kappa']))
+    # Indicative only (PROOF.md, "A proved packing ceiling"): price the idle multiset that attains the proved surrogate
+    # bound {1: 2431, 17: 1, 48: 4887} in place of the selected idle remainders. This is not a kappa bound.
+    ceiling_idle = Counter({1: 2431, 17: 1, 48: 4887})
+    base = Counter(a.as_profile(selplan['profile']))
+    base.subtract(old['idle'])
+    ceiling_profile = +(base+ceiling_idle)
+    assert sum(r*n for r, n in ceiling_profile.items()) == 1041408
+    pi = price(ceiling_profile)
+    assert Decimal(pi['kappa_decimal']) == Decimal(INDICATIVE_CEILING_KAPPA)
+    out['indicative_ceiling_price'] = dict(idle={str(k): v for k, v in sorted(ceiling_idle.items())},
+                                           kappa_decimal=pi['kappa_decimal'], complex_lower=pi['endpoint'])
+
+    if replay is not None:
+        rep = json.loads((replay/'REPLAY.json').read_text())
+        assert rep['status'] == 'PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY'
+        assert a.as_profile(rep['complex_profile']) == new['profile']
+        assert rep['kappa'] == pn['kappa'] and rep['complex_lower'] == pn['endpoint']
+        sys.path.insert(0, str(main/'research/pending-claims-independent-pricing'))
+        sweep = load('pricing', main/'research/pending-claims-independent-pricing/sweep.py')
+        claim = dict(pr=0, head='x', profile=new['profile'], live=14336, calls=144, complex_lower=rep['complex_lower'],
+                     record_kappa=rep['kappa'], claimed_kappa_decimal=rep['kappa_decimal'], bit_lower=rep['bit_lower'])
+        swept = sweep.price(claim)
+        keys = ('endpoint_certified', 'deficit_equals_W_minus_64N', 'halving', 'record_bit_is_pr589',
+                'kappa_equals_record', 'kappa_equals_title', 'kappa_exact_decimal', 'binding')
+        out['sweep'] = {k: swept.get(k) for k in keys}
+        assert all(out['sweep'][k] is True for k in keys[:6])
+        assert Decimal(out['sweep']['kappa_exact_decimal']) == Decimal(spec['expected']['kappa_decimal']) and out['sweep']['binding'] == 'complex'
+    if out_path is not None:
+        out_path.write_text(json.dumps(out, indent=1, default=str)+'\n')
+    print('PASS_INDEPENDENT_OWNER_AND_PRICING_CHECK', pn['kappa_decimal'], dict(sorted(new['idle'].items())),
+          'controls', new['controls'], 'sweep', replay is not None)
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, default=P.parents[1])
+    ap.add_argument('--replay', type=Path, help='strict replay work dir containing REPLAY.json (enables the PR1069 sweep)')
+    ap.add_argument('--out', type=Path)
+    args = ap.parse_args()
+    run(args.main.resolve(), args.replay and args.replay.resolve(), args.out)
diff --git a/research/complex-t16-two-stage-cycles/data/OWNERS.json.gz b/research/complex-t16-two-stage-cycles/data/OWNERS.json.gz
new file mode 100644
index 0000000000..aa664b8e35
Binary files /dev/null and b/research/complex-t16-two-stage-cycles/data/OWNERS.json.gz differ
diff --git a/research/complex-t16-two-stage-cycles/data/PLAN.json b/research/complex-t16-two-stage-cycles/data/PLAN.json
new file mode 100644
index 0000000000..99a48b1c72
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/data/PLAN.json
@@ -0,0 +1,85661 @@
+{
+  "status": "FROZEN_EXPLICIT_T16_TWO_BANK_DIRECT_SUM_OWNER_NOMINATION",
+  "mode": "gauge44-all144-t16-idle-concentration",
+  "K": 4,
+  "T": 16,
+  "M": 73,
+  "L": 9,
+  "live": 14336,
+  "deficit": 5120,
+  "profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62315,
+    "4": 20449,
+    "5": 11808,
+    "7": 5,
+    "8": 1152,
+    "16": 1,
+    "48": 4880
+  },
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diff --git a/research/complex-t16-two-stage-cycles/data/SPEC.json b/research/complex-t16-two-stage-cycles/data/SPEC.json
new file mode 100644
index 0000000000..fb46407cc6
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/data/SPEC.json
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diff --git a/research/complex-t16-two-stage-cycles/evidence/ADMISSION-CONTROLS.json b/research/complex-t16-two-stage-cycles/evidence/ADMISSION-CONTROLS.json
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index 0000000000..ff6eef2ab6
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "334722841145139/200000000000000000",
+  "input_sha256": {
+    "owner_audit": "c49a55129278231a2047237f90c0e84eecd1a6030771d28eb3f20eddaf470dd3",
+    "fresh_invoice": "53ab965b01b2b8861231be984104b0b6740d1f2a8c2ce1dfa4a8fdcbbdf9aaa7",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_258",
+    "gauge44:cold_helper_width_swap_270",
+    "gauge44:cold_helper_width_swap_282",
+    "gauge44:cold_helper_width_swap_294",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/ASSEMBLY.json b/research/complex-t16-two-stage-cycles/evidence/ASSEMBLY.json
new file mode 100644
index 0000000000..925cf3245f
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/ASSEMBLY.json
@@ -0,0 +1,346 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "334722841145139/200000000000000000",
+  "kappa_decimal": "0.001673614205725695",
+  "complex_lower": "83820994293071721251/50000000000000000000000",
+  "complex_decimal": "0.00167641988586143442502",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "2.284057953138420246258288880242548858864787923709216942926747012451152",
+  "complex_profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62315,
+    "4": 20449,
+    "5": 11808,
+    "7": 5,
+    "8": 1152,
+    "16": 1,
+    "48": 4880
+  },
+  "provider_counts": {
+    "gauge44": 144
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "335283976599811653119/200000000000000000000000",
+  "conservative_complex_decimal": "0.001676419882999058265595",
+  "conservative_kappa": "418403550718223/250000000000000000",
+  "conservative_kappa_decimal": "0.001673614202872892",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "335283976599811653119/200000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-65065847402241284216645094777755161671516625/26959946667150639794667015087019630673637144422540572481103610249216",
+        "-65065847402241284216645094777755161671516623/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "-24134266993731548642423/10000000000000000000000000000000000000000000000",
+        "-12067128496865774321141/5000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "419104970749764566399/250000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "6926628464338793538615366894518405075745543/13479973333575319897333507543509815336818572211270286240551805124608",
+        "865828558042349192326920861814800634468193/1684996666696914987166688442938726917102321526408785780068975640576"
+      ],
+      "base_two": [
+        "2569226503313973498061/5000000000000000000000000000000000000000000000",
+        "642307875828493374533/1250000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
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+      "cutoff_log2": "4774526629970"
+    },
+    {
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+    "leaf_saving_above_bit": "156037865031209153784351986758278293036565110364262698090184894508169961555045259110398757529994610229286964143738074903149892096802282589756337293215019540196430986560542694570023228539133297012845028325365134147906129328793896944819508667640001150405156703856933738213553851766892904811971641891432803706466660960829077756291490328248993231055726280970241/2560000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  },
+  "controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/BIT-SUPPLIER-CONTROLS.json b/research/complex-t16-two-stage-cycles/evidence/BIT-SUPPLIER-CONTROLS.json
new file mode 100644
index 0000000000..df4811b1fc
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/BIT-SUPPLIER-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.001673614205725695",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "15f6986a476bac76bcdc0bfcf51da115389b46f1950d2766b6822f757888b13a"
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/CEILING.json b/research/complex-t16-two-stage-cycles/evidence/CEILING.json
new file mode 100644
index 0000000000..fb838adfa1
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/CEILING.json
@@ -0,0 +1,281 @@
+{
+ "bins": {
+  "8": 10752,
+  "16": 7168,
+  "32": 7168,
+  "48": 7168
+ },
+ "helpers": {
+  "4": 8064,
+  "5": 4608,
+  "7": 4320,
+  "8": 17568,
+  "9": 34560
+ },
+ "idle_total": 237024,
+ "patterns": 1163,
+ "theorem1": {
+  "a": {
+   "4": 3,
+   "5": 3,
+   "7": 5,
+   "8": 6,
+   "9": 7
+  },
+  "A": {
+   "8": 6,
+   "16": 12,
+   "32": 24,
+   "48": 37
+  },
+  "bin_weight": 587776,
+  "helper_weight": 406944,
+  "slack_total": 180832,
+  "max_empty_cap48": 4887
+ },
+ "theorem2": {
+  "lambda_over_ln48": "36/37",
+  "bound_over_ln48": "8679936/37",
+  "bound_decimal": "908156.136",
+  "tight_patterns": [
+   [
+    8,
+    [
+     0,
+     0,
+     0,
+     1,
+     0
+    ],
+    0
+   ],
+   [
+    8,
+    [
+     2,
+     0,
+     0,
+     0,
+     0
+    ],
+    0
+   ],
+   [
+    16,
+    [
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+  ]
+ },
+ "theorem3": {
+  "rho_item": {
+   "slack": 34,
+   "free": 44
+  },
+  "bound": "4887 g(48) + g(17)",
+  "bound_decimal": "908139.013",
+  "float_full_knapsack": 908139.013
+ },
+ "this_map": {
+  "empty_cap48": 4880,
+  "E": 907271.883,
+  "surrogate_gap": 867.13,
+  "one_free_bins_by_cap_and_slack": {
+   "32,0": 2390,
+   "48,1": 2
+  }
+ }
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/CHECK.json b/research/complex-t16-two-stage-cycles/evidence/CHECK.json
new file mode 100644
index 0000000000..f34227a6d1
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/CHECK.json
@@ -0,0 +1,2279 @@
+{
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+  53336,
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+  53770,
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+  54050,
+  54311,
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+  58376,
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+  58622,
+  58974,
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+  59130,
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+  59301,
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+  59689,
+  59888,
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+  62715,
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+  64065,
+  64461,
+  65088,
+  65096,
+  65409,
+  65411,
+  65508,
+  67499,
+  67983
+ ],
+ "offset_only_rows": 367,
+ "all_strictly_inside": true,
+ "helper_once_per_call": true,
+ "majorization": {
+  "residual_total": 237024,
+  "bins": 32256,
+  "candidate_majorizes_selected": true,
+  "strict": true
+ },
+ "price_selected": {
+  "endpoint": "67018507072324140917/40000000000000000000000",
+  "endpoint_decimal": "0.001675462676808103522925",
+  "kappa": "836330098538459/500000000000000000",
+  "kappa_decimal": "0.001672660197076918"
+ },
+ "price_new": {
+  "endpoint": "83820994293071721251/50000000000000000000000",
+  "endpoint_decimal": "0.001676419885861434425020",
+  "kappa": "334722841145139/200000000000000000",
+  "kappa_decimal": "0.001673614205725695"
+ },
+ "price_new_conservative": {
+  "endpoint": "335283976599811653119/200000000000000000000000",
+  "endpoint_decimal": "0.001676419882999058265595",
+  "kappa": "418403550718223/250000000000000000",
+  "kappa_decimal": "0.001673614202872892"
+ },
+ "rel_gain": "954008648777/1672660197076918",
+ "indicative_ceiling_price": {
+  "idle": {
+   "1": 2431,
+   "17": 1,
+   "48": 4887
+  },
+  "kappa_decimal": "0.001674088611862992",
+  "complex_lower": "1676895884165954931459/1000000000000000000000000"
+ },
+ "sweep": {
+  "endpoint_certified": true,
+  "deficit_equals_W_minus_64N": true,
+  "halving": true,
+  "record_bit_is_pr589": true,
+  "kappa_equals_record": true,
+  "kappa_equals_title": true,
+  "kappa_exact_decimal": "0.001673614205725695",
+  "binding": "complex"
+ }
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/INDEPENDENT-T16.json b/research/complex-t16-two-stage-cycles/evidence/INDEPENDENT-T16.json
new file mode 100644
index 0000000000..95111e523f
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/INDEPENDENT-T16.json
@@ -0,0 +1,121 @@
+{
+  "status": "PASS_INDEPENDENT_T16_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+  "roles": 69120,
+  "calls": 144,
+  "source_events_per_replica": 30,
+  "expanded_replica_events": 480,
+  "bridge_events": 144,
+  "literal_windows": 288,
+  "checked_whole_helper_widths": 69120,
+  "checked_busy_family_windows": 69120,
+  "orthogonal_port_bases": 112,
+  "actual_73_axis_charts": 10011,
+  "checked_slice_prefixes": 32256,
+  "local_profile": {
+    "1": 2412,
+    "2": 418,
+    "3": 432,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 56,
+    "5": 32,
+    "7": 30,
+    "8": 122,
+    "9": 240
+  },
+  "idle": {
+    "1": 2392,
+    "2": 8,
+    "3": 107,
+    "4": 1,
+    "7": 5,
+    "16": 1,
+    "48": 4880
+  },
+  "profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62315,
+    "4": 20449,
+    "5": 11808,
+    "7": 5,
+    "8": 1152,
+    "16": 1,
+    "48": 4880
+  },
+  "live": 14336,
+  "physical": 14850,
+  "rank_mass": 1041408,
+  "deficit": 5120,
+  "namespace": {
+    "data": [
+      0,
+      14336
+    ],
+    "centres": [
+      14336,
+      14344
+    ],
+    "tableau": [
+      14344,
+      14848
+    ],
+    "coefficient": [
+      14848,
+      14850
+    ]
+  },
+  "local_prefix_bits": 68,
+  "local_prefix_from_native_receipt": true,
+  "local_profile_recounted": true,
+  "prefix_formula": {
+    "local_scalar": 68,
+    "input_l2": 37,
+    "invocations": 144,
+    "bridges": 144,
+    "margin": 4
+  },
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_stock_bits": 2642,
+  "physical_row_coefficient": 16469,
+  "row_limit": 20161,
+  "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+  "controls_rejected": [
+    {
+      "name": "private_namespace_collision",
+      "reason": "private-namespace collision"
+    },
+    {
+      "name": "copy_replica_alias",
+      "reason": "role invocation time"
+    },
+    {
+      "name": "missing_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "split_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "truncated_helper_width",
+      "reason": "whole-helper residual width"
+    },
+    {
+      "name": "cross_idle_boundary",
+      "reason": "strict bridge-aware idle window"
+    }
+  ],
+  "input_sha256": {
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/strict/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/strict/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/strict/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/local/INDEPENDENT-LOCAL-REPLAY.json": "13dd18297162569532983db1a2ab67926b064330cd7edd3587e7b546b2dedf17",
+    "/tmp/claude-1000/-home-pvv-repo-integer-mult-bounds/7f285b4f-6b62-4f2c-bb95-9f578ff78aed/scratchpad/expBL/vrun2/source/data/OWNERS.json.gz": "551fd1b3a75fa5fd67cfd8c00a6c77c2f893a5120cb0c0dd8a7699f25e9bddba"
+  }
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/REPLAY.json b/research/complex-t16-two-stage-cycles/evidence/REPLAY.json
new file mode 100644
index 0000000000..bceeee1b13
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/REPLAY.json
@@ -0,0 +1,112 @@
+{
+  "status": "PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY",
+  "kappa": "334722841145139/200000000000000000",
+  "kappa_decimal": "0.001673614205725695",
+  "conservative_kappa_decimal": "0.001673614202872892",
+  "complex_lower": "83820994293071721251/50000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "complex_profile": {
+    "1": 349720,
+    "2": 60200,
+    "3": 62315,
+    "4": 20449,
+    "5": 11808,
+    "7": 5,
+    "8": 1152,
+    "16": 1,
+    "48": 4880
+  },
+  "idle_remainder_profile": {
+    "1": 2392,
+    "2": 8,
+    "3": 107,
+    "4": 1,
+    "7": 5,
+    "16": 1,
+    "48": 4880
+  },
+  "complete_invocations": 144,
+  "roles": 69120,
+  "prefix_bits": 397,
+  "charged_prefix_bits": 512,
+  "physical_row_coefficient": 16469,
+  "retained_row_coefficient": 20161,
+  "actual_73_axis_charts": 10011,
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller_mutations": 15
+  },
+  "t8_kappa": "167166528321877/100000000000000000",
+  "spec_sha256": "e81f2dabf16bc4d56d427bf5bc4a06f05ce27fc6c539c3de4029cb5304ed9701",
+  "stages": [
+    {
+      "name": "restore-parent",
+      "seconds": 1.969,
+      "exit_code": 0,
+      "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+    },
+    {
+      "name": "bind8",
+      "seconds": 0.426,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "lift16",
+      "seconds": 3.366,
+      "exit_code": 0,
+      "log_sha256": "5734552201a17a15766f2257becf4bf6b7f00aede6f0a412067df2c159916853"
+    },
+    {
+      "name": "bind",
+      "seconds": 0.497,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 6.513,
+      "exit_code": 0,
+      "log_sha256": "80f3253de853c036fe5e5e7e9a4fcf44572253f11df490346d338d7775bae2b0"
+    },
+    {
+      "name": "audit",
+      "seconds": 20.773,
+      "exit_code": 0,
+      "log_sha256": "da22246506cd019cee09b2908f2080f1796b007dd6a1f525c6f5170b7bb76676"
+    },
+    {
+      "name": "invoice",
+      "seconds": 0.862,
+      "exit_code": 0,
+      "log_sha256": "8f7074e3f78a103318ded6362c8e9bc8fc0e8c1ea3b510e63b9b84b181452cb3"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.269,
+      "exit_code": 0,
+      "log_sha256": "4171f580e357579caab4b9f3dd8a26da3352e94a9871bfe3aa411243497816f9"
+    },
+    {
+      "name": "admission-controls",
+      "seconds": 0.359,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit-supplier-controls",
+      "seconds": 0.528,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent-t16",
+      "seconds": 0.836,
+      "exit_code": 0,
+      "log_sha256": "9a822ed55b91969189acb1bb1bbdcebafc800855952fbd5e91c5d977c29cbbf9"
+    }
+  ],
+  "scope": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification."
+}
diff --git a/research/complex-t16-two-stage-cycles/evidence/STAGES.json b/research/complex-t16-two-stage-cycles/evidence/STAGES.json
new file mode 100644
index 0000000000..5606efce92
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/evidence/STAGES.json
@@ -0,0 +1,68 @@
+[
+  {
+    "name": "restore-parent",
+    "seconds": 1.969,
+    "exit_code": 0,
+    "log_sha256": "fc3a01967636bd3173ee7e5049fae45b890e1fad4564b6acdd6aaca30a4e4ea5"
+  },
+  {
+    "name": "bind8",
+    "seconds": 0.426,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "lift16",
+    "seconds": 3.366,
+    "exit_code": 0,
+    "log_sha256": "5734552201a17a15766f2257becf4bf6b7f00aede6f0a412067df2c159916853"
+  },
+  {
+    "name": "bind",
+    "seconds": 0.497,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 6.513,
+    "exit_code": 0,
+    "log_sha256": "80f3253de853c036fe5e5e7e9a4fcf44572253f11df490346d338d7775bae2b0"
+  },
+  {
+    "name": "audit",
+    "seconds": 20.773,
+    "exit_code": 0,
+    "log_sha256": "da22246506cd019cee09b2908f2080f1796b007dd6a1f525c6f5170b7bb76676"
+  },
+  {
+    "name": "invoice",
+    "seconds": 0.862,
+    "exit_code": 0,
+    "log_sha256": "8f7074e3f78a103318ded6362c8e9bc8fc0e8c1ea3b510e63b9b84b181452cb3"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.269,
+    "exit_code": 0,
+    "log_sha256": "4171f580e357579caab4b9f3dd8a26da3352e94a9871bfe3aa411243497816f9"
+  },
+  {
+    "name": "admission-controls",
+    "seconds": 0.359,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  },
+  {
+    "name": "bit-supplier-controls",
+    "seconds": 0.528,
+    "exit_code": 0,
+    "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+  },
+  {
+    "name": "independent-t16",
+    "seconds": 0.836,
+    "exit_code": 0,
+    "log_sha256": "9a822ed55b91969189acb1bb1bbdcebafc800855952fbd5e91c5d977c29cbbf9"
+  }
+]
diff --git a/research/complex-t16-two-stage-cycles/search/aggbound.py b/research/complex-t16-two-stage-cycles/search/aggbound.py
new file mode 100644
index 0000000000..3e02af0c72
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/aggbound.py
@@ -0,0 +1,29 @@
+"""Aggregate ceiling (heuristic, not a proof): ignores calls, windows and R4 and packs the helper width counts
+into bins by capacity, maximising sum g(free) with g(f) = f ln f (scaled to integers). Coarser than winbound.py.
+The surrogate is only approximately linear in kappa, so this is not a certified kappa bound.
+Standalone: needs CPython 3.12 and ortools only."""
+import math, itertools
+from ortools.sat.python import cp_model
+W = [4, 5, 7, 8, 9]; N = {9: 240*144, 8: 122*144, 4: 56*144, 5: 32*144, 7: 30*144}
+B = {8: 10752, 16: 7168, 32: 7168, 48: 7168}
+g = lambda f: f*math.log(f) if f > 1 else 0.0
+def pats(cap):
+    out = []
+    def rec(i, rem, cur):
+        if i == len(W): out.append(tuple(cur)); return
+        for c in range(rem // W[i] + 1): rec(i+1, rem - c*W[i], cur + [c])
+    rec(0, cap, []); return out
+m = cp_model.CpModel(); obj = []; use = {w: [] for w in W}
+cur_obj = 0
+for cap, nb in B.items():
+    xs = []
+    for p in pats(cap):
+        s = sum(c*w for c, w in zip(p, W)); x = m.NewIntVar(0, nb, ''); xs.append(x)
+        obj.append(round(1e4*g(cap - s)) * x)
+        for c, w in zip(p, W):
+            if c: use[w].append(c * x)
+    m.Add(sum(xs) == nb)
+for w in W: m.Add(sum(use[w]) == N[w])
+m.Maximize(sum(obj)); s = cp_model.CpSolver(); s.parameters.max_time_in_seconds = 120; s.parameters.num_workers = 1
+st = s.Solve(m); print(s.StatusName(st), s.ObjectiveValue()/1e4, s.BestObjectiveBound()/1e4)
+cur = {1: 2346, 2: 3, 3: 154, 5: 9, 7: 36, 8: 2, 16: 7, 28: 1, 39: 1, 40: 1, 41: 2, 44: 41, 48: 4829}; print('current', sum(n*g(f) for f, n in cur.items()))
diff --git a/research/complex-t16-two-stage-cycles/search/buildcand.py b/research/complex-t16-two-stage-cycles/search/buildcand.py
new file mode 100644
index 0000000000..28bd364152
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/buildcand.py
@@ -0,0 +1,32 @@
+"""Build OWNERS/PLAN/SPEC for a candidate owner map from the selected PR1094 package (2077-style).
+argv: LIBDIR OWNERS_IN OUTDIR [sigmas]"""
+import sys, json, gzip, hashlib
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter
+from pathlib import Path
+rows = lib.read(sys.argv[2]); out = Path(sys.argv[3]); out.mkdir(parents=True)
+canon = lambda x: json.dumps(x, sort_keys=True, separators=(',', ':')).encode()
+dg = lambda b: hashlib.sha256(b).hexdigest()
+au = lib.audit(rows)
+plan = json.loads((lib.SEL/'PLAN.json').read_text()); spec = json.loads((lib.SEL/'SPEC.json').read_text())
+container = gzip.compress(json.dumps(rows).encode(), mtime=0)
+assert json.loads(gzip.decompress(container)) == rows
+profile = {str(k): v for k, v in sorted(au['profile'].items())}
+plan.update(profile=profile, assignment_sha256=dg(container), assignment_content_sha256=dg(canon(rows)))
+plan['replica_lift']['owners_file_sha256'] = dg(container)
+plan_bytes = (json.dumps(plan, indent=2) + '\n').encode()
+pn, pc = lib.price(au['profile']), lib.price(au['profile'], True)
+spec['data'] = dict(owners_sha256=dg(container), plan_sha256=dg(plan_bytes))
+e = spec['expected']
+from decimal import Decimal, localcontext
+from fractions import Fraction as Q
+def dec(x):
+    x = Q(x)
+    with localcontext() as ctx: ctx.prec = 70; return str(Decimal(x.numerator) / Decimal(x.denominator))
+e.update(complex_lower=pn['endpoint'], conservative_complex_lower=pc['endpoint'], kappa=pn['kappa'], kappa_decimal=dec(pn['kappa']),
+         conservative_kappa_decimal=dec(pc['kappa']), cross_replica_helper_roles=au['cross_replica_roles'],
+         idle_remainders=sum(au['idle'].values()), idle_remainder_profile={str(k): v for k, v in sorted(au['idle'].items())}, global_profile=profile)
+if len(sys.argv) > 4: e['actual_73column_sigmas'] = int(sys.argv[4])
+(out/'OWNERS.json.gz').write_bytes(container); (out/'PLAN.json').write_bytes(plan_bytes)
+(out/'SPEC.json').write_text(json.dumps(spec, indent=2) + '\n')
+print('built', out, pn['kappa_decimal'], pc['kappa_decimal'], au['idle'])
diff --git a/research/complex-t16-two-stage-cycles/search/chain.py b/research/complex-t16-two-stage-cycles/search/chain.py
new file mode 100644
index 0000000000..bdcbd2a482
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/chain.py
@@ -0,0 +1,156 @@
+"""Ejection-chain / cyclic-exchange search on a T16 owner map (final-state legality only).
+State = (hand width, hand time). Max-plus DP over states, gains g(f)=f ln f; exact replay + seed67 audit.
+argv: LIBDIR START_OWNERS OUT_PREFIX ROUNDS DEPTH"""
+import sys, math, json, gzip, time, copy
+sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np
+from collections import defaultdict
+start, outp, ROUNDS, L = sys.argv[2], sys.argv[3], int(sys.argv[4]), int(sys.argv[5])
+WS = [4, 5, 7, 8, 9]; WI = {w: i for i, w in enumerate(WS)}; T = 144; N = len(WS)*T
+sid = lambda w, t: WI[w]*T + t
+g = lib.g
+NEG = np.float32(-1e9)
+
+def build(m):
+    A = np.full((N, N), NEG, np.float32); wit = {}
+    absorb = np.full(N, NEG, np.float32); awit = {}
+    for k in m.cap:
+        f = m.free(k); mem = list(m.members[k]); fam = m.fam[k]
+        for t in m.allowed[k]:
+            famfree = fam not in m.occ[t]
+            if famfree:
+                for w in WS:
+                    if f >= w:
+                        s = sid(w, t); gn = g(f-w) - g(f)
+                        if gn > absorb[s]: absorb[s] = gn; awit[s] = k
+            for j in mem:
+                z = m.roles[j]; w2, t2 = z['width'], z['time']
+                if not (famfree or t2 == t): continue
+                d = sid(w2, t2)
+                for w in WS:
+                    if f + w2 - w < 0: continue
+                    s = sid(w, t); gn = g(f + w2 - w) - g(f)
+                    if gn > A[s, d] + 1e-9: A[s, d] = gn; wit[s, d] = [(k, j)]
+                    elif abs(gn - A[s, d]) <= 1e-9 and len(wit[s, d]) < 4: wit[s, d].append((k, j))
+    return A, wit, absorb, awit
+
+def maxplus(P, A):
+    out = np.full((N, N), NEG, np.float32); arg = np.zeros((N, N), np.int16)
+    for i in range(0, N, 24):
+        blk = P[i:i+24, :, None] + A[None, :, :]
+        arg[i:i+24] = blk.argmax(1); out[i:i+24] = blk.max(1)
+    return out, arg
+
+def paths(A):
+    Ps, args = [A], [None]
+    for d in range(1, L):
+        P, ar = maxplus(Ps[-1], A); Ps.append(P); args.append(ar)
+    return Ps, args
+
+def recon(Ps, args, d, i, j):
+    seq = [j]
+    while d > 0:
+        k = int(args[d][i, j]); seq.append(k); j = k; d -= 1
+    seq.append(i); return seq[::-1]  # states i -> ... -> j
+
+class Journal:
+    def __init__(self, m): self.m = m; self.bins = {}; self.roles = {}; self.occ = {}
+    def save(self, i):
+        m = self.m; k = m.bin(i); t = m.roles[i]['time']
+        if i not in self.roles: self.roles[i] = m.roles[i]
+        if k not in self.bins: self.bins[k] = (set(m.members[k]), m.used[k])
+        if t not in self.occ: self.occ[t] = set(m.occ[t])
+    def savebin(self, k, t):
+        m = self.m
+        if k not in self.bins: self.bins[k] = (set(m.members[k]), m.used[k])
+        if t not in self.occ: self.occ[t] = set(m.occ[t])
+    def undo(self):
+        m = self.m
+        for i, z in self.roles.items(): m.roles[i] = z
+        for k, (mem, u) in self.bins.items(): m.members[k] = mem; m.used[k] = u
+        for t, o in self.occ.items(): m.occ[t] = o
+        m._out = set()
+
+def try_apply(m, X, r0, states, end, wit, awit, keep=False):
+    """Exact replay with limbo on m in place (journaled). Returns (m, dE, moves, journal) or None (m restored)."""
+    J = Journal(m); m._out = set(); before = {}
+    def touch(k):
+        if k not in before: before[k] = m.free(k)
+    def lift(i): J.save(i); m.lift(i)
+    def put(i, k):
+        J.savebin(k, m.roles[i]['time']); return m.put(i, k)
+    touch(X); lift(r0); hand = r0; moves = []
+    def fail(): J.undo(); return None
+    for a, b in zip(states, states[1:]):
+        ok = False
+        for (k, j) in wit[a, b]:
+            if k in before or j in m._out or j == hand or m.bin(j) != k: continue
+            touch(k); lift(j)
+            if put(hand, k): moves.append((hand, k)); hand = j; ok = True; break
+            put(j, k); before.pop(k)
+        if not ok: return fail()
+    if end == 'X':
+        if not put(hand, X): return fail()
+        moves.append((hand, X))
+    else:
+        k = awit[states[-1]]
+        if k in before: return fail()
+        touch(k)
+        if not put(hand, k): return fail()
+        moves.append((hand, k))
+    assert not m._out
+    dE = sum(g(m.free(k)) - g(f) for k, f in before.items())
+    return m, dE, moves, J
+
+def round_(m):
+    t0 = time.time(); A, wit, absorb, awit = build(m); t1 = time.time()
+    Ps, args = paths(A); t2 = time.time()
+    stk = np.stack(Ps); best = np.max(stk, 0); bestd = np.argmax(stk, 0); del stk
+    cands = []
+    Tidx = np.arange(T)
+    for X in m.cap:
+        fX = m.free(X)
+        if not m.members[X]: continue
+        allowedX = np.zeros(T, bool); allowedX[list(m.allowed[X])] = True
+        famocc = np.array([m.fam[X] in m.occ[t] for t in range(T)])
+        for r0 in m.members[X]:
+            z = m.roles[r0]; w0, t0_ = z['width'], z['time']; i = sid(w0, t0_)
+            okT = allowedX & (~famocc | (Tidx == t0_))
+            for wk in WS:
+                if wk > fX + w0: continue
+                row = best[i, WI[wk]*T:(WI[wk]+1)*T]
+                tot = row + (g(fX + w0 - wk) - g(fX))
+                tot = np.where(okT, tot, -1e9)
+                for tk in np.nonzero(tot > 1e-6)[0]:
+                    cands.append((float(tot[tk]), X, r0, i, sid(wk, int(tk)), 'X'))
+            if absorb[i] + g(fX + w0) - g(fX) > 1e-6:
+                cands.append((float(absorb[i] + g(fX + w0) - g(fX)), X, r0, i, i, 'A0'))
+            # absorb endings
+            tot = best[i] + absorb + (g(fX + w0) - g(fX))
+            for j in np.nonzero(tot > 1e-6)[0]:
+                cands.append((float(tot[j]), X, r0, i, int(j), 'A'))
+    cands.sort(key=lambda c: -c[0])
+    print(f'build {t1-t0:.0f}s paths {time.time()-t1:.0f}s cands {len(cands)} top {[round(c[0],3) for c in cands[:5]]}', flush=True)
+    for c in cands[:5000]:
+        gain, X, r0, i, j, end = c
+        st = [i] if end == 'A0' else recon(Ps, args, int(bestd[i, j]), i, j)
+        if end == 'A0': end = 'A'
+        r = try_apply(m, X, r0, st, end, wit, awit)
+        if r and r[1] > 1e-6: return r[:3]
+        if r: r[3].undo()
+    return None
+
+m = lib.Limbo(lib.read(start)); m._out = set()
+base = lib.selroles; log = []
+print('start idle', dict(sorted(lib.idle_of(m.roles).items())), 'E', round(m.E(), 4), flush=True)
+for rnd in range(ROUNDS):
+    r = round_(m)
+    if not r: print('no improving chain found at depth', L); break
+    m, dE, moves = r
+    roles = lib.compact(m.roles); au = lib.audit(roles)
+    pr = lib.price(au['profile'])
+    log.append(dict(round=rnd, dE=dE, moves=[(i, list(k)) for i, k in moves], idle=au['idle'], kappa=pr['kappa_decimal']))
+    print('round', rnd, 'dE', round(dE, 4), 'moves', moves, 'idle', au['idle'], 'kappa', pr['kappa_decimal'], flush=True)
+    m.roles = roles
+    open(outp + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(roles).encode(), mtime=0))
+    json.dump(log, open(outp + '.log.json', 'w'), indent=1)
diff --git a/research/complex-t16-two-stage-cycles/search/chain2.py b/research/complex-t16-two-stage-cycles/search/chain2.py
new file mode 100644
index 0000000000..120fc1aaea
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/chain2.py
@@ -0,0 +1,53 @@
+"""Two-stage search: zero-gain cycles that raise free(X), then a second cycle on the same X (relaxed DP reused).
+argv: LIBDIR START OUT_PREFIX DEPTH"""
+import sys
+sys.argv = [sys.argv[0], sys.argv[1], sys.argv[2], sys.argv[3], '0', sys.argv[4]]
+exec(open(sys.argv[1] + '/chain.py').read().split("m = lib.Limbo")[0])
+from collections import Counter
+m = lib.Limbo(lib.read(start)); m._out = set()
+A, wit, absorb, awit = build(m); Ps, args = paths(A)
+stk = np.stack(Ps); best = stk.max(0); bestd = stk.argmax(0); del stk
+Tidx = np.arange(T)
+def closures(mm, X, thr):
+    fX = mm.free(X); out = []
+    allowedX = np.zeros(T, bool); allowedX[list(mm.allowed[X])] = True
+    famocc = np.array([mm.fam[X] in mm.occ[t] for t in range(T)])
+    for r0 in mm.members[X]:
+        z = mm.roles[r0]; w0, t0_ = z['width'], z['time']; i = sid(w0, t0_)
+        okT = allowedX & (~famocc | (Tidx == t0_))
+        for wk in WS:
+            if wk >= w0 or wk > fX + w0: continue   # X must strictly gain
+            tot = np.where(okT, best[i, WI[wk]*T:(WI[wk]+1)*T] + (g(fX + w0 - wk) - g(fX)), -1e9)
+            for tk in np.nonzero(tot > thr)[0]: out.append((float(tot[tk]), X, r0, i, sid(wk, int(tk))))
+    return sorted(out, key=lambda c: -c[0])
+stage1 = []
+for X in m.cap:
+    if m.members[X]: stage1 += closures(m, X, -1e-6)
+print('stage1 zero/positive X-gaining cycles (relaxed):', len(stage1), Counter(round(c[0], 3) for c in stage1).most_common(5), flush=True)
+byX = Counter(c[1] for c in stage1); print('distinct X', len(byX))
+found = None; tried = 0; perX = Counter(); sec_rel = Counter(); sec_exact = 0
+for c in stage1:
+    if perX[c[1]] >= 3: continue
+    perX[c[1]] += 1
+    tot, X, r0, i, j = c
+    r = try_apply(m, X, r0, recon(Ps, args, int(bestd[i, j]), i, j), 'X', wit, awit)
+    if not r: continue
+    m1, dE1, mv1, J1 = r; tried += 1
+    if dE1 > 1e-6: found = (m1, dE1, mv1); break
+    cl2 = closures(m1, X, -1e-6); sec_rel[len(cl2) > 0] += 1
+    for c2 in cl2[:200]:
+        tot2, _, r02, i2, j2 = c2
+        if tot2 + dE1 <= 1e-6 and m1.free(X) == 0: continue
+        r2 = try_apply(m1, X, r02, recon(Ps, args, int(bestd[i2, j2]), i2, j2), 'X', wit, awit)
+        if r2: sec_exact += 1
+        if r2 and dE1 + r2[1] > 1e-6: found = (r2[0], dE1 + r2[1], mv1 + r2[2]); break
+        if r2: r2[3].undo()
+    if not found: J1.undo()
+    if found or tried > 40000: break
+print('first cycles applied', tried, 'X with relaxed 2nd closures', dict(sec_rel), 'exact 2nd cycles', sec_exact)
+print('exact stage1 cycles tried', tried)
+if found:
+    mm, dE, moves = found; roles = lib.compact(mm.roles); au = lib.audit(roles); pr = lib.price(au['profile'])
+    print('FOUND dE', dE, 'moves', moves, 'idle', au['idle'], 'kappa', pr['kappa_decimal'])
+    open(outp + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(roles).encode(), mtime=0))
+else: print('NONE')
diff --git a/research/complex-t16-two-stage-cycles/search/compose.py b/research/complex-t16-two-stage-cycles/search/compose.py
new file mode 100644
index 0000000000..ee98e83fec
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/compose.py
@@ -0,0 +1,17 @@
+"""Composition test: apply each subset of PR2077's relocations to another owner map. argv: LIBDIR BASE_OWNERS PR2077_OWNERS"""
+import sys, itertools, json; sys.path.insert(0, sys.argv[1]); import lib
+A = lib.selroles; P = lib.read(sys.argv[2]); V = lib.read(sys.argv[3])
+key = lambda z: (z['owner_replica'], z['child'], z['port'])
+d77 = [i for i in range(len(A)) if key(A[i]) != key(V[i])]
+print('2077 relocations', d77, 'state in 1407:', [(i, key(A[i]), key(P[i]), key(V[i])) for i in d77])
+for r in range(1, len(d77)+1):
+    for sub in itertools.combinations(d77, r):
+        m = lib.Limbo(P); m._out = set(); ok = True
+        for i in sub: m.lift(i)
+        for i in sub:
+            if not m.put(i, key(V[i])): ok = False; break
+        if not ok: print(sub, 'illegal'); continue
+        roles = lib.compact(m.roles)
+        try: au = lib.audit(roles)
+        except Exception as e: print(sub, 'audit reject', e); continue
+        print(sub, 'idle', au['idle'], 'kappa', lib.price(au['profile'])['kappa_decimal'])
diff --git a/research/complex-t16-two-stage-cycles/search/glob.py b/research/complex-t16-two-stage-cycles/search/glob.py
new file mode 100644
index 0000000000..af985440e9
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/glob.py
@@ -0,0 +1,173 @@
+"""Global repack (session heuristic, no optimality claim). Stage 1: aggregated CP-SAT over bin classes (cap, allowed-set): pattern counts x[c,p], helper flows y[c,t,w],
+per-class per-time capacity sum_w y[c,t,w] <= n_c (R4: family windows are disjoint, so one helper per bin per call).
+Stage 2: per class, realise patterns on concrete bins with distinct times (greedy + CP-SAT fallback), then relocate roles.
+Bins of one (cap, allowed window) class are interchangeable, and inside a physical family the windows are disjoint,
+so R4 reduces to at most one helper per bin per call. Stage 1 keeps the per-(class, call) Hall constraints for every
+subset of widths (HALL=small: single widths and all widths only) and, with GR=1, Gale-Ryser-style constraints for
+several helpers of one width in a bin (they need distinct calls). Stage 1 is a relaxation of the bin-level problem,
+so stage 2 can fail on some classes; glob5.py is the stage 2 that was used.
+Writes OUT.stage1.json (x = pattern counts, y = flows) and, unless S1ONLY=1, OUT.OWNERS.json.gz.
+env: S1ONLY=1 (stage 1 only), HINT=<stage1.json> (warm start), FIX / FREE = JSON lists of class indices to fix to the
+start map or to leave free, FIXTO=1 (fix every class not in FIX/FREE to HINT), HALL=small, GR=1.
+argv: LIBDIR START OUT TL1 [NW] [SEED]   Needs CPython 3.12 and ortools."""
+import sys, math, json, gzip, random, time
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict
+from ortools.sat.python import cp_model
+start, out, TL1 = sys.argv[2], sys.argv[3], float(sys.argv[4])
+NW = int(sys.argv[5]) if len(sys.argv) > 5 else 1; SEED = int(sys.argv[6]) if len(sys.argv) > 6 else 0
+rng = random.Random(SEED)
+import os; STAGE1ONLY = os.environ.get('S1ONLY') == '1'
+FIX = set(json.loads(os.environ.get('FIX', '[]')))
+HINT = os.environ.get('HINT'); FREE = set(json.loads(os.environ.get('FREE', '[]'))); FIXTO = os.environ.get('FIXTO') == '1'
+hx0 = Counter(); hy0 = Counter()
+if HINT:
+    _d = json.load(open(HINT))
+    for ci, p, v in _d['x']: hx0[ci, tuple(p)] = v
+    for ci, t, w, v in _d['y']: hy0[ci, t, w] = v
+roles = lib.read(start); m = lib.Model(roles)
+W = [4, 5, 7, 8, 9]; g = lib.g; SC = 10000; gi = lambda f: round(SC * g(f))
+classes = defaultdict(list)
+for k in m.cap: classes[m.cap[k], frozenset(m.allowed[k])].append(k)
+CL = list(classes)
+D = Counter((z['time'], z['width']) for z in m.roles)
+def pats(cap):
+    o = []
+    def rec(i, rem, cur):
+        if i == len(W): o.append(tuple(cur)); return
+        for c in range(rem // W[i] + 1): rec(i + 1, rem - c * W[i], cur + [c])
+    rec(0, cap, []); return o
+P = {cap: pats(cap) for cap in (8, 16, 32, 48)}
+def pat_of(k): c = Counter(m.roles[i]['width'] for i in m.members[k]); return tuple(c[w] for w in W)
+md = cp_model.CpModel(); obj = []; ytw = defaultdict(list); X = {}; Y = {}
+for ci, key in enumerate(CL):
+    cap, al = key; bins = classes[key]; n = len(bins)
+    curp = Counter(pat_of(k) for k in bins); cury = Counter((m.roles[i]['time'], m.roles[i]['width']) for k in bins for i in m.members[k])
+    cw = defaultdict(list); xs = []
+    for p in P[cap]:
+        s = sum(c * w for c, w in zip(p, W))
+        if max(p) > n: continue
+        if sum(p) > len(al): continue
+        x = md.NewIntVar(0, n, ''); xs.append(x); X[ci, p] = x; md.AddHint(x, curp[p])
+        if gi(cap - s): obj.append(gi(cap - s) * x)
+        for c, w in zip(p, W):
+            if c: cw[w].append(c * x)
+    md.Add(sum(xs) == n)
+    pert = defaultdict(list)
+    for w in W:
+        ys = []
+        for t in al:
+            if D[t, w]:
+                y = md.NewIntVar(0, min(D[t, w], n), ''); ys.append(y); ytw[t, w].append(y); Y[ci, t, w] = y; pert[t].append(y)
+                md.AddHint(y, cury[t, w])
+        md.Add(sum(ys) == sum(cw[w]))
+    import itertools
+    loc = [(p, x) for p in P[cap] if (ci, p) in X for x in [X[ci, p]]]
+    hit = {}
+    for r in range(1, len(W) + 1):
+        for Sset in itertools.combinations(W, r):
+            hv = md.NewIntVar(0, n, ''); md.AddHint(hv, sum(curp[p] for p, x in loc if any(p[W.index(w)] for w in Sset))); md.Add(hv == sum(x for p, x in loc if any(p[W.index(w)] for w in Sset))); hit[Sset] = hv
+    for t in pert:
+        ws = [w for w in W if (ci, t, w) in Y]
+        for r in range(1, len(ws) + 1):
+            for Sset in itertools.combinations(ws, r):
+                if os.environ.get('HALL') == 'small' and 1 < r < len(ws): continue
+                md.Add(sum(Y[ci, t, w] for w in Sset) <= hit[Sset])
+    if os.environ.get('GR') == '1':
+        for wi, w in enumerate(W):
+            mx = max(p[wi] for p, x in loc)
+            tsw = [t for t in al if (ci, t, w) in Y]
+            for j in range(2, mx + 1):
+                sel = [(p, x) for p, x in loc if p[wi] >= j]
+                h = md.NewIntVar(0, n, ''); md.Add(h == sum(x for p, x in sel))
+                mts = []
+                for t in tsw:
+                    mt = md.NewIntVar(0, n, ''); md.Add(mt <= Y[ci, t, w]); md.Add(mt <= h); mts.append(mt)
+                md.Add(sum(p[wi] * x for p, x in sel) <= sum(mts))
+    if FIXTO and ci not in FIX and ci not in FREE:
+        for p, x in loc: md.Add(x == hx0[ci, p])
+        for w in W:
+            for t in al:
+                if (ci, t, w) in Y: md.Add(Y[ci, t, w] == hy0[ci, t, w])
+    if ci in FIX:
+        for p, x in loc: md.Add(x == curp[p])
+        for w in W:
+            for t in al:
+                if (ci, t, w) in Y: md.Add(Y[ci, t, w] == cury[t, w])
+for tw, d in D.items(): md.Add(sum(ytw[tw]) == d)
+cur_obj = sum(gi(m.free(k)) for k in m.cap)
+if HINT:
+    md.ClearHints(); hx = Counter(); hy = Counter(); dh = json.load(open(HINT))
+    for ci, p, v in dh['x']: hx[ci, tuple(p)] = v
+    for ci, t, w, v in dh['y']: hy[ci, t, w] = v
+    for key, v in X.items(): md.AddHint(v, hx[key])
+    for key, v in Y.items(): md.AddHint(v, hy[key])
+md.Maximize(sum(obj))
+sv = cp_model.CpSolver(); sv.parameters.max_time_in_seconds = TL1; sv.parameters.num_workers = NW; sv.parameters.random_seed = SEED; sv.parameters.repair_hint = True
+t0 = time.time(); st = sv.Solve(md)
+print('stage1', sv.StatusName(st), 'obj', sv.ObjectiveValue() / SC, 'bound', sv.BestObjectiveBound() / SC, 'current', cur_obj / SC, f'{time.time()-t0:.0f}s', flush=True)
+xv = {key: sv.Value(v) for key, v in X.items() if sv.Value(v)}; yv = {key: sv.Value(v) for key, v in Y.items() if sv.Value(v)}
+json.dump(dict(x=[[ci, list(p), v] for (ci, p), v in xv.items()], y=[[ci, t, w, v] for (ci, t, w), v in yv.items()]), open(out + '.stage1.json', 'w'))
+
+# Stage 2: realise per class
+byT = defaultdict(list)  # (t, w) -> role indices
+for i, z in enumerate(m.roles): byT[z['time'], z['width']].append(i)
+for v in byT.values(): rng.shuffle(v)
+new = [dict(z) for z in m.roles]; fails = 0
+def realise(ci):
+    cap, al = CL[ci]; bins = classes[CL[ci]]
+    plist = [p for (c, p), v in xv.items() if c == ci for _ in range(v)]
+    # keep bins with the same current pattern where possible (fewer relocations)
+    pool = defaultdict(list)
+    for k in bins: pool[pat_of(k)].append(k)
+    assign = {}; rest = []
+    for p in plist:
+        if pool[p]: assign[pool[p].pop()] = p
+        else: rest.append(p)
+    left = [k for v in pool.values() for k in v]
+    for k, p in zip(left, rest): assign[k] = p
+    items = [(t, w) for (c, t, w), v in yv.items() if c == ci for _ in range(v)]
+    # CP-SAT feasibility: z[b,t,w]
+    need = {k: dict(zip(W, assign[k])) for k in bins}
+    cnt = Counter(items)
+    mdl = cp_model.CpModel(); z = {}
+    bw = defaultdict(list); bt = defaultdict(list); tw = defaultdict(list)
+    curset = {(k, m.roles[i]['time'], m.roles[i]['width']) for k in bins for i in m.members[k]}
+    for k in bins:
+        for (t, w) in cnt:
+            if need[k][w]:
+                v = mdl.NewBoolVar(''); z[k, t, w] = v; bw[k, w].append(v); bt[k, t].append(v); tw[t, w].append(v)
+                mdl.AddHint(v, (k, t, w) in curset)
+    for k in bins:
+        for w in W:
+            if need[k][w]: mdl.Add(sum(bw[k, w]) == need[k][w])
+    for vs in bt.values():
+        if len(vs) > 1: mdl.AddAtMostOne(vs)
+    for key, c in cnt.items(): mdl.Add(sum(tw[key]) == c)
+    mdl.Maximize(sum(v for key, v in z.items() if key in curset))
+    s2 = cp_model.CpSolver(); s2.parameters.max_time_in_seconds = 60; s2.parameters.num_workers = NW
+    r = s2.Solve(mdl); print('class', ci, s2.StatusName(r), flush=True)
+    if r not in (cp_model.OPTIMAL, cp_model.FEASIBLE): return None
+    return [key for key, v in z.items() if s2.Value(v)]
+if STAGE1ONLY: sys.exit(0)
+place = defaultdict(list)  # (t,w) -> list of bins
+for ci in range(len(CL)):
+    res = realise(ci)
+    if res is None: print('class', ci, CL[ci][0], len(CL[ci][1]), 'INFEASIBLE', flush=True); fails += 1; continue
+    for (k, t, w) in res: place[t, w].append(k)
+if fails: print('stage2 fails', fails)
+if fails and STAGE1ONLY: sys.exit(1)
+# relocate: keep roles already in a chosen bin
+for tw, ks in place.items():
+    hs = byT[tw]; assert len(hs) == len(ks), tw
+    rem = Counter(ks); free_h = []
+    for i in hs:
+        b = m.bin(i)
+        if rem[b] > 0: rem[b] -= 1
+        else: free_h.append(i)
+    tgt = list(rem.elements()); assert len(tgt) == len(free_h)
+    for i, k in zip(free_h, tgt): new[i] = lib.relocate(new[i], *k); new[i]['offset'] = 10**6
+new = lib.compact(new)
+au = lib.audit(new); pr = lib.price(au['profile'])
+print('RESULT kappa', pr['kappa_decimal'], 'idle', au['idle'], 'moved', sum(1 for a, b in zip(roles, new) if (a['owner_replica'], a['child'], a['port']) != (b['owner_replica'], b['child'], b['port'])), flush=True)
+open(out + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(new).encode(), mtime=0))
diff --git a/research/complex-t16-two-stage-cycles/search/glob5.py b/research/complex-t16-two-stage-cycles/search/glob5.py
new file mode 100644
index 0000000000..6961ef1a62
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/glob5.py
@@ -0,0 +1,123 @@
+"""Stage 2 of the global repack (glob.py): realise a stage-1 class solution on concrete bins. Per class, patterns are
+assigned to bins (keeping each bin's current pattern where possible), then each width is placed by a max-flow from
+calls to bins with distinct calls per bin, over 40 random width orders / pattern assignments. Helpers left unplaced
+(80 in the session's run) are inserted greedily where they lower sum f ln f the least. Output: OUT.OWNERS.json.gz,
+audited (seed67 rules) and priced. Standard library only besides lib.py.
+argv: LIBDIR START STAGE1_JSON OUT [SEED]"""
+import sys, json, gzip, random, itertools
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict, deque
+start, s1, out = sys.argv[2], sys.argv[3], sys.argv[4]; SEED = int(sys.argv[5]) if len(sys.argv) > 5 else 0
+rng = random.Random(SEED)
+roles = lib.read(start); m = lib.Model(roles)
+W = [4, 5, 7, 8, 9]
+classes = defaultdict(list)
+for k in m.cap: classes[m.cap[k], frozenset(m.allowed[k])].append(k)
+CL = list(classes)
+d = json.load(open(s1))
+X = defaultdict(list); Y = defaultdict(Counter)
+for ci, p, v in d['x']: X[ci] += [tuple(p)] * v
+for ci, t, w, v in d['y']: Y[ci][t, w] += v
+def pat_of(k): c = Counter(m.roles[i]['width'] for i in m.members[k]); return tuple(c[w] for w in W)
+
+def maxflow(sup, cap_b, ok):
+    """sup: {t: s}, cap_b: {b: c}, ok(t,b) bool. Returns {(t,b)} with flow 1. Simple augmenting paths (BFS)."""
+    T = list(sup); B = list(cap_b)
+    flow = set(); fs = Counter(); fb = Counter()
+    adj = {t: [b for b in B if ok(t, b)] for t in T}
+    # greedy init
+    for t in sorted(T, key=lambda t: len(adj[t])):
+        for b in sorted(adj[t], key=lambda b: fb[b] - cap_b[b]):
+            if fs[t] >= sup[t]: break
+            if fb[b] < cap_b[b] and (t, b) not in flow: flow.add((t, b)); fs[t] += 1; fb[b] += 1
+    inb = defaultdict(set)
+    for (t, b) in flow: inb[b].add(t)
+    while True:
+        # BFS from times with spare supply to bins with spare capacity, alternating t->b (not in flow), b->t (in flow)
+        srcs = [t for t in T if fs[t] < sup[t]]
+        if not srcs: break
+        par = {('t', t): None for t in srcs}; q = deque(('t', t) for t in srcs); end = None
+        while q and end is None:
+            node = q.popleft()
+            if node[0] == 't':
+                t = node[1]
+                for b in adj[t]:
+                    if (t, b) in flow or ('b', b) in par: continue
+                    par[('b', b)] = node
+                    if fb[b] < cap_b[b]: end = ('b', b); break
+                    q.append(('b', b))
+            else:
+                b = node[1]
+                for t in inb[b]:
+                    if ('t', t) not in par: par[('t', t)] = node; q.append(('t', t))
+        if end is None: break
+        node = end
+        while par[node] is not None:
+            p = par[node]
+            if node[0] == 'b': flow.add((p[1], node[1])); inb[node[1]].add(p[1])
+            else: flow.discard((node[1], p[1])); inb[p[1]].discard(node[1])
+            node = p
+        fs[node[1]] += 1; fb[end[1]] += 1
+    return flow
+
+def realise(ci, tries=40):
+    bins = classes[CL[ci]]
+    pool = defaultdict(list)
+    for k in bins: pool[pat_of(k)].append(k)
+    best = (10**9, None)
+    for r in range(tries):
+        pl = X[ci][:]; rng.shuffle(pl); pp = {p: v[:] for p, v in pool.items()}; assign = {}; rest = []
+        for p in pl:
+            if pp.get(p): assign[pp[p].pop()] = p
+            else: rest.append(p)
+        left = [k for v in pp.values() for k in v]; rng.shuffle(left)
+        for k, p in zip(left, rest): assign[k] = p
+        order = sorted(W, key=lambda w: -sum(Y[ci][t, ww] for (t, ww) in Y[ci] if ww == w)) if r == 0 else rng.sample(W, 5)
+        used = {k: set() for k in bins}; res = []; miss = 0
+        for w in order:
+            sup = {t: c for (t, ww), c in Y[ci].items() if ww == w}
+            if not sup: continue
+            capb = {k: assign[k][W.index(w)] for k in bins if assign[k][W.index(w)]}
+            fl = maxflow(sup, capb, lambda t, b: t not in used[b])
+            for (t, b) in fl: used[b].add(t); res.append((b, t, w))
+            miss += sum(sup.values()) - len(fl)
+        if miss == 0: return res, 0
+        if miss < best[0]: best = (miss, res)
+    return best[1], best[0]
+place = defaultdict(list); fails = []
+for ci in range(len(CL)):
+    res, nb = realise(ci)
+    if nb: fails.append((ci, CL[ci][0], len(CL[ci][1]), nb)); print('partial', fails[-1], flush=True)
+    for (k, t, w) in res: place[t, w].append(k)
+print('fails', len(fails), 'unplaced', sum(f[3] for f in fails), flush=True)
+byT = defaultdict(list)
+for i, z in enumerate(m.roles): byT[z['time'], z['width']].append(i)
+new = [dict(z) for z in m.roles]; unpl = []
+used = Counter(); occ = defaultdict(set)
+for tw, ks in place.items():
+    hs = byT[tw]; assert len(hs) >= len(ks), tw
+    rem = Counter(ks); free_h = []
+    for i in hs:
+        b = m.bin(i)
+        if rem[b] > 0: rem[b] -= 1; used[b] += tw[1]; occ[tw[0]].add(m.fam[b])
+        else: free_h.append(i)
+    tgt = list(rem.elements())
+    for i, k in zip(free_h, tgt): new[i] = lib.relocate(new[i], *k); new[i]['offset'] = 10**6; used[k] += tw[1]; occ[tw[0]].add(m.fam[k])
+    unpl += free_h[len(tgt):]
+for tw in byT:
+    if tw not in place: unpl += byT[tw]
+print('unplaced roles', len(unpl), flush=True)
+unpl.sort(key=lambda i: -m.roles[i]['width'])
+for i in unpl:
+    t, w = m.roles[i]['time'], m.roles[i]['width']
+    best = None
+    for k in m.cap:
+        f = m.cap[k] - used[k]
+        if f >= w and t in m.allowed[k] and m.fam[k] not in occ[t]:
+            d = lib.g(f - w) - lib.g(f)
+            if best is None or d > best[0]: best = (d, k)
+    k = best[1]; new[i] = lib.relocate(new[i], *k); new[i]['offset'] = 10**6; used[k] += w; occ[t].add(m.fam[k])
+new = lib.compact(new)
+au = lib.audit(new); pr = lib.price(au['profile'])
+print('RESULT kappa', pr['kappa_decimal'], 'idle', au['idle'], flush=True)
+open(out + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(new).encode(), mtime=0))
diff --git a/research/complex-t16-two-stage-cycles/search/gloop.sh b/research/complex-t16-two-stage-cycles/search/gloop.sh
new file mode 100755
index 0000000000..bd3ad259c5
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/gloop.sh
@@ -0,0 +1,15 @@
+#!/bin/bash
+# Guided LNS of the fifth version (portable copy of the session's gloop.sh): repeated lns2.py guide steps toward one
+# fixed class-level target GUIDE (a winlp.py ip JSON), each on a random fraction (0.08-0.3) of the differing classes.
+# The first fifth-version checkpoint (kappa 0.001673373170972473) came from this loop; sloop.sh superseded it.
+# usage: search/gloop.sh DIR START_OWNERS GUIDE_JSON NW SEED ITERS     (env RUN: optional command prefix)
+# Needs uv, CPython 3.12, numpy and ortools. Run from the repository root.
+H=$(cd "$(dirname "$0")" && pwd)
+D=$1; mkdir -p "$D"; cp "$2" "$D/best.OWNERS.json.gz"; export OMP_NUM_THREADS=1
+PY="uv run -q --no-project --python 3.12 --with numpy --with ortools python -I"
+for n in $(seq 1 "$6"); do
+  fr=$(python3 -c "import random; random.seed($5*1000+$n); print(random.choice([0.08,0.12,0.15,0.2,0.3]))")
+  GUIDE=$3 GFRAC=$fr GMUL=2 NW=$4 DIV=0 TL2=30 $RUN $PY "$H/lns2.py" "$H" "$D/best.OWNERS.json.gz" "$D/t" 2 $(( $5*1000+n )) 120 guide 2>&1 \
+    | grep -E "^it|^final" | cut -c1-330 | sed "s/^/$(date +%T) fr=$fr /"
+  [ -f "$D/t.OWNERS.json.gz" ] && mv "$D/t.OWNERS.json.gz" "$D/best.OWNERS.json.gz"
+done
diff --git a/research/complex-t16-two-stage-cycles/search/lib.py b/research/complex-t16-two-stage-cycles/search/lib.py
new file mode 100644
index 0000000000..0e4de9240b
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/lib.py
@@ -0,0 +1,104 @@
+"""Shared loader: seed67 auditor geometry, bin model, pinned-engine pricing.
+Env: R = tree with the seed67 auditor, selected PR1094 data and engines; MAIN = tree with
+research/frontier1094-idle-star-ceiling. Both default to this repository checkout."""
+import os, sys, json, gzip, hashlib, importlib.util, math
+from pathlib import Path
+from collections import Counter, defaultdict
+from fractions import Fraction as Q
+ROOT = Path(__file__).resolve().parents[3]
+R = Path(os.environ.get('R', ROOT)); MAIN = Path(os.environ.get('MAIN', ROOT))
+def load(name, path):
+    s = importlib.util.spec_from_file_location(name, path); m = importlib.util.module_from_spec(s); s.loader.exec_module(m); return m
+def read(p):
+    p = Path(p); b = p.read_bytes(); return json.loads(gzip.decompress(b) if p.suffix == '.gz' else b)
+a = load('owners', R/'research/t16-owner-audit-seed67/verify.py')
+pins = read(R/'research/t16-owner-audit-seed67/SOURCES.json')['inputs']
+assert hashlib.sha256((R/a.TEMPLATE).read_bytes()).hexdigest() == pins['template_sha256']
+assert hashlib.sha256((R/a.PHASES).read_bytes()).hexdigest() == pins['data_phases_sha256']
+assert hashlib.sha256(gzip.decompress(a.WORD.read_bytes())).hexdigest() == pins['word_content_sha256']
+w = read(a.WORD); geo = a.geometry(read(R/a.TEMPLATE), read(R/a.PHASES)); widths = a.word_widths(w)
+local = a.as_profile(w['report']['local_profile'])
+SEL = R/'research/complex-t16-rare-pattern-exchanges/data'
+selplan = read(SEL/'PLAN.json'); selspec = read(SEL/'SPEC.json'); selroles = read(SEL/'OWNERS.json.gz')
+order = [tuple(x) for x in selplan['order']]
+span, callpos = a.windows(geo, order)
+
+def idle_of(roles):
+    used = Counter()
+    for z in roles: used[z['owner_replica'], z['child'], z['port']] += z['width']
+    idle = Counter()
+    for (o, c) in span:
+        for p in range(a.V):
+            f = geo['rank'][c] - used[o, c, p]
+            if f: idle[f] += 1
+    return idle
+
+def audit(roles, plan=selplan, controls=False):
+    idle = idle_of(roles)
+    r = a.audit(geo, widths, local, roles, plan, idle, 16)
+    if controls: r['controls'] = len(a.controls(geo, widths, local, roles, plan, idle, 16))
+    return r
+
+_eng = None
+def price(profile, bad=False):
+    global _eng
+    st = load('idlestar', MAIN/'research/frontier1094-idle-star-ceiling/analyze.py')
+    st.ROOT = R; st.ENGINE_ROOT = R/'research/complex-k492-owner-repair/vendor/multicold/engines'
+    if _eng is None: _eng = (st, tuple(st.load_engine(n) for n in ('moment', 'base_two_moment', 'outer')))
+    baseline = json.loads((R/'research/community-frontier1094-audit/ASSEMBLY.json').read_text())
+    return _eng[0].price(Counter({int(k): v for k, v in profile.items()}), bad, baseline, _eng[1])
+
+def compact(roles):
+    """Re-serialize offsets as a prefix per bin, preserving within-bin order by old offset."""
+    out = [dict(z) for z in roles]; byb = defaultdict(list)
+    for i, z in enumerate(out): byb[z['owner_replica'], z['child'], z['port']].append(i)
+    for k, v in byb.items():
+        off = 0
+        for i in sorted(v, key=lambda i: out[i]['offset']):
+            out[i]['offset'] = off; off += out[i]['width']
+    return out
+
+def relocate(z, owner, child, port):
+    pair, side = geo['place'][child]
+    return dict(z, owner_replica=owner, child=child, port=port, copy=owner*a.V+port,
+                family=owner*a.FAMILIES_PER_REPLICA+(2*pair+side)*a.V+port)
+
+class Model:
+    """Bins (owner, child, port); legal-move oracle mirroring R3-R6."""
+    def __init__(self, roles):
+        self.roles = [dict(z) for z in roles]
+        self.cap = {}; self.allowed = {}; self.fam = {}
+        for (o, c), (lo, hi) in span.items():
+            pair, side = geo['place'][c]
+            calls = {t for t, key in enumerate(order) if lo < callpos[key] < hi and (o, pair) != (key[1], geo['stage_pair'][key[0]])}
+            for p in range(a.V):
+                k = (o, c, p); self.cap[k] = geo['rank'][c]; self.allowed[k] = calls
+                self.fam[k] = o*a.FAMILIES_PER_REPLICA+(2*pair+side)*a.V+p
+        self.members = defaultdict(set); self.used = Counter(); self.occ = defaultdict(set)
+        for i, z in enumerate(self.roles):
+            k = (z['owner_replica'], z['child'], z['port']); self.members[k].add(i); self.used[k] += z['width']
+            assert self.fam[k] not in self.occ[z['time']]; self.occ[z['time']].add(self.fam[k])
+    def bin(self, i): z = self.roles[i]; return (z['owner_replica'], z['child'], z['port'])
+    def free(self, k): return self.cap[k] - self.used[k]
+    def can(self, i, k, also_free=0):
+        z = self.roles[i]; t = z['time']
+        return k != self.bin(i) and self.free(k) + also_free >= z['width'] and t in self.allowed[k] and self.fam[k] not in self.occ[t]
+    def move(self, i, k):
+        z = self.roles[i]; old = self.bin(i); t = z['time']
+        self.members[old].discard(i); self.used[old] -= z['width']; self.occ[t].discard(self.fam[old])
+        self.members[k].add(i); self.used[k] += z['width']; self.occ[t].add(self.fam[k])
+        self.roles[i] = relocate(z, *k); self.roles[i]['offset'] = 10**6  # placeholder; compact() fixes
+    def E(self):
+        return sum(f*math.log(f) for k in self.cap if (f := self.free(k)) > 1)
+
+def g(f): return f*math.log(f) if f > 1 else 0.0
+
+class Limbo(Model):
+    def lift(self, i):
+        z = self.roles[i]; k = self.bin(i); t = z['time']
+        self.members[k].discard(i); self.used[k] -= z['width']; self.occ[t].discard(self.fam[k]); self._out.add(i)
+    def put(self, i, k):
+        z = self.roles[i]; t = z['time']
+        if not (self.free(k) >= z['width'] and t in self.allowed[k] and self.fam[k] not in self.occ[t]): return False
+        self.members[k].add(i); self.used[k] += z['width']; self.occ[t].add(self.fam[k]); self._out.discard(i)
+        self.roles[i] = relocate(z, *k); return True
diff --git a/research/complex-t16-two-stage-cycles/search/lns.py b/research/complex-t16-two-stage-cycles/search/lns.py
new file mode 100644
index 0000000000..38b91c811c
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/lns.py
@@ -0,0 +1,219 @@
+"""Large-neighbourhood search with CP-SAT on a T16 owner map.
+Neighbourhood = a set of physical families (columns). Every bin of a chosen family is in the neighbourhood,
+so R4 (one helper per family per call) is internal. Helpers of the neighbourhood are re-assigned by
+(time, width) class to bins of the neighbourhood (R5 windows / R3 active pair via Model.allowed, R6 capacity).
+Objective: maximise sum over bins of round(SC * g(free)), g(f) = f ln f; accepted only if exact kappa rises.
+argv: LIBDIR START OUT_PREFIX ITERS SEED [TL] [MODE] [...]
+env: NW = CP-SAT workers per solve (default 2), DIV=1 plateau step, TL2 = time limit of the DIV re-solve.
+Modes: fam (default), set:<calls>, time, early<k>, queue, tgt:..., and f3 (calls drawn from the window of a bin
+with free capacity 2, 3, 6, 7, 9 or 10; used by loopx.sh), and evac (used by loopy.sh): 1-3 stranded cap-48 bins
+(0 < used <= 20), bins with spare room and full bins whose windows contain some of the stranded helpers' calls,
+and a few empty bins; all their helpers are freed and re-packed exactly (env NB = neighbourhood size, default 200).
+kappa values are compared as Decimal, never as strings (the pinned assembler can drop trailing zeros)."""
+import sys, math, json, gzip, random, time
+from decimal import Decimal
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict
+from ortools.sat.python import cp_model
+start, outp, ITERS, SEED = sys.argv[2], sys.argv[3], int(sys.argv[4]), int(sys.argv[5])
+TL = float(sys.argv[6]) if len(sys.argv) > 6 else 30.0
+import os; NW = int(os.environ.get('NW', 2)); DIV = os.environ.get('DIV') == '1'; TL2 = float(os.environ.get('TL2', 60))
+rng = random.Random(SEED)
+SC = 10000
+def gi(f): return round(SC * lib.g(f))
+
+roles = lib.read(start)
+def kappa_of(roles):
+    au = lib.audit(roles); return lib.price(au['profile'])['kappa_decimal'], au['idle']
+best_k, best_idle = kappa_of(roles)
+print('start', best_k, best_idle, flush=True)
+
+def setup(roles):
+    m = lib.Model(roles)
+    fambins = defaultdict(list)
+    for k in m.cap: fambins[m.fam[k]].append(k)
+    return m, fambins
+
+m, fambins = setup(roles)
+grp = defaultdict(list)   # (owner, pair-side id) -> families
+for f, bins in fambins.items():
+    o, c, p = bins[0]; pair, side = lib.geo['place'][c]; grp[o, 2*pair+side].append(f)
+famtimes = {f: set().union(*(m.allowed[k] for k in bins)) for f, bins in fambins.items()}
+
+def frag(f): return sum(1 for k in fambins[f] if 0 < m.free(k) < m.cap[k])
+
+def pick():
+    """Choose families: seed groups with fragments, then groups whose windows overlap."""
+    fr = [f for f in fambins if frag(f)]
+    f0 = rng.choice(fr); o0, c0, _ = fambins[f0][0]
+    T0 = famtimes[f0]
+    gkeys = list(grp)
+    # score groups by overlap of times with T0
+    ov = sorted(gkeys, key=lambda g: -len(famtimes[grp[g][0]] & T0) + rng.random() * 3)
+    ng = rng.choice([2, 3, 4, 5, 6])
+    chosen = [g for g in ov[:12] if len(famtimes[grp[g][0]] & T0)]
+    rng.shuffle(chosen); chosen = chosen[:ng]
+    g0 = [g for g in grp if f0 in grp[g]][0]
+    if g0 not in chosen: chosen.append(g0)
+    budget = rng.choice([60, 90, 120, 160])
+    per = max(4, budget // len(chosen))
+    fams = {f0}
+    for g in chosen:
+        fs = grp[g][:]
+        rng.shuffle(fs)
+        fs.sort(key=lambda f: -(frag(f) > 0) * rng.random())
+        # mix fragment and full / empty families
+        fams.update(fs[:per])
+    return sorted(fams)
+
+DELTA = None
+def solve(bins, H):
+    Hs = set(H)
+    D = Counter((m.roles[i]['time'], m.roles[i]['width']) for i in H)
+    byt = defaultdict(list)
+    for (t, w) in D: byt[t].append(w)
+    resid = {k: m.cap[k] - sum(m.roles[i]['width'] for i in m.members[k] if i not in Hs) for k in bins}
+    fixocc = defaultdict(set)
+    for t in byt:
+        fixocc[t] = set(m.occ[t]) - {m.fam[m.bin(i)] for i in H if m.roles[i]['time'] == t}
+    mdl = cp_model.CpModel(); y = {}
+    for k in bins:
+        for t in m.allowed[k]:
+            if t not in byt or m.fam[k] in fixocc[t]: continue
+            for w in byt[t]:
+                if w <= resid[k]: y[k, t, w] = mdl.NewBoolVar('')
+    cur = Counter(); obj0 = 0
+    for i in H: z = m.roles[i]; cur[m.bin(i), z['time'], z['width']] += 1
+    for k in bins: obj0 += gi(m.free(k))
+    byk = defaultdict(list); bytw = defaultdict(list); byft = defaultdict(list)
+    for (k, t, w), v in y.items():
+        byk[k].append((w, v)); bytw[t, w].append(v); byft[m.fam[k], t].append(v)
+        mdl.AddHint(v, cur[k, t, w])
+    for (k, t, w), c in cur.items(): assert (k, t, w) in y, (k, t, w)
+    for tw, d in D.items(): mdl.Add(sum(bytw[tw]) == d)
+    for vs in byft.values():
+        if len(vs) > 1: mdl.AddAtMostOne(vs)
+    obj = []; ohf = defaultdict(list); N0 = Counter()
+    for k in bins:
+        cap = resid[k]; f0 = m.free(k)
+        oh = [mdl.NewBoolVar('') for f in range(cap + 1)]
+        mdl.AddExactlyOne(oh)
+        mdl.Add(sum(f * b for f, b in enumerate(oh)) == cap - sum(w * v for w, v in byk[k]))
+        for f, b in enumerate(oh): mdl.AddHint(b, f == f0)
+        obj += [gi(f) * b for f, b in enumerate(oh) if gi(f)]
+        for f, b in enumerate(oh): ohf[f].append(b)
+        N0[f0] += 1
+    if DELTA:
+        for f in ohf:
+            mdl.Add(sum(ohf[f]) == N0[f] + DELTA.get(f, 0))
+    mdl.Maximize(sum(obj))
+    sv = cp_model.CpSolver(); sv.parameters.max_time_in_seconds = TL; sv.parameters.num_workers = NW; sv.parameters.repair_hint = True
+    sv.parameters.random_seed = rng.randrange(1 << 30)
+    st = sv.Solve(mdl)
+    info = dict(bins=len(bins), helpers=len(H), vars=len(y), status=sv.StatusName(st), obj0=obj0)
+    if st not in (cp_model.OPTIMAL, cp_model.FEASIBLE): return None, info
+    info['obj'] = sv.ObjectiveValue(); info['bound'] = sv.BestObjectiveBound()
+    if sv.ObjectiveValue() <= obj0 and not DIV: return None, info
+    # phase 2: keep the objective, minimise relocations (or, with DIV on a plateau, randomly maximise them)
+    best = int(sv.ObjectiveValue()); vals = {key: sv.Value(v) for key, v in y.items()}
+    mdl.ClearHints()
+    for key, v in y.items(): mdl.AddHint(v, vals[key])
+    mdl.Add(sum(obj) >= best)
+    if best <= obj0: mdl.Maximize(sum(rng.randrange(1, 4) * v for key, v in y.items() if not cur[key]))
+    else: mdl.Maximize(sum(v for key, v in y.items() if cur[key]))
+    sv2 = cp_model.CpSolver(); sv2.parameters.max_time_in_seconds = TL2; sv2.parameters.num_workers = NW
+    st2 = sv2.Solve(mdl)
+    if st2 in (cp_model.OPTIMAL, cp_model.FEASIBLE): sv = sv2; info['kept'] = sv2.ObjectiveValue()
+    # reconstruct
+    pool = defaultdict(list)
+    for i in H: z = m.roles[i]; pool[z['time'], z['width']].append(i)
+    want = defaultdict(list)
+    for (k, t, w), v in y.items():
+        if sv.Value(v): want[t, w].append(k)
+    new = [dict(z) for z in m.roles]
+    for tw, ks in want.items():
+        hs = pool[tw]; rem = list(ks); free_h = []
+        for i in hs:
+            if m.bin(i) in rem: rem.remove(m.bin(i))
+            else: free_h.append(i)
+        assert len(free_h) == len(rem)
+        for i, k in zip(free_h, rem):
+            new[i] = lib.relocate(new[i], *k); new[i]['offset'] = 10**6
+    return lib.compact(new), info
+
+MODE = sys.argv[7] if len(sys.argv) > 7 else 'fam'
+EMPTYOK = {16: 17}
+QUEUE = []
+def pick_times():
+    if MODE.startswith('early'):
+        hi = int(MODE[5:] or 15); n = rng.choice([4, 5, 5, 6, 6, 7])
+        return set(rng.sample(range(hi + 1), n))
+    if MODE == 'queue':
+        if not QUEUE:
+            sets = sorted({tuple(sorted(m.allowed[k])) for k in m.cap if 0 < m.free(k) < m.cap[k]}, key=len)
+            for a in sets:
+                if len(a) <= 6: QUEUE.append(set(a))
+                else:
+                    for j in range(0, len(a), 4): QUEUE.append(set(a[j:j+5]))
+            rng.shuffle(QUEUE); print('queue', len(QUEUE), flush=True)
+        return QUEUE.pop()
+    if MODE == 'f3': fr = [k for k in m.cap if m.free(k) in (2, 3, 6, 7, 9, 10)]
+    else: fr = [k for k in m.cap if 0 < m.free(k) < m.cap[k]]
+    k0 = rng.choice(fr); al = sorted(m.allowed[k0])
+    n = rng.choice([1, 2, 2, 3, 3, 4]) if MODE != 'f3' else rng.choice([2, 3, 4, 5, 6])
+    return set(rng.sample(al, min(n, len(al))))
+def nbhd_times(Ts):
+    H = [i for i, z in enumerate(m.roles) if z['time'] in Ts]
+    hb = {m.bin(i) for i in H}
+    bins = [k for k in m.cap if k in hb or (4 <= m.free(k) < EMPTYOK.get(m.cap[k], m.cap[k]) and m.allowed[k] & Ts)]
+    return bins, H
+NB = int(os.environ.get('NB', 200))
+def pick_evac():
+    """Stranded bins (cap 48, 0 < used <= 20) + bins with spare that share times with them + full bins of the same classes."""
+    st = [k for k in m.cap if m.cap[k] == 48 and 0 < m.cap[k] - m.free(k) <= 20]
+    if not st: st = [k for k in m.cap if 0 < m.free(k) < m.cap[k] and m.free(k) >= 4]
+    k0s = rng.sample(st, min(len(st), rng.choice([1, 1, 2, 3])))
+    T0 = {m.roles[i]["time"] for k in k0s for i in m.members[k]}
+    nb = rng.choice([NB // 2, NB, NB, int(NB * 1.5)])
+    cand = [k for k in m.cap if k not in k0s and m.allowed[k] & T0 and m.free(k) < m.cap[k]]
+    spare = [k for k in cand if m.free(k) > 0]; full = [k for k in cand if m.free(k) == 0]
+    rng.shuffle(spare); rng.shuffle(full)
+    # bias toward bins with larger spare
+    spare.sort(key=lambda k: -m.free(k) * rng.random())
+    a = spare[:int(nb * rng.choice([0.3, 0.5, 0.7]))]
+    sel = set(k0s) | set(a)
+    # full bins: prefer those whose allowed set overlaps chosen spare bins' classes
+    rest = nb - len(sel); sel |= set(full[:max(0, rest)])
+    # also some empty cap-48 bins allowing T0 (lets a 2-for-1 consolidation happen)
+    emp = [k for k in m.cap if m.free(k) == m.cap[k] and m.allowed[k] & T0]; rng.shuffle(emp); sel |= set(emp[:rng.choice([0, 2, 5])])
+    return sorted(sel)
+DLIST = []
+if MODE.startswith('tgt:'):
+    for x in sys.argv[8].split(';'):
+        a, b = x.split('>'); d = Counter(map(int, b.split('+'))); d.subtract(Counter(map(int, a.split('+'))))
+        d[0] += len(a.split('+')) - len(b.split('+')); DLIST.append({f: v for f, v in d.items() if v})
+    ITERS = len(DLIST)
+for it in range(ITERS):
+    t0 = time.time()
+    if DLIST: DELTA = DLIST[it]; print('delta', DELTA, flush=True)
+    if MODE.startswith('evac'):
+        bins = pick_evac(); H = [i for k in bins for i in m.members[k]]; tag = ('evac', len(bins))
+    elif MODE == 'fam':
+        fams = pick(); bins = [k for f in fams for k in fambins[f]]; H = [i for k in bins for i in m.members[k]]; tag = len(fams)
+    else:
+        Ts = set(map(int, MODE[4:].split(','))) if MODE[:4] in ('set:', 'tgt:') else pick_times(); bins, H = nbhd_times(Ts); tag = sorted(Ts)
+    res, info = solve(bins, H)
+    msg = f"it {it} {tag} {info} {time.time()-t0:.1f}s"
+    if res is not None:
+        try:
+            k, idle = kappa_of(res)
+        except Exception as e:
+            print(msg, 'AUDIT REJECT', e, flush=True); continue
+        msg += f" kappa {k} idle {idle}"
+        if Decimal(k) > Decimal(best_k) or (DIV and Decimal(k) == Decimal(best_k)):   # never compare kappa strings
+            best_k, best_idle, roles = k, idle, res
+            m, fambins = setup(roles)
+            open(outp + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(roles).encode(), mtime=0))
+            msg += ' ** NEW BEST'
+    print(msg, flush=True)
+print('final', best_k, best_idle)
diff --git a/research/complex-t16-two-stage-cycles/search/lns2.py b/research/complex-t16-two-stage-cycles/search/lns2.py
new file mode 100644
index 0000000000..76c1af3f27
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/lns2.py
@@ -0,0 +1,271 @@
+"""Large-neighbourhood search with CP-SAT on a T16 owner map (fifth version): lns.py plus two neighbourhood modes.
+The helpers of the neighbourhood's bins are re-assigned by (time, width) class to those bins (windows and the active
+pair via Model.allowed, capacity, at most one helper per family per call), maximising sum over bins of
+round(SC * g(free)), g(f) = f ln f; a result is accepted only if the exact kappa rises (compared as Decimal).
+argv: LIBDIR START OUT_PREFIX ITERS SEED [TL] [MODE] [...]
+Modes as in lns.py (fam, set:<calls>, time, early<k>, queue, tgt:..., f3, evac) and:
+  guide: neighbourhood from a stage-1 class target (env GUIDE = a winlp.py ip JSON): for a random fraction GFRAC of
+         the classes whose target differs, up to GMUL x (excess + 1) bins holding helpers whose class (call, width)
+         count must drop, and up to GMUL x (excess + 1) bins whose pattern count must drop. The CP-SAT model then
+         maximises the surrogate exactly over that neighbourhood (used by sloop.sh, fifth version).
+  rc:    lossy small bins plus 1-3 partly filled cap-48 bins sharing their calls (tried in the session; no shipped
+         checkpoint came from it).
+env: NW = CP-SAT workers per solve (default 2), DIV=1 plateau step, TL2 = time limit of the DIV re-solve,
+     NB = neighbourhood size for evac/rc, RESTRICT=1 limits each bin's free value to a few values (not used in sloop.sh).
+kappa values are compared as Decimal, never as strings (the pinned assembler can drop trailing zeros)."""
+import sys, math, json, gzip, random, time
+from decimal import Decimal
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict
+from ortools.sat.python import cp_model
+start, outp, ITERS, SEED = sys.argv[2], sys.argv[3], int(sys.argv[4]), int(sys.argv[5])
+TL = float(sys.argv[6]) if len(sys.argv) > 6 else 30.0
+import os; NW = int(os.environ.get('NW', 2)); DIV = os.environ.get('DIV') == '1'; TL2 = float(os.environ.get('TL2', 60))
+rng = random.Random(SEED)
+SC = 10000
+def gi(f): return round(SC * lib.g(f))
+
+roles = lib.read(start)
+def kappa_of(roles):
+    au = lib.audit(roles); return lib.price(au['profile'])['kappa_decimal'], au['idle']
+best_k, best_idle = kappa_of(roles)
+print('start', best_k, best_idle, flush=True)
+
+def setup(roles):
+    m = lib.Model(roles)
+    fambins = defaultdict(list)
+    for k in m.cap: fambins[m.fam[k]].append(k)
+    return m, fambins
+
+m, fambins = setup(roles)
+grp = defaultdict(list)   # (owner, pair-side id) -> families
+for f, bins in fambins.items():
+    o, c, p = bins[0]; pair, side = lib.geo['place'][c]; grp[o, 2*pair+side].append(f)
+famtimes = {f: set().union(*(m.allowed[k] for k in bins)) for f, bins in fambins.items()}
+
+def frag(f): return sum(1 for k in fambins[f] if 0 < m.free(k) < m.cap[k])
+
+def pick():
+    """Choose families: seed groups with fragments, then groups whose windows overlap."""
+    fr = [f for f in fambins if frag(f)]
+    f0 = rng.choice(fr); o0, c0, _ = fambins[f0][0]
+    T0 = famtimes[f0]
+    gkeys = list(grp)
+    # score groups by overlap of times with T0
+    ov = sorted(gkeys, key=lambda g: -len(famtimes[grp[g][0]] & T0) + rng.random() * 3)
+    ng = rng.choice([2, 3, 4, 5, 6])
+    chosen = [g for g in ov[:12] if len(famtimes[grp[g][0]] & T0)]
+    rng.shuffle(chosen); chosen = chosen[:ng]
+    g0 = [g for g in grp if f0 in grp[g]][0]
+    if g0 not in chosen: chosen.append(g0)
+    budget = rng.choice([60, 90, 120, 160])
+    per = max(4, budget // len(chosen))
+    fams = {f0}
+    for g in chosen:
+        fs = grp[g][:]
+        rng.shuffle(fs)
+        fs.sort(key=lambda f: -(frag(f) > 0) * rng.random())
+        # mix fragment and full / empty families
+        fams.update(fs[:per])
+    return sorted(fams)
+
+DELTA = None
+RESTRICT = os.environ.get('RESTRICT') == '1'
+def solve(bins, H):
+    Hs = set(H)
+    D = Counter((m.roles[i]['time'], m.roles[i]['width']) for i in H)
+    byt = defaultdict(list)
+    for (t, w) in D: byt[t].append(w)
+    resid = {k: m.cap[k] - sum(m.roles[i]['width'] for i in m.members[k] if i not in Hs) for k in bins}
+    fixocc = defaultdict(set)
+    for t in byt:
+        fixocc[t] = set(m.occ[t]) - {m.fam[m.bin(i)] for i in H if m.roles[i]['time'] == t}
+    mdl = cp_model.CpModel(); y = {}
+    for k in bins:
+        for t in m.allowed[k]:
+            if t not in byt or m.fam[k] in fixocc[t]: continue
+            for w in byt[t]:
+                if w <= resid[k]: y[k, t, w] = mdl.NewBoolVar('')
+    cur = Counter(); obj0 = 0
+    for i in H: z = m.roles[i]; cur[m.bin(i), z['time'], z['width']] += 1
+    for k in bins: obj0 += gi(m.free(k))
+    byk = defaultdict(list); bytw = defaultdict(list); byft = defaultdict(list)
+    for (k, t, w), v in y.items():
+        byk[k].append((w, v)); bytw[t, w].append(v); byft[m.fam[k], t].append(v)
+        mdl.AddHint(v, cur[k, t, w])
+    for (k, t, w), c in cur.items(): assert (k, t, w) in y, (k, t, w)
+    for tw, d in D.items(): mdl.Add(sum(bytw[tw]) == d)
+    for vs in byft.values():
+        if len(vs) > 1: mdl.AddAtMostOne(vs)
+    obj = []; ohf = defaultdict(list); N0 = Counter()
+    for k in bins:
+        cap = resid[k]; f0 = m.free(k)
+        okf = set(range(cap + 1)) if not RESTRICT else ({0, cap, f0, resid[k]} | ({1} if m.cap[k] == 32 else set()) | ({3} if m.cap[k] == 16 else set()))
+        okf = {f for f in okf if 0 <= f <= cap}
+        oh = [mdl.NewBoolVar('') if f in okf else mdl.NewConstant(0) for f in range(cap + 1)]
+        mdl.AddExactlyOne(oh)
+        mdl.Add(sum(f * b for f, b in enumerate(oh)) == cap - sum(w * v for w, v in byk[k]))
+        for f, b in enumerate(oh):
+            if f in okf: mdl.AddHint(b, f == f0)
+        obj += [gi(f) * b for f, b in enumerate(oh) if gi(f) and f in okf]
+        for f, b in enumerate(oh): ohf[f].append(b)
+        N0[f0] += 1
+    if DELTA:
+        for f in ohf:
+            mdl.Add(sum(ohf[f]) == N0[f] + DELTA.get(f, 0))
+    mdl.Maximize(sum(obj))
+    sv = cp_model.CpSolver(); sv.parameters.max_time_in_seconds = TL; sv.parameters.num_workers = NW; sv.parameters.repair_hint = True
+    sv.parameters.random_seed = rng.randrange(1 << 30)
+    st = sv.Solve(mdl)
+    info = dict(bins=len(bins), helpers=len(H), vars=len(y), status=sv.StatusName(st), obj0=obj0)
+    if st not in (cp_model.OPTIMAL, cp_model.FEASIBLE): return None, info
+    info['obj'] = sv.ObjectiveValue(); info['bound'] = sv.BestObjectiveBound()
+    if sv.ObjectiveValue() <= obj0 and not DIV: return None, info
+    # phase 2: keep the objective, minimise relocations (or, with DIV on a plateau, randomly maximise them)
+    best = int(sv.ObjectiveValue()); vals = {key: sv.Value(v) for key, v in y.items()}
+    mdl.ClearHints()
+    for key, v in y.items(): mdl.AddHint(v, vals[key])
+    mdl.Add(sum(obj) >= best)
+    if best <= obj0: mdl.Maximize(sum(rng.randrange(1, 4) * v for key, v in y.items() if not cur[key]))
+    else: mdl.Maximize(sum(v for key, v in y.items() if cur[key]))
+    sv2 = cp_model.CpSolver(); sv2.parameters.max_time_in_seconds = TL2; sv2.parameters.num_workers = NW
+    st2 = sv2.Solve(mdl)
+    if st2 in (cp_model.OPTIMAL, cp_model.FEASIBLE): sv = sv2; info['kept'] = sv2.ObjectiveValue()
+    # reconstruct
+    pool = defaultdict(list)
+    for i in H: z = m.roles[i]; pool[z['time'], z['width']].append(i)
+    want = defaultdict(list)
+    for (k, t, w), v in y.items():
+        if sv.Value(v): want[t, w].append(k)
+    new = [dict(z) for z in m.roles]
+    for tw, ks in want.items():
+        hs = pool[tw]; rem = list(ks); free_h = []
+        for i in hs:
+            if m.bin(i) in rem: rem.remove(m.bin(i))
+            else: free_h.append(i)
+        assert len(free_h) == len(rem)
+        for i, k in zip(free_h, rem):
+            new[i] = lib.relocate(new[i], *k); new[i]['offset'] = 10**6
+    return lib.compact(new), info
+
+MODE = sys.argv[7] if len(sys.argv) > 7 else 'fam'
+EMPTYOK = {16: 17}
+QUEUE = []
+def pick_times():
+    if MODE.startswith('early'):
+        hi = int(MODE[5:] or 15); n = rng.choice([4, 5, 5, 6, 6, 7])
+        return set(rng.sample(range(hi + 1), n))
+    if MODE == 'queue':
+        if not QUEUE:
+            sets = sorted({tuple(sorted(m.allowed[k])) for k in m.cap if 0 < m.free(k) < m.cap[k]}, key=len)
+            for a in sets:
+                if len(a) <= 6: QUEUE.append(set(a))
+                else:
+                    for j in range(0, len(a), 4): QUEUE.append(set(a[j:j+5]))
+            rng.shuffle(QUEUE); print('queue', len(QUEUE), flush=True)
+        return QUEUE.pop()
+    if MODE == 'f3': fr = [k for k in m.cap if m.free(k) in (2, 3, 6, 7, 9, 10)]
+    else: fr = [k for k in m.cap if 0 < m.free(k) < m.cap[k]]
+    k0 = rng.choice(fr); al = sorted(m.allowed[k0])
+    n = rng.choice([1, 2, 2, 3, 3, 4]) if MODE != 'f3' else rng.choice([2, 3, 4, 5, 6])
+    return set(rng.sample(al, min(n, len(al))))
+def nbhd_times(Ts):
+    H = [i for i, z in enumerate(m.roles) if z['time'] in Ts]
+    hb = {m.bin(i) for i in H}
+    bins = [k for k in m.cap if k in hb or (4 <= m.free(k) < EMPTYOK.get(m.cap[k], m.cap[k]) and m.allowed[k] & Ts)]
+    return bins, H
+DLIST = []
+NB = int(os.environ.get('NB', 200))
+def pick_evac():
+    """Stranded bins (cap 48, 0 < used <= 20) + bins with spare that share times with them + full bins of the same classes."""
+    st = [k for k in m.cap if m.cap[k] == 48 and 0 < m.cap[k] - m.free(k) <= 20]
+    if not st: st = [k for k in m.cap if 0 < m.free(k) < m.cap[k] and m.free(k) >= 4]
+    k0s = rng.sample(st, min(len(st), rng.choice([1, 1, 2, 3])))
+    T0 = {m.roles[i]["time"] for k in k0s for i in m.members[k]}
+    nb = rng.choice([NB // 2, NB, NB, int(NB * 1.5)])
+    cand = [k for k in m.cap if k not in k0s and m.allowed[k] & T0 and m.free(k) < m.cap[k]]
+    spare = [k for k in cand if m.free(k) > 0]; full = [k for k in cand if m.free(k) == 0]
+    rng.shuffle(spare); rng.shuffle(full)
+    # bias toward bins with larger spare
+    spare.sort(key=lambda k: -m.free(k) * rng.random())
+    a = spare[:int(nb * rng.choice([0.3, 0.5, 0.7]))]
+    sel = set(k0s) | set(a)
+    # full bins: prefer those whose allowed set overlaps chosen spare bins' classes
+    rest = nb - len(sel); sel |= set(full[:max(0, rest)])
+    # also some empty cap-48 bins allowing T0 (lets a 2-for-1 consolidation happen)
+    emp = [k for k in m.cap if m.free(k) == m.cap[k] and m.allowed[k] & T0]; rng.shuffle(emp); sel |= set(emp[:rng.choice([0, 2, 5])])
+    return sorted(sel)
+def pick_rc():
+    """Seeds: many lossy bins (cap16 free 3/16/7 etc.), plus 1-3 full cap-48 targets sharing times, plus full bins of overlapping classes."""
+    lossy = [k for k in m.cap if m.cap[k] < 48 and m.free(k) >= 2]
+    nA = rng.choice([8, 16, 24, 40])
+    k0 = rng.choice(lossy); T0 = set(m.allowed[k0])
+    close = sorted(lossy, key=lambda k: -len(m.allowed[k] & T0) / len(m.allowed[k] | T0) - 0.3 * rng.random())
+    A = close[:nA]; T0 = set().union(*(m.allowed[k] for k in A))
+    tg = [k for k in m.cap if m.cap[k] == 48 and m.free(k) < 48 and m.allowed[k] & T0]
+    tg = rng.sample(tg, min(len(tg), rng.choice([1, 2, 3])))
+    Th = {m.roles[i]['time'] for k in A + tg for i in m.members[k]}
+    nb = rng.choice([NB // 2, NB, int(NB * 1.5), 2 * NB])
+    cand = [k for k in m.cap if k not in A and k not in tg and m.free(k) < m.cap[k] and m.allowed[k] & Th]
+    rng.shuffle(cand)
+    # prefer bins holding 7s/8s/4s/5s at the hot times (the exchange currency)
+    cand.sort(key=lambda k: -sum(1 for i in m.members[k] if m.roles[i]['time'] in Th and m.roles[i]['width'] != 9) * rng.random())
+    sel = set(A) | set(tg) | set(cand[:nb])
+    emp = [k for k in m.cap if m.free(k) == m.cap[k] and m.allowed[k] & Th]; rng.shuffle(emp); sel |= set(emp[:rng.choice([0, 2, 4])])
+    return sorted(sel)
+def pick_guide():
+    """Neighbourhood from a stage-1 class target (env GUIDE): bins holding helpers whose class (t,w) count must drop, bins whose pattern count must drop."""
+    W = [4, 5, 7, 8, 9]; d = json.load(open(os.environ['GUIDE']))
+    cls = defaultdict(list)
+    for k in m.cap: cls[m.cap[k], frozenset(m.allowed[k])].append(k)
+    CL = list(cls); cid = {k: i for i, c in enumerate(CL) for k in cls[c]}
+    pat = {k: tuple(Counter(m.roles[i]['width'] for i in m.members[k])[w] for w in W) for k in m.cap}
+    cx = Counter((cid[k], pat[k]) for k in m.cap); cy = Counter((cid[m.bin(i)], z['time'], z['width']) for i, z in enumerate(m.roles))
+    nx = Counter({(ci, tuple(p)): v for ci, p, v in d['x']}); ny = Counter({(ci, t, w): v for ci, t, w, v in d['y']})
+    FR = float(os.environ.get('GFRAC', 1.0)); MUL = float(os.environ.get('GMUL', 2.0))
+    keys = [kk for kk in set(cx) | set(nx) if nx[kk] < cx[kk]]
+    ykeys = [kk for kk in set(cy) | set(ny) if ny[kk] < cy[kk]]
+    sel = set()
+    chosen_cls = set(rng.sample(sorted({kk[0] for kk in keys} | {kk[0] for kk in ykeys}), max(1, int(FR * len({kk[0] for kk in keys} | {kk[0] for kk in ykeys})))))
+    for (ci, p) in keys:
+        if ci not in chosen_cls: continue
+        bs = [k for k in cls[CL[ci]] if pat[k] == p]; rng.shuffle(bs); sel |= set(bs[:int(MUL * (cx[ci, p] - nx[ci, p])) + 1])
+    for (ci, t, w) in ykeys:
+        if ci not in chosen_cls: continue
+        bs = [k for k in cls[CL[ci]] if any(m.roles[i]['time'] == t and m.roles[i]['width'] == w for i in m.members[k])]
+        rng.shuffle(bs); sel |= set(bs[:int(MUL * (cy[ci, t, w] - ny[ci, t, w])) + 1])
+    print('guide classes', len(chosen_cls), 'bins', len(sel), flush=True)
+    return sorted(sel)
+if MODE.startswith('tgt:'):
+    for x in sys.argv[8].split(';'):
+        a, b = x.split('>'); d = Counter(map(int, b.split('+'))); d.subtract(Counter(map(int, a.split('+'))))
+        d[0] += len(a.split('+')) - len(b.split('+')); DLIST.append({f: v for f, v in d.items() if v})
+    ITERS = len(DLIST)
+for it in range(ITERS):
+    t0 = time.time()
+    if DLIST: DELTA = DLIST[it]; print('delta', DELTA, flush=True)
+    if MODE == 'guide':
+        bins = pick_guide(); H = [i for k in bins for i in m.members[k]]; tag = ('guide', len(bins))
+    elif MODE == 'rc':
+        bins = pick_rc(); H = [i for k in bins for i in m.members[k]]; tag = ('rc', len(bins))
+    elif MODE.startswith('evac'):
+        bins = pick_evac(); H = [i for k in bins for i in m.members[k]]; tag = ('evac', len(bins))
+    elif MODE == 'fam':
+        fams = pick(); bins = [k for f in fams for k in fambins[f]]; H = [i for k in bins for i in m.members[k]]; tag = len(fams)
+    else:
+        Ts = set(map(int, MODE[4:].split(','))) if MODE[:4] in ('set:', 'tgt:') else pick_times(); bins, H = nbhd_times(Ts); tag = sorted(Ts)
+    res, info = solve(bins, H)
+    msg = f"it {it} {tag} {info} {time.time()-t0:.1f}s"
+    if res is not None:
+        try:
+            k, idle = kappa_of(res)
+        except Exception as e:
+            print(msg, 'AUDIT REJECT', e, flush=True); continue
+        msg += f" kappa {k} idle {idle}"
+        if Decimal(k) > Decimal(best_k) or (DIV and Decimal(k) == Decimal(best_k)):   # never compare kappa strings
+            best_k, best_idle, roles = k, idle, res
+            m, fambins = setup(roles)
+            open(outp + '.OWNERS.json.gz', 'wb').write(gzip.compress(json.dumps(roles).encode(), mtime=0))
+            msg += ' ** NEW BEST'
+    print(msg, flush=True)
+print('final', best_k, best_idle)
diff --git a/research/complex-t16-two-stage-cycles/search/loop3.sh b/research/complex-t16-two-stage-cycles/search/loop3.sh
new file mode 100755
index 0000000000..71c633e24b
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/loop3.sh
@@ -0,0 +1,20 @@
+#!/bin/bash
+# Improvement loop used for the kappa search (portable copy of the session's loop3.sh; logic unchanged).
+# Alternate: chain2.py (one/two-stage ejection cycles, depth D) while it finds a strictly improving step;
+# when it finds none, run one CP-SAT plateau-diversification step of lns.py (DIV=1: keep the surrogate
+# objective, then randomly maximise relocations) on a random neighbourhood mode, and continue from its output.
+# Each accepted map is written as <OUT_PREFIX><n>.OWNERS.json.gz. Finite heuristic; no optimality claim.
+# usage: search/loop3.sh START_OWNERS OUT_PREFIX     env: D (default 8), MAXN (default 200 steps),
+#        RUN (optional command prefix, e.g. a memory-capped systemd scope; the session used MemoryMax=4G)
+# Needs uv, CPython 3.12, numpy and ortools. Run from the repository root (lib.py reads the selected data there).
+H=$(cd "$(dirname "$0")" && pwd)
+cur=$1; P=$2; n=0; D=${D:-8}; MAXN=${MAXN:-200}
+while [ $n -lt $MAXN ]; do
+  n=$((n+1))
+  out=$($RUN uv run -q --no-project --python 3.12 --with numpy python -I "$H/chain2.py" "$H" "$cur" "$P$n" "$D" 2>&1 | tail -1)
+  if [ -f "$P$n.OWNERS.json.gz" ]; then cur=$P$n.OWNERS.json.gz; echo "chain2 $n $(echo "$out" | grep -o 'idle.*')"; continue; fi
+  n=$((n+1)); modes=("set:0,1,2,3,4" "early8" "early15" "time" "fam"); md=${modes[$((RANDOM % 5))]}
+  r=$(DIV=1 TL2=40 $RUN uv run -q --no-project --python 3.12 --with numpy --with ortools python -I "$H/lns.py" "$H" "$cur" "$P$n" 1 $((n+700+RANDOM)) 60 "$md" 2>&1 | grep "^it" | grep -o "status.*" | cut -c1-60; true)
+  [ -f "$P$n.OWNERS.json.gz" ] && cur=$P$n.OWNERS.json.gz
+  echo "div $n $md $r -> $cur"
+done
diff --git a/research/complex-t16-two-stage-cycles/search/loopx.sh b/research/complex-t16-two-stage-cycles/search/loopx.sh
new file mode 100755
index 0000000000..02d1f6e36b
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/loopx.sh
@@ -0,0 +1,32 @@
+#!/bin/bash
+# Improvement loop used after the global repack (portable copy of the session's loopX.sh; logic unchanged).
+# Like loop3.sh it alternates chain2.py (ejection cycles, depth 8) while it finds a strictly improving step with
+# one CP-SAT plateau step of lns.py (DIV=1) on a random neighbourhood mode, now including the f3 mode (bins with
+# free capacity 2, 3, 6, 7, 9 or 10). Unlike loop3.sh it keeps only the current map and the best one by exact
+# kappa (score.py), and writes every new best as DIR/k_<kappa>.OWNERS.json.gz. Finite heuristic; no optimum.
+# usage: search/loopx.sh DIR START_OWNERS NW SEED [MAXN]
+#   NW = CP-SAT workers per lns.py solve; MAXN = steps (default 100000, stop by hand).
+#   env RUN: optional command prefix, e.g. a memory-capped systemd scope (the session used MemoryMax=4G).
+# Needs uv, CPython 3.12, numpy and ortools. Run from the repository root (lib.py reads the selected data there).
+H=$(cd "$(dirname "$0")" && pwd)
+D=$1; cur=$2; NW=$3; SEED=$4; MAXN=${5:-100000}; mkdir -p "$D"
+PY="uv run -q --no-project --python 3.12 --with numpy --with ortools python -I"
+bestk=$($RUN $PY "$H/score.py" "$H" "$cur" | awk '{print $2}')
+cp "$cur" "$D/best.OWNERS.json.gz"; cp "$cur" "$D/cur.OWNERS.json.gz"; cur=$D/cur.OWNERS.json.gz
+echo "start $bestk"
+RANDOM=$SEED; n=0
+gt() { python3 -c "import sys; from decimal import Decimal as D; sys.exit(0 if D('$1') > D('$2') else 1)"; }
+newcur() { mv "$1" "$D/cur.OWNERS.json.gz"; k=$2
+  if [ -n "$k" ] && gt "$k" "$bestk"; then bestk=$k; cp "$D/cur.OWNERS.json.gz" "$D/best.OWNERS.json.gz"
+    cp "$D/cur.OWNERS.json.gz" "$D/k_$k.OWNERS.json.gz"; echo "$(date +%T) NEW BEST $k step $n"; fi; }
+while [ $n -lt "$MAXN" ]; do
+  n=$((n+1))
+  out=$($RUN $PY "$H/chain2.py" "$H" "$cur" "$D/t" 8 2>&1 | tail -1)
+  if [ -f "$D/t.OWNERS.json.gz" ]; then k=$(echo "$out" | grep -o 'kappa [0-9.]*' | awk '{print $2}')
+    echo "$(date +%T) chain2 $n $(echo "$out" | grep -o 'idle.*')"; newcur "$D/t.OWNERS.json.gz" "$k"; continue; fi
+  n=$((n+1)); modes=("set:0,1,2,3,4" "early8" "time" "time" "f3" "f3" "fam" "early15" "time" "f3"); md=${modes[$((RANDOM % 10))]}
+  r=$(NW=$NW DIV=1 TL2=40 $RUN $PY "$H/lns.py" "$H" "$cur" "$D/t" 1 $((SEED*100000+n+RANDOM)) 60 "$md" 2>&1 | grep "^it")
+  k=$(echo "$r" | grep -o 'kappa [0-9.]*' | awk '{print $2}')
+  [ -f "$D/t.OWNERS.json.gz" ] && newcur "$D/t.OWNERS.json.gz" "$k"
+  echo "$(date +%T) div $n $md $(echo "$r" | grep -o "status.*" | cut -c1-50) k=$k"
+done
diff --git a/research/complex-t16-two-stage-cycles/search/loopy.sh b/research/complex-t16-two-stage-cycles/search/loopy.sh
new file mode 100755
index 0000000000..314d60ec8b
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/loopy.sh
@@ -0,0 +1,33 @@
+#!/bin/bash
+# Improvement loop of the fourth version (portable copy of the session's loopY.sh). Same as loopx.sh except the
+# neighbourhood mode mix, which now includes the evac mode of lns.py (stranded cap-48 bins plus bins whose windows
+# contain some of their calls, re-packed exactly; env NB = neighbourhood size, default 200). It alternates chain2.py
+# (ejection cycles, depth 8) while it finds a strictly improving step with one CP-SAT plateau step of lns.py
+# (DIV=1) on a random mode (evac, time, f3, early15). It keeps only the current map and the best one by exact
+# kappa (score.py, compared as Decimal), and writes every new best as DIR/k_<kappa>.OWNERS.json.gz. Finite heuristic; no optimum.
+# usage: search/loopy.sh DIR START_OWNERS NW SEED [MAXN]
+#   NW = CP-SAT workers per lns.py solve; MAXN = steps (default 100000, stop by hand).
+#   env RUN: optional command prefix, e.g. a memory-capped systemd scope (the session used MemoryMax=4G).
+# Needs uv, CPython 3.12, numpy and ortools. Run from the repository root (lib.py reads the selected data there).
+H=$(cd "$(dirname "$0")" && pwd)
+D=$1; cur=$2; NW=$3; SEED=$4; MAXN=${5:-100000}; mkdir -p "$D"
+PY="uv run -q --no-project --python 3.12 --with numpy --with ortools python -I"
+bestk=$($RUN $PY "$H/score.py" "$H" "$cur" | awk '{print $2}')
+cp "$cur" "$D/best.OWNERS.json.gz"; cp "$cur" "$D/cur.OWNERS.json.gz"; cur=$D/cur.OWNERS.json.gz
+echo "start $bestk"
+RANDOM=$SEED; n=0
+gt() { python3 -c "import sys; from decimal import Decimal as D; sys.exit(0 if D('$1') > D('$2') else 1)"; }
+newcur() { mv "$1" "$D/cur.OWNERS.json.gz"; k=$2
+  if [ -n "$k" ] && gt "$k" "$bestk"; then bestk=$k; cp "$D/cur.OWNERS.json.gz" "$D/best.OWNERS.json.gz"
+    cp "$D/cur.OWNERS.json.gz" "$D/k_$k.OWNERS.json.gz"; echo "$(date +%T) NEW BEST $k step $n"; fi; }
+while [ $n -lt "$MAXN" ]; do
+  n=$((n+1))
+  out=$($RUN $PY "$H/chain2.py" "$H" "$cur" "$D/t" 8 2>&1 | tail -1)
+  if [ -f "$D/t.OWNERS.json.gz" ]; then k=$(echo "$out" | grep -o 'kappa [0-9.]*' | awk '{print $2}')
+    echo "$(date +%T) chain2 $n $(echo "$out" | grep -o 'idle.*')"; newcur "$D/t.OWNERS.json.gz" "$k"; continue; fi
+  n=$((n+1)); modes=("evac" "evac" "time" "time" "f3" "f3" "evac" "early15" "time" "f3"); md=${modes[$((RANDOM % 10))]}
+  r=$(NB=${NB:-200} NW=$NW DIV=1 TL2=40 $RUN $PY "$H/lns.py" "$H" "$cur" "$D/t" 1 $((SEED*100000+n+RANDOM)) 60 "$md" 2>&1 | grep "^it")
+  k=$(echo "$r" | grep -o 'kappa [0-9.]*' | awk '{print $2}')
+  [ -f "$D/t.OWNERS.json.gz" ] && newcur "$D/t.OWNERS.json.gz" "$k"
+  echo "$(date +%T) div $n $md $(echo "$r" | grep -o "status.*" | cut -c1-50) k=$k"
+done
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_cls1.py b/research/complex-t16-two-stage-cycles/search/mindiff_cls1.py
new file mode 100644
index 0000000000..d1a7ff92d9
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_cls1.py
@@ -0,0 +1,137 @@
+"""Min-diff toward the selected map A at a target idle profile, class level, stage 1 (HiGHS MIP). Bins of one (cap, allowed-window) class are interchangeable, and at
+most one helper per bin per call. Variables: pattern counts x[c,p] (width multiplicities per bin), flows y[c,t,w]
+(helpers of call t, width w hosted by class c). Constraints: class sizes, width balance, demand per (t, w),
+Hall per (c, t) for single widths and for all widths, idle profile = target. Objective: maximise
+sum min(y, yA) (an upper bound on placements of A that can be kept), tie-break: fewer pattern changes.
+If solved to optimality without FIX/KEEP, 69,120 minus the kept flow bounds the relocations from below within this
+relaxation (up to the small tie-break weight EPS). Stage 1 is a relaxation of the bin-level problem, so
+mindiff_cls2.py can find a class unrealisable; such classes are then fixed to A (FIX) and stage 1 is re-solved.
+argv: LIBDIR TARGET_OWNERS OUT_JSON TIME_LIMIT [START_OWNERS (warm start; must have the target profile)]
+env: FIX = JSON list of class indices kept exactly as in A (used when stage 2 cannot realise a class);
+     KEEP = a previous stage-1 JSON whose (x, y) every class outside FIX and FREE (JSON list) keeps exactly
+     (FREE classes pay a small cost for moving away from KEEP's flows);
+     BAN = JSON list of [class, pattern] pairs forbidden in that class (fourth version: class 9 cannot host
+     eleven bins of four width-4 helpers, which need four distinct calls each; Hall alone does not see this).
+Needs CPython 3.12, numpy, scipy, highspy. Single thread."""
+import sys, json, time, itertools
+sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np, highspy
+from scipy.sparse import coo_matrix
+from collections import Counter, defaultdict
+A = lib.selroles; F = lib.read(sys.argv[2]); OUT = sys.argv[3]; TL = float(sys.argv[4])
+m = lib.Model(A); W = [4, 5, 7, 8, 9]
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+cls = defaultdict(list)
+for k in sorted(m.cap): cls[m.cap[k], frozenset(m.allowed[k])].append(k)
+CL = list(cls); cid = {k: ci for ci, key in enumerate(CL) for k in cls[key]}
+D = Counter((z['time'], z['width']) for z in A)
+T = lib.idle_of(F)
+cnt = defaultdict(Counter); yA = Counter()
+for z in A: cnt[B(z)][z['width']] += 1; yA[cid[B(z)], z['time'], z['width']] += 1
+xA = Counter((cid[k], tuple(cnt[k][w] for w in W)) for k in m.cap)
+def pats(cap):
+    o = []
+    def rec(i, rem, cur):
+        if i == len(W): o.append(tuple(cur)); return
+        for c in range(rem // W[i] + 1): rec(i + 1, rem - c * W[i], cur + [c])
+    rec(0, cap, []); return o
+P = {cap: pats(cap) for cap in (8, 16, 32, 48)}
+var_lo, var_hi, cost, integ = [], [], [], []
+def var(lo, hi, c=0.0, i=True):
+    var_lo.append(lo); var_hi.append(hi); cost.append(c); integ.append(i); return len(var_lo) - 1
+R, Cc, V, lo, hi = [], [], [], [], []
+def con(e, l, h):
+    r = len(lo)
+    for j, v in e: R.append(r); Cc.append(j); V.append(v)
+    lo.append(l); hi.append(h)
+X = {}; Y = {}; prof = defaultdict(list); DV = {}; KV = {}; HV = {}
+EPS = 1e-3
+for ci, (cap, al) in enumerate(CL):
+    n = len(cls[CL[ci]]); ws = defaultdict(list)
+    for p in P[cap]:
+        if sum(p) > len(al) or max(p) > n: continue
+        j = var(0, n); X[ci, p] = j
+        f = cap - sum(c * w for c, w in zip(p, W))
+        if f: prof[f].append(j)
+        for c, w in zip(p, W):
+            if c: ws[w].append((j, c))
+        if xA[ci, p]:   # d >= xA - x, cost EPS per lost pattern bin
+            d = var(0, n, EPS, False); con([(d, 1), (j, 1)], xA[ci, p], np.inf); DV[ci, p] = d
+    con([(j, 1) for (c2, p), j in X.items() if c2 == ci], n, n)
+    pert = defaultdict(dict)
+    for w in W:
+        ys = []
+        for t in sorted(al):
+            if D[t, w]:
+                j = var(0, min(D[t, w], n)); Y[ci, t, w] = j; ys.append((j, 1)); pert[t][w] = j
+                if yA[ci, t, w]:
+                    k = var(0, yA[ci, t, w], -1.0, False); con([(k, 1), (j, -1)], -np.inf, 0); KV[ci, t, w] = k
+        con(ys + [(j, -c) for j, c in ws[w]], 0, 0)
+    # Hall: per t and width w, y <= bins whose pattern holds w; all widths: sum_w y <= nonempty bins
+    hv = {}
+    for w in W + [0]:   # hv[w] = bins whose pattern holds width w (0: any helper); aggregated once per class
+        hv[w] = var(0, n, 0.0, False); HV[ci, w] = hv[w]
+        con([(hv[w], 1)] + [(j, -1) for (c2, p), j in X.items() if c2 == ci and (p[W.index(w)] if w else sum(p))], 0, 0)
+    for t, d in pert.items():
+        for w, j in d.items(): con([(j, 1), (hv[w], -1)], -np.inf, 0)
+        if len(d) > 1: con([(j, 1) for j in d.values()] + [(hv[0], -1)], -np.inf, 0)
+byTW = defaultdict(list)
+for (ci, t, w), j in Y.items(): byTW[t, w].append((j, 1))
+for tw, d in D.items(): con(byTW[tw], d, d)
+import os
+FIX = set(json.loads(os.environ.get('FIX', '[]')))   # classes kept exactly as in A (x = xA, y = yA)
+for (ci, p), j in X.items():
+    if ci in FIX: con([(j, 1)], xA[ci, p], xA[ci, p])
+for (ci, t, w), j in Y.items():
+    if ci in FIX: con([(j, 1)], yA[ci, t, w], yA[ci, t, w])
+BAN = json.loads(os.environ.get('BAN', '[]'))   # [[class, pattern], ...] forbidden (x = 0); used when stage 2
+for ci, p in BAN:                                 # shows a pattern needs more distinct calls than the class can give
+    con([(X[ci, tuple(p)], 1)], 0, 0)
+if BAN: print('banned', BAN, flush=True)
+KEEP = os.environ.get('KEEP')   # stage-1 JSON: classes not in FREE (and not in FIX) keep its (x, y) exactly
+if KEEP:
+    FREE = set(json.loads(os.environ.get('FREE', '[]'))); kd = json.load(open(KEEP))
+    kx = Counter({(ci, tuple(p)): v for ci, p, v in kd['x']}); ky = Counter({(ci, t, w): v for ci, t, w, v in kd['y']})
+    for (ci, p), j in X.items():
+        if ci not in FIX and ci not in FREE: con([(j, 1)], kx[ci, p], kx[ci, p])
+    for (ci, t, w), j in Y.items():
+        if ci not in FIX and ci not in FREE: con([(j, 1)], ky[ci, t, w], ky[ci, t, w])
+    for (ci, t, w), j in Y.items():   # free classes: small cost for moving away from KEEP's flows
+        if ci in FREE and ci not in FIX:
+            e = var(0, np.inf, 1e-4, False); con([(e, 1), (j, -1)], -ky[ci, t, w], np.inf); con([(e, 1), (j, 1)], ky[ci, t, w], np.inf)
+    print('kept from', KEEP, 'free classes', sorted(FREE), flush=True)
+print('fixed classes', sorted(FIX), flush=True)
+for v in sorted(set(prof) | set(T)): con([(j, 1) for j in prof[v]], T[v], T[v])
+nv = len(var_lo); Mx = coo_matrix((V, (R, Cc)), shape=(len(lo), nv)).tocsc()
+print('vars', nv, 'cons', len(lo), 'A flows', sum(yA.values()), flush=True)
+h = highspy.Highs(); h.setOptionValue('time_limit', TL); h.setOptionValue('threads', 1); h.setOptionValue('mip_rel_gap', 1e-6)
+lp = highspy.HighsLp(); lp.num_col_ = nv; lp.num_row_ = len(lo); lp.col_cost_ = np.array(cost)
+lp.col_lower_ = np.array(var_lo, float); lp.col_upper_ = np.array(var_hi, float)
+lp.row_lower_ = np.array(lo, float); lp.row_upper_ = np.array(hi, float)
+lp.a_matrix_.format_ = highspy.MatrixFormat.kColwise
+lp.a_matrix_.start_ = Mx.indptr; lp.a_matrix_.index_ = Mx.indices; lp.a_matrix_.value_ = Mx.data.astype(float)
+lp.integrality_ = [highspy.HighsVarType.kInteger if i else highspy.HighsVarType.kContinuous for i in integ]
+h.passModel(lp)
+if len(sys.argv) > 5:
+    S0 = lib.read(sys.argv[5]); assert lib.idle_of(S0) == T
+    c0 = defaultdict(Counter); y0 = Counter()
+    for z in S0: c0[B(z)][z['width']] += 1; y0[cid[B(z)], z['time'], z['width']] += 1
+    x0 = Counter((cid[k], tuple(c0[k][w] for w in W)) for k in m.cap)
+    v0 = np.zeros(nv)
+    for key, j in X.items(): v0[j] = x0[key]
+    for key, j in Y.items(): v0[j] = y0[key]
+    for key, j in DV.items(): v0[j] = max(0, xA[key] - x0[key])
+    for key, j in KV.items(): v0[j] = min(yA[key], y0[key])
+    for (ci, w), j in HV.items(): v0[j] = sum(v for (c2, p), v in x0.items() if c2 == ci and (p[W.index(w)] if w else sum(p)))
+    s0 = highspy.HighsSolution(); s0.col_value = list(v0); s0.value_valid = True
+    print('setSolution', h.setSolution(s0), 'start kept', sum(v0[j] for j in KV.values()), flush=True)
+t0 = time.time(); h.run()
+info = h.getInfo(); xs = np.array(h.getSolution().col_value)
+print('status', h.modelStatusToString(h.getModelStatus()), 'obj', info.objective_function_value, 'bound', info.mip_dual_bound, f'{time.time()-t0:.0f}s', flush=True)
+xv = [[ci, list(p), int(round(xs[j]))] for (ci, p), j in X.items() if round(xs[j])]
+yv = [[ci, t, w, int(round(xs[j]))] for (ci, t, w), j in Y.items() if round(xs[j])]
+kept = sum(min(v, yA[ci, t, w]) for ci, t, w, v in yv)
+chg = [ci for ci in range(len(CL)) if Counter({tuple(p): v for c2, p, v in xv if c2 == ci}) != Counter({p: v for (c2, p), v in xA.items() if c2 == ci})
+       or {(t, w): v for c2, t, w, v in yv if c2 == ci} != {(t, w): v for (c2, t, w), v in yA.items() if c2 == ci}]
+print('kept flow', kept, 'relocated >=', len(A) - kept, 'changed classes', len(chg), 'dual bound kept', -info.mip_dual_bound, flush=True)
+json.dump(dict(x=xv, y=yv, changed=chg, bound=-info.mip_dual_bound), open(OUT, 'w'))
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_cls2.py b/research/complex-t16-two-stage-cycles/search/mindiff_cls2.py
new file mode 100644
index 0000000000..8897d69ca6
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_cls2.py
@@ -0,0 +1,128 @@
+"""Min-diff, class level, stage 2 (per changed class of mindiff_cls1.py): realise the stage-1 class solution on concrete bins, keeping as
+many (bin, call, width) placements of A as possible. Unchanged classes keep A. Per class: z[b,t,w] in {0,1} for every
+(t, w) the class hosts; at most one helper per bin per call; class flows y[c,t,w] exact; every bin's free value is
+one of the class's stage-1 free values, with their counts exact. CP-SAT (hint = A, repair_hint) finds a start, then
+HiGHS (warm started) improves it or proves it optimal. Each class result is cached as CACHE/<class>.json.
+argv: LIBDIR STAGE1_JSON CACHE_DIR TL_CPSAT TL_HIGHS PART/NPARTS cp|hi   (run cp first, then hi)
+      LIBDIR STAGE1_JSON CACHE_DIR OUT_TRIPLES_JSON merge   (union with A's unchanged classes; checks the result)
+Needs CPython 3.12; cp: ortools; hi: numpy, scipy, highspy (one thread each)."""
+import sys, json, time, os
+sys.path.insert(0, sys.argv[1]); import lib
+MODE = sys.argv[-1]   # cp: CP-SAT start; hi: HiGHS from the cached start; merge
+# ortools and highspy cannot be loaded in one process (clashing HiGHS symbols), hence two passes.
+if MODE == 'cp': from ortools.sat.python import cp_model
+elif MODE == 'hi':
+    import numpy as np, highspy
+    from scipy.sparse import coo_matrix
+from collections import Counter, defaultdict
+A = lib.selroles; s1 = json.load(open(sys.argv[2])); CACHE = sys.argv[3]; os.makedirs(CACHE, exist_ok=True)
+if MODE == 'merge':
+    m = lib.Model(A); B = lambda z: (z['owner_replica'], z['child'], z['port'])
+    cls = {}
+    for k in sorted(m.cap): cls.setdefault((m.cap[k], frozenset(m.allowed[k])), []).append(k)
+    cid = {k: ci for ci, key in enumerate(cls) for k in cls[key]}
+    TA = {(B(z), z['time'], z['width']) for z in A}; ch = set(s1['changed'])
+    out = {tr for tr in TA if cid[tr[0]] not in ch}
+    for ci in ch: out |= {(tuple(k), t, w) for k, t, w in json.load(open(f'{CACHE}/{ci}.json'))['triples']}
+    fill = Counter()
+    for k, t, w in out: fill[k] += w
+    idle = Counter(m.cap[k] - fill[k] for k in m.cap if m.cap[k] - fill[k])
+    prof = Counter()
+    for ci, p, v in s1['x']:
+        f = list(cls)[ci][0] - sum(c * w for c, w in zip(p, [4, 5, 7, 8, 9]))
+        if f: prof[f] += v
+    assert len(out) == len(A) and idle == prof and Counter((t, w) for k, t, w in out) == Counter((z['time'], z['width']) for z in A)
+    assert max(Counter((m.fam[k], t) for k, t, w in out).values()) == 1 and all(t in m.allowed[k] for k, t, w in out)
+    print('merged: idle', dict(sorted(idle.items())), 'kept', len(out & TA), 'relocated', len(A) - len(out & TA))
+    json.dump(dict(triples=sorted(out)), open(sys.argv[4], 'w')); sys.exit(0)
+TLC = float(sys.argv[4]) if len(sys.argv) > 4 else 60; TLH = float(sys.argv[5]) if len(sys.argv) > 5 else 120
+PART, NP = map(int, (sys.argv[6] if len(sys.argv) > 6 else '0/1').split('/'))
+m = lib.Model(A); W = [4, 5, 7, 8, 9]
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+cls = defaultdict(list)
+for k in sorted(m.cap): cls[m.cap[k], frozenset(m.allowed[k])].append(k)
+CL = list(cls); cid = {k: ci for ci, key in enumerate(CL) for k in cls[key]}
+TA = {(B(z), z['time'], z['width']) for z in A}
+fillA = Counter()
+for z in A: fillA[B(z)] += z['width']
+y = defaultdict(Counter); fv = defaultdict(Counter)
+for ci, t, w, v in s1['y']: y[ci][t, w] = v
+for ci, p, v in s1['x']: fv[ci][CL[ci][0] - sum(c * w for c, w in zip(p, W))] += v
+for ci in s1['changed'][PART::NP]:
+    path = f'{CACHE}/{ci}.json'
+    if os.path.exists(path): continue
+    cap = CL[ci][0]; bins = cls[CL[ci]]; TW = sorted(y[ci]); vals = sorted(fv[ci]); t0 = time.time()
+    C = [(b, t, w) for b in bins for (t, w) in TW]
+    bytw = defaultdict(list); bybt = defaultdict(list); bybin = defaultdict(list)
+    for j, (b, t, w) in enumerate(C): bytw[t, w].append(j); bybt[b, t].append(j); bybin[b].append((j, w))
+    nA = sum(1 for tr in TA if cid[tr[0]] == ci)
+    if MODE == 'cp':
+        md = cp_model.CpModel(); z = [md.NewBoolVar('') for _ in C]; o = {}
+        for tw in TW: md.Add(sum(z[j] for j in bytw[tw]) == y[ci][tw])
+        for js in bybt.values():
+            if len(js) > 1: md.AddAtMostOne(z[j] for j in js)
+        for b in bins:
+            for v in vals: o[b, v] = md.NewBoolVar(''); md.AddHint(o[b, v], cap - fillA[b] == v)
+            md.AddExactlyOne(o[b, v] for v in vals)
+            md.Add(sum(w * z[j] for j, w in bybin[b]) + sum(v * o[b, v] for v in vals) == cap)
+        for v in vals: md.Add(sum(o[b, v] for b in bins) == fv[ci][v])
+        for j, tr in enumerate(C): md.AddHint(z[j], tr in TA)
+        md.Maximize(sum(z[j] for j, tr in enumerate(C) if tr in TA))
+        sv = cp_model.CpSolver(); sv.parameters.max_time_in_seconds = TLC; sv.parameters.num_workers = 1; sv.parameters.repair_hint = True
+        st = sv.Solve(md); cps = sv.StatusName(st)
+        x0 = None
+        if st in (cp_model.OPTIMAL, cp_model.FEASIBLE):
+            x0 = [sv.Value(v) for v in z]; ov = {key: sv.Value(v) for key, v in o.items()}
+        cpk = sv.ObjectiveValue() if x0 else None
+        sp = path.replace('.json', '.cp.json')
+        if st == cp_model.OPTIMAL:
+            sol = [C[j] for j in range(len(C)) if x0[j]]
+            print('class', ci, 'cap', cap, 'cpsat OPTIMAL A rows', nA, 'kept', int(cpk), f'{time.time()-t0:.0f}s', flush=True)
+            json.dump(dict(ci=ci, kept=int(cpk), nA=nA, bound=int(cpk), triples=sol), open(path, 'w'))
+        else:
+            print('class', ci, 'cap', cap, 'cpsat', cps, cpk, f'{time.time()-t0:.0f}s', flush=True)
+            json.dump(dict(x0=x0, ov=[[b, v, x] for (b, v), x in ov.items()] if x0 else None, cpk=cpk), open(sp, 'w'))
+        continue
+    sp = path.replace('.json', '.cp.json'); d0 = json.load(open(sp)); x0 = d0['x0']; cpk = d0['cpk']; cps = 'cached'
+    ov = {(tuple(b), v): x for b, v, x in d0['ov']} if x0 else None
+    best = x0; hs = 'skipped'
+    if True:
+        R, Cc, V, lo, hi = [], [], [], [], []
+        def con(e, l, h):
+            r = len(lo)
+            for j, v in e: R.append(r); Cc.append(j); V.append(v)
+            lo.append(l); hi.append(h)
+        for tw in TW: con([(j, 1) for j in bytw[tw]], y[ci][tw], y[ci][tw])
+        for js in bybt.values():
+            if len(js) > 1: con([(j, 1) for j in js], 0, 1)
+        nv = len(C); oh = defaultdict(list); oid = {}
+        for b in bins:
+            ids = list(range(nv, nv + len(vals))); nv += len(vals)
+            con(bybin[b] + [(i, v) for i, v in zip(ids, vals)], cap, cap); con([(i, 1) for i in ids], 1, 1)
+            for i, v in zip(ids, vals): oh[v].append(i); oid[b, v] = i
+        for v in vals: con([(i, 1) for i in oh[v]], fv[ci][v], fv[ci][v])
+        c = np.zeros(nv)
+        for j, tr in enumerate(C):
+            if tr in TA: c[j] = -1
+        Mx = coo_matrix((V, (R, Cc)), shape=(len(lo), nv)).tocsc()
+        h = highspy.Highs(); h.setOptionValue('output_flag', False); h.setOptionValue('time_limit', TLH); h.setOptionValue('threads', 1)
+        lp = highspy.HighsLp(); lp.num_col_ = nv; lp.num_row_ = len(lo); lp.col_cost_ = c
+        lp.col_lower_ = np.zeros(nv); lp.col_upper_ = np.ones(nv)
+        lp.row_lower_ = np.array(lo, float); lp.row_upper_ = np.array(hi, float)
+        lp.a_matrix_.format_ = highspy.MatrixFormat.kColwise
+        lp.a_matrix_.start_ = Mx.indptr; lp.a_matrix_.index_ = Mx.indices; lp.a_matrix_.value_ = Mx.data.astype(float)
+        lp.integrality_ = [highspy.HighsVarType.kInteger] * nv
+        h.passModel(lp)
+        if x0:
+            v0 = np.zeros(nv); v0[:len(C)] = x0
+            for key, i in oid.items(): v0[i] = ov[key]
+            s0 = highspy.HighsSolution(); s0.col_value = list(v0); s0.value_valid = True; h.setSolution(s0)
+        h.run(); hs = h.modelStatusToString(h.getModelStatus()); xs = np.array(h.getSolution().col_value)
+        if xs.size == nv and h.getInfo().primal_solution_status == 2 and (x0 is None or -h.getInfo().objective_function_value >= cpk):
+            best = [int(v > 0.5) for v in xs[:len(C)]]
+        hb = -h.getInfo().mip_dual_bound; hb = round(hb) if abs(hb) < 1e9 else hb
+    if best is None:
+        print('class', ci, 'cap', cap, 'FAIL', cps, hs, flush=True); continue
+    sol = [C[j] for j in range(len(C)) if best[j]]; keep = sum(tr in TA for tr in sol)
+    print('class', ci, 'cap', cap, 'cpsat', cps, cpk, 'highs', hs, 'A rows', nA, 'kept', keep, 'bound', hb, f'{time.time()-t0:.0f}s', flush=True)
+    json.dump(dict(ci=ci, kept=keep, nA=nA, bound=hb, triples=sol), open(path, 'w'))
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_lns.py b/research/complex-t16-two-stage-cycles/search/mindiff_lns.py
new file mode 100644
index 0000000000..d671f5882f
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_lns.py
@@ -0,0 +1,148 @@
+"""LNS toward the selected map A under an exact idle-profile constraint (min-diff search).
+
+State: class-level placements (bin, call, width). Helpers of one (call, width) class are interchangeable for the
+owner rules R3-R6, so a state fixes the owner map up to that relabelling (realize.py picks the labels).
+Each bin's fill is either A's or F's (F = the equivalent-profile target map, e.g. the LNS/CP-SAT best). A step frees
+a neighbourhood of bins grown by BFS over the current diff graph; the rows of each class currently in those bins may
+move among the candidate placements (A's, F's, current) of those bins. The per-free-value bin counts inside the
+neighbourhood are preserved, so the global idle profile (hence kappa) is unchanged. Each sub-MIP (HiGHS, warm
+started at the current state) maximises the placements shared with A.
+argv: LIBDIR F_OWNERS START_TRIPLES_JSON OUT_JSON ITERS SEED [NBINS] [TL]
+Needs CPython 3.12, numpy, scipy, highspy. Single thread."""
+import sys, json, random, time
+sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np, highspy
+from scipy.sparse import coo_matrix
+from collections import Counter, defaultdict, deque
+A = lib.selroles; F = lib.read(sys.argv[2])
+cur = {(tuple(k), t, w) for k, t, w in json.load(open(sys.argv[3]))['triples']}
+OUT, ITERS, rng = sys.argv[4], int(sys.argv[5]), random.Random(int(sys.argv[6]))
+NB = int(sys.argv[7]) if len(sys.argv) > 7 else 300
+TL = float(sys.argv[8]) if len(sys.argv) > 8 else 60
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+m = lib.Model(A)
+TA = {(B(z), z['time'], z['width']) for z in A}
+TF = {(B(z), z['time'], z['width']) for z in F}
+fillA, fillF = Counter(), Counter()
+for z in A: fillA[B(z)] += z['width']
+for z in F: fillF[B(z)] += z['width']
+candbin = defaultdict(set)
+for tr in TA | TF: candbin[tr[0]].add(tr)
+DA = Counter((z['time'], z['width']) for z in A)
+
+
+def idle(trs):
+    fill = Counter()
+    for k, t, w in trs: fill[k] += w
+    out = Counter()
+    for k in m.cap:
+        f = m.cap[k] - fill[k]
+        if f: out[f] += 1
+    return out
+
+
+target = idle(TF)
+assert idle(cur) == target, 'start profile differs from F'
+
+
+def check(trs):
+    assert len(trs) == len(A) and idle(trs) == target
+    assert Counter((t, w) for k, t, w in trs) == DA
+    assert max(Counter((m.fam[k], t) for k, t, w in trs).values()) == 1
+    assert all(t in m.allowed[k] for k, t, w in trs)
+
+
+def graph(trs):
+    adj = defaultdict(set); diff = (TA - trs) | (trs - TA)
+    bycls = defaultdict(list); byft = defaultdict(set)
+    for k, t, w in diff: bycls[t, w].append(k)
+    for tr in TA | trs: byft[m.fam[tr[0]], tr[1]].add(tr[0])
+    for ks in bycls.values():
+        for a in ks:
+            adj[a].update(b for b in ks if b != a)
+    for k, t, w in diff:
+        for k2 in byft[m.fam[k], t]:
+            if k2 != k: adj[k].add(k2); adj[k2].add(k)
+    return adj, sorted({tr[0] for tr in diff})
+
+
+def solve(trs, N):
+    N = set(N)
+    inN = {tr for tr in trs if tr[0] in N}
+    D = Counter((t, w) for k, t, w in inN)
+    occ_out = {(m.fam[k], t) for k, t, w in trs if k not in N}
+    C = set(inN)
+    for k in N: C |= candbin[k]
+    C = sorted(tr for tr in C if (tr[1], tr[2]) in D and (m.fam[tr[0]], tr[1]) not in occ_out)
+    n = len(C); rows, cols, vals, lo, hi = [], [], [], [], []
+
+    def con(e, l, h):
+        r = len(lo)
+        for j, v in e: rows.append(r); cols.append(j); vals.append(v)
+        lo.append(l); hi.append(h)
+    bycls = defaultdict(list); bybin = defaultdict(list); byft = defaultdict(list)
+    for j, (k, t, w) in enumerate(C):
+        bycls[t, w].append(j); bybin[k].append((j, w)); byft[m.fam[k], t].append(j)
+    for tw, d in D.items(): con([(j, 1) for j in bycls[tw]], d, d)
+    for js in byft.values():
+        if len(js) > 1: con([(j, 1) for j in js], 0, 1)
+    fillc = Counter()
+    for k, t, w in inN: fillc[k] += w
+    nv = n; bid = {}
+    for k in N:
+        if fillA[k] == fillF[k] or fillc[k] not in (fillA[k], fillF[k]):
+            con([(j, w) for j, w in bybin[k]], fillc[k], fillc[k]); continue
+        i = nv; nv += 1; bid[k] = i
+        con([(j, w) for j, w in bybin[k]] + [(i, -(fillF[k] - fillA[k]))], fillA[k], fillA[k])
+    vs = set()
+    for k in bid: vs |= {m.cap[k] - fillF[k], m.cap[k] - fillA[k]}
+    for v in vs - {0}:
+        e, rhs = [], 0
+        for k, i in bid.items():
+            co = int(m.cap[k] - fillF[k] == v) - int(m.cap[k] - fillA[k] == v)
+            if co: e.append((i, co)); rhs += co * int(fillc[k] == fillF[k])
+        con(e, rhs, rhs)
+    c = np.zeros(nv)
+    for j, tr in enumerate(C):
+        if tr in TA: c[j] = -1
+    M = coo_matrix((vals, (rows, cols)), shape=(len(lo), nv)).tocsc()
+    h = highspy.Highs(); h.setOptionValue('output_flag', False)
+    h.setOptionValue('time_limit', TL); h.setOptionValue('threads', 1)
+    lp = highspy.HighsLp(); lp.num_col_ = nv; lp.num_row_ = len(lo); lp.col_cost_ = c
+    lp.col_lower_ = np.zeros(nv); lp.col_upper_ = np.ones(nv)
+    lp.row_lower_ = np.array(lo, float); lp.row_upper_ = np.array(hi, float)
+    lp.a_matrix_.format_ = highspy.MatrixFormat.kColwise
+    lp.a_matrix_.start_ = M.indptr; lp.a_matrix_.index_ = M.indices; lp.a_matrix_.value_ = M.data.astype(float)
+    lp.integrality_ = [highspy.HighsVarType.kInteger] * nv
+    h.passModel(lp)
+    x0 = np.zeros(nv)
+    for j, tr in enumerate(C): x0[j] = tr in inN
+    for k, i in bid.items(): x0[i] = fillc[k] == fillF[k]
+    s0 = highspy.HighsSolution(); s0.col_value = list(x0); s0.value_valid = True
+    h.setSolution(s0); h.run()
+    xs = np.array(h.getSolution().col_value)
+    if xs.size != nv: return None, 0
+    new = {C[j] for j in range(n) if xs[j] > 0.5}
+    gain = sum(tr in TA for tr in new) - sum(tr in TA for tr in inN)
+    return (trs - inN) | new, gain
+
+
+best = len(TA & cur)
+print('start kept', best, 'relocated', len(A) - best, flush=True)
+for it in range(ITERS):
+    t0 = time.time()
+    adj, dbins = graph(cur)
+    if not dbins: break
+    seed = rng.choice(dbins); N = [seed]; seen = {seed}; q = deque([seed])
+    size = rng.choice([NB // 2, NB, NB * 2])
+    while q and len(N) < size:
+        a = q.popleft(); nb = sorted(adj[a]); rng.shuffle(nb)
+        for b in nb:
+            if b not in seen: seen.add(b); N.append(b); q.append(b)
+    new, gain = solve(cur, N)
+    if new is not None and gain > 0:
+        check(new); cur = new; best += gain
+        json.dump(dict(triples=sorted(cur)), open(OUT, 'w'))
+    print(f'it {it} N {len(N)} gain {gain} kept {best} relocated {len(A)-best} {time.time()-t0:.1f}s', flush=True)
+json.dump(dict(triples=sorted(cur)), open(OUT, 'w'))
+print('final relocated', len(A) - best)
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_lns2.py b/research/complex-t16-two-stage-cycles/search/mindiff_lns2.py
new file mode 100644
index 0000000000..08ca2d73d0
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_lns2.py
@@ -0,0 +1,122 @@
+"""Second-phase min-diff LNS toward the selected map A. Inside the neighbourhood every legal placement (bin, call, width) of the rows it holds is
+a candidate (not only A's or F's), each bin's free capacity is any value already present among the neighbourhood's
+bins, and the number of bins per free value is preserved (so the global idle profile and kappa are unchanged).
+Maximises placements shared with A (HiGHS, warm start = current state).
+Each iteration frees a random subset (30/60/90/all) of the differing bins plus up to EXTRA sampled bins (sharing a
+physical family with a differing bin, or partly filled). Unlike mindiff_lns.py, fills are not restricted to A's or F's.
+argv: LIBDIR START_TRIPLES_JSON OUT_JSON ITERS SEED [EXTRA] [TL]
+Needs CPython 3.12, numpy, scipy, highspy. Single thread."""
+import sys, json, random, time
+sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np, highspy
+from scipy.sparse import coo_matrix
+from collections import Counter, defaultdict
+A = lib.selroles
+cur = {(tuple(k), t, w) for k, t, w in json.load(open(sys.argv[2]))['triples']}
+OUT, ITERS, rng = sys.argv[3], int(sys.argv[4]), random.Random(int(sys.argv[5]))
+EXTRA = int(sys.argv[6]) if len(sys.argv) > 6 else 200
+TL = float(sys.argv[7]) if len(sys.argv) > 7 else 120
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+m = lib.Model(A)
+TA = {(B(z), z['time'], z['width']) for z in A}
+DA = Counter((z['time'], z['width']) for z in A)
+
+
+def idle(trs):
+    fill = Counter()
+    for k, t, w in trs: fill[k] += w
+    return Counter(m.cap[k] - fill[k] for k in m.cap if m.cap[k] - fill[k])
+
+
+target = idle(cur)
+
+
+def check(trs):
+    assert len(trs) == len(A) and idle(trs) == target
+    assert Counter((t, w) for k, t, w in trs) == DA
+    assert max(Counter((m.fam[k], t) for k, t, w in trs).values()) == 1
+    assert all(t in m.allowed[k] for k, t, w in trs)
+
+
+def solve(trs, N):
+    N = set(N)
+    inN = {tr for tr in trs if tr[0] in N}
+    D = Counter((t, w) for k, t, w in inN)
+    wt = defaultdict(set)
+    for t, w in D: wt[t].add(w)
+    occ_out = {(m.fam[k], t) for k, t, w in trs if k not in N}
+    C = sorted((k, t, w) for k in N for t in m.allowed[k] if t in wt and (m.fam[k], t) not in occ_out
+               for w in wt[t] if w <= m.cap[k])
+    C = sorted(set(C) | inN)
+    n = len(C); rows, cols, vals, lo, hi = [], [], [], [], []
+
+    def con(e, l, h):
+        r = len(lo)
+        for j, v in e: rows.append(r); cols.append(j); vals.append(v)
+        lo.append(l); hi.append(h)
+    bycls = defaultdict(list); bybin = defaultdict(list); byft = defaultdict(list)
+    for j, (k, t, w) in enumerate(C):
+        bycls[t, w].append(j); bybin[k].append((j, w)); byft[m.fam[k], t].append(j)
+    for tw, d in D.items(): con([(j, 1) for j in bycls[tw]], d, d)
+    for js in byft.values():
+        if len(js) > 1: con([(j, 1) for j in js], 0, 1)
+    fillc = Counter()
+    for k, t, w in inN: fillc[k] += w
+    cnt0 = Counter(m.cap[k] - fillc[k] for k in N)
+    vs = sorted(v for v in cnt0 if v)
+    nv = n; ohs = defaultdict(list); x0x = {}
+    for k in N:
+        opts = [v for v in vs if v <= m.cap[k]]
+        ids = list(range(nv, nv + len(opts))); nv += len(opts)
+        con([(j, w) for j, w in bybin[k]] + [(i, v) for i, v in zip(ids, opts)], m.cap[k], m.cap[k])
+        if len(ids) > 1: con([(i, 1) for i in ids], 0, 1)
+        for i, v in zip(ids, opts): ohs[v].append(i); x0x[i] = (m.cap[k] - fillc[k] == v)
+    for v in vs: con([(i, 1) for i in ohs[v]], cnt0[v], cnt0[v])
+    c = np.zeros(nv)
+    for j, tr in enumerate(C):
+        if tr in TA: c[j] = -1
+    M = coo_matrix((vals, (rows, cols)), shape=(len(lo), nv)).tocsc()
+    h = highspy.Highs(); h.setOptionValue('output_flag', False)
+    h.setOptionValue('time_limit', TL); h.setOptionValue('threads', 1)
+    lp = highspy.HighsLp(); lp.num_col_ = nv; lp.num_row_ = len(lo); lp.col_cost_ = c
+    lp.col_lower_ = np.zeros(nv); lp.col_upper_ = np.ones(nv)
+    lp.row_lower_ = np.array(lo, float); lp.row_upper_ = np.array(hi, float)
+    lp.a_matrix_.format_ = highspy.MatrixFormat.kColwise
+    lp.a_matrix_.start_ = M.indptr; lp.a_matrix_.index_ = M.indices; lp.a_matrix_.value_ = M.data.astype(float)
+    lp.integrality_ = [highspy.HighsVarType.kInteger] * nv
+    h.passModel(lp)
+    x0 = np.zeros(nv)
+    for j, tr in enumerate(C): x0[j] = tr in inN
+    for i, v in x0x.items(): x0[i] = v
+    s0 = highspy.HighsSolution(); s0.col_value = list(x0); s0.value_valid = True
+    h.setSolution(s0); h.run()
+    xs = np.array(h.getSolution().col_value)
+    info = h.getInfo()
+    stat = (h.modelStatusToString(h.getModelStatus()), len(N), n, round(-info.mip_dual_bound))
+    if xs.size != nv: return None, 0, stat
+    new = {C[j] for j in range(n) if xs[j] > 0.5}
+    gain = sum(tr in TA for tr in new) - sum(tr in TA for tr in inN)
+    return (trs - inN) | new, gain, stat
+
+
+best = len(TA & cur)
+print('start relocated', len(A) - best, 'profile', dict(sorted(target.items())), flush=True)
+allbins = sorted(m.cap)
+for it in range(ITERS):
+    t0 = time.time()
+    diffb = {tr[0] for tr in (TA - cur) | (cur - TA)}
+    # extras: bins sharing a family with a diff bin, bins with free capacity, random others
+    fams = {m.fam[k] for k in diffb}
+    fillc = Counter()
+    for k, t, w in cur: fillc[k] += w
+    pool1 = [k for k in allbins if k not in diffb and m.fam[k] in fams]
+    pool2 = [k for k in allbins if k not in diffb and 0 < m.cap[k] - fillc[k] < m.cap[k]]
+    ex = set(rng.sample(pool1, min(len(pool1), EXTRA // 2))) | set(rng.sample(pool2, min(len(pool2), EXTRA // 2)))
+    sub = set(rng.sample(sorted(diffb), min(len(diffb), rng.choice([30, 60, 90, 400]))))
+    new, gain, stat = solve(cur, sub | ex)
+    if new is not None and gain > 0:
+        check(new); cur = new; best += gain
+        json.dump(dict(triples=sorted(cur)), open(OUT, 'w'))
+    print(f'it {it} {stat} gain {gain} relocated {len(A)-best} {time.time()-t0:.1f}s', flush=True)
+json.dump(dict(triples=sorted(cur)), open(OUT, 'w'))
+print('final relocated', len(A) - best)
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_mip.py b/research/complex-t16-two-stage-cycles/search/mindiff_mip.py
new file mode 100644
index 0000000000..dbd8ace010
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_mip.py
@@ -0,0 +1,87 @@
+"""Min-diff re-assignment MIP (HiGHS): an owner map with the same idle profile (hence the same kappa) as a target
+map F that keeps as many placements of the selected PR1094 map A as possible.
+
+Helpers of one (call, width) class are interchangeable for the owner rules R3-R6 (they read only the call and
+the width), so the model works on class placements x[bin, call, width] in {0, 1}, with candidates = placements
+used by A or by F (or by START). Constraints: every class keeps its count; at most one helper per physical
+family per call (R4); windows/active pair (R3/R5) hold because every candidate is a placement of a legal map.
+  fill: every bin keeps F's fill exactly.
+  two:  every bin's fill is A's or F's (one 0/1 choice per bin where they differ); the number of bins per idle
+        value is linear in those choices and is fixed to F's idle profile.
+Objective: maximise placements shared with A. realize.py turns the class solution into owner rows.
+argv: LIBDIR F_OWNERS OUT_JSON MODE(fill|two) TIME_LIMIT START_JSON(triples, or -)
+Needs CPython 3.12, numpy, scipy, highspy. Single thread."""
+import sys, json, time
+sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np
+import highspy
+from scipy.sparse import coo_matrix
+from collections import Counter, defaultdict
+Fp, OUT, MODE, TL, START = sys.argv[2], sys.argv[3], sys.argv[4], float(sys.argv[5]), sys.argv[6]
+assert MODE in ('fill', 'two')
+A = lib.selroles; F = lib.read(Fp)
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+m = lib.Model(A)
+TA = {(B(z), z['time'], z['width']) for z in A}; TF = {(B(z), z['time'], z['width']) for z in F}
+st = None if START == '-' else {(tuple(k), t, w) for k, t, w in json.load(open(START))['triples']}
+C = sorted(TA | TF | (st or set())); n = len(C)
+D = Counter((z['time'], z['width']) for z in A)
+fillA, fillF = Counter(), Counter()
+for z in A: fillA[B(z)] += z['width']
+for z in F: fillF[B(z)] += z['width']
+idleA, idleF = lib.idle_of(A), lib.idle_of(F)
+rows_, cols, vals, lo, hi = [], [], [], [], []
+
+
+def con(entries, l, h):
+    r = len(lo)
+    for j, v in entries: rows_.append(r); cols.append(j); vals.append(v)
+    lo.append(l); hi.append(h)
+
+
+bycls = defaultdict(list); bybin = defaultdict(list); byft = defaultdict(list)
+for j, (k, t, w) in enumerate(C):
+    assert t in m.allowed[k] and w <= m.cap[k]
+    bycls[t, w].append(j); bybin[k].append((j, w)); byft[m.fam[k], t].append(j)
+for tw, d in D.items(): con([(j, 1) for j in bycls[tw]], d, d)
+for js in byft.values():
+    if len(js) > 1: con([(j, 1) for j in js], 0, 1)
+nv = n; bin_ids = {}
+for k, e in bybin.items():
+    if MODE == 'fill' or fillA[k] == fillF[k]:
+        con([(j, w) for j, w in e], fillF[k], fillF[k]); continue
+    i = nv; nv += 1; bin_ids[k] = i          # 1 = F's fill, 0 = A's fill
+    con([(j, w) for j, w in e] + [(i, -(fillF[k] - fillA[k]))], fillA[k], fillA[k])
+if MODE == 'two':
+    for v in sorted(set(idleF) | set(idleA)):
+        ent = [(i, co) for k, i in bin_ids.items()
+               if (co := int(m.cap[k] - fillF[k] == v) - int(m.cap[k] - fillA[k] == v))]
+        con(ent, idleF[v] - idleA[v], idleF[v] - idleA[v])
+c = np.zeros(nv)
+for j, t in enumerate(C):
+    if t in TA: c[j] = -1
+M = coo_matrix((vals, (rows_, cols)), shape=(len(lo), nv)).tocsc()
+print('vars', nv, 'cons', len(lo), flush=True)
+t0 = time.time()
+h = highspy.Highs(); h.setOptionValue('time_limit', TL); h.setOptionValue('mip_rel_gap', 0.0); h.setOptionValue('threads', 1)
+lp = highspy.HighsLp(); lp.num_col_ = nv; lp.num_row_ = len(lo)
+lp.col_cost_ = c; lp.col_lower_ = np.zeros(nv); lp.col_upper_ = np.ones(nv)
+lp.row_lower_ = np.array(lo, float); lp.row_upper_ = np.array(hi, float)
+lp.a_matrix_.format_ = highspy.MatrixFormat.kColwise
+lp.a_matrix_.start_ = M.indptr; lp.a_matrix_.index_ = M.indices; lp.a_matrix_.value_ = M.data.astype(float)
+lp.integrality_ = [highspy.HighsVarType.kInteger] * nv
+h.passModel(lp)
+if st is not None:
+    x0 = np.zeros(nv)
+    for j, tr in enumerate(C): x0[j] = tr in st
+    fill0 = Counter()
+    for (k, t, w) in st: fill0[k] += w
+    for k, i in bin_ids.items(): x0[i] = fill0[k] == fillF[k]
+    s0 = highspy.HighsSolution(); s0.col_value = list(x0); s0.value_valid = True
+    print('setSolution', h.setSolution(s0), 'start obj', -float(c @ x0), flush=True)
+h.run()
+info = h.getInfo(); xs = np.array(h.getSolution().col_value)
+print('status', h.modelStatusToString(h.getModelStatus()), 'obj', info.objective_function_value,
+      'bound', info.mip_dual_bound, f'{time.time()-t0:.0f}s', flush=True)
+sol = [C[j] for j in range(n) if xs[j] > 0.5]
+json.dump(dict(mode=MODE, obj=-info.objective_function_value, bound=-info.mip_dual_bound, triples=sol), open(OUT, 'w'))
diff --git a/research/complex-t16-two-stage-cycles/search/mindiff_reuse.py b/research/complex-t16-two-stage-cycles/search/mindiff_reuse.py
new file mode 100644
index 0000000000..5a6986f195
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/mindiff_reuse.py
@@ -0,0 +1,14 @@
+"""Min-diff helper: copy per-class mindiff_cls2.py results from an old cache to a new one for every changed class whose
+stage-1 (x, y) is the same in the old and the new mindiff_cls1.py solution. Standard library only.
+argv: OLD_STAGE1_JSON NEW_STAGE1_JSON OLD_CACHE NEW_CACHE"""
+import sys, json, os, shutil
+from collections import Counter
+a, b, ca, cb = sys.argv[1:5]; A1 = json.load(open(a)); B1 = json.load(open(b)); os.makedirs(cb, exist_ok=True)
+def key(d, ci): return (sorted((tuple(p), v) for c, p, v in d['x'] if c == ci), sorted((t, w, v) for c, t, w, v in d['y'] if c == ci))
+n = 0
+for ci in B1['changed']:
+    f = f'{ca}/{ci}.json'
+    if ci in A1['changed'] and key(A1, ci) == key(B1, ci) and os.path.exists(f):
+        d = json.load(open(f)); ny = sum(v for c, t, w, v in B1['y'] if c == ci)
+        if len(d['triples']) == ny: shutil.copy(f, f'{cb}/{ci}.json'); n += 1
+print('reused', n, 'of', len(B1['changed']), 'changed classes')
diff --git a/research/complex-t16-two-stage-cycles/search/realize.py b/research/complex-t16-two-stage-cycles/search/realize.py
new file mode 100644
index 0000000000..a4a4412ce7
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/realize.py
@@ -0,0 +1,80 @@
+"""Turn a min-diff class solution (triples (bin, call, width)) into an owner map closest to the selected map A:
+keep A's helper label wherever A's (bin, call, width) placement is kept, assign the rest of each class arbitrarily
+(deterministically), then choose each bin's serialization order to maximise rows whose offset equals A's
+(contiguous offsets from 0, R6), then audits (seed67 rules) and prices the result.
+argv: LIBDIR SOL_JSON OUT_OWNERS. Standard library only."""
+import sys, json, gzip, itertools
+sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict
+A = lib.selroles; sol = json.load(open(sys.argv[2]))
+B = lambda z: (z['owner_replica'], z['child'], z['port'])
+trip = {(tuple(k), t, w) for k, t, w in sol['triples']}
+assert len(trip) == len(A)
+rows = [dict(z) for z in A]
+left = defaultdict(list)   # class -> unplaced row indices
+used = set()
+for i, z in enumerate(A):
+    c = (B(z), z['time'], z['width'])
+    if c in trip: used.add(c)
+    else: left[z['time'], z['width']].append(i)
+free = defaultdict(list)
+for c in sorted(trip - used): free[c[1], c[2]].append(c[0])
+for tw, idx in left.items():
+    assert len(idx) == len(free[tw])
+    for i, k in zip(sorted(idx), free[tw]): rows[i] = lib.relocate(rows[i], *k)
+# per-bin order: maximise rows at A's offset
+bybin = defaultdict(list)
+for i, z in enumerate(rows): bybin[B(z)].append(i)
+def tiles(gaps, ws):
+    """Can the multiset ws exactly tile the gap lengths? (small: brute force via DP over assignment)"""
+    ws = sorted(ws, reverse=True)
+    def rec(j, g):
+        if j == len(ws): return all(x == 0 for x in g)
+        seen = set()
+        for a in range(len(g)):
+            if g[a] >= ws[j] and g[a] not in seen:
+                seen.add(g[a]); g2 = list(g); g2[a] -= ws[j]
+                if rec(j + 1, g2): return True
+        return False
+    return rec(0, list(gaps))
+def layout(fixed, rest, fill):
+    """fixed: list of (offset, width, i) kept at A offsets; rest: (width, i). Return {i: offset} or None."""
+    fixed = sorted(fixed); pos = 0; gaps = []
+    for o, w, i in fixed:
+        if o < pos: return None
+        gaps.append((pos, o - pos)); pos = o + w
+    if pos > fill: return None
+    gaps.append((pos, fill - pos))
+    if not tiles([g for _, g in gaps], [w for w, _ in rest]): return None
+    # realise the tiling greedily with backtracking
+    rest = sorted(rest, reverse=True); out = {i: o for o, w, i in fixed}
+    def rec(j, g):
+        if j == len(rest): return all(x[1] == 0 for x in g)
+        w, i = rest[j]
+        for a in range(len(g)):
+            if g[a][1] >= w:
+                g2 = list(g); g2[a] = (g[a][0] + w, g[a][1] - w); out[i] = g[a][0]
+                if rec(j + 1, g2): return True
+        return False
+    assert rec(0, gaps); return out
+stat = Counter()
+for k, idx in bybin.items():
+    fill = sum(rows[i]['width'] for i in idx)
+    cand = [i for i in idx if B(A[i]) == k]          # kept placements, candidates to keep A's offset
+    other = [i for i in idx if B(A[i]) != k]
+    best = None
+    for r in range(len(cand), -1, -1):
+        for S in itertools.combinations(cand, r):
+            L = layout([(A[i]['offset'], A[i]['width'], i) for i in S],
+                       [(rows[i]['width'], i) for i in idx if i not in S], fill)
+            if L is not None: best = L; break
+        if best is not None: break
+        if len(cand) > 14 and r < len(cand) - 3: raise SystemExit(f'bin {k} too hard')
+    for i, o in best.items(): rows[i]['offset'] = o
+for z, a in zip(rows, A):
+    assert all(z[f] == a[f] for f in ('stage', 'replica', 'time', 'helper', 'width'))
+au = lib.audit(rows)
+pr = lib.price(au['profile'])
+ch = sum(a != z for a, z in zip(A, rows)); rel = sum(B(a) != B(z) for a, z in zip(A, rows))
+print('changed', ch, 'relocated', rel, 'offset_only', ch - rel, 'idle', dict(sorted(au['idle'].items())), 'kappa', pr['kappa_decimal'])
+open(sys.argv[3], 'wb').write(gzip.compress(json.dumps(rows).encode(), mtime=0))
diff --git a/research/complex-t16-two-stage-cycles/search/score.py b/research/complex-t16-two-stage-cycles/search/score.py
new file mode 100644
index 0000000000..06e50ab650
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/score.py
@@ -0,0 +1,4 @@
+"""Print the exact kappa (pinned engines) and idle profile of owner maps. argv: LIBDIR OWNERS..."""
+import sys; sys.path.insert(0, sys.argv[1]); import lib
+for f in sys.argv[2:]:
+    au = lib.audit(lib.read(f)); print(f, lib.price(au['profile'])['kappa_decimal'], au['idle'], flush=True)
diff --git a/research/complex-t16-two-stage-cycles/search/sloop.sh b/research/complex-t16-two-stage-cycles/search/sloop.sh
new file mode 100755
index 0000000000..275f6e7674
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/sloop.sh
@@ -0,0 +1,28 @@
+#!/bin/bash
+# Improvement loop of the fifth version (portable copy of the session's sloop.sh / sloop2.sh; sloop2.sh only made the
+# CP-SAT worker count of the realisation step an env setting, NW2). Each step:
+#  1. winlp.py ip: re-solve the class-level model (pattern counts and flows per (capacity, window) class, R4
+#     aggregate cuts) warm-started from the current map, with a random subset of 12, 18 or 24 classes free (drawn
+#     from the classes that differ from TARGET, a full-model optimum JSON) and all others fixed; change penalty
+#     PEN=1000, minimum surrogate gain GAIN=1;
+#  2. lns2.py guide: realise that class target on concrete bins by two CP-SAT neighbourhood solves around the bins
+#     whose class (call, width) count or pattern count must drop, maximising the surrogate exactly; a result is kept
+#     only if the exact kappa rises (Decimal comparison).
+# Finite heuristic; no optimum. Every new best is written as DIR/k_<step>.OWNERS.json.gz.
+# usage: search/sloop.sh DIR START_OWNERS TARGET_JSON SEED ITERS
+#   env RUN: optional command prefix, e.g. a memory-capped systemd scope (the session used MemoryMax=5G);
+#   env NW2: CP-SAT workers of the realisation step (default 2).
+# Needs uv, CPython 3.12, numpy, scipy and ortools. Run from the repository root (lib.py reads the selected data there).
+H=$(cd "$(dirname "$0")" && pwd)
+D=$1; mkdir -p "$D"; [ -f "$D/best.OWNERS.json.gz" ] || cp "$2" "$D/best.OWNERS.json.gz"
+export OMP_NUM_THREADS=1
+PY="uv run -q --no-project --python 3.12 --with numpy --with scipy --with ortools python -I"
+for n in $(seq 1 "$5"); do
+  sd=$(( $4*1000+n )); fr=$(( 12 + sd % 3 * 6 ))
+  FREE=$fr SEED=$sd FREEFROM=$3 PEN=1000 GAIN=1 $RUN $PY "$H/winlp.py" "$H" "$D/best.OWNERS.json.gz" ip 120 1 2 "$D/s1.json" > "$D/s1.log" 2>&1
+  st=$(grep -E "^(FEASIBLE|OPTIMAL|INFEASIBLE|UNKNOWN)" "$D/s1.log" | cut -c1-60)
+  if ! echo "$st" | grep -qE "^(FEASIBLE|OPTIMAL)"; then echo "$(date +%T) $n s1 $st"; continue; fi
+  GUIDE=$D/s1.json GFRAC=1 GMUL=2 NW=${NW2:-2} DIV=0 TL2=30 $RUN $PY "$H/lns2.py" "$H" "$D/best.OWNERS.json.gz" "$D/t" 2 $sd 150 guide 2>&1 \
+    | grep -E "^it|^guide" | cut -c1-260 | sed "s/^/$(date +%T) $n [$st] /"
+  [ -f "$D/t.OWNERS.json.gz" ] && mv "$D/t.OWNERS.json.gz" "$D/best.OWNERS.json.gz" && cp "$D/best.OWNERS.json.gz" "$D/k_$n.OWNERS.json.gz"
+done
diff --git a/research/complex-t16-two-stage-cycles/search/winbound.py b/research/complex-t16-two-stage-cycles/search/winbound.py
new file mode 100644
index 0000000000..5d4330b57e
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/winbound.py
@@ -0,0 +1,46 @@
+"""Window-aware relaxation (heuristic ceiling, not a proof): bins grouped by (cap, allowed window) class; helpers by
+(call, width); pattern counts per class, flows of (call, width) helpers into classes. It drops the per-bin
+constraints (one helper per bin per call, which also covers R4) and so over-estimates the surrogate
+sum f ln f over idle fragments. The surrogate is only approximately linear in kappa, so the printed CP-SAT bound
+is an optimistic ceiling for the surrogate, not a certified kappa bound.
+argv: LIBDIR OWNERS [TIME_LIMIT] [WORKERS]   Needs CPython 3.12 and ortools."""
+import sys, math; sys.path.insert(0, sys.argv[1]); import lib
+from collections import Counter, defaultdict
+from ortools.sat.python import cp_model
+m = lib.Model(lib.read(sys.argv[2])); TL = float(sys.argv[3]) if len(sys.argv) > 3 else 300
+W = [4, 5, 7, 8, 9]; g = lib.g
+cls = Counter((m.cap[k], frozenset(m.allowed[k])) for k in m.cap)
+print('classes', len(cls))
+D = Counter((z['time'], z['width']) for z in m.roles)
+def pats(cap):
+    out = []
+    def rec(i, rem, cur):
+        if i == len(W): out.append(tuple(cur)); return
+        for c in range(rem // W[i] + 1): rec(i+1, rem - c*W[i], cur + [c])
+    rec(0, cap, []); return out
+P = {cap: pats(cap) for cap in (8, 16, 32, 48)}
+md = cp_model.CpModel(); obj = []; ytw = defaultdict(list); X = {}
+for ci, ((cap, al), n) in enumerate(cls.items()):
+    xs = []; cw = defaultdict(list)
+    for p in P[cap]:
+        s = sum(c*w for c, w in zip(p, W)); x = md.NewIntVar(0, n, ''); xs.append(x); X[ci, p] = x
+        if g(cap - s): obj.append(round(1e4*g(cap - s)) * x)
+        for c, w in zip(p, W):
+            if c: cw[w].append(c * x)
+    md.Add(sum(xs) == n)
+    for w in W:
+        ys = []
+        for t in al:
+            if D[t, w]: y = md.NewIntVar(0, D[t, w] * n, ''); ys.append(y); ytw[t, w].append(y)
+        md.Add(sum(ys) == sum(cw[w]))
+for tw, d in D.items(): md.Add(sum(ytw[tw]) == d)
+md.Maximize(sum(obj)); s = cp_model.CpSolver(); s.parameters.max_time_in_seconds = TL; s.parameters.num_workers = int(sys.argv[4]) if len(sys.argv) > 4 else 2
+st = s.Solve(md); print(s.StatusName(st), 'obj', s.ObjectiveValue()/1e4, 'bound', s.BestObjectiveBound()/1e4)
+prof = Counter()
+for (ci, p), x in X.items():
+    v = s.Value(x)
+    if v:
+        cap = list(cls)[ci][0]; f = cap - sum(c*w for c, w in zip(p, W))
+        if f: prof[f] += v
+print('profile', dict(sorted(prof.items())))
+print('current', sum(g(m.free(k)) for k in m.cap))
diff --git a/research/complex-t16-two-stage-cycles/search/winlp.py b/research/complex-t16-two-stage-cycles/search/winlp.py
new file mode 100644
index 0000000000..cf1fb01ca0
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/search/winlp.py
@@ -0,0 +1,136 @@
+"""Class-level window LP/IP for the T16 owner bins with aggregate family-time (R4) cuts (fifth version).
+Classes = (capacity, allowed calls); variables x[class, pattern] (bins of the class with that width multiset) and
+y[class, call, width] (helpers of that call and width hosted by the class); constraints: class sizes, width balance,
+demand per (call, width), and for every group of classes that share physical families (64 groups) and every call,
+at most (number of families in the group) helpers of that call. Objective: the surrogate sum g(free), g(f) = f ln f.
+It is a relaxation of the bin-level problem (no per-bin call distinctness beyond the R4 aggregate), used here
+only as a search guide; the proved ceiling is ceiling_bound.py (PROOF.md).
+argv: LIBDIR OWNERS MODE(lp|ip) [TL] [R4=1] [WORKERS] [OUT_JSON]
+ip mode (CP-SAT) env: HINT = JSON solution to hint (default: the OWNERS map's own class solution);
+  FREE = n and SEED: only n classes, drawn at random, may change (all others are fixed to the OWNERS map);
+  FREEFROM = a full-model ip JSON (target): draw the FREE classes only from classes whose (x, y) differ from it;
+  PEN = penalty per unit of |x - x_cur| and |y - y_cur| (change penalty); GAIN = required surrogate gain over the
+  OWNERS map (in surrogate units). With PEN, the objective is surrogate*1e4 - PEN * (total change).
+Needs CPython 3.12, numpy, scipy (lp) or ortools (ip)."""
+import sys, math, json; sys.path.insert(0, sys.argv[1]); import lib
+import numpy as np, scipy.sparse as sp
+from collections import Counter, defaultdict
+m = lib.Model(lib.read(sys.argv[2])); MODE = sys.argv[3]; TL = float(sys.argv[4]) if len(sys.argv) > 4 else 600
+R4 = (sys.argv[5] if len(sys.argv) > 5 else '1') == '1'
+W = [4, 5, 7, 8, 9]; g = lib.g
+cls = defaultdict(list)
+for k in m.cap: cls[m.cap[k], frozenset(m.allowed[k])].append(k)
+CL = list(cls); cid = {}
+for i, c in enumerate(CL):
+    for k in cls[c]: cid[k] = i
+fam = defaultdict(set)
+for k in m.cap: fam[m.fam[k]].add(cid[k])
+groups = Counter(frozenset(v) for v in fam.values())
+D = Counter((z['time'], z['width']) for z in m.roles)
+def pats(cap):
+    out = []
+    def rec(i, rem, cur):
+        if i == len(W): out.append(tuple(cur)); return
+        for c in range(rem // W[i] + 1): rec(i+1, rem - c*W[i], cur + [c])
+    rec(0, cap, []); return out
+P = {cap: pats(cap) for cap in (8, 16, 32, 48)}
+var = []; obj = []
+for ci, (cap, al) in enumerate(CL):
+    for p in P[cap]: var.append(('x', ci, p)); obj.append(g(cap - sum(a*w for a, w in zip(p, W))))
+for ci, (cap, al) in enumerate(CL):
+    for t in al:
+        for w in W:
+            if D[t, w] and w <= cap: var.append(('y', ci, t, w)); obj.append(0.0)
+idx = {v: i for i, v in enumerate(var)}
+rows = []; rhs = []; sense = []
+def add(coefs, s, b): rows.append(coefs); sense.append(s); rhs.append(b)
+xby = defaultdict(list); yby = defaultdict(list)
+for v in var:
+    if v[0] == 'x': xby[v[1]].append(v)
+    else: yby[v[1], v[3]].append(v)
+for ci, (cap, al) in enumerate(CL):
+    add([(idx[v], 1) for v in xby[ci]], '=', len(cls[CL[ci]]))
+    for j, w in enumerate(W):
+        co = [(idx[v], -v[2][j]) for v in xby[ci] if v[2][j]] + [(idx[v], 1) for v in yby[ci, w]]
+        if co: add(co, '=', 0)
+ytw = defaultdict(list)
+for v in var:
+    if v[0] == 'y': ytw[v[2], v[3]].append(idx[v])
+for tw, d in D.items(): add([(i, 1) for i in ytw[tw]], '=', d)
+if R4:
+    yct = defaultdict(list)
+    for v in var:
+        if v[0] == 'y': yct[v[1], v[2]].append(idx[v])
+    for G, n in groups.items():
+        ts = set().union(*(CL[c][1] for c in G))
+        for t in ts:
+            co = [(i, 1) for c in G for i in yct.get((c, t), [])]
+            if co: add(co, '<', n)
+print('vars', len(var), 'rows', len(rows), 'groups', len(groups), flush=True)
+if MODE == 'lp':
+    from scipy.optimize import linprog
+    def mat(sel):
+        r = []; c = []; d = []
+        for ri, j in enumerate(sel):
+            for i, a in rows[j]: r.append(ri); c.append(i); d.append(a)
+        return sp.csr_matrix((d, (r, c)), shape=(len(sel), len(var)))
+    eq = [j for j, s in enumerate(sense) if s == '=']; le = [j for j, s in enumerate(sense) if s == '<']
+    res = linprog(-np.array(obj), A_eq=mat(eq), b_eq=[rhs[j] for j in eq], A_ub=mat(le) if le else None, b_ub=[rhs[j] for j in le] if le else None, method='highs')
+    print('LP', -res.fun, res.status)
+    x = res.x; prof = Counter()
+    for v, i in idx.items():
+        if v[0] == 'x' and x[i] > 1e-6:
+            cap = CL[v[1]][0]; f = cap - sum(a*w for a, w in zip(v[2], W))
+            if f: prof[f] += x[i]
+    print('profile', {f: round(n, 2) for f, n in sorted(prof.items())})
+else:
+    from ortools.sat.python import cp_model
+    md = cp_model.CpModel(); X = []
+    for i, v in enumerate(var):
+        ub = len(cls[CL[v[1]]]) if v[0] == 'x' else D[v[2], v[3]]
+        X.append(md.NewIntVar(0, ub, ''))
+    for co, s, b in zip(rows, sense, rhs):
+        e = sum(a*X[i] for i, a in co)
+        md.Add(e == b) if s == '=' else md.Add(e <= b)
+    # hint from current map
+    cur = Counter()
+    for k in m.cap:
+        c = Counter(m.roles[i]['width'] for i in m.members[k]); cur[cid[k], tuple(c[w] for w in W)] += 1
+    ycur = Counter((cid[m.bin(i)], z['time'], z['width']) for i, z in enumerate(m.roles))
+    import os
+    if os.environ.get('HINT'):
+        hd = json.load(open(os.environ['HINT'])); hx = Counter({(ci, tuple(p)): v for ci, p, v in hd['x']}); hy = Counter({(ci, t, w): v for ci, t, w, v in hd['y']})
+        for v, i in idx.items(): md.AddHint(X[i], hx[v[1], v[2]] if v[0] == 'x' else hy[v[1], v[2], v[3]])
+    else:
+        for v, i in idx.items(): md.AddHint(X[i], cur[v[1], v[2]] if v[0] == 'x' else ycur[v[1], v[2], v[3]])
+    import os, random
+    if os.environ.get('FREE'):
+        rr = random.Random(int(os.environ.get('SEED', 0)))
+        pool = list(range(len(CL)))
+        if os.environ.get('FREEFROM'):
+            fd = json.load(open(os.environ['FREEFROM'])); fx = Counter({(ci, tuple(p)): v for ci, p, v in fd['x']}); fy = Counter({(ci, t, w): v for ci, t, w, v in fd['y']})
+            ch = {kk[0] for kk in set(fx) | set(cur) if fx[kk] != cur[kk]} | {kk[0] for kk in set(fy) | set(ycur) if fy[kk] != ycur[kk]}
+            pool = sorted(ch)
+        FREE = set(rr.sample(pool, min(len(pool), int(os.environ['FREE']))))
+        print('free classes', sorted(FREE), flush=True)
+        for v, i in idx.items():
+            if v[1] not in FREE: md.Add(X[i] == (cur[v[1], v[2]] if v[0] == 'x' else ycur[v[1], v[2], v[3]]))
+    PEN = int(os.environ.get('PEN', 0)); GAIN = float(os.environ.get('GAIN', 0))
+    E = sum(round(1e4*o)*X[i] for i, o in enumerate(obj) if o)
+    if PEN:
+        Ecur = sum(round(1e4*g(m.free(k))) for k in m.cap); pen = []
+        for v, i in idx.items():
+            c0 = cur[v[1], v[2]] if v[0] == 'x' else ycur[v[1], v[2], v[3]]
+            d = md.NewIntVar(0, 10**6, ''); md.Add(d >= X[i] - c0); md.Add(d >= c0 - X[i]); pen.append(d)
+        md.Add(E >= Ecur + round(1e4*GAIN))
+        md.Maximize(E - PEN * sum(pen))
+    else: md.Maximize(E)
+    s = cp_model.CpSolver(); s.parameters.max_time_in_seconds = TL; s.parameters.num_workers = int(sys.argv[6]) if len(sys.argv) > 6 else 1
+    st = s.Solve(md); print(s.StatusName(st), 'obj', s.ObjectiveValue()/1e4, 'bound', s.BestObjectiveBound()/1e4)
+    prof = Counter(); sol = []
+    for v, i in idx.items():
+        val = s.Value(X[i])
+        if v[0] == 'x' and val:
+            cap = CL[v[1]][0]; f = cap - sum(a*w for a, w in zip(v[2], W)); prof[f] += val; sol.append([v[1], list(v[2]), val])
+    print('profile', dict(sorted(prof.items())))
+    json.dump({'x': sol, 'y': [[v[1], v[2], v[3], s.Value(X[i])] for v, i in idx.items() if v[0] == 'y' and s.Value(X[i])]}, open(sys.argv[7] if len(sys.argv) > 7 else 'winip.json', 'w'))
diff --git a/research/complex-t16-two-stage-cycles/verify.py b/research/complex-t16-two-stage-cycles/verify.py
new file mode 100644
index 0000000000..9868a02d8a
--- /dev/null
+++ b/research/complex-t16-two-stage-cycles/verify.py
@@ -0,0 +1,116 @@
+"""Reconstruct the T16 owner map from the selected PR1094 map and DIFF-vs-selected.json, run the
+unchanged strict T16 admission, then the independent seed67 owner audit, exact pricing and PR1069 sweep,
+and finally the proved packing ceiling (ceiling_bound.py)."""
+from decimal import Decimal
+from pathlib import Path
+import argparse
+import hashlib
+import importlib.util
+import json
+import os
+import shutil
+import subprocess
+import sys
+import tarfile
+import tempfile
+
+if not __debug__:
+    raise RuntimeError('Assertions must remain enabled')
+P = Path(__file__).resolve().parent
+sha = lambda p: hashlib.sha256(p.read_bytes()).hexdigest()
+CONTROLS = dict(admission=69, bit_supplier=12, independent_t16=6, controller_mutations=15)
+KAPPA_DECIMAL = '0.001673614205725695'
+SIGMAS = 10011
+
+
+def run(main, work):
+    pins = json.loads((P/'INPUTS.json').read_text())
+    for name, h in pins.items():
+        assert sha(main/name) == h, 'Changed dependency: '+name
+    package_pins = json.loads((P/'MANIFEST.json').read_text())
+    actual = {f.relative_to(P).as_posix(): sha(f) for f in P.rglob('*')
+              if f.is_file() and f != P/'MANIFEST.json' and '__pycache__' not in f.parts}
+    assert actual == package_pins, 'Package inventory mismatch'
+
+    # 1. Byte-exact PLAN/SPEC and content-exact OWNERS from selected PR1094 + DIFF.
+    modspec = importlib.util.spec_from_file_location('t16_owner_build', P/'build.py')
+    mod = importlib.util.module_from_spec(modspec)
+    modspec.loader.exec_module(mod)
+    blobs = mod.derive(main)
+    for name, b in zip(('OWNERS.json.gz', 'PLAN.json', 'SPEC.json'), blobs):
+        assert b == (P/'data'/name).read_bytes(), 'Reconstruction mismatch: '+name
+
+    # 2. Unchanged PR1087 strict verifier on the overlaid data.
+    source = work/'source'
+    source.mkdir(parents=True)
+    archive = main/'research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz'
+    with tarfile.open(archive) as t:
+        for m in t.getmembers():
+            assert m.isfile() and (source/m.name).resolve().is_relative_to(source.resolve())
+        t.extractall(source, filter='data')
+    original = json.loads((source/'MANIFEST.json').read_text())
+    assert {f.relative_to(source).as_posix(): sha(f) for f in source.rglob('*')
+            if f.is_file() and f != source/'MANIFEST.json'} == original
+    for name in ('OWNERS.json.gz', 'PLAN.json', 'SPEC.json'):
+        shutil.copyfile(P/'data'/name, source/'data'/name)
+    local = work/'local'
+    local.mkdir()
+    local_pins = json.loads((P/'LOCAL-PINS.json').read_text())
+    with tarfile.open(main/'research/community-frontier1094-audit/selected-replay.tar.gz') as t:
+        prefix = 'candidate/strict/global/base/providers/gauge44/'
+        for name, h in local_pins.items():
+            member = t.getmember(prefix+name)
+            assert member.isfile()
+            b = t.extractfile(member).read()
+            assert hashlib.sha256(b).hexdigest() == h
+            (local/name).write_bytes(b)
+    # No discovery, source reconstruction, optimizer, credential environment,
+    # or native cold rebuild. The full controller and invoice are regenerated.
+    env = {k: os.environ[k] for k in ('PATH', 'SYSTEMROOT', 'WINDIR', 'TMPDIR', 'TEMP', 'TMP') if k in os.environ}
+    env.update(PYTHONNOUSERSITE='1', PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0')
+    subprocess.run([sys.executable, '-E', '-S', '-B', str(source/'verify_t16.py'),
+                    '--main', str(main), '--local', str(local), '--work', str(work/'strict')], env=env, check=True)
+    result = json.loads((work/'strict/REPLAY.json').read_text())
+    target = json.loads((P/'CANDIDATE.json').read_text())
+    assert result['status'] == 'PASS_GAUGE44_T16_STRICT_GLOBAL_REPLAY'
+    assert result['kappa'] == target['expected_updates']['kappa']
+    # Decimal comparisons throughout: the native assembler and the SPEC may differ only in trailing zeros.
+    assert Decimal(result['conservative_kappa_decimal']) == Decimal(target['expected_updates']['conservative_kappa_decimal'])
+    assert result['complex_profile'] == target['expected_updates']['global_profile']
+    assert result['idle_remainder_profile'] == target['expected_updates']['idle_remainder_profile']
+    assert result['actual_73_axis_charts'] == target['expected_updates']['actual_73column_sigmas'] == SIGMAS
+    assert result['controls'] == CONTROLS
+
+    # 3. Independent seed67 owner audit, pinned-engine pricing and PR1069 sweep.
+    subprocess.run([sys.executable, '-I', '-B', str(P/'check.py'), '--main', str(main),
+                    '--replay', str(work/'strict'), '--out', str(work/'CHECK.json')], env=env, check=True)
+    check = json.loads((work/'CHECK.json').read_text())
+    assert Decimal(check['price_new']['kappa_decimal']) == Decimal(result['kappa_decimal']) == Decimal(KAPPA_DECIMAL)
+    assert check['majorization']['candidate_majorizes_selected'] is True
+    assert check['changed_rows'] == mod.CHANGED_ROWS and len(check['relocated_rows']) == mod.RELOCATED_ROWS
+
+    # 4. Proved packing ceiling (PROOF.md): exact integer checks, standard library only.
+    subprocess.run([sys.executable, '-I', '-B', str(P/'ceiling_bound.py'), '--data', str(P/'data'),
+                    '--out', str(work/'CEILING.json')], env=env, check=True)
+    ceiling = json.loads((work/'CEILING.json').read_text())
+    assert ceiling['theorem1']['slack_total'] == 180832 and ceiling['theorem1']['max_empty_cap48'] == 4887
+    assert Decimal(ceiling['theorem3']['bound_decimal']) == Decimal('908139.013')
+    assert ceiling['this_map']['empty_cap48'] == check['candidate']['idle'].get('48', check['candidate']['idle'].get(48))
+    for name, h in pins.items():
+        assert sha(main/name) == h
+    print('PASS_T16_OWNER_MAP', result['kappa_decimal'], result['idle_remainder_profile'],
+          'changed', check['changed_rows'], 'relocated', len(check['relocated_rows']),
+          'ceiling: empty cap-48 <=', ceiling['theorem1']['max_empty_cap48'], 'E <=', ceiling['theorem3']['bound_decimal'])
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--main', type=Path, default=P.parents[1])
+    ap.add_argument('--work', type=Path)
+    args = ap.parse_args()
+    if args.work:
+        args.work.mkdir(parents=True, exist_ok=False)
+        run(args.main.resolve(), args.work.resolve())
+    else:
+        with tempfile.TemporaryDirectory(prefix='two-stage-cycles-') as d:
+            run(args.main.resolve(), Path(d))