research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (κ = 0.0017297760894)

research/rank7-coupled-586-588-carrier-fold/.gitattributes

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+# Keep vendored, data, allocation and evidence bytes exact (the repository default normalizes text).
+* -text

research/rank7-coupled-586-588-carrier-fold/ALLOCATION-PINS.json

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+{
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/FILL.json.gz": "68b8bae90144248774b1920cd27f9519caa3dc427704d8a9da6d4c491d912fc4",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/PROFILE.json": "a815694364065a6d1275c59c17235f4cf400d28d8f7fe3bb3314c57c35dee44c",
+  "allocation/PROVIDERS.json": "52eb0d85caa7b2d4a93acdf5011f52b793f61ddca86235fb03cd9a09397ad4cd",
+  "allocation/SEARCH.json": "aff630fad679c7c5773f16f92dce6234e5b5519626861e9bd83b9884f002066f",
+  "allocation/baseline/CLAIM.json": "656a4c93411b078753783513e2e71b1722a56e7b70120264a38118811982fa77",
+  "allocation/baseline/ORDER.json": "d559a1dcb83707724afc0310f6ef8e3a36ad6cda0a895ca6abae9d6f39a0fc76",
+  "allocation/baseline/PROFILE.json": "6de8ac1fd628cdd2afa5a43872da69c7dab9d7219bdc318f9db55fd8ccdb5eb2",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+}

research/rank7-coupled-586-588-carrier-fold/CLAIM.json

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+{
+  "admitted_package_manifest_sha256": "15a6773d8bc13aa55e7a3b4efb21963fbdd6e23262b3b6376072de8fa3279b50",
+  "baseline_head": "e2ca469b08385d3d5e29a918d66dbefaf889e9f3",
+  "baseline_kappa": "17240352247481048785499999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2969,
+  "baseline_status": "FINITE_NATIVE_OWNER_AND_MOMENT_CANDIDATE_OUTER_PENDING",
+  "calls": 666,
+  "complex_lower": "864888044702560167119/500000000000000000000000",
+  "declared_edits": {
+    "count": 4,
+    "edits_sha256": "47831d52490e3a3b8ed0569ff644582ea23f60e2ef900c2301d04c60bd73f5d4",
+    "lowered_helpers": [
+      586,
+      588
+    ],
+    "previous_kappa": "0.0017290339826465135177169999999999999999999998999999999999999999999999",
+    "previous_pr": 2979
+  },
+  "fill_sha256": "68b8bae90144248774b1920cd27f9519caa3dc427704d8a9da6d4c491d912fc4",
+  "fixed_inventory_cap": {
+    "cap_lower": "17297774946785970118869/10000000000000000000000000",
+    "cap_lower_decimal": "0.0017297774946785970118869",
+    "cap_upper": "1729777494678597011887/1000000000000000000000000",
+    "cap_upper_decimal": "0.0017297774946785970118870",
+    "realized": "below the fractional optimum by the recorded gap (check_cap.py); the cap basis is fractional at T74"
+  },
+  "gain": "717608082126931961/125000000000000000000000",
+  "helpers": 408,
+  "independent_inputs": 632,
+  "kappa": "17297760894051203342379999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017297760894051203342379999999999999999999998999999999999999999999999",
+  "kappa_interval": [
+    "0.0017297760894051203342384",
+    "0.0017297760894051203342385"
+  ],
+  "kappa_lower": "0.0017297760894051203342384",
+  "kappa_upper": "0.0017297760894051203342385",
+  "live_families": 66304,
+  "local_profile": {
+    "1": 2433,
+    "2": 724,
+    "3": 228,
+    "4": 102,
+    "5": 20,
+    "8": 8
+  },
+  "native_receipt_sha256": "165999eb606809540d37a9c30d569e778ee1818d04c10a4b5e5f7e548cc3624a",
+  "physical_families": 66813,
+  "previous_claims": {
+    "pr2942": {
+      "claim_file": "comparators/PR2942-CLAIM.json",
+      "gain": "3479884770953003121/500000000000000000000000",
+      "head": "a027b0f6fdb0ab2b42ba10fc31b53960166bf2bf",
+      "kappa": "17228163198632143279959999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "pr": 2942
+    },
+    "pr2957": {
+      "claim_file": "comparators/PR2957-CLAIM.json",
+      "gain": "6058674334382163267/1000000000000000000000000",
+      "head": "b74b25f3ccc84c16e1a801d73b2f47e5ea764c78",
+      "kappa": "17237174150707381709709999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "pr": 2957
+    },
+    "pr2966": {
+      "claim_file": "comparators/PR2966-CLAIM.json",
+      "gain": "2870908440834078413/500000000000000000000000",
+      "head": "e62d3eb9005117d82a9babcfa937ecc53237c490",
+      "kappa": "17240342725234521774119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "pr": 2966
+    },
+    "pr2969": {
+      "claim_file": "allocation/baseline/CLAIM.json",
+      "gain": "717608082126931961/125000000000000000000000",
+      "head": "e2ca469b08385d3d5e29a918d66dbefaf889e9f3",
+      "kappa": "17240352247481048785499999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "pr": 2969
+    },
+    "pr2979": {
+      "claim_file": "comparators/PR2979-CLAIM.json",
+      "gain": "742106758606816521/1000000000000000000000000",
+      "head": "be191346391661f4d35fc0d1508d0a6029572576",
+      "kappa": "17290339826465135177169999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+      "pr": 2979
+    }
+  },
+  "profile": {
+    "1": 1637692,
+    "2": 482184,
+    "3": 156741,
+    "39": 1,
+    "4": 67932,
+    "48": 28256,
+    "5": 14710,
+    "8": 5328
+  },
+  "release_receipt_sha256": "80b89fbbe1c77154940b81f9202bedccca43a9dda7606c4bfd09cb7e62e63856",
+  "replicas": 74,
+  "scope": "Conditional finite supplier/outer certificate for PR2979s words (mdumitrean: joint rank-7 end frames, five further paired extractions, fourteen PR2957 rewrites) with two declared restore edit blocks (R1_E42, R2_E7) and two coupled B+restore carrier-fold rewrites (B_586_438, B_588_440) lowering entering helpers 586 and 588 from width 7 to width 6, paired with the literal T74 allocation FILL.json.gz (T74_optimal_idle39). Inherited all-size/compiler/theorem hypotheses remain. No selected-frontier change or independent-human-review claim.",
+  "source_manifest_sha256": "fa3e2d855ac5298ecc849e596d79dcef7a72668a276b6524585bc0cd616ce474",
+  "stages": {
+    "stage1": {
+      "frame_edits": 139,
+      "groups": {
+        "A": {
+          "W": [
+            256,
+            128,
+            64,
+            38,
+            20,
+            10,
+            1
+          ],
+          "helpers": [
+            331,
+            450,
+            451,
+            508,
+            509
+          ]
+        },
+        "B": {
+          "W": [
+            256,
+            128,
+            64,
+            34,
+            17,
+            11,
+            4
+          ],
+          "helpers": [
+            299,
+            448,
+            449,
+            484,
+            485
+          ]
+        },
+        "C": {
+          "W": [
+            256,
+            128,
+            64,
+            32,
+            19,
+            11,
+            6
+          ],
+          "helpers": [
+            452,
+            453,
+            532,
+            533
+          ]
+        },
+        "D": {
+          "W": [
+            256,
+            128,
+            64,
+            37,
+            21,
+            8,
+            3
+          ],
+          "helpers": [
+            454,
+            455,
+            556,
+            557
+          ]
+        },
+        "V45": {
+          "W": [
+            256,
+            128,
+            64,
+            35,
+            16,
+            11,
+            5
+          ],
+          "helpers": [
+            249,
+            251,
+            265,
+            267
+          ]
+        }
+      },
+      "kind": "joint codimension-2 end-frame lowering (frame-only)",
+      "record_sha256": "5fbfce004330ebc1fbac8de264614fe295f1a074811b478db4892c3bc3852cd3"
+    },
+    "stage2": {
+      "extractions": [
+        {
+          "helper": 226,
+          "normal": 42,
+          "step": 1
+        },
+        {
+          "helper": 228,
+          "normal": 42,
+          "step": 2
+        },
+        {
+          "helper": 230,
+          "normal": 42,
+          "step": 3
+        },
+        {
+          "helper": 363,
+          "normal": 7,
+          "step": 4
+        },
+        {
+          "helper": 395,
+          "normal": 7,
+          "step": 5
+        }
+      ],
+      "kind": "rank-8 paired input/output extractions"
+    },
+    "stage3": {
+      "applier_sha256": "2509f1335e47543f8814b42d6bf83032b30c5899b4f7cc62a6adc03f5138ae13",
+      "count": 14,
+      "kind": "declared exactness-preserving gate rewrites (Jeremy Kothe, PR2957), re-addressed",
+      "rewrites_sha256": "a37ade675876e4f5b00b33066c84f495fccd264863b7eb5d813837b1d01c3e7d"
+    }
+  },
+  "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+  "width_inventory": {
+    "4": 26,
+    "5": 2,
+    "6": 18,
+    "7": 50,
+    "8": 99,
+    "9": 213
+  },
+  "zero_buffers": 91
+}

research/rank7-coupled-586-588-carrier-fold/CREDITS.md

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+# Credits
+
+- **PR #2908, Jeremy Diviney**: the paired input/output extraction, its compensation rule `C*S`, the exact two-sided certificate (`structure.py`, vendored unchanged) and the closed-adapter admission chain.
+- **PR #2917, Mason Hale**: the nine paired extractions and 82-endpoint words under PR2942, the refit/compose producer model that stage 2 follows, the T74 chronology (ORDER/DISPATCH), the allocation checker, moment auditor, extension stage and adapter derivation reused here.
+- **PR #2957 / #2948 / #2966, Jeremy Kothe (jeremykothe2)**: the fourteen declared exactness-preserving gate rewrites in five classes (R-retime, A3779-cut-start-read, PM-carrier-lender-entry, B-carrier-retime, A-commuting-swap) and their pure applier (`vendor/declared_rewrites.py`, vendored unchanged); stage 3 composes exactly these rewrites onto this package's stage-2 word (`data/REWRITES-2957.json`, re-addressed with exact preimages). PR2966 composed the same rewrites onto our PR2942 words.
+- **PR #2969, Dugongue**: the PR2942 + PR2957 composition at T370 and its cap-level headline nomination, this package's comparator and moment baseline (`allocation/baseline/`). Our stage 3 composes the same fourteen rewrites, here onto the stage-2 word.
+- **PR #2918 (research/helper408-rank7-pairing), RossRichardson**: the fixed-cut rank-seven obstruction for helper408; this package's census of fresh rank-7 extractions reproduces it exactly and is consistent with it.
+- **PR #2894 / #2833, Jeremy Kothe**: the preload re-synthesis supplier, the frame accounting and inverse-reverse cleanup (`vendor/preload_move.py`), the source materializer and the inherited supplier lineage.
+- **PR #2857 / #2848, Yiyang Lu (Lyy-iiis)**: the shared-kernel words, the staged native/overlay tooling and the chronological flow model and realization (edge colouring) used to construct the allocation; PR2843 (Marius-Paul Dumitrean) is that flow model's starting point.
+- **PR #2863 / #2839, Dugongue**: the packing lineage and the PR2839 owner engine.
+- **Tekalign**: the independent owner/chronology checker (`allocation/vendor/independent_owners.py`) and admission tooling.
+- **icekylinx**: the exact free-operator auditor retained as `vendor/audit_local.py` (PR2833).
+- **themilkman216**: the observation that a cap-level allocation of these inventories needs a T whose basic counts are integral, which the allocation's degenerate-face step builds on.
+- **Gareth Davidson (bitplane), PR #1995 / #2013**: the fixed-word terminal-subspace bounds that frame stage 1's scope; earlier rank-seven helper ends on other words are in `research/complex-rank7-end-pair`, `research/k8-rank7-composition` and the PR1090/PR1104 lineage (credited there).
+- **PR #2930 / #2942, Marius-Paul Dumitrean**: the cap allocation of PR2917's words, the four normal-45 extractions under these words, the relaxation tools and the overlay/producer conventions reused here.
+- **PR #2979, Marius-Paul Dumitrean (with substantial AI assistance from Anthropic Claude via Claude Code)**: the codimension-2 census on paired-extraction words, the joint end-frame lowering of 22 restored helpers in five groups (stage 1), the five further extractions it makes profitable (stage 2), the exact composition with PR2957's rewrites (stage 3), the producer and local verification for all three stages, the overlay stage `rank7-joint-endframes` with its rebuild guards, the adapter generalization to six width classes, the literal T74 allocation of the changed inventory, its relaxation certificates and recorded gap, and the complete fresh replay.
+- **PR #3015, Jeremy Kothe (jeremykothe2)**: the declared literal edit stage (`edits/`, `tools/build_edits.py`) with its independent review (`edits/edits_review.py`), and edit R1 on PR #2979's restore section (carrier 61 for register 63).
+- **PR #3042, dcharb78 (with AI assistance)**: the six restore carrier/pivot skips (`R1_E42` at `restore[162:188]`, `26 -> 33` gates skipping `{22, 40, 54, 63}`, and `R2_E7` at `restore[190:203]`, `13 -> 15` gates skipping `{5, 73}`) on PR #2979's words that serve as the direct starting words for `B_586_438` and `B_588_440`.
+- **New here (dcharb78, with AI assistance)**: the two coupled `B` + `restore` dying-helper carrier folds (`B_586_438` and `B_588_440`, `6` hunks / `6 -> 5` gates each) and `helper_final` lowerings on entering helpers `586` ($E_{30} \to V_{30,76,82}$) and `588` ($E_{30} \to V_{30,97,127}$) shifting the helper width inventory from `{4:26, 5:2, 6:16, 7:52, 8:99, 9:213}` to `{4:26, 5:2, 6:18, 7:50, 8:99, 9:213}` (`+665` net profit per helper, `+1,330` joint), the literal `T74_optimal_idle39` allocation (`allocation/FILL.json.gz`), the 21-control per-word edit review (`edits/edits_review.py`) and 100-control four-stage replay (`verify.py`), and the re-derived paid profile, cap certificate (`certificates/RELAX-CAP.json`), and complete fresh-native admission and release receipts. PR #2979 (mdumitrean), PR #3015 (jeremykothe2), and PR #3042 (dcharb78) are credited first.

research/rank7-coupled-586-588-carrier-fold/EDIT-PINS.json

@@ -0,0 +1,7 @@
+{
+  "edits/EDITS.json": "47831d52490e3a3b8ed0569ff644582ea23f60e2ef900c2301d04c60bd73f5d4",
+  "edits/FINAL-WORD-base.json.gz": "300a9b8ad1d554f0e6f84f43f3f5fd870a5b4e5f81ad856900b6e8999684892e",
+  "edits/FINAL-WORD-extra.json.gz": "495d030f1e03b90e954dad3043994f03293d41b9ed220a3beaef849df435d3f0",
+  "edits/declared_edits.py": "4871287e859c6451b53adbd602eb209ad62acc7f3c6eb88106be3010044ef82b",
+  "edits/edits_review.py": "2fca291cc254f61ed3528de2b95e59e54c578d7fbdec0e5c0c330350d4fbda32"
+}