Research: bound joint helper-end and frame contractions of the selected k8 word

research/selected-k8-endpoint-contractions/EXPECTED.json

@@ -0,0 +1,164 @@
+{
+  "a_bracket": [
+    "845099025151/500000000000000",
+    "1690198050303/1000000000000000"
+  ],
+  "attaining_contracted_ends": [
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+    580,
+    581
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+  "bills": {
+    "1690198050303/1000000000000000": [
+      "164831441711219711256809062548369701947902785692060484013862439/57896044618658097711785492504343953926634992332820282019728792003956564819968",
+      "329662883422439422513618125096739403895805571384120968027724915/115792089237316195423570985008687907853269984665640564039457584007913129639936"
+    ],
+    "35491136290869/20000000000000000": [
+      "28366093828269560521727384830766206250226840555885609297121176345453932379/115792089237316195423570985008687907853269984665640564039457584007913129639936",
+      "221610108033355941575995193990360986329897191842856322633759190198858847/904625697166532776746648320380374280103671755200316906558262375061821325312"
+    ],
+    "845099025151/500000000000000": [
+      "-817584525779388915848662239543911811389968483603640981013099/14474011154664524427946373126085988481658748083205070504932198000989141204992",
+      "-6540676206235111326789297916351294491119747868829127848104755/115792089237316195423570985008687907853269984665640564039457584007913129639936"
+    ]
+  },
+  "ceiling_ratio_upper": "563399350101/563351369696",
+  "component_sizes": {
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+    "10": 4,
+    "197": 1,
+    "21": 5,
+    "23": 1,
+    "326": 1,
+    "691": 1,
+    "9": 2,
+    "90": 3
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+  "domain_sizes": {
+    "16": 30,
+    "2": 1144,
+    "5": 613
+  },
+  "duality": {
+    "columns": 23456,
+    "components": 135,
+    "distinct_reduced_vectors": 443,
+    "positive": 8529,
+    "rows": 18033,
+    "zero": 14927
+  },
+  "duals_sha256": "c83cfcd8020913c3d358399ae2bd16fb95e8aaee7c47c4112bc6807653f296d0",
+  "forced_ends": [
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+    275,
+    277,
+    282,
+    289,
+    291,
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+    305,
+    307,
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+    385,
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+    394
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+  "free_ends": [
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+    449,
+    450,
+    451,
+    452,
+    453,
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+    455,
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+    584,
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+    586,
+    587,
+    588,
+    589,
+    590,
+    591
+  ],
+  "free_gates": 1741,
+  "gates": 5413,
+  "graph": {
+    "cone_edges": 106,
+    "cone_helpers": 78,
+    "cones_sha256": "5546e8ad5d979e0eaf618a4adbb333a7ec6b3528ef71bbf659b05ba2e5fc0004",
+    "domains_sha256": "dc1778d2f5e671e7f308b336daa7f45815ea86f081bf52c538212e051ed68e0e",
+    "edge_count": 10328,
+    "edges_sha256": "4f30b8c3c22b7e70bf48ce5398212512081acb7fed4a61ad67873bc032218e62",
+    "node_count": 6941,
+    "nodes_sha256": "a7783e87cfc4705d7c0400612aeb5beaea96f36fad64f27a892c47aef6952233"
+  },
+  "idle_mass": 1650,
+  "kappa_cap": "1690198050303/1001690198050303",
+  "local_mass": 5582,
+  "primal_sha256": "462c3fef57ad4711e7767450c31e3f29d78ada18f54070df436510359386e3de",
+  "profile": {
+    "1": 2400,
+    "2": 446,
+    "3": 416,
+    "4": 142,
+    "5": 82,
+    "8": 8
+  },
+  "restricted_ends": 78,
+  "schema": "selected-k8-endpoint-contraction-bound-v1",
+  "scope": "fixed scalar word and entrances; all nested restricted helper ends and gate frames; full idle charge; no global supplier or new kappa",
+  "status": "PASS_SELECTED_K8_ENDPOINT_CONTRACTION_BOUND",
+  "target_a": "35491136290869/20000000000000000",
+  "word_sha256": "c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8"
+}

research/selected-k8-endpoint-contractions/INPUTS.json

@@ -0,0 +1,14 @@
+{
+  "research/r480-owner-optimum/inputs/local/FULL-WORD.json.gz": "WORD.json.gz",
+  "research/gauge44-slots/construction/slots/SLOT-PINS-k8.json": "SLOT-PINS.json",
+  "research/complex-x4-frame-bound/model.py": "frame_model.py",
+  "research/complex-x4-frame-bound/gen_duals.py": "gen_duals.py",
+  "research/complex-x4-frame-bound/README.md": "FRAME-METHOD.md",
+  "research/complex-local-word-ceiling/ceiling.py": "ceiling.py",
+  "research/complex-local-word-ceiling/README.md": "CEILING.md",
+  "research/gauge44-slots/independent/audit_local.py": "audit_local.py",
+  "research/k8-rank7-composition/data/END-RECIPE.json": "END-RECIPE.json",
+  "research/k8-rank7-composition/construct.py": "construct.py",
+  "research/k8-rank7-composition/README.md": "END-WITNESS.md",
+  "research/selected1042-lineage-resolution98/README.md": "WORD-LINEAGE.md"
+}

research/selected-k8-endpoint-contractions/NOTICE.md

@@ -0,0 +1,40 @@
+# Attribution and license
+
+Prepared by Gareth Davidson (@bitplane), with substantial OpenAI Codex
+assistance in the mathematics, implementation, certificates, checks and
+writing. Apache-2.0. No independent human or proof-assistant review is claimed.
+
+The complete frame-domain and local-polytope method is navinor's retained
+`complex-x4-frame-bound`, following chafreaky/PR557, ntedvs/PR776 and Rohan
+Guliani/PR815. The original model, generator and README are copied unchanged
+under references. This package extends the model with variable nested
+endpoint nodes and excess prices relative to idle work. Nomination code
+adapts navinor's generator, which discloses Claude Code assistance.
+
+The source utilities, dual-checking structure, independent bitset/integer-root
+implementation and controls are adapted from Gareth Davidson's PR1671,
+mathematical commit `11fbeaf34609147c124323c2f5e74fc450dad931`, with disclosed
+OpenAI Codex assistance. They are modified here to reconstruct the changed
+endpoint domain, cone edges, primal attainment and variable-mass cost model.
+The predecessor's fixed-endpoint theorem is not assumed to prove this result.
+The two implementations have the same AI-assisted author and share source
+utilities and candidate certificate data.
+
+Alexander Schwartzman's PR1030 constructs rank-seven helper ends, and
+Cinna Davis (@1337isnot1337) transfers that mechanism to the selected k8 word
+in PR1090. The retained recipe, constructor and README preserve attribution;
+the exact two-end recipe is replayed as a native positive control. Particular
+smaller ends are not claimed as a new mechanism here. Arham Tahir's PR1583
+establishes endpoint rigidity with the gate frames fixed, a different scope.
+
+Douglas Colkitt's PR1240 supplies the retained exact ceiling engine and
+planning model, following Sagar Thakrar's PR1012 coverage law. The selected
+word and hosting line retain Jeremy Kothe, Rohan Arun, Hao Yan/FanPUYen,
+icekylinx and the cumulative geometry, controller, ownership, native compiler,
+bit-supplier and upstream credits in the selected review. The retained local
+auditor credits icekylinx and OpenAI GPT-6 Astra assistance. Woklerx supplied
+the word-lineage reconciliation used to avoid the stale R492 predecessor.
+
+Every references file is an unchanged copy, with exact source SHA256 and
+Git-blob pins in SOURCES.json. Selected records, frozen predecessors,
+upstream source archives and inherited licenses remain unchanged.