Research: four helper placements improve selected T16 kappa

research/complex-t16-vacancy-chain/CANDIDATE.json

@@ -0,0 +1,29 @@
+{
+  "baseline_kappa": "836330098538459/500000000000000000",
+  "expected_updates": {
+    "complex_lower": "1675466538131846067921/1000000000000000000000000",
+    "conservative_complex_lower": "1675466535270375507923/1000000000000000000000000",
+    "kappa": "418166011373521/250000000000000000",
+    "cross_replica_helper_roles": 57481,
+    "idle_remainders": 7524,
+    "idle_remainder_profile": {
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+      "3": 375,
+      "7": 8,
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+    "global_profile": {
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+      "48": 4866
+    },
+    "conservative_kappa_decimal": "0.001672664042642178",
+    "kappa_decimal": "0.001672664045494084"
+  },
+  "gain_percent": "0.0002300776435480056370430715177769732180669752459068794341827305690837412"
+}

research/complex-t16-vacancy-chain/LOCAL-PINS.json

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+{
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+  "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"
+}

research/complex-t16-vacancy-chain/MANIFEST.json

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+{
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+  "SOURCES.json": "4255ca7bf9ef25db0b5d0a4263c2194a79f43757b2b980c45c3bc8748de3041c",
+  "MOVES.json": "be12fa564ea7c3509f13a6e751379436c20c7b9e1bbf15685258001c474a24c6",
+  "VERIFY.json": "4744b59f6ef0f0ab99a3599b6926f1347e46e7b81542b520cfb56d9ed930dc92",
+  "CANDIDATE.json": "c8db55b8ef354b5df17d86f41f80a1fdbf54d70614272e52eb5bc56e1738c53a",
+  "TASK.json": "c8680eebc5c3725b80b721090dce7dee72dedb18c5282df9992e5edd9267d695",
+  "LOCAL-PINS.json": "c9e7ad3818f2a841ea0d224089ca2f975caff2d04cc12b55f072fca88df53140",
+  "README.md": "3f803b76f43fff9a738b6fbf45711b920405182d8de62769478d4d9b0b83aea4",
+  "OVERLAP.json": "ed0552ac37e974e09b96220ed73b21bbf4a89e342c94d6665bdaebd85d7549af",
+  "INPUTS.json": "cb968989e14e85b554c3ccbb3f981eec8c2cb44d4deb9735781c51e7623997cb",
+  "VALIDATION.json": "aa90996c79852512db53a2e1138d37eccf404c012fcf6a6a94cb123575881e42",
+  "verify.py": "ec56bac0d8f2f59338498132fc91db6a216dcda2074c2bcf8bf8d6a81001abf0",
+  "evidence/ASSEMBLY.json": "b0285f3f1744c07ace830600ea0e904043ff8f497720084a9c0826678f9301d3",
+  "evidence/BIT-SUPPLIER-CONTROLS.json": "2cd71c4df0157fc1ce9b2d7c983f9f91308724b307376ad2857223c95b5631c9",
+  "evidence/REPLAY.json": "6b6ef7dfed5e0a2a47a153422e7bcba17d30f9183218f576df694a42acab5047",
+  "evidence/ADMISSION-CONTROLS.json": "4965de78ce4c735c1cf8b193641dd80818edf6f320d1b4720c77d964324e3b79",
+  "evidence/STAGES.json": "c43c03e932611f4885057b7c9f6dc291b1ca8f6d100481a56722d063ae0ad5c7",
+  "data/SPEC.json": "e3868a1fe9740fb4f8557aeaaa4dc00a204078ef183605221b7e21eaf6bc551c",
+  "data/PLAN.json": "954e0df66558321570d9a98e1d47ebbc7540f53cf9522c1fb63b03847fd570bc",
+  "data/OWNERS.json.gz": "76df9a5b1c4f3c1e13a2e3c7946b35499a16307da90513f3a19edc7e6b598f34"
+}

research/complex-t16-vacancy-chain/MOVES.json

@@ -0,0 +1,118 @@
+[
+  {
+    "index": 2010,
+    "before": {
+      "child": 0,
+      "copy": 102,
+      "family": 326,
+      "helper": 90,
+      "offset": 9,
+      "owner_replica": 0,
+      "port": 102,
+      "replica": 0,
+      "stage": 1,
+      "time": 4,
+      "width": 4
+    },
+    "after": {
+      "child": 8,
+      "copy": 1335,
+      "family": 10631,
+      "helper": 90,
+      "offset": 40,
+      "owner_replica": 11,
+      "port": 103,
+      "replica": 0,
+      "stage": 1,
+      "time": 4,
+      "width": 4
+    }
+  },
+  {
+    "index": 4474,
+    "before": {
+      "child": 0,
+      "copy": 246,
+      "family": 2038,
+      "helper": 154,
+      "offset": 9,
+      "owner_replica": 2,
+      "port": 22,
+      "replica": 9,
+      "stage": 1,
+      "time": 9,
+      "width": 4
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+    "after": {
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+      "copy": 1335,
+      "family": 10631,
+      "helper": 154,
+      "offset": 44,
+      "owner_replica": 11,
+      "port": 103,
+      "replica": 9,
+      "stage": 1,
+      "time": 9,
+      "width": 4
+    }
+  },
+  {
+    "index": 34306,
+    "before": {
+      "child": 8,
+      "copy": 1335,
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+      "offset": 40,
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+      "time": 71,
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+      "copy": 198,
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+      "helper": 226,
+      "offset": 25,
+      "owner_replica": 1,
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+      "stage": 1,
+      "time": 71,
+      "width": 7
+    }
+  },
+  {
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+    "before": {
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+      "copy": 198,
+      "family": 1318,
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+      "owner_replica": 1,
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+      "time": 96,
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+      "stage": 6,
+      "time": 96,
+      "width": 7
+    }
+  }
+]

research/complex-t16-vacancy-chain/OVERLAP.json

@@ -0,0 +1,168 @@
+{
+  "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+  "searched_at": "2026-10-14T18:42:15.593356+00:00",
+  "terms": [
+    "vacancy",
+    "H8-H7",
+    "H7-2",
+    "four-helper"
+  ],
+  "coverage": {
+    "open_prs": {
+      "fetched_at": "2026-10-14T18:40:44.452390+00:00",
+      "complete_pagination": true,
+      "records": 347
+    },
+    "discussions": {
+      "fetched_at": "2026-10-14T18:42:15.528286+00:00",
+      "complete_pagination": true,
+      "records": 723
+    }
+  },
+  "local_records": 327,
+  "warnings": [],
+  "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+  "matches_total": 9,
+  "matches": [
+    {
+      "number": 1695,
+      "title": "Claim: Five-helper cyclic basis changes on the R439 D map",
+      "kind": "discussion",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1695",
+      "updated_at": "2026-10-14T08:20:33Z",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "corporated PR967 helper-star word, PR1015/PR923 B blocks, the PR1040 target retune lineage, and the four-helper search in `research/r439-helper-quartets-seed07/`. The fresh overlap helper at 2026-10-14 07:13 UTC covered 385 open PRs and 337 Discussions with complete pagination and returned no match for this exact scope. Nearby open work #1333 (binary affine register theorem) and #1662 (UT4 central tariff) changes the address algebra/object and is not imported. No novelty guarantee is inferred fr"
+    },
+    {
+      "number": 1544,
+      "title": "DONE: exact three-helper / four-target dirty shear costs",
+      "kind": "discussion-comment",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1544#discussioncomment-18917361",
+      "updated_at": "2026-10-14T06:38:26Z",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "**CLAIM** \u2014 four-helper / four-target dirty shear costs (the open next question of PR1557)\n\nQuestion: for every binary 4-by-4 K, does target feedback lower the minimum unit-cost single-source XOR count of the fully restored dirty shear `(h,y) -> (h,y+Kh)` (same model and two alphabets as PR1306/PR1557: eight arbitrary dirty registers, no extra registers)?\nBase / predecessors: main `418e40eb`; PR1306 (@commdata2338) and PR1557 (@bbMisk) model, census and handoff.\nMethod and domain: all 65,536 K a"
+    },
+    {
+      "kind": "local-readme",
+      "title": "research/r439-helper-quartets-seed07/README.md",
+      "path": "research/r439-helper-quartets-seed07/README.md",
+      "sha256": "251ebba7c9c721c36f357a8515533717560c27ac9a7a2dbe653c4ba3eebefe38",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "# A four-helper fusion below the R439 disjoint-pair floor\n\nOne four-helper change reduces the frozen PR941 circuit from **11,949 to\n11,946 complete ADDs**, including preparation and restoration. It crosses\nthe **11,948-ADD disjoint-pair floor** certified by PR941, whose integer dual\ncertificate is replayed here. The new helper graph is a connected four-node\npath, outside that class. No new kappa is claimed.\n\nThis is a small construction and an exact bounded search result. It is not\nthe cheapest "
+    },
+    {
+      "kind": "local-readme",
+      "title": "research/u8-e4-gap-fill/README.md",
+      "path": "research/u8-e4-gap-fill/README.md",
+      "sha256": "cbde1d1483b451437e9a9cefe939cc5263edfc207ba4441564c5310ad45cca8d",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": " construction changes one of the 333 local invocations in PR942's T37\nconstruction. It reverses one four-helper entrance-promotion group, then\nmoves the four enlarged helpers into four existing unit gaps. The nominated\nouter exponent is\n\n\\[\n\\kappa=0.001661961039655941,\n\\]\n\nan increase of `0.000000000491941994` over PR942's\n`0.001661960547713947`. Both figures use the repository's retained conditional\ninteger-multiplication framework, whose running-time claim is\n\\(T(n)=O(n(\\log n)^{1-\\kappa})\\). "
+    },
+    {
+      "kind": "pr",
+      "number": 1183,
+      "title": "Conditional kappa 0.001675603180601302: mixed entrance providers on T37 owners",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1183",
+      "head": "9e7ccda21f28f5dd0397aa04a596e4f0e1d75d1d",
+      "updated_at": "2026-10-14T05:30:16Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "683629385640127295304%** above PR1169's 0.001675568675201533.\n\nIn 23 of 333 calls, three additional four-helper entrance groups (619, 627, 651) use narrower entrance frames. Within-call whole-helper exchanges place the twelve affected roles in twelve distinct one-axis gaps before widening them from four to five axes. The 69 group instances consume 276 actual idle axes. All 159,840 roles remain whole; idle profile is H1=558, H48=11374. Aggregate paid delta is -828 H1 +552 H2 +276 H3 -276 H4. This"
+    },
+    {
+      "kind": "pr",
+      "number": 1192,
+      "title": "Conditional kappa 0.001675670695307702: cross-call T37 entrance augmentation",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1192",
+      "head": "970793428d346b4aa8d8fa2af03aa6dd5ad6f994",
+      "updated_at": "2026-10-14T05:30:37Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "stronger provider now occupies 68 of 333 calls (45 additional calls). Each extra call changes three four-helper entrance groups. Actual source-window-compatible exchanges preserve whole helpers and per-call physical-family uniqueness. The additional 135 group instances consume 540 more unit gaps, leaving idle H1=18, H48=11374. All 159,840 roles remain whole and the deficit is unchanged. Aggregate profile is H1=785598, H2=167466, H3=138012, H4=42474, H5=27306, H8=2664, H48=11374.\n\nVerification pa"
+    },
+    {
+      "kind": "pr",
+      "number": 1218,
+      "title": "Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1218",
+      "head": "0aa147977ad226f9d777d6a21a610ab037985b1e",
+      "updated_at": "2026-10-14T06:10:04Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "2887%** above PR1207's 0.001675807682652000.\n\nThere are 125 base calls and 208 calls with one extra four-helper entrance group. This consumes 16 more unit gaps than PR1207's 68 calls with three added groups. Both final words preserve PR1193's ordered helper widths, common ports and centre frames. Profiles:\n- Base (125 calls): H1=2358, H2=504, H3=410, H4=130, H5=82, H8=8.\n- Extra (208 calls): H1=2350, H2=512, H3=414, H4=126, H5=82, H8=8.\n- Idle: H1=2, H48=11374.\n- Complete: H1=783552, H2=169496, "
+    },
+    {
+      "kind": "pr",
+      "number": 1154,
+      "title": "Conditional kappa = 0.001673260706543984: adaptive joint kernel demotion on PR1117",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1154",
+      "head": "390de2866a03758e7f4ddbb2846e5b2ee4e72154",
+      "updated_at": "2026-10-14T05:29:23Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "ending stock\n\nPR1117 supplies the rank-seven end word and its T16 owner schedule. PR1111 supplies a four-helper entrance-demotion recipe. Applying one fixed provider everywhere ignores the actual pending capacities. This package constructs and checks five joint local prefixes and chooses the prefix separately at every literal call:\n\n1. Groups are ordered **635, 603, 611, 619, 627**. Their helper indices are respectively `(411,413,414,415)`, `(379,381,382,383)`, `(387,389,390,391)`, `(395,397,398"
+    },
+    {
+      "kind": "pr",
+      "number": 1048,
+      "title": "Research: the bit paid profile is the whole bit supplier \u2014 exact pricer, and the reframing class is exhausted at #589 (no \u03ba claim)",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1048",
+      "head": "07730cd8302c378607259a9ad0efb73e0b57a2f2",
+      "updated_at": "2026-10-13T17:18:47Z",
+      "draft": false,
+      "state": "open",
+      "matched_terms": [
+        "four-helper"
+      ],
+      "score": 1,
+      "excerpt": "fferent R439 lineage (post-PR915/PR967), and\n  **#1045** crosses PR941's disjoint-pair floor with a four-helper fusion. Different words, different\n  accounting, different move classes.\n* Those results are cited from their own packages and were **not** re-run here.\n\n## Scope and limits\n\n* Finite, exact audit of two specific words and one move class. Not an optimality theorem over bit\n  words, and **not** an exclusion of three-or-more-move escapes of the plateau.\n* The two-move search is complete "
+    }
+  ],
+  "subsequent_review": {
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2077#issuecomment-6176996271",
+    "reviewer": "philippeVV",
+    "disclosed_ai_assistance": "substantial Claude assistance",
+    "scope": "Reviewer-reported CPython3.12 full strict and registered replay, metadata check, separate seed67 owner audit; no blocking finding",
+    "same_supplier_predecessor": {
+      "pr": 1407,
+      "kappa": "0.001672680818492982",
+      "overlapping_rows": [
+        2010,
+        34306
+      ],
+      "composition": "not valid as written; needs a new combined assignment and complete replay",
+      "head": "d8640f5b7ae99b43f5d56146cb94ca62b8b3835d",
+      "package": "research/astra-ultra-hosting-20261013",
+      "owners_sha256": "28bc3da38d97d0cc87ec2526c8163943fc3c0929352a06c407ad5d7232962e72",
+      "owners_git_blob": "814d8e8e2d7240d4131748853138c2a80eb10ee0"
+    }
+  }
+}