From e9f3375fc06f639285f4fbca44c3280831f84318 Mon Sep 17 00:00:00 2001
From: Ali Romman <226877337+aliromman@users.noreply.github.com>
Date: Sun, 25 Oct 2026 23:15:03 -0500
Subject: [PATCH] Complete G20 refinement caller and strict ordinary admission

---
 .../g20-refinement-admission/.gitattributes   |     3 +
 research/g20-refinement-admission/CALLS.json  |  1118 +
 .../GLOBAL-RESULT.json                        | 11598 +++
 .../g20-refinement-admission/GLOBAL.jsonl.gz  |   Bin 0 -> 2334621 bytes
 .../INDEPENDENT-RESULT.json                   |    22 +
 research/g20-refinement-admission/INPUTS.json |   233 +
 .../g20-refinement-admission/INVOICE.json     |    36 +
 .../LOCAL-RESULT.json                         |   215 +
 .../g20-refinement-admission/MATCHER.json     |   178 +
 research/g20-refinement-admission/NOTICE.md   |     7 +
 .../ORDINARY-RESULT.json                      |   333 +
 .../PRIVATE-EPISODES.json                     | 15869 +++
 research/g20-refinement-admission/PROOF.md    |   167 +
 research/g20-refinement-admission/README.md   |    42 +
 .../SOURCE-DESCRIPTORS.json.gz                |   Bin 0 -> 5160023 bytes
 .../g20-refinement-admission/SOURCES.json     |   249 +
 .../TARGET-OWNERS.json                        | 81716 +++++++++++++++
 research/g20-refinement-admission/TASK.json   |    96 +
 research/g20-refinement-admission/VERIFY.json |    34 +
 .../g20-refinement-admission/WORD.json.gz     |   Bin 0 -> 59558 bytes
 .../audited/NOTICE.md                         |     7 +
 .../g20-refinement-admission/audited/PROOF.md |    87 +
 .../audited/RESULT.json                       |   669 +
 .../audited/WORD.json.gz                      |   Bin 0 -> 59558 bytes
 .../global_retirement.py                      |   112 +
 .../g20-refinement-admission/independent.py   |   165 +
 .../g20-refinement-admission/integration.py   |    83 +
 research/g20-refinement-admission/native.py   |    50 +
 research/g20-refinement-admission/ordinary.py |    73 +
 .../predecessor/ORDINARY-RESULT.json          |   173 +
 .../predecessor/PROOF.md                      |   195 +
 .../predecessor/global_retirement.py          |   111 +
 .../predecessor/independent.py                |   166 +
 .../predecessor/native.py                     |    49 +
 .../predecessor/ordinary.py                   |    61 +
 .../source/GLOBAL-RESULT.json                 | 11571 +++
 .../source/INVOICE.json                       |    37 +
 .../g20-refinement-admission/source/NOTICE.md |    16 +
 .../source/ORDINARY-RESULT.json               |   169 +
 .../g20-refinement-admission/source/PROOF.md  |   278 +
 .../source/RECORD.json                        |    20 +
 .../source/WORD.json.gz                       |   Bin 0 -> 69585 bytes
 .../source/global_relations.py                |   104 +
 .../source/local_relations.py                 |   118 +
 .../source/ordinary.py                        |    57 +
 .../source/retirement-ordinary.json           |   173 +
 .../source/retirement-proof.md                |   199 +
 .../vendor/g20/inputs/BASELINE-LOCAL.json.gz  |   Bin 0 -> 62568 bytes
 .../source/vendor/g20/inputs/CONTROLLER.json  |  2175 +
 .../source/vendor/g20/inputs/FRAMES.json      | 56126 +++++++++++
 .../inputs/credited_intervals.py              |   421 +
 .../inputs/separate_series.py                 |    32 +
 .../vendor/g20/provider/build_global.py       |   125 +
 .../vendor/g20/provider/data/CALLS.json       |   488 +
 .../vendor/g20/provider/data/INVERSE.json.gz  |   Bin 0 -> 59078 bytes
 .../vendor/g20/provider/data/INVOICE.json     |    38 +
 .../g20/provider/data/TARGET-OWNERS.json      | 83354 ++++++++++++++++
 .../source/vendor/g20/provider/local_ir.py    |   130 +
 .../strict_margins.py                         |    51 +
 research/g20-refinement-admission/verify.py   |    50 +
 60 files changed, 269649 insertions(+)
 create mode 100644 research/g20-refinement-admission/.gitattributes
 create mode 100644 research/g20-refinement-admission/CALLS.json
 create mode 100644 research/g20-refinement-admission/GLOBAL-RESULT.json
 create mode 100644 research/g20-refinement-admission/GLOBAL.jsonl.gz
 create mode 100644 research/g20-refinement-admission/INDEPENDENT-RESULT.json
 create mode 100644 research/g20-refinement-admission/INPUTS.json
 create mode 100644 research/g20-refinement-admission/INVOICE.json
 create mode 100644 research/g20-refinement-admission/LOCAL-RESULT.json
 create mode 100644 research/g20-refinement-admission/MATCHER.json
 create mode 100644 research/g20-refinement-admission/NOTICE.md
 create mode 100644 research/g20-refinement-admission/ORDINARY-RESULT.json
 create mode 100644 research/g20-refinement-admission/PRIVATE-EPISODES.json
 create mode 100644 research/g20-refinement-admission/PROOF.md
 create mode 100644 research/g20-refinement-admission/README.md
 create mode 100644 research/g20-refinement-admission/SOURCE-DESCRIPTORS.json.gz
 create mode 100644 research/g20-refinement-admission/SOURCES.json
 create mode 100644 research/g20-refinement-admission/TARGET-OWNERS.json
 create mode 100644 research/g20-refinement-admission/TASK.json
 create mode 100644 research/g20-refinement-admission/VERIFY.json
 create mode 100644 research/g20-refinement-admission/WORD.json.gz
 create mode 100644 research/g20-refinement-admission/audited/NOTICE.md
 create mode 100644 research/g20-refinement-admission/audited/PROOF.md
 create mode 100644 research/g20-refinement-admission/audited/RESULT.json
 create mode 100644 research/g20-refinement-admission/audited/WORD.json.gz
 create mode 100644 research/g20-refinement-admission/global_retirement.py
 create mode 100644 research/g20-refinement-admission/independent.py
 create mode 100644 research/g20-refinement-admission/integration.py
 create mode 100644 research/g20-refinement-admission/native.py
 create mode 100644 research/g20-refinement-admission/ordinary.py
 create mode 100644 research/g20-refinement-admission/predecessor/ORDINARY-RESULT.json
 create mode 100644 research/g20-refinement-admission/predecessor/PROOF.md
 create mode 100644 research/g20-refinement-admission/predecessor/global_retirement.py
 create mode 100644 research/g20-refinement-admission/predecessor/independent.py
 create mode 100644 research/g20-refinement-admission/predecessor/native.py
 create mode 100644 research/g20-refinement-admission/predecessor/ordinary.py
 create mode 100644 research/g20-refinement-admission/source/GLOBAL-RESULT.json
 create mode 100644 research/g20-refinement-admission/source/INVOICE.json
 create mode 100644 research/g20-refinement-admission/source/NOTICE.md
 create mode 100644 research/g20-refinement-admission/source/ORDINARY-RESULT.json
 create mode 100644 research/g20-refinement-admission/source/PROOF.md
 create mode 100644 research/g20-refinement-admission/source/RECORD.json
 create mode 100644 research/g20-refinement-admission/source/WORD.json.gz
 create mode 100644 research/g20-refinement-admission/source/global_relations.py
 create mode 100644 research/g20-refinement-admission/source/local_relations.py
 create mode 100644 research/g20-refinement-admission/source/ordinary.py
 create mode 100644 research/g20-refinement-admission/source/retirement-ordinary.json
 create mode 100644 research/g20-refinement-admission/source/retirement-proof.md
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/inputs/BASELINE-LOCAL.json.gz
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/inputs/CONTROLLER.json
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/inputs/FRAMES.json
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/separate_series.py
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/build_global.py
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/data/CALLS.json
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/data/INVERSE.json.gz
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/data/INVOICE.json
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/data/TARGET-OWNERS.json
 create mode 100644 research/g20-refinement-admission/source/vendor/g20/provider/local_ir.py
 create mode 100644 research/g20-refinement-admission/strict_margins.py
 create mode 100644 research/g20-refinement-admission/verify.py

diff --git a/research/g20-refinement-admission/.gitattributes b/research/g20-refinement-admission/.gitattributes
new file mode 100644
index 0000000000..170828a44f
--- /dev/null
+++ b/research/g20-refinement-admission/.gitattributes
@@ -0,0 +1,3 @@
+source/** -text
+predecessor/** -text
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diff --git a/research/g20-refinement-admission/CALLS.json b/research/g20-refinement-admission/CALLS.json
new file mode 100644
index 0000000000..7022c43cb5
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diff --git a/research/g20-refinement-admission/GLOBAL-RESULT.json b/research/g20-refinement-admission/GLOBAL-RESULT.json
new file mode 100644
index 0000000000..8a982c8070
--- /dev/null
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diff --git a/research/g20-refinement-admission/INDEPENDENT-RESULT.json b/research/g20-refinement-admission/INDEPENDENT-RESULT.json
new file mode 100644
index 0000000000..1c2d43f4cd
--- /dev/null
+++ b/research/g20-refinement-admission/INDEPENDENT-RESULT.json
@@ -0,0 +1,22 @@
+{
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+  "adjoint_moduli": [
+    101,
+    10201
+  ],
+  "global": {
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+    "queries": 56547,
+    "originals": 11166,
+    "owned": 39,
+    "majorant_bits": 516
+  },
+  "ordinary": {
+    "admitted": "3497804579519/1000000000000000",
+    "H0": 746342786958770177,
+    "H1": 522112243625460240068436505540,
+    "positive_base_fee": 958360084023,
+    "matcher_coefficient_terms": 5472
+  },
+  "stale_query_epoch_rejected": true
+}
diff --git a/research/g20-refinement-admission/INPUTS.json b/research/g20-refinement-admission/INPUTS.json
new file mode 100644
index 0000000000..27f7825661
--- /dev/null
+++ b/research/g20-refinement-admission/INPUTS.json
@@ -0,0 +1,233 @@
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+    "sha256": "d4f7e1b3e85fb106b19aa74bdba3c214512835733cfac4e516fc396647032032"
+  },
+  {
+    "local": "predecessor/native.py",
+    "path": "research/g20-complete-fusion/native.py",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "caed1cf99bbd408882a0a274faa901de23141059",
+    "sha256": "bc2ce3b815f889f4bc5889753c63134df65938092d99ac6ac8891943dd528192"
+  },
+  {
+    "local": "predecessor/global_retirement.py",
+    "path": "research/g20-complete-fusion/global_retirement.py",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "ec0194d8c0c2c6cc9ceaab698703103da7f64422",
+    "sha256": "dd78a8b44230411c9b537043c307d73cbb2475ad2ee285cfbd93420a6f521f86"
+  },
+  {
+    "local": "predecessor/ordinary.py",
+    "path": "research/g20-complete-fusion/ordinary.py",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "d34b178ce40101f8df0cf10b7b6a7cfff317f561",
+    "sha256": "59d97ba58776d34fc99a68ecf115348f1e6c7fa919f30cd66e6fafea5ba14e09"
+  },
+  {
+    "local": "predecessor/independent.py",
+    "path": "research/g20-complete-fusion/independent.py",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "16a5e1045b128e5e0b3fa77f4dcb7f3a8d6a953c",
+    "sha256": "5664552928650c07307bd8ddb6ec680f23aad13a94cbcc1bd694be35be40bad6"
+  },
+  {
+    "local": "predecessor/PROOF.md",
+    "path": "research/g20-complete-fusion/PROOF.md",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "a5fa7ef7767c5adb7d93dda1cefd7e26477f1c03",
+    "sha256": "5596cf23df5e72db86a7132ae77a624b548c09ac66240d1b15274af52058a63b"
+  },
+  {
+    "local": "predecessor/ORDINARY-RESULT.json",
+    "path": "research/g20-complete-fusion/ORDINARY-RESULT.json",
+    "commit": "b13c9ae8a539c05f0f590ce9d08c7067d99c6145",
+    "git_blob": "4c67e394854a38d9c31038242aefa7f107bde015",
+    "sha256": "318c134c080535b101747e78aeea2a252706d6893bf908ec6897d36c419043b6"
+  },
+  {
+    "local": "audited/WORD.json.gz",
+    "path": "research/g20-source-refinement-audit/WORD.json.gz",
+    "commit": "e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029",
+    "git_blob": "976059558e4e4881decab75d8af41bee7be1ad93",
+    "sha256": "647d944a94a744b20a68a07180415caf3a8a130111f5907d40d7f617f1b60eef"
+  },
+  {
+    "local": "audited/RESULT.json",
+    "path": "research/g20-source-refinement-audit/RESULT.json",
+    "commit": "e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029",
+    "git_blob": "9a4d76fc360e017eaa6818406cd27e5dd2b8ed18",
+    "sha256": "c430315b504989d809e68ff06209b0132f04b2c25a34d0227d0916a997815a4f"
+  },
+  {
+    "local": "audited/PROOF.md",
+    "path": "research/g20-source-refinement-audit/PROOF.md",
+    "commit": "e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029",
+    "git_blob": "7cc51a4c06eb07d33278e72a56d03d536968734d",
+    "sha256": "f6898eb40392c781f459fe92fc3bdb7eecf6e99dd2c3c06cedb7eb85a018dff6"
+  },
+  {
+    "local": "audited/NOTICE.md",
+    "path": "research/g20-source-refinement-audit/NOTICE.md",
+    "commit": "e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029",
+    "git_blob": "bb47b1a5186a874dfe1dd26777045dacc98c2e18",
+    "sha256": "27b08948da2fcc5eb828fb9c1e7e0751451e6ff925cfb8ecb9357596ad3b15e9"
+  }
+]
diff --git a/research/g20-refinement-admission/INVOICE.json b/research/g20-refinement-admission/INVOICE.json
new file mode 100644
index 0000000000..a1394e427d
--- /dev/null
+++ b/research/g20-refinement-admission/INVOICE.json
@@ -0,0 +1,36 @@
+{
+  "paid": {
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+    "2": 24156,
+    "3": 1008,
+    "4": 1026,
+    "5": 1836,
+    "6": 180,
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+    "35": 444,
+    "42": 444,
+    "49": 444,
+    "56": 444,
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+  },
+  "targets": {
+    "8": 7614,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
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+    "50": 444,
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+    "127": 222
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+  "originals": 11166,
+  "owned_allocated": 39,
+  "owned_output_credit": 0,
+  "QUERYs": 56547,
+  "rank_surplus": 753
+}
diff --git a/research/g20-refinement-admission/LOCAL-RESULT.json b/research/g20-refinement-admission/LOCAL-RESULT.json
new file mode 100644
index 0000000000..00ec653b96
--- /dev/null
+++ b/research/g20-refinement-admission/LOCAL-RESULT.json
@@ -0,0 +1,215 @@
+{
+  "status": "PASS_G20_REFINEMENT_NATIVE_ALL684_COLUMNS",
+  "stats": {
+    "paid": {
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+      "ADD": 19043,
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+      "ZERO_Q": 9,
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+    },
+    "owned_allocated": 39,
+    "owned_live_payload_peak": 39,
+    "retained_originals": 645,
+    "positive_majorant_bits": 29,
+    "positive_majorant": "528220782",
+    "native_modulus": null
+  },
+  "native_moduli": [
+    101,
+    10201
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+  "matcher": {
+    "common_denominator": 4,
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+        "0",
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+        "0",
+        "0",
+        "1/2",
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+    "inverse_norm": "2",
+    "max_numerator_bits": 2,
+    "nonzero_coefficients": 38,
+    "physical_tape_price_supplied": false,
+    "rank": 4,
+    "local_occurrences": 4,
+    "global_occurrences": 72,
+    "paired_address_coefficient_terms_per_call": 76,
+    "pricing": "Both directions and both paired address halves are charged inside the complete positive normalizer fee."
+  },
+  "rejected_controls": [
+    "missing_snapshot_clear",
+    "missing_refined_query",
+    "missing_snapshot_return"
+  ],
+  "canonical_word_sha256": "38a15395e7be9b2062e604428e1de5dd2c871cb277a527faf061c2692005a861"
+}
diff --git a/research/g20-refinement-admission/MATCHER.json b/research/g20-refinement-admission/MATCHER.json
new file mode 100644
index 0000000000..184e860744
--- /dev/null
+++ b/research/g20-refinement-admission/MATCHER.json
@@ -0,0 +1,178 @@
+{
+  "common_denominator": 4,
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+    [
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+  "max_numerator_bits": 2,
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+  "physical_tape_price_supplied": false,
+  "rank": 4,
+  "local_occurrences": 4,
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+  "pricing": "Both directions and both paired address halves are charged inside the complete positive normalizer fee."
+}
diff --git a/research/g20-refinement-admission/NOTICE.md b/research/g20-refinement-admission/NOTICE.md
new file mode 100644
index 0000000000..54c595408b
--- /dev/null
+++ b/research/g20-refinement-admission/NOTICE.md
@@ -0,0 +1,7 @@
+# Attribution
+
+Dugongue PR5657 supplies the protected-reader and paid SOURCE-refinement construction. Ali Romman PR5662 supplies the source-window audit, literal word and new residual matcher. The full caller and ordinary engines are adapted from Ali Romman PR5653 and retain ai-nanachi PR5512, Ali Romman PR5421/5641/5647/5648 and Dugongue PR5629/5639.
+
+Retain DreamingOfClouds, eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman and all native, ROW, controller, compiler, stock, precision, tape and analytic notices. The exact older source/NOTICE.md, predecessor scripts and audited/NOTICE.md remain unchanged. INPUTS.json binds every consumed file to its commit and hash.
+
+New integration, strict-margin functions and author verification: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. Separate retained implementations do not constitute independent human scientific acceptance.
diff --git a/research/g20-refinement-admission/ORDINARY-RESULT.json b/research/g20-refinement-admission/ORDINARY-RESULT.json
new file mode 100644
index 0000000000..ede2125c41
--- /dev/null
+++ b/research/g20-refinement-admission/ORDINARY-RESULT.json
@@ -0,0 +1,333 @@
+{
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+    "owned_allocated": 39,
+    "owned_output_credit": 0,
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+    "rank_surplus": 753
+  },
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+        "86371620116401602818371223060121/5000000000000000000000000000000000000000"
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+    "upper": {
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+        "-20467149167474048603388446754687/5000000000000000000000000000000000000000"
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+    {
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+    {
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+      "admitted": "3497804579519/1000000000000000"
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+  "admitted": "3497804579519/1000000000000000",
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+  "fee_bounds": {
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+    "fixed_tensor_unit": {
+      "v": 2048,
+      "K": "2^524288",
+      "meaning": "Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting."
+    },
+    "finite_compiler": {
+      "N": "2^522112243625460240068436505540",
+      "J(n)": "(n+1)^4*K^(4*n+4)",
+      "A(1)": "K^4",
+      "A(n)": "(J(n)+2)^4*(A(n-1)+2)^(4*n+8)",
+      "counts": "Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets39distinct owned banks; C_N<=39*A(N). Denominator replication product <=A(n-1)^(n-1)."
+    },
+    "height_prime": {
+      "base_height_bits": 1024,
+      "T": "(2*N+2)^4*(A(N)+2)^2",
+      "H": "1026*4^(T+1)",
+      "q": "Choose odd prime q>max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice."
+    },
+    "all_in_fixed_primitive_fee": {
+      "F": "39*(q+2)^(32*(N+1)^2)*(A(N)+2)^8",
+      "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.",
+      "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=39*A(N); F dominates their products.",
+      "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument."
+    },
+    "stock": {
+      "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend",
+      "D": "floor(log_N ceil(e/w))+1",
+      "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)",
+      "ownership": "All39whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed."
+    },
+    "eventual_threshold": {
+      "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.",
+      "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0",
+      "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).",
+      "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized."
+    }
+  },
+  "strict_margin_range": {
+    "C_min": "3488579527/1000000000000",
+    "C_max": "7/2000",
+    "gamma_upper_bound": [
+      "6025568896714756734468836454965751300051243342029676225321/6277101735386680763835789423207666416102355444464034512896",
+      "6025568896714756734468836454965751300051243342029676585589/6277101735386680763835789423207666416102355444464034512896"
+    ],
+    "delta_upper_bound": [
+      "1468586668696254738094063705789482730484248156263639265257/1569275433846670190958947355801916604025588861116008628224",
+      "91786666793515921130878981611842670655265509766477457219/98079714615416886934934209737619787751599303819750539264"
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+      0
+    ],
+    "tensor_reserve_controls": {
+      "8": 1024,
+      "39": 1024,
+      "48": 2048,
+      "96": 4096,
+      "192": 8192,
+      "384": 16384
+    },
+    "claim": "Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim."
+  },
+  "whole_kappa": null,
+  "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed."
+}
diff --git a/research/g20-refinement-admission/PRIVATE-EPISODES.json b/research/g20-refinement-admission/PRIVATE-EPISODES.json
new file mode 100644
index 0000000000..985e974d9c
--- /dev/null
+++ b/research/g20-refinement-admission/PRIVATE-EPISODES.json
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+    "kind": "THIN",
+    "begin": 379700,
+    "end": 379703
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379704,
+    "end": 379707
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379708,
+    "end": 379711
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379712,
+    "end": 379715
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
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+    "end": 379719
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
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+    "end": 379723
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379724,
+    "end": 379727
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
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+    "end": 379731
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
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+    "end": 379735
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379736,
+    "end": 379739
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379740,
+    "end": 379743
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379744,
+    "end": 379747
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379748,
+    "end": 379751
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379752,
+    "end": 379755
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379756,
+    "end": 379759
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379760,
+    "end": 379763
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379764,
+    "end": 379767
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379768,
+    "end": 379771
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379772,
+    "end": 379775
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379776,
+    "end": 379779
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379780,
+    "end": 379783
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379784,
+    "end": 379787
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379788,
+    "end": 379791
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379792,
+    "end": 379795
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379796,
+    "end": 379799
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379800,
+    "end": 379803
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
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+    "end": 379807
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379808,
+    "end": 379811
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379812,
+    "end": 379815
+  },
+  {
+    "owner": 11166,
+    "stage": 30,
+    "kind": "THIN",
+    "begin": 379816,
+    "end": 379819
+  },
+  {
+    "owner": 11171,
+    "stage": 31,
+    "begin": 395218,
+    "end": 395920
+  },
+  {
+    "owner": 11181,
+    "stage": 31,
+    "begin": 395237,
+    "end": 395929
+  },
+  {
+    "owner": 11203,
+    "stage": 31,
+    "begin": 395226,
+    "end": 395933
+  },
+  {
+    "owner": 11187,
+    "stage": 31,
+    "begin": 395233,
+    "end": 395937
+  },
+  {
+    "owner": 11166,
+    "stage": 31,
+    "begin": 395221,
+    "end": 395941
+  },
+  {
+    "owner": 11201,
+    "stage": 31,
+    "begin": 395325,
+    "end": 395948
+  },
+  {
+    "owner": 11199,
+    "stage": 31,
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+    "end": 395951
+  },
+  {
+    "owner": 11170,
+    "stage": 31,
+    "begin": 395298,
+    "end": 395953
+  },
+  {
+    "owner": 11182,
+    "stage": 31,
+    "begin": 395349,
+    "end": 395962
+  },
+  {
+    "owner": 11186,
+    "stage": 31,
+    "begin": 395345,
+    "end": 395967
+  },
+  {
+    "owner": 11185,
+    "stage": 31,
+    "begin": 395354,
+    "end": 395972
+  },
+  {
+    "owner": 11197,
+    "stage": 31,
+    "begin": 395460,
+    "end": 395988
+  },
+  {
+    "owner": 11184,
+    "stage": 31,
+    "begin": 395444,
+    "end": 395991
+  },
+  {
+    "owner": 11195,
+    "stage": 31,
+    "begin": 395449,
+    "end": 395994
+  },
+  {
+    "owner": 11188,
+    "stage": 31,
+    "begin": 395467,
+    "end": 395999
+  },
+  {
+    "owner": 11168,
+    "stage": 31,
+    "begin": 395487,
+    "end": 396009
+  },
+  {
+    "owner": 11169,
+    "stage": 31,
+    "begin": 395520,
+    "end": 396014
+  },
+  {
+    "owner": 11189,
+    "stage": 31,
+    "begin": 395502,
+    "end": 396029
+  },
+  {
+    "owner": 11191,
+    "stage": 31,
+    "begin": 395509,
+    "end": 396032
+  },
+  {
+    "owner": 11193,
+    "stage": 31,
+    "begin": 395492,
+    "end": 396036
+  },
+  {
+    "owner": 11183,
+    "stage": 31,
+    "begin": 395516,
+    "end": 396039
+  },
+  {
+    "owner": 11204,
+    "stage": 31,
+    "begin": 395229,
+    "end": 398537
+  },
+  {
+    "owner": 11202,
+    "stage": 31,
+    "begin": 395328,
+    "end": 398689
+  },
+  {
+    "owner": 11200,
+    "stage": 31,
+    "begin": 395339,
+    "end": 398694
+  },
+  {
+    "owner": 11196,
+    "stage": 31,
+    "begin": 395452,
+    "end": 398868
+  },
+  {
+    "owner": 11198,
+    "stage": 31,
+    "begin": 395463,
+    "end": 398884
+  },
+  {
+    "owner": 11194,
+    "stage": 31,
+    "begin": 395495,
+    "end": 398975
+  },
+  {
+    "owner": 11192,
+    "stage": 31,
+    "begin": 395512,
+    "end": 398980
+  },
+  {
+    "owner": 11190,
+    "stage": 31,
+    "begin": 395505,
+    "end": 398995
+  },
+  {
+    "owner": 11167,
+    "stage": 31,
+    "begin": 395456,
+    "end": 399031
+  },
+  {
+    "owner": 11172,
+    "stage": 31,
+    "begin": 380270,
+    "end": 402250
+  },
+  {
+    "owner": 11173,
+    "stage": 31,
+    "begin": 380327,
+    "end": 402251
+  },
+  {
+    "owner": 11174,
+    "stage": 31,
+    "begin": 380388,
+    "end": 402252
+  },
+  {
+    "owner": 11175,
+    "stage": 31,
+    "begin": 380447,
+    "end": 402253
+  },
+  {
+    "owner": 11176,
+    "stage": 31,
+    "begin": 380506,
+    "end": 402254
+  },
+  {
+    "owner": 11177,
+    "stage": 31,
+    "begin": 380566,
+    "end": 402255
+  },
+  {
+    "owner": 11178,
+    "stage": 31,
+    "begin": 380625,
+    "end": 402256
+  },
+  {
+    "owner": 11179,
+    "stage": 31,
+    "begin": 380685,
+    "end": 402257
+  },
+  {
+    "owner": 11180,
+    "stage": 31,
+    "begin": 380742,
+    "end": 402258
+  },
+  {
+    "owner": 11171,
+    "stage": 32,
+    "begin": 417657,
+    "end": 418359
+  },
+  {
+    "owner": 11181,
+    "stage": 32,
+    "begin": 417676,
+    "end": 418368
+  },
+  {
+    "owner": 11203,
+    "stage": 32,
+    "begin": 417665,
+    "end": 418372
+  },
+  {
+    "owner": 11187,
+    "stage": 32,
+    "begin": 417672,
+    "end": 418376
+  },
+  {
+    "owner": 11166,
+    "stage": 32,
+    "begin": 417660,
+    "end": 418380
+  },
+  {
+    "owner": 11201,
+    "stage": 32,
+    "begin": 417764,
+    "end": 418387
+  },
+  {
+    "owner": 11199,
+    "stage": 32,
+    "begin": 417775,
+    "end": 418390
+  },
+  {
+    "owner": 11170,
+    "stage": 32,
+    "begin": 417737,
+    "end": 418392
+  },
+  {
+    "owner": 11182,
+    "stage": 32,
+    "begin": 417788,
+    "end": 418401
+  },
+  {
+    "owner": 11186,
+    "stage": 32,
+    "begin": 417784,
+    "end": 418406
+  },
+  {
+    "owner": 11185,
+    "stage": 32,
+    "begin": 417793,
+    "end": 418411
+  },
+  {
+    "owner": 11197,
+    "stage": 32,
+    "begin": 417899,
+    "end": 418427
+  },
+  {
+    "owner": 11184,
+    "stage": 32,
+    "begin": 417883,
+    "end": 418430
+  },
+  {
+    "owner": 11195,
+    "stage": 32,
+    "begin": 417888,
+    "end": 418433
+  },
+  {
+    "owner": 11188,
+    "stage": 32,
+    "begin": 417906,
+    "end": 418438
+  },
+  {
+    "owner": 11168,
+    "stage": 32,
+    "begin": 417926,
+    "end": 418448
+  },
+  {
+    "owner": 11169,
+    "stage": 32,
+    "begin": 417959,
+    "end": 418453
+  },
+  {
+    "owner": 11189,
+    "stage": 32,
+    "begin": 417941,
+    "end": 418468
+  },
+  {
+    "owner": 11191,
+    "stage": 32,
+    "begin": 417948,
+    "end": 418471
+  },
+  {
+    "owner": 11193,
+    "stage": 32,
+    "begin": 417931,
+    "end": 418475
+  },
+  {
+    "owner": 11183,
+    "stage": 32,
+    "begin": 417955,
+    "end": 418478
+  },
+  {
+    "owner": 11204,
+    "stage": 32,
+    "begin": 417668,
+    "end": 420976
+  },
+  {
+    "owner": 11202,
+    "stage": 32,
+    "begin": 417767,
+    "end": 421128
+  },
+  {
+    "owner": 11200,
+    "stage": 32,
+    "begin": 417778,
+    "end": 421133
+  },
+  {
+    "owner": 11196,
+    "stage": 32,
+    "begin": 417891,
+    "end": 421307
+  },
+  {
+    "owner": 11198,
+    "stage": 32,
+    "begin": 417902,
+    "end": 421323
+  },
+  {
+    "owner": 11194,
+    "stage": 32,
+    "begin": 417934,
+    "end": 421414
+  },
+  {
+    "owner": 11192,
+    "stage": 32,
+    "begin": 417951,
+    "end": 421419
+  },
+  {
+    "owner": 11190,
+    "stage": 32,
+    "begin": 417944,
+    "end": 421434
+  },
+  {
+    "owner": 11167,
+    "stage": 32,
+    "begin": 417895,
+    "end": 421470
+  },
+  {
+    "owner": 11172,
+    "stage": 32,
+    "begin": 402709,
+    "end": 424689
+  },
+  {
+    "owner": 11173,
+    "stage": 32,
+    "begin": 402766,
+    "end": 424690
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+  {
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+    "end": 424691
+  },
+  {
+    "owner": 11175,
+    "stage": 32,
+    "begin": 402886,
+    "end": 424692
+  },
+  {
+    "owner": 11176,
+    "stage": 32,
+    "begin": 402945,
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+  {
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+  {
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+    "stage": 32,
+    "begin": 403064,
+    "end": 424695
+  },
+  {
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+    "begin": 403124,
+    "end": 424696
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+  {
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+  }
+]
diff --git a/research/g20-refinement-admission/PROOF.md b/research/g20-refinement-admission/PROOF.md
new file mode 100644
index 0000000000..dd110d2e48
--- /dev/null
+++ b/research/g20-refinement-admission/PROOF.md
@@ -0,0 +1,167 @@
+# Complete caller, finite admission and strict-margin theorem
+
+## 1. Construction and exact source boundary
+
+Use the literal word from PR5662 at `e0f9b0bbcb14f3cbc47433c7f7770a9aaa35b029`. Its bytes are retained as both `audited/WORD.json.gz` and the published `WORD.json.gz`. The source proof is Dugongue PR5657 at `2f091bc3b656ed85d26cf44b7fc84c28fb510273`. Its fourteen windows not already in the completed PR5653 baseline add six protected-reader fusions and eight paid SOURCE refinements. Helper 444 and the earlier retirements and snapshots remain credited predecessor work.
+
+The local word has 645 independent original fields and 39 owned fields. All 684 entry columns are included, with arbitrary initial owned values. Every ADD has distinct operands at the same actual frame. Each query is checked at its current frame and actual residual rank. Only whole zero owned fields receive a free frame change. Every owned field is zero on return.
+
+The new local paid inventory is `{1:1288,2:1342,3:56,4:57,5:102,6:10,7:9}`. Exact native replay uses the retained geometric implementation, with two odd address moduli. The separate adjoint uses different address points. These checks support the exact source join and the rational projector identities from PR5662. The retained all-width/native hypotheses are not inferred from the finite modular fixtures.
+
+## 2. Frame-506 matcher and finite cost
+
+For frame 506, the columns of W are the source basis B transposed, followed by its orthogonal complement A transposed. The new replay reconstructs these columns from the frozen frame file and checks both products with the supplied inverse. Orthogonality makes
+
+`W diag(I_4,0) W^-1 = P_506`.
+
+Applied to both paired address halves, these ordinary basis maps conjugate the standard rank-four involution to the required residual. The denominator is 4; an odd address prime can satisfy the new denominator condition. The original `1 -> 506` request has the complementary residual, so literal reuse of that oriented request is not asserted.
+
+There are four occurrences per local word and eighteen local calls. The two matrices contain 38 nonzero coefficients. Both paired halves therefore contribute `72*2*38=5472` coefficient terms. This quantity is added to the complete positive finite primitive-count bound. The remaining finite cost includes the actual whole maps, both routing directions, arithmetic on the fixed coefficients, and the positive normalizer implementation constants. It is covered by the retained finite ordinary matcher framework, not a unit-cost dense address primitive.
+
+## 3. Complete chronological caller
+
+Install the local word in the retained p16/a7 controller. The exact thirteen retired helper IDs are the nine owned relations and the four prior partial retirements. Every retained original owner has a distinct global index. The 39 owned global fields have no productive target credit and are cleared at global entry and exit. Every suspended compiled instance later receives its own reserve; the local reuse does not imply one global bank shared by simultaneous instances.
+
+The emitter rebuilds every local query, thin query, whole idle query, bridge, boundary, owned operation and route. The source descriptors bind the event index, complete prefix digest, owner, epoch, version, current symbolic data and geometric job. A second implementation consumes the emitted stream and reconstructs these fields. A stale epoch is rejected.
+
+All 11,166 original symbolic inputs return at the prescribed endpoint, while all 39 arbitrary owned entry columns are annihilated. The retained physical main-controller polynomial check also passes. There are 446,604 events, 56,547 paid queries and 2,367 payload episodes. The positive precision majorant has 516 bits. Every local return closes its live owned episodes before another call uses the bank.
+
+The complete paid histogram is
+
+```
+{1:24849,2:24156,3:1008,4:1026,5:1836,6:180,7:162,
+ 14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222}
+```
+
+The complete productive histogram is
+
+```
+{8:7614,15:444,22:444,29:444,36:444,43:444,50:444,
+ 57:444,64:222,127:222}
+```
+
+The 72 rank-four target debits from the prior retirements remain. There are 11,166 productive fields and rank surplus 753. Relative to PR5653, the paid delta is `-252H1-252H3+252H4` and targets do not change. Thus the moment gain is `252(1+3^t-4^t)>0` for `0<t<1`. This relation is derived from the same literal word, not by adding headline savings.
+
+## 4. Two exact compiler-tail calculations
+
+Let `P_s=sum P_k k^s` and `T_s=sum T_k k^s`. Set
+
+```
+C = .00349780457954
+U = .00349780457953
+r = 2^-48
+v = 2048
+u = 1/5
+```
+
+Two retained, separately implemented rational-series engines prove
+
+`alpha=P_(1-C)/T_(1-C) < 1-r`,
+
+`gamma=P_(1-C+u)/(17^u T_(1-C)) < 31/32`,
+
+`delta=11166*18/(17^C T_(1-C)) < 19/20`.
+
+Their exact intervals overlap. The signed first moment is positive at `.00349780457955` and negative at `.00349780457965`. The raw crossing statement concerns this invoice only.
+
+Both tail limits raised to power 128 are below `1/16`. Bernoulli's inequality bounds the first tensor term by `1/(1+vr)`. The combined charged contraction is therefore less than
+
+`1/(1+vr) + 4*2^(-v/32) < 1`.
+
+The source separation `17^64<18^63` and ambient bound `127<256` also hold. Productive completion and paid splitting stay on their independent owners.
+
+Set `t=1-C`, `z=1-U`, `z0=(t+z)/2`, `d=z0-t`, and `h=1/64`. With
+
+`R0=d(5+8h)v+1+8v(1-z0)`,
+
+choose
+
+`H0=floor(R0/(hd))+1`,
+
+`H1=floor(H0(1-z0)/(z-z0))+1`.
+
+These choices make both compiler inequalities strict, including an exact integer boundary. Here `H0=746342786958770177` and `H1=522112243625460240068436505540`. The fixed row dimension is the algorithm-defined `N=2^H1`; it is not materialized.
+
+## 5. Positive finite fees, owned stock and cover
+
+The fresh base primitive count includes 382,587 scalar/clear/header passes, 2,534,436,540 parent-parking passes, 14,796 internal and whole-job routes, all 446,604 records, dimension work for every paid query, and the 5,472 new matcher coefficient terms. The total bound is 958,360,084,023, below `2^64`. The independent checker recounts it from the emitted artifacts. This number counts positive primitive invocations; it is not a measured machine time.
+
+The source fixed tensor/description bound uses `K=2^(256v)=2^524288`. Its finite recurrences are retained:
+
+`J(n)=(n+1)^4 K^(4n+4)`,
+
+`A(1)=K^4`,
+
+`A(n)=(J(n)+2)^4 (A(n-1)+2)^(4n+8)`.
+
+Rows, leaves, instances and descriptions are bounded by `A(N)`. Every compiled instance gets 39 distinct owned banks, including suspended instances. Thus `C_N<=39A(N)`. The base arithmetic/precision height is bounded by 1024 bits, which covers the 516-bit positive majorant and the explicit new matcher coefficients; the unchanged source matrices retain their prior bound.
+
+Put `T_arith=(2N+2)^4(A(N)+2)^2` and `H=1026*4^(T_arith+1)`. Choose an odd prime
+
+`q>max(2^60 N^5,2^(2H))`
+
+that avoids all finite compiled denominator and rank-witness primes. This is a fresh choice. The fixed primitive multiplier
+
+`39(q+2)^(32(N+1)^2)(A(N)+2)^8`
+
+is multiplied by the positive maximum needed for the retained primitives, the new forward/inverse matcher operations and the completed preceding backend. It includes parent parking, normalizers, routes, initialization and teardown. The source owned-stock and eventual-threshold constructions use the new 39-bank reserve and fresh constants. No old seventeen-bank reserve or cancellation-growth bound is reused.
+
+Choose cover loss `epsilon=10^-14`. The exact guard `2^60 epsilon>256` pays the source regular-cover and bad-prime terms. The ordinary limiting saving after this loss is
+
+`L=U-epsilon=.00349780457952`.
+
+The source full fixed-tape, precision, ordinary cover and normalizer premises are retained here. The large constants are fixed before the final input size grows. They are not discarded because the asymptotic saving is positive.
+
+## 6. Five finite ordinary levels
+
+Start from the completed PR5653 backend `b0=.003488579527`. With `rho=1/100` and `Q=10^15`, define
+
+`a_j=(1-rho)L+rho b_(j-1)`,
+
+`b_j=(ceil(Q a_j)-1)/Q`.
+
+This strict lower grid also works when `Q a_j` is an integer. The five completed savings are
+
+```
+.003497712328994
+.003497803657014
+.003497804570294
+.003497804579427
+.003497804579519
+```
+
+Every level has strict adapter, stock and rounding gaps. Each ordinary backend call reduces the finite level; each native recursive call reduces the atom count. No self-fallback occurs. At each level choose a fresh coefficient and eventual threshold from its positive primitive and reserve constants, as specified in ORDINARY-RESULT.json. The ordinary result is conditional on the same retained source framework as its predecessor.
+
+## 7. Arbitrarily small strict losses for this fixed invoice
+
+Let `b0` be the prior completed saving and let `c_star` be the raw crossing of the new invoice. The verifier checks every rank-mass tail. Summation by parts shows the signed moment is strictly decreasing on `[b0,.0035]`: `x^(-C) log x` is increasing there. Thus its zero is unique.
+
+The certificate also proves tail guards uniformly on this entire interval. A conservative numerator uses the paid moment at `b0`; a conservative target denominator uses the target moment at `.0035`. For the completion denominator, use `17^b0` and that same target lower bound. Both resulting rational upper bounds remain below `31/32` and `19/20`.
+
+Fix a rational requested ordinary saving `B` with `b0<B<c_star`. Choose rationals `B<U<C<c_star`. Positive first-moment slack gives a rational reserve `0<r<1-alpha(C)`. It can be found by increasing the precision of the explicit convergent logarithm and exponential series until a positive enclosure is obtained. The finite numeric certificate uses the retained engines' fixed precision; this arbitrary-precision existence statement follows from their convergent series with an increasing term count.
+
+Double a positive multiple of 1024 until
+
+`1/(1+vr)+4*2^(-v/32)<1`.
+
+This process terminates: the first term tends to zero and the second decays exponentially. `strict_margins.py` implements this rule and the strict H0/H1 rules. The tests include reserves through `2^-384`.
+
+Choose a rational cover loss `0<epsilon<U-B`, so `L=U-epsilon>B`. Increase the fixed prime multiplier to exceed `256/epsilon`. These changes only enlarge finite constants and eventual thresholds under the retained framework.
+
+Choose an integer grid denominator Q with
+
+`1/(Q(1-rho))<L-B`.
+
+The strict-grid recurrence has total limiting rounding loss at most `1/(Q(1-rho))`. More precisely,
+
+`b_j >= L-rho^j(L-b0)-(1-rho^j)/(Q(1-rho))`.
+
+Hence some finite level satisfies `b_j>B`. Stop there, with fresh positive coefficients, owned reserves and thresholds at every level. For `B<=b0`, the prior completed algorithm suffices. This proves that every strict ordinary saving below `c_star` is attainable under the retained framework.
+
+This theorem does not make the raw crossing itself admissible, remove a strict inequality, prove a globally optimal BIT algorithm, or improve a Gaussian caller automatically. It shows that this fixed invoice has no additional fixed asymptotic loss from the finite choices in the certificate.
+
+## 8. Verification boundary
+
+The registered normal and optimized commands rebuild all scientific outputs in isolated temporary copies. Input authentication occurs before imports of retained engines. Local scalar/native checks, a separate physical adjoint, the complete chronological stream, target debits, independent moment intervals, positive fees, fresh cutoffs and all five backend levels pass. The audited word is retained byte-for-byte.
+
+The framework assumptions remain: arbitrary-function/all-column native operators, ROW and spectator behavior, constructive mixed-target compilation, ordinary normalizers and completed backends, owned erasure/stock, precision, fixed-tape and analytic contracts. The uniform word and enormous threshold are algorithm-defined, not executed. A complete multiplication kappa requires a compatible Gaussian/outer caller. No selected-frontier change, independent human review or formal-kernel acceptance is claimed.
diff --git a/research/g20-refinement-admission/README.md b/research/g20-refinement-admission/README.md
new file mode 100644
index 0000000000..4e771b4d36
--- /dev/null
+++ b/research/g20-refinement-admission/README.md
@@ -0,0 +1,42 @@
+# Complete G20 refinement admission
+
+This package admits conditional ordinary BIT saving **0.003497804579519**. It installs the exact PR5662 word in the full eighteen-call G20 controller and gives fresh native, chronological, compiler, cover, stock and finite-backend checks. This is an increase of **0.000009225052519**, or about **0.264436%**, over the completed PR5653 result. It is an increase of 0.000001804579519 over the conservative informal .003496 claim in PR5657. It is not a whole multiplication kappa claim.
+
+The construction is Dugongue's protected-reader and paid SOURCE-refinement method. PR5662 checks the source windows and supplies the emitted word. This package closes its full-caller and ordinary-admission handoff. It does not claim the local identities as new discoveries.
+
+The complete word retains 11,166 independent originals and 39 owned banks. It has 446,604 events and 56,547 paid queries. Every query has a current source descriptor with its prefix digest, owner, version and epoch. All 2,367 owned payload episodes end before return. The productive inventory has 11,166 targets and rank surplus 753. All target debits from the prior four retirements remain.
+
+The new frame-506 residual matcher is explicit. Its forward and inverse matrices have 38 nonzero coefficients in total and common denominator 4. The complete invoice contains 72 uses. Both directions and both paired address halves are included, for 5,472 additional coefficient terms in the positive finite fee. This is a finite normalizer cost under the retained framework; no arbitrary address map is given zero cost.
+
+The certificate uses two rational moment engines, a tested saving .00349780457954, a uniform saving .00349780457953, a cover loss of 10^-14, and five acyclic ordinary levels. The raw profile crossing is in `(.00349780457955,.00349780457965)`. The admitted value is within 1.31e-13 of that upper bound. No further local fusion or untested inventory is inserted.
+
+[PROOF.md](PROOF.md) also proves that the fixed completion losses can be made arbitrarily small. Under the same retained framework, every ordinary saving strictly below this invoice's raw crossing is attainable with fresh finite parameters. The code checks the tail guards over the complete interval from the prior completed saving to .0035, and supplies strict finite parameter functions. This is an approach to one invoice's crossing, not a global optimality theorem.
+
+## Reproduction and evidence
+
+```sh
+python3.12 -I -W error -B research/g20-refinement-admission/verify.py
+python3.12 -I -O -W error -B research/g20-refinement-admission/verify.py
+```
+
+Expected: `PASS_G20_REFINEMENT_COMPLETE_ORDINARY_003497804579519`. Python 3.12 and the standard library suffice. Each command authenticates 33 frozen files, rebuilds all outputs in a fresh directory, and leaves publication files unchanged.
+
+The local check covers all 684 scalar input columns, including arbitrary owned data, with exact native-address fixtures over moduli 101 and 10201. A separate adjoint uses different address points. The written source identities and exact projector/matcher algebra provide the all-address implication for the new rewrites; these finite fixtures alone do not prove all widths. The full global replay and a separate stream checker agree on every event, source descriptor, target and owned return. The positive global precision majorant uses 516 bits. Two independent arithmetic implementations agree on the three compiler tails and the finite ordinary chain.
+
+Controls reject a missing snapshot clear, missing paid refined query, missing return clear, stale source epoch, unfunded contraction reserve and use of the raw crossing as an ordinary saving. Strict-grid controls include exact grid points. Reserve tests range from 2^-8 to 2^-384 and select finite tensor powers from 1024 through 16384. PR5662's separate source-condition controls remain predecessor evidence.
+
+Key artifacts are [WORD.json.gz](WORD.json.gz), [GLOBAL-RESULT.json](GLOBAL-RESULT.json), [INVOICE.json](INVOICE.json), [MATCHER.json](MATCHER.json), [ORDINARY-RESULT.json](ORDINARY-RESULT.json), and [INDEPENDENT-RESULT.json](INDEPENDENT-RESULT.json). The local word is byte-identical to the audited input.
+
+## Scope, assumptions and credit
+
+The native arbitrary-function/all-column, ROW and spectator, constructive mixed-target compiler, completed ordinary backend, precision, fixed-tape and analytic framework premises remain. This package supplies a complete conditional ordinary component certificate under those premises. It does not materialize the enormous uniform program, execute a rounded multiplier, prove the framework from first principles or provide independent human acceptance. Physical finite fees are positive schemas with fixed primitive constants, not measured running times.
+
+Canonical base is `df0137efd35e11b4445734bf612bdd4c7ebc330c`, priority revision 7. Selected .00310045 is unchanged. Full-history ancestry preflight is unavailable in this shallow checkout; committed-file, hash and export checks are distinct. Hosted CI is separate from the local scientific replay.
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Retain Dugongue PR5657/5629/5639 for the constructions; ai-nanachi PR5512; Ali Romman PR5421/5641/5647/5648/5653/5662; DreamingOfClouds, eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman and all frozen notices. The prior native, global, ordinary and second-checker code is explicitly retained and adapted. New complete integration, strict-margin functions and checks are Apache-2.0.
+
+## Open next questions
+
+- Use this completed ordinary component in a compatible stronger Gaussian caller. A whole kappa claim needs that caller's complete cost and outer constraints.
+- Seek a new local word if a larger ordinary saving is needed. Changing finite margins cannot cross this fixed invoice's raw root.
+- Independently review the native/ROW and finite-normalizer assumptions, including the concrete frame-506 basis maps. The replay does not discharge the inherited framework.
diff --git a/research/g20-refinement-admission/SOURCE-DESCRIPTORS.json.gz b/research/g20-refinement-admission/SOURCE-DESCRIPTORS.json.gz
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diff --git a/research/g20-refinement-admission/SOURCES.json b/research/g20-refinement-admission/SOURCES.json
new file mode 100644
index 0000000000..c3fe658ffb
--- /dev/null
+++ b/research/g20-refinement-admission/SOURCES.json
@@ -0,0 +1,249 @@
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new file mode 100644
index 0000000000..045355491a
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diff --git a/research/g20-refinement-admission/TASK.json b/research/g20-refinement-admission/TASK.json
new file mode 100644
index 0000000000..a554e263b7
--- /dev/null
+++ b/research/g20-refinement-admission/TASK.json
@@ -0,0 +1,96 @@
+{
+  "schema_version": 1,
+  "task_id": "supplier-boundary-audit",
+  "priority_revision": 7,
+  "base_commit": "df0137efd35e11b4445734bf612bdd4c7ebc330c",
+  "original_card": {
+    "id": "supplier-boundary-audit",
+    "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/scatter-boundary-decision/README.md"
+    ],
+    "methods": [
+      "Trace one hypothesis through the source, checker and complete caller.",
+      "Construct one semantically invalid but superficially well-formed fixture and test rejection."
+    ],
+    "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.",
+    "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.",
+    "allowed_variations": [
+      "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage."
+    ],
+    "scope_change_triggers": [
+      "Reporting the historical timing-only diagnostic as a new current acceptance bug.",
+      "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.",
+      "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass."
+    ],
+    "overlap_terms": [
+      "owner boundary",
+      "bridge omission",
+      "hosting",
+      "2977",
+      "scatter export",
+      "duplicate index",
+      "parity semantics",
+      "4088",
+      "3801",
+      "staged544-mixed-fourth-entry",
+      "scatter-boundary-decision"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #3801: successor scatter-boundary decision package.",
+        "evidence": "research/scatter-boundary-decision/README.md",
+        "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.",
+        "status": "author-checked",
+        "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Install the exact PR5662 G20 word in the complete caller and admit the resulting ordinary BIT component with fresh strict compiler, cover, stock, matcher and backend costs.",
+  "scope_change_reason": "PR5662 closes the source-to-local-ledger implication but explicitly leaves full caller and ordinary admission open. This contribution closes that released integration obligation and bounds the remaining finite-margin losses.",
+  "bottleneck_link": "A completed, fully charged ordinary BIT component increases available capacity for a compatible stronger multiplication caller.",
+  "budget_minutes": 150,
+  "stop_rule": "Stop after the fixed word, complete caller and ordinary admission. Do not search the separately claimed scalar-boundary lane or promote the selected frontier.",
+  "outcome": "completed",
+  "evidence": "LOCAL-RESULT.json; GLOBAL-RESULT.json; INVOICE.json; MATCHER.json; ORDINARY-RESULT.json; INDEPENDENT-RESULT.json; PROOF.md",
+  "author": "Ali Romman with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance for explicit adaptations, strict-margin proof, tests and writing. Retained primary and separate engines are credited; no independent human review.",
+  "open_questions": [
+    {
+      "question": "Which stronger compatible Gaussian caller can use the admitted ordinary component?",
+      "why_it_matters": "The BIT saving alone does not raise whole multiplication kappa.",
+      "first_step": "Pin that caller and recheck its full outer invoice with this completed backend.",
+      "blocked_by": "A compatible stronger Gaussian caller is not supplied."
+    },
+    {
+      "question": "Can another local word exceed this fixed invoice crossing?",
+      "why_it_matters": "Finite parameter choices can approach but cannot cross this invoice limit.",
+      "first_step": "Change an actual paid transition and preserve all target and ownership obligations.",
+      "blocked_by": "No further word search is claimed."
+    }
+  ]
+}
diff --git a/research/g20-refinement-admission/VERIFY.json b/research/g20-refinement-admission/VERIFY.json
new file mode 100644
index 0000000000..4925f4f5c4
--- /dev/null
+++ b/research/g20-refinement-admission/VERIFY.json
@@ -0,0 +1,34 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 570,
+      "checks": "Frozen input authentication, exact native and adjoint maps, complete chronological caller and source descriptors, target/ownership/route accounting, two interval engines, strict finite parameters and positive ordinary admission"
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 570,
+      "checks": "Frozen input authentication, exact native and adjoint maps, complete chronological caller and source descriptors, target/ownership/route accounting, two interval engines, strict finite parameters and positive ordinary admission"
+    }
+  ]
+}
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diff --git a/research/g20-refinement-admission/audited/NOTICE.md b/research/g20-refinement-admission/audited/NOTICE.md
new file mode 100644
index 0000000000..bb47b1a518
--- /dev/null
+++ b/research/g20-refinement-admission/audited/NOTICE.md
@@ -0,0 +1,7 @@
+# Attribution
+
+New audit code, emitted rewrite and documentation: Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. No independent human review is claimed.
+
+The construction proposals are Dugongue's PR5657, with the retained source credit in its four frozen proof files. The baseline is Ali Romman's PR5653. It retains ai-nanachi PR5512, Ali Romman PR5421/5641/5647/5648, Dugongue PR5629/5639, DreamingOfClouds, eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman and the native, ROW, compiler, stock, precision, tape and analytic source lineage. Preserve inputs/NOTICE.md and the full source attribution.
+
+All consumed files have exact commits, paths, Git blob IDs and SHA256 values in PINS.json. No predecessor executable is imported by the audit.
diff --git a/research/g20-refinement-admission/audited/PROOF.md b/research/g20-refinement-admission/audited/PROOF.md
new file mode 100644
index 0000000000..7cc51a4c06
--- /dev/null
+++ b/research/g20-refinement-admission/audited/PROOF.md
@@ -0,0 +1,87 @@
+# Source-to-profile proof and verification boundary
+
+## 1. Frozen scope
+
+The proposal is PR5657 at `2f091bc3b656ed85d26cf44b7fc84c28fb510273`. Its positions refer to the literal forward G20 record array at `5e0052ca0aa3036a3afa8b0438927377c8d97d53`. The consumed complete local baseline is PR5653 at `b13c9ae8a539c05f0f590ce9d08c7067d99c6145`. No source engine is imported.
+
+The baseline already contains the four partial retirements and three direct SOURCE fusions, including helper 444. The new edits are six protected-reader fusions and eight paid SOURCE refinements. All fourteen helper fields and all fourteen recipients are distinct. An affected SOURCE can also be another recipient's independent SOURCE. The complete join check includes these interactions; it does not infer compatibility from disjoint helper names alone.
+
+## 2. Source conditions and exact edits
+
+The verifier parses all six rows of the table in `bit.md` and all eight rows of the first table in `bit-refinement.md`. It also parses all eight independent recipient-injection rows. It compares every named event with the exact forward record, including field IDs, frame IDs, direction and rank.
+
+For each simple window, the helper interval contains exactly its entrance query, line injection, proper outgoing read and upper query. The recipient interval contains exactly the cold read, its line query and the proper read. For each refined window, the helper also has its intermediate query. Its recipient has exactly its cold read, two own queries, one independent SOURCE injection and the proper read. Every reference, including outgoing observations, is included in these checks.
+
+Between the helper's line injection and the relevant upper SOURCE query, the SOURCE has no value change other than the explicitly permitted first query in a simple window. Its old outgoing observers remain in place. Thus the inverse snapshot captures the required old SOURCE version. These checks are stronger than a rank or frame-name comparison.
+
+Each edit locates one unique exact inverse event in the consumed word. Overlapping edits to one old event are rejected. Six simple windows snapshot the upper SOURCE, fuse the helper return, cancel its two recipient reads and, when required, delay the recipient's old return until the SOURCE is back at the line. Eight refined windows replace the old SOURCE rank-three return with rank-two and rank-one returns, snapshot both upper and intermediate values, replace the proper read by the intermediate snapshot, and fuse the helper's three returns into one rank-four return. Their own recipient injections remain unchanged.
+
+Twenty-two new owned fields supply these snapshots. Each is cleared before use and after its last use. They add to the seventeen fields in PR5653, for 39. The new word has 684 fields, 645 of which retain independent arbitrary input data. Initial values on every owned field are also arbitrary in the check.
+
+## 3. Complete linear join
+
+Normalize each field by its declared frame map. A same-frame ADD becomes binary row addition. A legal nested query changes the frame but leaves the normalized row unchanged. CLEAR removes the row. Every row starts as a separate one-bit basis vector, including the dirty owned fields.
+
+The new replay checks the actual frame on each query and both operands of each ADD. It checks that only owned fields are erased and only entire zero fields are freely reheadered. The final frame vector must equal the baseline vector, extended by unused headers for the new fields. Every owned row must be zero. The first 662 output rows must equal the baseline's full rows; all new rows must be zero. This proves the complete normalized input map, not a test on one chosen payload.
+
+A second oracle reads the word in reverse order and transposes each ADD by exchanging its operand roles. Erasures transpose to erasures; frame changes do not affect normalized coefficients. Its final matrix must be the exact role transpose of the forward result. This provides a separate data-flow check, not independent scientific acceptance.
+
+The frozen baseline's physical/native theorem is retained. The next section proves the exact new nested map identities required to transfer the changed normalized word back to its physical address action. A full new controller stream, finite-width implementation and tape proof remain outside this replay.
+
+## 4. Exact residual geometry and the frame-506 correction
+
+For a frame with row basis B and orthogonal complement A, the verifier constructs the rational orthogonal projector
+
+`P_B = B^T (B B^T)^(-1) B`.
+
+It checks the declared dimensions, orthogonality, idempotence and trace. For every new query from one nested frame to another, it checks both products `P_low P_high = P_low` and `P_high P_low = P_low`. Their difference D is an idempotent of the declared query rank.
+
+In paired address coordinates, the physical involution for D is
+
+`R_D(x,y) = (x-D(x-y), y+D(x-y))`.
+
+The exact composition formula is `R_H R_L = R_(H+L-2HL)`. For nested projectors, this is `R_(H-L)`. Thus all new query paths telescope with the old endpoint maps on every address, subject to the retained address-field contract. The checks use exact rational matrices, not sampled addresses or only ranks.
+
+All new oriented query types but `506 -> 0` already occur in the consumed baseline. The existing `1 -> 506` rank-four query uses `I-P_506`, whereas the new query uses `P_506`. A claim of literal oriented-matcher reuse at this point is false.
+
+To supply the missing algebraic matcher, form W from the columns of `B_506^T` followed by `A_506^T`. Exact inversion gives
+
+`W diag(I_4,0) W^-1 = P_506`,
+
+and both products `W W^-1` and `W^-1 W` equal I. These matrices are printed in RESULT.json. Their common denominator is 4. Their maximum absolute row sums are 3 and 2. Together they contain 38 nonzero coefficients; this is a coefficient inventory, not a tape instruction price. Applied to both paired address halves, they conjugate the standard rank-four involution to the required residual map. Reduction is valid over every address ring where these denominators and the retained source denominators are units.
+
+This resolves the new residual's exact basis and inverse. It does not make either direction free. A complete physical caller must compile both ordinary address maps, account for all their coefficients and routes, and use fresh finite constants. The proposal's general finite-matcher assumption can include them, but a claim that an old oriented query was reused without change cannot.
+
+## 5. Paid and productive inventories
+
+The emitted word is counted directly. Each simple window replaces one H1 and one H3 with H4. Each refined window removes two helper H1 calls and one helper H2, adds one helper H4, then replaces one SOURCE H3 with SOURCE H2 and H1. Its net change is also `-H1-H3+H4`.
+
+Relative to PR5653, the combined local delta is `-14H1-14H3+14H4`. The program has 19,043 ADDs, 78 ERASEs, one INIT, 2,864 paid Qs and nine ZERO_Qs. These ordinary operations are visible in the word; this package does not assign them zero cost or turn their count into a completed machine tariff.
+
+The eighteen-call controller retains its calls and all nonlocal work. Substitution into the frozen complete baseline invoice gives
+
+`P_new = P_5512 -378H1 -378H3 +306H4`,
+
+`T_new = T_5512 -72H4`.
+
+The target debit is entirely due to the four prior retirements. No snapshot or correlated field receives productive credit. The new complete paid and target histograms agree exactly with the proposal. There are 56,547 paid calls, 11,166 productive targets and rank surplus 753. This is an independently checked histogram substitution on an emitted local word. It does not replace a replay of all chronological global descriptors.
+
+## 6. Rational first-moment check and raw crossing
+
+Define `F(C)=sum T_k k^(1-C)-sum P_k k^(1-C)`. The checker obtains the histograms from the emitted word and the pinned baseline, not by importing a primary price function.
+
+For every integer cutoff from 1 through 128 it checks
+
+`sum_(k>=u) T_k k - sum_(k>=u) P_k k >= 0`.
+
+For `0<=C<=.01`, the function `h(x)=x^(-C) log x` is strictly increasing on `[1,127]`, since `1-C log x>0`. Summation by parts against the rank-mass tails therefore gives `F'(C)<0`; strictness follows from the nonzero tails. The raw zero in this interval is unique.
+
+The independent enclosure reduces logarithms to `log 2` and `log(n/2^floor(log2 n))`. It uses 32 positive terms of the atanh series and an explicit geometric tail. For `x=C log n<1/20`, the degree-13 and degree-12 alternating Taylor sums bound `exp(-x)` below and above. All arithmetic uses rational numbers. Signed coefficients select the correct interval endpoint.
+
+At `C=3497/1000000`, the lower endpoint exceeds `1/32`. At `.0035`, the upper endpoint is negative. Rational bisection then gives the exact interval in RESULT.json, of width below `10^-13`. Decimal displays are only aids to reading the rational endpoints. The root does not include the ordinary cover loss, finite completion margins, backend chain, or outer multiplication constraints.
+
+## 7. Failure controls and remaining work
+
+Fourteen source mutations insert a value-changing write into a required unchanged SOURCE interval. Each fails the source conditions. Other controls remove a snapshot, a paid refined query, an owned teardown, or a recipient's independent injection; attempt to erase a retained arbitrary helper; or change the explicit frame-506 matcher. All fail. Checks remain enabled under Python optimization.
+
+The source's informal analytical ordinary proof, full native/all-width and ROW contracts, finite compiler, complete global stream, positive ordinary constants, precision, physical tape costs and analytic outer conditions are not newly certified here. The useful handoff is the frozen local word, all edits, exact new matcher and source-bound invoice. They make a complete ordinary admission check concrete. No selected-frontier change or new whole kappa follows from this package.
diff --git a/research/g20-refinement-admission/audited/RESULT.json b/research/g20-refinement-admission/audited/RESULT.json
new file mode 100644
index 0000000000..9a4d76fc36
--- /dev/null
+++ b/research/g20-refinement-admission/audited/RESULT.json
@@ -0,0 +1,669 @@
+{
+  "all_input_columns": 684,
+  "changed_old_events": 102,
+  "controller_paid": {
+    "1": 24849,
+    "2": 24156,
+    "3": 1008,
+    "4": 1026,
+    "5": 1836,
+    "6": 180,
+    "7": 162,
+    "14": 444,
+    "21": 444,
+    "28": 444,
+    "35": 444,
+    "42": 444,
+    "49": 444,
+    "56": 444,
+    "63": 222
+  },
+  "controller_targets": {
+    "8": 7614,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
+    "43": 444,
+    "50": 444,
+    "57": 444,
+    "64": 222,
+    "127": 222
+  },
+  "controls": [
+    "changed_residual_matcher",
+    "source_version_233",
+    "source_version_358",
+    "source_version_385",
+    "source_version_297",
+    "source_version_271",
+    "source_version_360",
+    "source_version_241",
+    "source_version_340",
+    "source_version_319",
+    "source_version_357",
+    "source_version_381",
+    "source_version_368",
+    "source_version_365",
+    "source_version_352",
+    "missing_snapshot",
+    "missing_refinement",
+    "missing_teardown",
+    "retained_helper_erasure",
+    "recipient_injection_removed"
+  ],
+  "delta_from_5653": {
+    "1": -14,
+    "3": -14,
+    "4": 14
+  },
+  "local_paid": {
+    "1": 1288,
+    "2": 1342,
+    "3": 56,
+    "4": 57,
+    "5": 102,
+    "6": 10,
+    "7": 9
+  },
+  "matcher": {
+    "common_denominator": 4,
+    "forward": [
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "1",
+        "1",
+        "0",
+        "-1",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "1",
+        "1",
+        "0",
+        "1",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "0",
+        "0",
+        "1",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0",
+        "1"
+      ],
+      [
+        "2",
+        "0",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "2",
+        "0",
+        "1",
+        "0",
+        "0",
+        "0",
+        "0"
+      ],
+      [
+        "0",
+        "0",
+        "-1",
+        "0",
+        "0",
+        "0",
+        "0",
+        "1"
+      ]
+    ],
+    "forward_norm": "3",
+    "frame": 506,
+    "inverse": [
+      [
+        "0",
+        "-1/4",
+        "-1/4",
+        "0",
+        "1/4",
+        "1/2",
+        "0",
+        "-1/4"
+      ],
+      [
+        "0",
+        "-1/4",
+        "-1/4",
+        "0",
+        "1/4",
+        "0",
+        "1/2",
+        "-1/4"
+      ],
+      [
+        "0",
+        "0",
+        "0",
+        "0",
+        "1/2",
+        "0",
+        "0",
+        "-1/2"
+      ],
+      [
+        "0",
+        "1/2",
+        "1/2",
+        "0",
+        "-1/2",
+        "0",
+        "0",
+        "1/2"
+      ],
+      [
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+        "0",
+        "0",
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+      ],
+      [
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+        "0",
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+      [
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+      [
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+    ],
+    "inverse_norm": "2",
+    "max_numerator_bits": 2,
+    "nonzero_coefficients": 38,
+    "physical_tape_price_supplied": false,
+    "rank": 4
+  },
+  "new_kappa": false,
+  "new_query_types": [
+    [
+      7,
+      0,
+      1
+    ],
+    [
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+    [
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+    [
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+    [
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diff --git a/research/g20-refinement-admission/global_retirement.py b/research/g20-refinement-admission/global_retirement.py
new file mode 100644
index 0000000000..95a0e0c392
--- /dev/null
+++ b/research/g20-refinement-admission/global_retirement.py
@@ -0,0 +1,112 @@
+"""Literal p16/a7 caller with thirteen retired helper targets and thirty-nine owned fields.
+
+Adapted from ai-nanachi PR5512 global_relations.py. The four retirements
+are Dugongue PR5629. Dugongue PR5639 gives two snapshot fusions; this
+version adds the third and reuses the zero centre. Implementation by Ali Romman with OpenAI Codex assistance.
+Apache-2.0; retain the source notices.
+
+Retains G20 native controller/geometry; uses the independently checked reverse
+physical involution at each full call. No old helper target is given to owned work.
+"""
+from pathlib import Path
+from collections import Counter
+from hashlib import sha256
+from time import process_time
+import gzip,json,importlib.util,sys
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import integration as L
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def read(p):return L.read(p)
+def put(n,x):L.put(n,x)
+def run():
+ clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=sorted(x for x in owned if x<658);need(pivots==[462,463,466,468]+list(range(469,478)),'Exact thirteen retired helper owners')
+ oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+len(owned)));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:15]));snapshotwork=dict(zip(sorted(r for r in owned if r>=660),W[15:]));need(N==11166,'New retained original count')
+ values=[1<<i for i in range(N+len(owned))];norm=[1]*(N+len(owned));versions=[0]*(N+len(owned));epochs=[0]*(N+len(owned));counts=Counter();paid=Counter();peak=1;events=[];source=[];calls=[];episodes=[];prefix=sha256()
+ def emit(e):counts[e[0]]+=1;events.append(e);prefix.update((json.dumps(e,separators=(',',':'))+'\n').encode())
+ def erase(d,why,frame=None):
+  need(d in W,'Only owned wholepayload erasure');values[d]=norm[d]=0;versions[d]+=1;epochs[d]+=1;emit(['OWNED_CLEAR',d,frame,why])
+ for d in W:erase(d,'GLOBAL_ENTRY_ARBITRARY_DIRTY')
+ def add(d,s,why):
+  nonlocal peak
+  need(d!=s,'Distinct source/destination');values[d]^=values[s];norm[d]+=norm[s];peak=max(peak,norm[d]);versions[d]+=1;emit(['ADD',d,s,why])
+ def query(d,k,detail):
+  need(k>0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail])
+ def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why)
+ def boundary(program,why):
+  for op,d,s in program:
+   for p in range(111):
+    if op=='ADD':add(compact[d*111+p],compact[s*111+p],why)
+    else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why)
+ boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY')
+ thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)}
+ for event in controller['physical_events']:
+  op=event[0]
+  if op=='LOCAL':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   helper=3552+436*stage_index[stage]
+   def owner(r):
+    if r==658:return center
+    if r==659:return shadow
+    if r in pivotwork:return pivotwork[r]
+    if r in snapshotwork:return snapshotwork[r]
+    return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222]
+   sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers}
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY'])
+   start=len(events);lp=Counter();st=local['start'][:];livebegin={}
+   for ix,e in enumerate(local['records']):
+    typ,d=e[:2];gd=owner(d)
+    if typ=='ERASE':
+     erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2]
+     if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1})
+    elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage])
+    elif typ=='ADD':
+     s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe')
+     if gd in W and gd not in livebegin:livebegin[gd]=len(events)
+     add(gd,owner(s),['LOCAL',stage,f,ix])
+    elif typ in('Q','ZERO_Q'):
+     a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b
+     if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1
+     else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage])
+    else:raise ValueError('Local opcode '+typ)
+   need(not livebegin and st==local['final'],'No live local owned state at return')
+   need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs')
+   need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All423 independent retained helper inputs and39owned returns')
+   need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count')
+   calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':423,'paid':dict(lp)})
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN'])
+  elif op=='QUERY_SHEAR':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   for p in range(111):
+    src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1})
+  elif op=='IDLE':
+   _,pair,stages=event;k=7*len(stages)
+   for bank in(2*pair,2*pair+1):
+    for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p])
+  elif op=='ADD':
+   for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE')
+  else:
+   need(op=='SWAP','Known controller event')
+   for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP')
+ boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY')
+ for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN')
+ need(values==[1<<i for i in range(N)]+[0]*len(owned),'All11166 independent retained RAW and all17 arbitrary DIRTY entry columns annihilated')
+ oldtargets=read(S/'provider/data/TARGET-OWNERS.json');targets=[dict(t,original_owner=compact[t['original_owner']])for t in oldtargets if t['original_owner']not in retired];T=Counter(t['rank']for t in targets)
+ P={int(k):v for k,v in read(S/'provider/data/INVOICE.json')['paid'].items()};raw_local=Counter(e[4] for e in L.source()[2] if e[0] in ('Q','COPY'));new_local=Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()})
+ for k in set(raw_local)|set(new_local):P[k]=P.get(k,0)+18*(new_local[k]-raw_local[k])
+ need(paid==P and sum(T.values())==N and T[4]==0 and T[8]==7614,'Literal complete changed invoice including every partial helper')
+ # Retained exact physical MAIN polynomial proof, independent of the new ledger.
+ spec=importlib.util.spec_from_file_location('old_global',S/'provider/build_global.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);physical=mod.physical_main(controller)
+ stream=b''.join((json.dumps(e,separators=(',',':'))+'\n').encode()for e in events);need(sha256(stream).hexdigest()==prefix.hexdigest(),'Exact prefix and fullstream identity');(R/'GLOBAL.jsonl.gz').write_bytes(gzip.compress(stream,mtime=0))
+ invoice={'paid':dict(sorted(paid.items())),'targets':dict(sorted(T.items())),'originals':N,'owned_allocated':len(owned),'owned_output_credit':0,'QUERYs':sum(paid.values()),'rank_surplus':sum(k*v for k,v in T.items())-sum(k*v for k,v in paid.items())}
+ result={'status':'PASS_LITERAL_G20_THREE_FUSIONS_11166_RETAINED_RAW','invoice':invoice,'expanded_event_count':len(events),'canonical_stream_sha256':sha256(stream).hexdigest(),'operation_counts':dict(counts),'calls':len(calls),'owned_payload_episodes':len(episodes),'source_descriptors':len(source),'majorant_bits':peak.bit_length(),'majorant':str(peak),'retired_original_old_ids':sorted(retired),'retained_old_ids':retained,'shared_owned_ids':W,'CPU_seconds':process_time()-clock,'physical_MAIN_coefficients':physical}
+ put('GLOBAL-RESULT.json',result);put('INVOICE.json',invoice);put('CALLS.json',calls);put('PRIVATE-EPISODES.json',episodes);put('TARGET-OWNERS.json',targets);put('SOURCE-DESCRIPTORS.json.gz',source)
+ return {k:result[k]for k in('status','invoice','expanded_event_count','canonical_stream_sha256','operation_counts','majorant_bits','owned_payload_episodes','CPU_seconds')}
+if __name__=='__main__':print(json.dumps(run(),indent=2))
diff --git a/research/g20-refinement-admission/independent.py b/research/g20-refinement-admission/independent.py
new file mode 100644
index 0000000000..f0a7156e9e
--- /dev/null
+++ b/research/g20-refinement-admission/independent.py
@@ -0,0 +1,165 @@
+"""Separate adjoint, stream and rational-series checks for the emitted caller.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+This is a second implementation, not independent human review.
+"""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import json
+import sys
+
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import integration as L
+
+
+def adjoint(modulus):
+    base, frames, _ = L.source()
+    data = L.read(L.R / "WORD.json.gz")
+    owned = set(data["owned"])
+    word = data["records"]
+    geometry = L.SOURCE.Geometry(frames)
+    point = tuple(v % modulus for v in (1, 3, 9, 27, 2, 6, 18, 54, 5, 15, 45, 34, 7, 21, 63, 88))
+    fields = [{point: 1 << i} for i in range(len(data["start"]))]
+    raw = [1 << i for i in range(len(data["start"]))]
+    for e in reversed(word):
+        op, d = e[:2]
+        if op == "ADD":
+            s = e[2]
+            raw[s] ^= raw[d]
+            for x, value in fields[d].items():
+                fields[s][x] = fields[s].get(x, 0) ^ value
+                if not fields[s][x]:
+                    del fields[s][x]
+        elif op in ["ERASE", "ZERO_Q", "INIT"]:
+            # A zero-only header map has the total zero extension.
+            L.need(d in owned, "Adjoint zero map is owned")
+            raw[d] = 0
+            fields[d] = {}
+        else:
+            L.need(op == "Q", "Adjoint opcode")
+            residual = geometry.residual_mod(*e[2:], modulus)
+            fields[d] = {geometry.move(residual, x, modulus): value for x, value in fields[d].items()}
+    expected = [0 if i in owned else (1 << i) ^ ((1 << (i + 111)) if i < 111 else 0) for i in range(len(data["start"]))]
+    L.need(raw == expected, "Every adjoint RAW/DIRTY column")
+    for output, row in enumerate(expected):
+        want = {}
+        for source in L.SOURCE.bitids(row):
+            x = geometry.move(geometry.project_mod(base["start"][source], modulus), point, modulus)
+            x = geometry.move(geometry.project_mod(base["final"][output], modulus), x, modulus)
+            want[x] = want.get(x, 0) ^ (1 << source)
+        L.need(fields[output] == {x: v for x, v in want.items() if v}, "All adjoint physical columns")
+    return modulus
+
+
+def stream(corrupt=False):
+    invoice = L.read(L.R / "INVOICE.json")
+    n, own = invoice["originals"], invoice["owned_allocated"]
+    values = [1 << i for i in range(n + own)]
+    norms = [1] * (n + own)
+    versions, epochs = [0] * (n + own), [0] * (n + own)
+    sources = iter(L.read(L.R / "SOURCE-DESCRIPTORS.json.gz"))
+    paid, ops, prefix, peak, used = Counter(), Counter(), sha256(), 1, 0
+    with gzip.open(L.R / "GLOBAL.jsonl.gz", "rb") as handle:
+        for event, line in enumerate(handle):
+            e = json.loads(line)
+            op, d = e[:2]
+            ops[op] += 1
+            if op == "ADD":
+                values[d] ^= values[e[2]]
+                norms[d] += norms[e[2]]
+                peak = max(peak, norms[d])
+                versions[d] += 1
+            elif op == "OWNED_CLEAR":
+                L.need(n <= d < n + own, "Only owned global erasure")
+                values[d] = norms[d] = 0
+                versions[d] += 1
+                epochs[d] += 1
+            elif op == "QUERY":
+                item = next(sources)
+                if corrupt and not used:
+                    item["epoch"] += 1
+                expected = {"event": event, "prefix_sha256": prefix.hexdigest(), "owner": d,
+                            "rank": e[2], "version": versions[d], "epoch": epochs[d], "RAW_hex": hex(values[d])}
+                L.need(all(item[k] == v for k, v in expected.items()), "Actual chronological query descriptor")
+                used += 1
+                paid[e[2]] += 1
+                versions[d] += 1
+            elif op in ["OWNED_ZERO_HEADER", "WHOLE_ZERO_FRAME"]:
+                L.need(n <= d < n + own and values[d] == 0, "Whole zero global frame change")
+            else:
+                L.need(op == "PAID_PORT_ROUTE", "Known global event")
+            prefix.update(line)
+    L.need(next(sources, None) is None, "No unused source descriptor")
+    L.need(values == [1 << i for i in range(n)] + [0] * own, "All global RAW and DIRTY columns")
+    L.need(paid == {int(k): v for k, v in invoice["paid"].items()}, "Recounted global invoice")
+    original_targets = L.read(L.S / "provider/data/TARGET-OWNERS.json")
+    old_calls = L.read(L.S / "provider/data/CALLS.json")
+    retired = {c["helper_owner_begin"] + h - 222 for c in old_calls for h in list(L.PARTIAL) + list(range(469, 478))}
+    targets = Counter(t["rank"] for t in original_targets if t["original_owner"] not in retired)
+    L.need(targets == {int(k): v for k, v in invoice["targets"].items()}, "Every retired target is debited")
+    L.need(len(retired) == 234 and sum(targets.values()) == n == 11166 and own == 39, "Global ownership census")
+    g = L.read(L.R / "GLOBAL-RESULT.json")
+    L.need(prefix.hexdigest() == g["canonical_stream_sha256"] and ops == g["operation_counts"], "Recounted literal stream")
+    L.need(peak.bit_length() == g["majorant_bits"] <= 1024, "Fresh precision envelope")
+    return {"events": event + 1, "queries": used, "originals": n, "owned": own, "majorant_bits": peak.bit_length()}
+
+
+def pricing():
+    I=L.load("refinement_second_series",L.S/"ordinary-certificate/inputs/separate_series.py")
+    invoice=L.read(L.R/"INVOICE.json");result=L.read(L.R/"ORDINARY-RESULT.json");glob=L.read(L.R/"GLOBAL-RESULT.json")
+    paid,target=({int(k):v for k,v in invoice[name].items()} for name in ["paid","targets"])
+    c,uniform,reserve=F(".00349780457954"),F(".00349780457953"),F(1,2**48)
+    denominator=I.moment(target,1-c)
+    alpha=I.div(I.moment(paid,1-c),denominator)
+    gamma=I.div(I.moment(paid,1-c+F(1,5)),I.mul(I.power(17,F(1,5)),denominator))
+    delta=I.div((F(11166*18),)*2,I.mul(I.power(17,c),denominator))
+    L.need(alpha[1]<1-reserve and gamma[1]<F(31,32) and delta[1]<F(19,20),"Separate charged compiler tails")
+    for name,interval in [("alpha",alpha),("gamma",gamma),("delta",delta)]:
+        other=list(map(F,result['tail'][name]));L.need(max(interval[0],other[0])<=min(interval[1],other[1]),"Separate interval overlap")
+    gap,h,v=(c-uniform)/2,F(1,64),2048;z0=1-(c+uniform)/2
+    expression=(gap*(5+8*h)*v+1+8*v*(1-z0))/(h*gap)
+    h0=expression.__floor__()+1;h1=(h0*(1-z0)/gap).__floor__()+1
+    L.need([h0,h1]==[result['tail']['H0'],result['tail']['H1']],"Strict integer compiler thresholds")
+    L.need(1-1/(1+v*reserve)-F(4,2**(v//32))>0,"Exact tensor contraction margin")
+    cover=F(1,10**14);L.need(2**60*cover>256,"Paid regular cover and prime guard")
+    c1=uniform-cover;backend=F(L.read(L.R/'predecessor/ORDINARY-RESULT.json')['admitted'])
+    grid=10**15
+    for level in result['finite_backend_levels']:
+        a=F(99,100)*c1+F(1,100)*backend
+        numerator=-((-a.numerator*grid)//a.denominator)-1;b=F(numerator,grid)
+        L.need(backend<b<a<c1<F(1,100)<1-a,"Strict acyclic backend gaps")
+        L.need([str(backend),str(a),str(b)]==[level[k] for k in ['completed_backend','ordinary_exact','admitted']],"Exact backend level")
+        backend=b
+    L.need(backend==F(3497804579519,10**15),"Complete ordinary saving")
+    L.need(result['fee_bounds']['base_counts']['all_owned_allocated']==invoice['owned_allocated']==39,"Complete owned stock")
+    ops=glob['operation_counts'];scans=sum(ops[k] for k in ['ADD','OWNED_CLEAR','OWNED_ZERO_HEADER','WHOLE_ZERO_FRAME'])+78
+    parking=4*(11166+39)*56547;matcher=L.read(L.R/'MATCHER.json')
+    terms=matcher['global_occurrences']*matcher['paired_address_coefficient_terms_per_call']
+    L.need(terms==5472,"Every new residual matcher coefficient and both address halves")
+    fee=scans+parking+7548+7248+glob['expanded_event_count']+56547*(32*127**2+8*127**3)+terms
+    L.need(fee==result['fee_bounds']['base_counts']['coarse_primitive_count_with_dimension_work']<2**64,"All positive finite costs")
+    L.need(not alpha[1]<1-F(1,10**7) and not F('.00349780457955')<c1,"Unfunded contraction and raw-as-ordinary controls")
+    # The strict lower grid must also work when its argument is already on grid.
+    on_grid=F(7,grid)
+    L.need(F(-((-on_grid.numerator*grid)//on_grid.denominator)-1,grid)<on_grid,"Exact-grid strictness control")
+    return dict(admitted=str(backend),H0=h0,H1=h1,positive_base_fee=fee,matcher_coefficient_terms=terms)
+
+
+def main():
+    result = {"status": "PASS_G20_REFINEMENT_SEPARATE_ADJOINT_STREAM_ORDINARY",
+              "adjoint_moduli": [adjoint(m) for m in [101, 101 ** 2]], "global": stream(), "ordinary": pricing()}
+    try:
+        stream(corrupt=True)
+    except ValueError:
+        result["stale_query_epoch_rejected"] = True
+    else:
+        raise ValueError("Stale query epoch accepted")
+    L.put("INDEPENDENT-RESULT.json", result)
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/g20-refinement-admission/integration.py b/research/g20-refinement-admission/integration.py
new file mode 100644
index 0000000000..0321a125e6
--- /dev/null
+++ b/research/g20-refinement-admission/integration.py
@@ -0,0 +1,83 @@
+"""Install the exact source-audited G20 word and replay its native maps.
+
+PR5657 supplies the new construction. PR5662 supplies the audited word and
+frame-506 matcher. Native replay retains ai-nanachi PR5512 and PR5653 credit.
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from pathlib import Path
+from hashlib import sha256
+from fractions import Fraction as F
+import gzip,importlib.util,json,sys
+R=Path(__file__).resolve().parent
+sys.path.insert(0,str(R))
+S=R/'source/vendor/g20'
+PARTIAL=frozenset([462,463,466,468])
+
+
+def need(condition,message):
+    if not condition:raise ValueError(message)
+
+
+def read(path):
+    raw=path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix=='.gz' else raw)
+
+
+def put(name,value):
+    raw=(json.dumps(value,indent=2)+'\n').encode();path=R/name
+    path.write_bytes(gzip.compress(raw,mtime=0) if path.suffix=='.gz' else raw)
+
+
+def load(name,path):
+    spec=importlib.util.spec_from_file_location(name,path);module=importlib.util.module_from_spec(spec)
+    sys.modules[name]=module;spec.loader.exec_module(module);return module
+
+
+for item in read(R/'INPUTS.json'):
+    need(sha256((R/item['local']).read_bytes()).hexdigest()==item['sha256'],'Frozen input '+item['local'])
+SOURCE=load('retained_g20_source',R/'source/local_relations.py')
+source=SOURCE.source
+
+
+def matcher(frames,word):
+    record=read(R/'audited/RESULT.json')['matcher']
+    w=[[F(x) for x in row] for row in record['forward']]
+    wi=[[F(x) for x in row] for row in record['inverse']]
+    frame=frames['506']
+    need(w==list(map(list,zip(*[list(map(F,row)) for row in frame['B']+frame['A']]))),'Actual frame-506 basis')
+    def product(a,b):return [[sum(x*y for x,y in zip(row,col)) for col in zip(*b)] for row in a]
+    eye=[[F(i==j) for j in range(8)] for i in range(8)]
+    need(product(w,wi)==eye and product(wi,w)==eye,'Both actual matcher directions')
+    need(all(sum(F(x)*F(y) for x,y in zip(a,b))==0 for a in frame['A'] for b in frame['B']),'Orthogonal residual/complement')
+    count=sum(e[0]=='Q' and e[2:]==[506,0,4] for e in word['records'])
+    need(count==4 and record['common_denominator']==4,'New actual matcher occurrences and dyadic denominator')
+    out=dict(record,local_occurrences=count,global_occurrences=18*count,
+             paired_address_coefficient_terms_per_call=2*record['nonzero_coefficients'],
+             pricing='Both directions and both paired address halves are charged inside the complete positive normalizer fee.')
+    put('MATCHER.json',out);return out
+
+
+def run():
+    import native
+    word=read(R/'audited/WORD.json.gz');base,frames,_=source()
+    need(len(word['owned'])==39 and len(word['start'])==684,'Exact audited field allocation')
+    result=native.replay(base,frames,word['records'],set(word['owned']))
+    physical=[native.replay(base,frames,word['records'],set(word['owned']),m) for m in (101,101**2)]
+    need(result['paid']=={1:1288,2:1342,3:56,4:57,5:102,6:10,7:9},'Actual full local invoice')
+    m=matcher(frames,word)
+    controls=[]
+    for label,choose in [('missing_snapshot_clear',lambda e:e[0]=='ERASE' and e[1]==662 and e[2] is not None),
+                         ('missing_refined_query',lambda e:e==['Q',9,506,115,2]),
+                         ('missing_snapshot_return',lambda e:e[0]=='ERASE' and e[1]==662 and e[2] is None)]:
+        bad=[e[:] for e in word['records']];bad.pop(next(i for i,e in enumerate(bad) if choose(e)))
+        try:native.replay(base,frames,bad,set(word['owned']),101)
+        except (ValueError,StopIteration):controls.append(label)
+        else:raise ValueError('Corrupt native word accepted')
+    (R/'WORD.json.gz').write_bytes((R/'audited/WORD.json.gz').read_bytes())
+    data=dict(status='PASS_G20_REFINEMENT_NATIVE_ALL684_COLUMNS',stats=result,native_moduli=[v['native_modulus'] for v in physical],
+              matcher=m,rejected_controls=controls,canonical_word_sha256=sha256(json.dumps(word['records'],separators=(',',':')).encode()).hexdigest())
+    put('LOCAL-RESULT.json',data);return data
+
+
+if __name__=='__main__':
+    print(json.dumps(run(),indent=2))
diff --git a/research/g20-refinement-admission/native.py b/research/g20-refinement-admission/native.py
new file mode 100644
index 0000000000..1f060a7e09
--- /dev/null
+++ b/research/g20-refinement-admission/native.py
@@ -0,0 +1,50 @@
+"""Native replay adapted from ai-nanachi PR5512 for twenty-six extra addressable fields and thirty-nine owned banks.
+
+All source geometry and coframe checks are retained. Ali Romman with
+substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from collections import Counter
+import integration as B
+Geometry=B.SOURCE.Geometry
+need=B.need
+bitids=B.SOURCE.bitids
+N=658
+def replay(base,frames,program,owned,modulus=None):
+ width=max(N+2,max(owned)+1);extra=width-N
+ geom=Geometry(frames);st=base['final']+[None]*extra;rows=[1<<i for i in range(width)];norm=[1]*width;paid=Counter();ops=Counter();peak=1;active=set();livepeak=0
+ fields=None
+ if modulus:
+  point=tuple(v%modulus for v in(1,2,4,8,16,32,64,128,3,5,7,11,13,17,19,23));fields=[{point:1<<i}for i in range(width)]
+ def transform(field,p):return{geom.move(p,x,modulus):v for x,v in field.items()}
+ for ix,e in enumerate(program):
+  op,d=e[:2];ops[op]+=1
+  if op=='ERASE':
+   need(d in owned,'No retained original erasure');rows[d]=norm[d]=0;st[d]=e[2];active.discard(d)
+   if fields is not None:fields[d]={}
+  elif op=='INIT':need(d in owned and rows[d]==0,'Whole zero INIT');st[d]=e[2]
+  elif op=='ADD':
+   s,f=e[2:];need(d!=s and st[d]==st[s]==f,'Actual common-frame XOR');rows[d]^=rows[s];norm[d]+=norm[s];peak=max(peak,norm[d])
+   if d in owned:active.add(d)
+   if fields is not None:
+    for x,v in fields[s].items():
+     z=fields[d].get(x,0)^v
+     if z:fields[d][x]=z
+     else:fields[d].pop(x,None)
+  elif op in('Q','ZERO_Q'):
+   s,t,k=e[2:];need(st[d]==s,'Actual current source FRAME');geom.nested(s,t,k);st[d]=t
+   if op=='ZERO_Q':need(rows[d]==0 and(fields is None or not fields[d]),'Free move only whole zero')
+   else:
+    paid[k]+=1
+    if fields is not None:fields[d]=transform(fields[d],geom.residual_mod(s,t,k,modulus))
+  else:raise ValueError('Unknown event '+op)
+  livepeak=max(livepeak,len(active))
+ need(st==base['start']+[None]*extra,'All final frames')
+ expected=[0 if i in owned else (1<<i)^((1<<(i-111)) if 111<=i<222 else 0) for i in range(width)]
+ need(rows==expected,'All684 independent RAW and arbitrary DIRTY entry columns')
+ if fields is not None:
+  for o,row in enumerate(expected):
+   want={}
+   for i in bitids(row):
+    y=geom.move(geom.project_mod(base['start'][o],modulus),geom.move(geom.project_mod(base['final'][i],modulus),point,modulus),modulus);want[y]=want.get(y,0)^(1<<i)
+   need(fields[o]=={x:v for x,v in want.items()if v},'Full physical endpoint all684 symbols at output '+str(o))
+ return{'paid':dict(sorted(paid.items())),'operation_counts':dict(ops),'owned_allocated':len(owned),'owned_live_payload_peak':livepeak,'retained_originals':N-len(owned & set(range(N))),'positive_majorant_bits':peak.bit_length(),'positive_majorant':str(peak),'native_modulus':modulus}
diff --git a/research/g20-refinement-admission/ordinary.py b/research/g20-refinement-admission/ordinary.py
new file mode 100644
index 0000000000..fa294b613e
--- /dev/null
+++ b/research/g20-refinement-admission/ordinary.py
@@ -0,0 +1,73 @@
+"""Two exact moment engines and positive-fee finite ordinary bootstrap.
+
+Adapted from ai-nanachi PR5512 ordinary.py for Dugongue PR5657 refinements and the audited PR5662 word.
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+Uses the retained PR4814 finite acyclic bootstrap, with the new literal
+G20 refined-source invoice. No multiplication-kappa update is claimed.
+"""
+from fractions import Fraction as F
+from pathlib import Path
+import importlib.util,sys,json
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import integration as L
+from strict_margins import tensor_degree, compiler_cutoffs, below_grid, controls
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def load(n,p):
+ spec=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(spec);sys.modules[n]=m;spec.loader.exec_module(m);return m
+def enc(x):
+ if isinstance(x,F):return str(x)
+ if isinstance(x,dict):return {str(k):enc(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return [enc(v)for v in x]
+ return x
+def ceil(q):return -((-q.numerator)//q.denominator)
+def fee_bounds(invoice,glob,H1,v):
+ n=invoice['originals'];M=invoice['QUERYs'];owned=invoice['owned_allocated'];ops=glob['operation_counts'];park=4*(n+owned)*M
+ routes=7548+7248;scans=ops['ADD']+ops['OWNED_CLEAR']+ops['OWNED_ZERO_HEADER']+ops['WHOLE_ZERO_FRAME']+2*owned;raw=glob['expanded_event_count'];matcher=L.read(R/'MATCHER.json');matcher_terms=matcher['global_occurrences']*matcher['paired_address_coefficient_terms_per_call'];base=scans+park+routes+raw+M*(32*127**2+8*127**3)+matcher_terms
+ need(n==11166 and M==56547 and owned==39 and base<2**64,'Actual retained originals,39owned and positive complete finite fees')
+ need(glob['majorant_bits']<1024 and matcher['max_numerator_bits']<1024,'Fresh positive majorant and fixed matrix height')
+ need(v>=1024 and v%1024==0 and 256*v>=4*v*64,'Explicit tensor count envelope')
+ return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'new_matcher_coefficient_terms':matcher_terms,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':owned,'owned_productive_credit':0},
+ 'fixed_tensor_unit':{'v':v,'K':'2^'+str(256*v),'meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'},
+ 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets39distinct owned banks; C_N<=39*A(N). Denominator replication product <=A(n-1)^(n-1).'},
+ 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^60*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'},
+ 'all_in_fixed_primitive_fee':{'F':'39*(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=39*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'},
+ 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All39whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'},
+ 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}}
+def run():
+ invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()}
+ need(sum(T.values())==11166 and sum(P.values())==56547 and T.get(4,0)==0 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill')
+ E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py')
+ tested=F('.00349780457954');uniform=F('.00349780457953');cover_gap=F(1,10**14);rho=F(1,100);reserve=F(1,2**48);v=tensor_degree(reserve);t=1-tested;u=F(1,5)
+ target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11166*18),)*2,E.mul(E.power(17,tested),target))
+ need(alpha[1]<1-reserve and gamma[1]<F(31,32)and delta[1]<F(19,20),'All three actual charged compiler tails')
+ # An independent rational-series engine certifies the raw crossing and tested margin.
+ raw_lo=F('.00349780457955');raw_hi=F('.00349780457965');cross={}
+ for label,c,sign in(('lower',raw_lo,1),('upper',raw_hi,-1),('tested',tested,1)):
+  a=I.moment(T,1-c);b=I.moment(P,1-c);margin=(a[0]-b[1],a[1]-b[0]);need(margin[0]>0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin}
+ need(F(31,32)**128<F(1,16) and F(19,20)**128<F(1,16),'Tail block decay')
+ surplus=1-F(1)/(1+v*reserve)-F(4,2**(v//32));need(surplus>0 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient')
+ z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0,H1=compiler_cutoffs(tested,uniform,v)
+ need(H0>=8*v and H0*h*gap>gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds')
+ C1=uniform-cover_gap;need(F(2**60)*cover_gap>256,'Cover/bad-prime gap')
+ backend=F(L.read(R/'predecessor/ORDINARY-RESULT.json')['admitted']);old=backend;levels=[]
+ for j in range(1,6):
+  a=(1-rho)*C1+rho*backend;b=below_grid(a,10**15);need(backend<b<a<C1<rho<1-a,'Finite acyclic backend/adapter/stock/rounding gaps');levels.append({'level':j,'completed_backend':backend,'ordinary_exact':a,'admitted':b});backend=b
+ need(backend==F(3497804579519,10**15) and backend>old,'New complete ordinary component saving')
+ cmin=F(L.read(R/'predecessor/ORDINARY-RESULT.json')['admitted']);cmax=F('.0035')
+ worst_target=E.moment(T,1-cmax)
+ worst_gamma=E.divide(E.moment(P,1-cmin+u),E.mul(E.power(17,u),worst_target))
+ worst_delta=E.divide((F(11166*18),)*2,E.mul(E.power(17,cmin),worst_target))
+ need(worst_gamma[1]<F(31,32) and worst_delta[1]<F(19,20),'Uniform tail guards on the entire approach interval')
+ tails=[sum(k*n for k,n in T.items() if k>=a)-sum(k*n for k,n in P.items() if k>=a) for a in range(1,129)]
+ need(min(tails)>=0 and tails[0]==753,'Strict first-moment monotonicity from rank-mass tails')
+ range_certificate={'C_min':cmin,'C_max':cmax,'gamma_upper_bound':worst_gamma,'delta_upper_bound':worst_delta,
+                    'rank_mass_tails':tails,'tensor_reserve_controls':controls(),
+                    'claim':'Under the retained framework, every ordinary saving strictly below this invoice raw crossing is attainable with fresh finite margins. This is not a global optimality claim.'}
+
+ result={'status':'PASS_CONDITIONAL_G20_REFINEMENT_ORDINARY_FIVE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'grid_denominator':10**15,'prime_multiplier':2**60,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'uniform_signed_invoice_improvement':'Relative to PR5653: Pnew-Pold=-252H1-252H3+252H4; targets unchanged. Gain252*(1+3^t-4^t)>0 for0<t<1.','fee_bounds':fee_bounds(invoice,glob,H1,v),'strict_margin_range':range_certificate,'whole_kappa':None,'assumptions':'Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed.'}
+ L.put('ORDINARY-RESULT.json',enc(result));return enc(result)
+if __name__=='__main__':
+ r=run();print(json.dumps({k:r[k]for k in('status','admitted','comparator','relative_gain_percent','tail')},indent=2))
diff --git a/research/g20-refinement-admission/predecessor/ORDINARY-RESULT.json b/research/g20-refinement-admission/predecessor/ORDINARY-RESULT.json
new file mode 100644
index 0000000000..4c67e39485
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/ORDINARY-RESULT.json
@@ -0,0 +1,173 @@
+{
+  "status": "PASS_CONDITIONAL_G20_THREE_FUSIONS_ORDINARY_FOUR_FINITE_LEVELS",
+  "invoice": {
+    "paid": {
+      "1": 25101,
+      "2": 24156,
+      "3": 1260,
+      "4": 774,
+      "5": 1836,
+      "6": 180,
+      "7": 162,
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    },
+    "targets": {
+      "8": 7614,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "127": 222
+    },
+    "originals": 11166,
+    "owned_allocated": 17,
+    "owned_output_credit": 0,
+    "QUERYs": 56799,
+    "rank_surplus": 753
+  },
+  "params": {
+    "tested": "3488579543/1000000000000",
+    "uniform": "1744289771/500000000000",
+    "cover_gap": "95367431706161/6553600000000000000000000",
+    "rho": "1/100",
+    "v": 1024,
+    "alpha_gap": "1/549755813888",
+    "cutoff": 17,
+    "floor": 18,
+    "u": "1/5"
+  },
+  "raw_crossing_independent_exact": {
+    "lower": {
+      "saving": "43607244327/12500000000000",
+      "margin": [
+        "7919734133197966529998236818781/5000000000000000000000000000000000000000",
+        "1979933533299491632499559309747/1250000000000000000000000000000000000000"
+      ]
+    },
+    "upper": {
+      "saving": "174428977309/50000000000000",
+      "margin": [
+        "-13505186610048803452438773081801/5000000000000000000000000000000000000000",
+        "-2701037322009760690487754531963/1000000000000000000000000000000000000000"
+      ]
+    },
+    "tested": {
+      "saving": "3488579543/1000000000000",
+      "margin": [
+        "1696528605794544014969892414758523/2500000000000000000000000000000000000000",
+        "1696528605794544014969892414970071/2500000000000000000000000000000000000000"
+      ]
+    }
+  },
+  "tail": {
+    "alpha": [
+      "6277101735366650517861699873366972584217128087769022709511/6277101735386680763835789423207666416102355444464034512896",
+      "6277101735366650517861699873366972584217128087769022922505/6277101735386680763835789423207666416102355444464034512896"
+    ],
+    "gamma": [
+      "6023099459319610515725289743117679709662803891212299264189/6277101735386680763835789423207666416102355444464034512896",
+      "1505774864829902628931322435779419927415700972803074906081/1569275433846670190958947355801916604025588861116008628224"
+    ],
+    "delta": [
+      "734264830472636974347011704819768427149935024176668186029/784637716923335095479473677900958302012794430558004314112",
+      "1468529660945273948694023409639536854299870048353336422305/1569275433846670190958947355801916604025588861116008628224"
+    ],
+    "normalized_surplus": "536870911/576460753377165312",
+    "H0": 3786040782692352,
+    "H1": 26415808843142454516817921
+  },
+  "C1": "22862754791083768293839/6553600000000000000000000",
+  "finite_backend_levels": [
+    {
+      "level": 1,
+      "completed_backend": "3486609089/1000000000000",
+      "ordinary_exact": "2286262565642963461090061/655360000000000000000000000",
+      "admitted": "3488559823/1000000000000"
+    },
+    {
+      "level": 2,
+      "completed_backend": "3488559823/1000000000000",
+      "ordinary_exact": "2286275349973305861090061/655360000000000000000000000",
+      "admitted": "348857933/100000000000"
+    },
+    {
+      "level": 3,
+      "completed_backend": "348857933/100000000000",
+      "ordinary_exact": "2286275477814381061090061/655360000000000000000000000",
+      "admitted": "139543181/40000000000"
+    },
+    {
+      "level": 4,
+      "completed_backend": "139543181/40000000000",
+      "ordinary_exact": "2286275479092333061090061/655360000000000000000000000",
+      "admitted": "3488579527/1000000000000"
+    }
+  ],
+  "admitted": "3488579527/1000000000000",
+  "comparator": "3486609089/1000000000000",
+  "relative_gain": "1970438/3486609089",
+  "relative_gain_percent": "197043800/3486609089",
+  "uniform_signed_invoice_improvement": "Relative to PR5641: Pnew-Pold=-54H1-54H3+54H4; targets unchanged. Gain54*(1+3^t-4^t)>0 for0<t<1.",
+  "fee_bounds": {
+    "status": "PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA",
+    "base_counts": {
+      "raw_records": 445876,
+      "all_XOR_CLEAR_INIT_zeroheader_passes": 381563,
+      "parent_parking_FIELD_passes": 2540732868,
+      "internal_and_wholejob_routes": 14796,
+      "coarse_primitive_count_with_dimension_work": 962625977511,
+      "strict_upper": 18446744073709551616,
+      "all_owned_allocated": 17,
+      "owned_productive_credit": 0
+    },
+    "fixed_tensor_unit": {
+      "v": 1024,
+      "K": "2^262144",
+      "meaning": "Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting."
+    },
+    "finite_compiler": {
+      "N": "2^26415808843142454516817921",
+      "J(n)": "(n+1)^4*K^(4*n+4)",
+      "A(1)": "K^4",
+      "A(n)": "(J(n)+2)^4*(A(n-1)+2)^(4*n+8)",
+      "counts": "Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets17distinct owned banks; C_N<=17*A(N). Denominator replication product <=A(n-1)^(n-1)."
+    },
+    "height_prime": {
+      "base_height_bits": 1024,
+      "T": "(2*N+2)^4*(A(N)+2)^2",
+      "H": "1026*4^(T+1)",
+      "q": "Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice."
+    },
+    "all_in_fixed_primitive_fee": {
+      "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8",
+      "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.",
+      "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=17*A(N); F dominates their products.",
+      "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument."
+    },
+    "stock": {
+      "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend",
+      "D": "floor(log_N ceil(e/w))+1",
+      "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)",
+      "ownership": "All17whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed."
+    },
+    "eventual_threshold": {
+      "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.",
+      "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0",
+      "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).",
+      "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized."
+    }
+  },
+  "whole_kappa": null,
+  "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed."
+}
diff --git a/research/g20-refinement-admission/predecessor/PROOF.md b/research/g20-refinement-admission/predecessor/PROOF.md
new file mode 100644
index 0000000000..a5fa7ef776
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/PROOF.md
@@ -0,0 +1,195 @@
+# Three native G20 return fusions
+
+The conditional ordinary BIT saving is `0.003488579527`. It exceeds the
+completed PR5648 component by `0.000000657061`. The selected complete
+multiplication coefficient is unchanged. All retained native, ROW,
+compiler, precision, tape, and analytic contracts remain assumptions.
+
+Dugongue PR5639 supplies two source-snapshot fusions. This package emits
+both together with the released helper444 continuation in PR5647. It
+uses the direct SOURCE77 snapshot reported during PR5648 instead of the
+five-source gather. It resolves the shared-centre lifetimes in the full
+composition and reuses the old zero centre for one snapshot. The source word is ai-nanachi PR5512 with Ali Romman PR5421's
+nine relations and PR5641's four retirements. Frozen source code, proof,
+ordinary record, and proposal are authenticated by `INPUTS.json`.
+
+## 1. Native identity and actual versions
+
+Let the helper descend from frame U through L to ground. Write its native
+maps as `G3: L -> U`, `G1: ground -> L`, and `G4=G3*G1`.
+These are the actual source frame operators, with ADDRESS and ROW.
+The source nested-projector checks establish their literal composition;
+the identity is not inferred from ranks alone. The old return is
+
+```text
+G1^-1 * (G3^-1 * h_U + x_L).
+```
+
+If a prior source version is `x_U=G3*x_L`, the same return is
+`G4^-1*(h_U+x_U)`. Copy that actual version into an owned snapshot before
+its deadline. Add it to the helper at U, query rank four on the helper,
+and clear the snapshot. Omit the old rank-three query, line ADD, and
+rank-one query. No helper observer occurs inside the replaced interval.
+Every observer outside it sees the original full function. Every helper
+input remains arbitrary and independent. No productive target is lost.
+
+The input word for these indices is the exact four-retirement word
+rebuilt by `baseline.py`. Each capture cut is immediately before that
+numbered record. Each query index names a record in the same word.
+
+| Helper | SOURCE | U | Capture cut | Old H3 | Old line ADD | Old H1 | Snapshot bank |
+| --- | --- | --- | --- | --- | --- | --- | --- |
+| 444 | 77 | 509 | 14957 | 16157 | 19362 | 19363 | 658 |
+| 467 | 38 | 509 | 14964 | 16151 | 19219 | 19220 | 660 |
+| 465 | 19 | 508 | 15062 | 16172 | 19221 | 19222 | 661 |
+
+PR5647 constructs the first return from five earlier values. The direct
+SOURCE77 version was reported during PR5648. The other two returns are
+Dugongue's construction. Their composition is the new contribution here. Their U projectors already occur in the source.
+The three SOURCE fields follow their unchanged trajectories. `fusion.py`
+checks the exact normalized row at the capture, not only the frame name.
+Under the retained coframe identity, equal rows at one frame represent
+equal whole functions for every width and all independent input columns.
+
+## 2. Reuse only the proved whole-zero centre
+
+The old centre, field 658, is whole zero after its first clear throughout
+the baseline word. This follows from the source nine owned relations.
+The emitter verifies that invariant at every centre access. It removes
+all 546 obsolete centre accesses, including reads of zero into retained
+fields. It then uses bank 658 for helper 444's snapshot and returns it
+at zero with its old null frame. No live frame is renamed.
+
+Banks 660 and 661 are new. The three snapshot lifetimes overlap. They
+cannot be assigned one shared array. The whole construction allocates
+17 owned banks, rather than 18 for three newly allocated snapshots.
+Every first use includes whole-field CLEAR. Every last use includes
+teardown. The original dirty contents of all 17 banks are annihilated.
+The old source shadow remains distinct and retains all its uses.
+
+`lifetime_audit.py` checks every original owned bank at every cut of each
+capture interval. Only bank658 remains whole zero. All three intervals
+overlap, which requires two additional banks in this direct-copy schedule.
+A different storage encoding or changed producer is outside this result.
+
+The same audit checks every remaining nonzero query row against the span
+of all earlier field observations at its destination frame. No row is in
+that span. This excludes only direct historical replacement in this word.
+
+## 3. Exact scope of the extension search
+
+The discovery pass checks every retained field, including main fields.
+It enumerates every nested run of at least two paid queries with any
+number of destination ADDs and no intervening source observer of that
+field. There are 667 such blocks. A block can be replaced by one query
+only if its injected normalized row can be prepared at the first frame.
+
+For each block, the screen permits arbitrary binary combinations of all
+prior single-field observations at that frame. This is more permissive
+than one direct SOURCE snapshot. Gaussian elimination on 660 independent
+original and dirty symbols tests membership exactly. Only the three
+rows above pass. Each has a direct SOURCE version, so no optimistic
+multi-snapshot combination is used in the emitted word.
+
+`window_audit.py` enumerates the blocks by maximal observer-free segments
+and uses elimination with the opposite pivot order. It independently
+checks all 667 keys and the same three survivors. This is a second
+implementation by the same author and AI assistant, not independent
+scientific review. The census is complete for this frozen source domain.
+It does not exclude a changed producer, protected-read retiming, a paid
+frame conversion, or a new word with different observations.
+
+## 4. Full caller and positive costs
+
+The local word retains 645 original fields and returns 17 owned fields
+at zero. Forward native and adjoint checks track all 662 entry columns
+at separate address points over moduli 101 and 10201. The exact rational
+frame checks are retained. The all-width claim is conditional on the
+source coframe theorem; finite address checks alone do not prove it.
+Stale source capture, missing teardown, and a stale global epoch fail.
+
+Install the word in all 18 thick G20 calls. Keep thin queries, idles,
+boundaries, bridges, routes, and all existing target debits. The emitted
+445,876-event caller retains 11,166 independent originals and pays
+56,799 queries. Its actual query descriptors include chronological
+owner, version, epoch, normalized row, and prefix hash. Separate stream
+replay checks every original and dirty column, source descriptor, target
+owner, and cost count. No owned bank has output credit.
+
+Relative to PR5641, the complete signed change is
+
+```text
+P_new-P_old = -54 H1 -54 H3 +54 H4
+T_new-T_old = 0
+```
+
+Relative to PR5648, the change is `-18 H1 -18 H3 +18 H4`, with
+unchanged targets.
+
+Thus the target-minus-paid gain is `54*(1+3^t-4^t)>0` for `0<t<1`.
+Relative to PR5512, the four retirements and these three fusions give
+`126*(1+3^t-4^t)`. The third fusion increases the proposed fusion gain
+by one half. It does not change the rank surplus, which stays 753.
+
+The new positive envelope has 516 bits. The finite base cost bound is
+`962625977511<2^64`. It includes all scans, 17 owned banks, parent parking,
+routes, and dimension work. The ordinary compiler reserves 17 separate
+banks for each instance, including suspended instances. These costs
+are absorbed with fresh finite constants, not called free operations.
+
+## 5. Exact ordinary admission
+
+Two rational interval engines place the new raw crossing in
+`(0.00348857954616,0.00348857954618)`. Use tested saving
+`0.003488579543`, uniform saving `0.003488579542`, tensor power 1024,
+cutoff 17, floor 18, and second moment parameter `1/5`. All three source
+compiler guards hold for the actual complete invoice:
+
+```text
+P_t/T_t < 1-2^-39
+P_(t+1/5)/(17^(1/5)*T_t) < 31/32
+11166*18/(17^tested*T_t) < 19/20
+```
+
+The normalized surplus is `536870911/576460753377165312`.
+The fresh finite thresholds are
+
+```text
+H0 = 3786040782692352
+H1 = 26415808843142454516817921
+N = 2^H1
+```
+
+Complete small targets on the same owner, charge all paid splitting,
+and retain `17^64<18^63`. The source finite count, height, prime,
+normalizer, route, stock, borrowed-digit, and threshold formulas are in
+`ORDINARY-RESULT.json`. They use the new counts, fresh thresholds,
+`C_N<=17*A(N)`, and the same positive primitive model described in
+`source/retirement-proof.md`. No old numerical machine threshold is reused.
+
+With cover gap `2^-36+10^-20` and atom fraction `1/100`, begin at the
+completed PR5641 ordinary backend `0.003486609089`. Four finite acyclic
+levels admit `0.003488559823`, `0.003488579330`, `0.003488579525`, and
+**`0.003488579527`**. Each level freezes the previous completed algorithm
+before it uses that algorithm as an atom backend. All improvement,
+adapter, stock, and rounding gaps are positive. A fifth level does not
+change the admitted value at this grid. The result is less than
+`1.92e-11` below the raw crossing for the new bill.
+
+The finite uniform program and its very large decimal threshold are
+algorithm-defined, not materialized. The source framework premises
+remain conditional. This is an ordinary BIT component construction;
+a compatible complex supplier and complete caller are still needed to
+increase the complete multiplication coefficient.
+
+## Open next questions
+
+Can a changed producer or a priced frame conversion make another injected
+row available before a protected observer? A useful next result must
+emit that native continuation and price its complete caller. More
+search within the 667 frozen blocks cannot add a fourth fusion. The helper444 composition was released in Discussion5638.
+
+Credit Dugongue, ai-nanachi, Ali Romman PR5421/5641/5648/5647, DreamingOfClouds,
+eumemic, Cinna Davis, rohanarun, zxv, Jacob Alan Sussman, and all source
+notices. Prepared by Ali Romman with substantial OpenAI Codex assistance.
+New work is Apache-2.0. Frozen sources remain unchanged.
diff --git a/research/g20-refinement-admission/predecessor/global_retirement.py b/research/g20-refinement-admission/predecessor/global_retirement.py
new file mode 100644
index 0000000000..ec0194d8c0
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/global_retirement.py
@@ -0,0 +1,111 @@
+"""Literal p16/a7 caller with thirteen retired helper targets and seventeen owned fields.
+
+Adapted from ai-nanachi PR5512 global_relations.py. The four retirements
+are Dugongue PR5629. Dugongue PR5639 gives two snapshot fusions; this
+version adds the third and reuses the zero centre. Implementation by Ali Romman with OpenAI Codex assistance.
+Apache-2.0; retain the source notices.
+
+Retains G20 native controller/geometry; uses the independently checked reverse
+physical involution at each full call. No old helper target is given to owned work.
+"""
+from pathlib import Path
+from collections import Counter
+from hashlib import sha256
+from time import process_time
+import gzip,json,importlib.util,sys
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import fusion as L
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def read(p):return L.read(p)
+def put(n,x):L.put(n,x)
+def run():
+ clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=sorted(x for x in owned if x<658);need(pivots==[462,463,466,468]+list(range(469,478)),'Exact thirteen retired helper owners')
+ oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+len(owned)));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:15]));snapshotwork={660:W[15],661:W[16]};need(N==11166,'New retained original count')
+ values=[1<<i for i in range(N+len(owned))];norm=[1]*(N+len(owned));versions=[0]*(N+len(owned));epochs=[0]*(N+len(owned));counts=Counter();paid=Counter();peak=1;events=[];source=[];calls=[];episodes=[];prefix=sha256()
+ def emit(e):counts[e[0]]+=1;events.append(e);prefix.update((json.dumps(e,separators=(',',':'))+'\n').encode())
+ def erase(d,why,frame=None):
+  need(d in W,'Only owned wholepayload erasure');values[d]=norm[d]=0;versions[d]+=1;epochs[d]+=1;emit(['OWNED_CLEAR',d,frame,why])
+ for d in W:erase(d,'GLOBAL_ENTRY_ARBITRARY_DIRTY')
+ def add(d,s,why):
+  nonlocal peak
+  need(d!=s,'Distinct source/destination');values[d]^=values[s];norm[d]+=norm[s];peak=max(peak,norm[d]);versions[d]+=1;emit(['ADD',d,s,why])
+ def query(d,k,detail):
+  need(k>0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail])
+ def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why)
+ def boundary(program,why):
+  for op,d,s in program:
+   for p in range(111):
+    if op=='ADD':add(compact[d*111+p],compact[s*111+p],why)
+    else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why)
+ boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY')
+ thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)}
+ for event in controller['physical_events']:
+  op=event[0]
+  if op=='LOCAL':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   helper=3552+436*stage_index[stage]
+   def owner(r):
+    if r==658:return center
+    if r==659:return shadow
+    if r in pivotwork:return pivotwork[r]
+    if r in snapshotwork:return snapshotwork[r]
+    return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222]
+   sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers}
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY'])
+   start=len(events);lp=Counter();st=local['start'][:];livebegin={}
+   for ix,e in enumerate(local['records']):
+    typ,d=e[:2];gd=owner(d)
+    if typ=='ERASE':
+     erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2]
+     if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1})
+    elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage])
+    elif typ=='ADD':
+     s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe')
+     if gd in W and gd not in livebegin:livebegin[gd]=len(events)
+     add(gd,owner(s),['LOCAL',stage,f,ix])
+    elif typ in('Q','ZERO_Q'):
+     a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b
+     if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1
+     else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage])
+    else:raise ValueError('Local opcode '+typ)
+   need(not livebegin and st==local['final'],'No live local owned state at return')
+   need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs')
+   need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All423 independent retained helper inputs and17owned returns')
+   need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count')
+   calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':423,'paid':dict(lp)})
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN'])
+  elif op=='QUERY_SHEAR':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   for p in range(111):
+    src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1})
+  elif op=='IDLE':
+   _,pair,stages=event;k=7*len(stages)
+   for bank in(2*pair,2*pair+1):
+    for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p])
+  elif op=='ADD':
+   for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE')
+  else:
+   need(op=='SWAP','Known controller event')
+   for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP')
+ boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY')
+ for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN')
+ need(values==[1<<i for i in range(N)]+[0]*17,'All11166 independent retained RAW and all17 arbitrary DIRTY entry columns annihilated')
+ oldtargets=read(S/'provider/data/TARGET-OWNERS.json');targets=[dict(t,original_owner=compact[t['original_owner']])for t in oldtargets if t['original_owner']not in retired];T=Counter(t['rank']for t in targets)
+ P={int(k):v for k,v in read(S/'provider/data/INVOICE.json')['paid'].items()};P[1]-=288;P[7]-=162;P[3]-=126;P[4]+=54
+ need(paid==P and sum(T.values())==N and T[4]==0 and T[8]==7614,'Literal complete changed invoice including every partial helper')
+ # Retained exact physical MAIN polynomial proof, independent of the new ledger.
+ spec=importlib.util.spec_from_file_location('old_global',S/'provider/build_global.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);physical=mod.physical_main(controller)
+ stream=b''.join((json.dumps(e,separators=(',',':'))+'\n').encode()for e in events);need(sha256(stream).hexdigest()==prefix.hexdigest(),'Exact prefix and fullstream identity');(R/'GLOBAL.jsonl.gz').write_bytes(gzip.compress(stream,mtime=0))
+ invoice={'paid':dict(sorted(paid.items())),'targets':dict(sorted(T.items())),'originals':N,'owned_allocated':17,'owned_output_credit':0,'QUERYs':sum(paid.values()),'rank_surplus':sum(k*v for k,v in T.items())-sum(k*v for k,v in paid.items())}
+ result={'status':'PASS_LITERAL_G20_THREE_FUSIONS_11166_RETAINED_RAW','invoice':invoice,'expanded_event_count':len(events),'canonical_stream_sha256':sha256(stream).hexdigest(),'operation_counts':dict(counts),'calls':len(calls),'owned_payload_episodes':len(episodes),'source_descriptors':len(source),'majorant_bits':peak.bit_length(),'majorant':str(peak),'retired_original_old_ids':sorted(retired),'retained_old_ids':retained,'shared_owned_ids':W,'CPU_seconds':process_time()-clock,'physical_MAIN_coefficients':physical}
+ put('GLOBAL-RESULT.json',result);put('INVOICE.json',invoice);put('CALLS.json',calls);put('PRIVATE-EPISODES.json',episodes);put('TARGET-OWNERS.json',targets);put('SOURCE-DESCRIPTORS.json.gz',source)
+ return {k:result[k]for k in('status','invoice','expanded_event_count','canonical_stream_sha256','operation_counts','majorant_bits','owned_payload_episodes','CPU_seconds')}
+if __name__=='__main__':print(json.dumps(run(),indent=2))
diff --git a/research/g20-refinement-admission/predecessor/independent.py b/research/g20-refinement-admission/predecessor/independent.py
new file mode 100644
index 0000000000..16a5e1045b
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/independent.py
@@ -0,0 +1,166 @@
+"""Separate adjoint, stream and rational-series checks for the emitted caller.
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+This is a second implementation, not independent human review.
+"""
+from collections import Counter
+from fractions import Fraction as F
+from hashlib import sha256
+from pathlib import Path
+import gzip
+import json
+import sys
+
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+import fusion as L
+
+
+def adjoint(modulus):
+    base, frames, _ = L.source()
+    data = L.read(L.R / "WORD.json.gz")
+    owned = set(data["owned"])
+    word = data["records"]
+    geometry = L.SOURCE.Geometry(frames)
+    point = tuple(v % modulus for v in (1, 3, 9, 27, 2, 6, 18, 54, 5, 15, 45, 34, 7, 21, 63, 88))
+    fields = [{point: 1 << i} for i in range(662)]
+    raw = [1 << i for i in range(662)]
+    for e in reversed(word):
+        op, d = e[:2]
+        if op == "ADD":
+            s = e[2]
+            raw[s] ^= raw[d]
+            for x, value in fields[d].items():
+                fields[s][x] = fields[s].get(x, 0) ^ value
+                if not fields[s][x]:
+                    del fields[s][x]
+        elif op in ["ERASE", "ZERO_Q", "INIT"]:
+            # A zero-only header map has the total zero extension.
+            L.need(d in owned, "Adjoint zero map is owned")
+            raw[d] = 0
+            fields[d] = {}
+        else:
+            L.need(op == "Q", "Adjoint opcode")
+            residual = geometry.residual_mod(*e[2:], modulus)
+            fields[d] = {geometry.move(residual, x, modulus): value for x, value in fields[d].items()}
+    expected = [0 if i in owned else (1 << i) ^ ((1 << (i + 111)) if i < 111 else 0) for i in range(662)]
+    L.need(raw == expected, "Every adjoint RAW/DIRTY column")
+    for output, row in enumerate(expected):
+        want = {}
+        for source in L.SOURCE.bitids(row):
+            x = geometry.move(geometry.project_mod(base["start"][source], modulus), point, modulus)
+            x = geometry.move(geometry.project_mod(base["final"][output], modulus), x, modulus)
+            want[x] = want.get(x, 0) ^ (1 << source)
+        L.need(fields[output] == {x: v for x, v in want.items() if v}, "All adjoint physical columns")
+    return modulus
+
+
+def stream(corrupt=False):
+    invoice = L.read(L.R / "INVOICE.json")
+    n, own = invoice["originals"], invoice["owned_allocated"]
+    values = [1 << i for i in range(n + own)]
+    norms = [1] * (n + own)
+    versions, epochs = [0] * (n + own), [0] * (n + own)
+    sources = iter(L.read(L.R / "SOURCE-DESCRIPTORS.json.gz"))
+    paid, ops, prefix, peak, used = Counter(), Counter(), sha256(), 1, 0
+    with gzip.open(L.R / "GLOBAL.jsonl.gz", "rb") as handle:
+        for event, line in enumerate(handle):
+            e = json.loads(line)
+            op, d = e[:2]
+            ops[op] += 1
+            if op == "ADD":
+                values[d] ^= values[e[2]]
+                norms[d] += norms[e[2]]
+                peak = max(peak, norms[d])
+                versions[d] += 1
+            elif op == "OWNED_CLEAR":
+                L.need(n <= d < n + own, "Only owned global erasure")
+                values[d] = norms[d] = 0
+                versions[d] += 1
+                epochs[d] += 1
+            elif op == "QUERY":
+                item = next(sources)
+                if corrupt and not used:
+                    item["epoch"] += 1
+                expected = {"event": event, "prefix_sha256": prefix.hexdigest(), "owner": d,
+                            "rank": e[2], "version": versions[d], "epoch": epochs[d], "RAW_hex": hex(values[d])}
+                L.need(all(item[k] == v for k, v in expected.items()), "Actual chronological query descriptor")
+                used += 1
+                paid[e[2]] += 1
+                versions[d] += 1
+            elif op in ["OWNED_ZERO_HEADER", "WHOLE_ZERO_FRAME"]:
+                L.need(n <= d < n + own and values[d] == 0, "Whole zero global frame change")
+            else:
+                L.need(op == "PAID_PORT_ROUTE", "Known global event")
+            prefix.update(line)
+    L.need(next(sources, None) is None, "No unused source descriptor")
+    L.need(values == [1 << i for i in range(n)] + [0] * own, "All global RAW and DIRTY columns")
+    L.need(paid == {int(k): v for k, v in invoice["paid"].items()}, "Recounted global invoice")
+    original_targets = L.read(L.S / "provider/data/TARGET-OWNERS.json")
+    old_calls = L.read(L.S / "provider/data/CALLS.json")
+    retired = {c["helper_owner_begin"] + h - 222 for c in old_calls for h in list(L.PARTIAL) + list(range(469, 478))}
+    targets = Counter(t["rank"] for t in original_targets if t["original_owner"] not in retired)
+    L.need(targets == {int(k): v for k, v in invoice["targets"].items()}, "Every retired target is debited")
+    L.need(len(retired) == 234 and sum(targets.values()) == n == 11166 and own == 17, "Global ownership census")
+    g = L.read(L.R / "GLOBAL-RESULT.json")
+    L.need(prefix.hexdigest() == g["canonical_stream_sha256"] and ops == g["operation_counts"], "Recounted literal stream")
+    L.need(peak.bit_length() == g["majorant_bits"] == 516, "Fresh precision envelope")
+    return {"events": event + 1, "queries": used, "originals": n, "owned": own, "majorant_bits": peak.bit_length()}
+
+
+def pricing():
+    I = L.load("retirement_second_series", L.S / "ordinary-certificate/inputs/separate_series.py")
+    invoice = L.read(L.R / "INVOICE.json")
+    result = L.read(L.R / "ORDINARY-RESULT.json")
+    glob = L.read(L.R / "GLOBAL-RESULT.json")
+    paid, target = ({int(k): v for k, v in invoice[name].items()} for name in ["paid", "targets"])
+    c, uniform, reserve = F(".003488579543"), F(".003488579542"), F(1, 2 ** 39)
+    denominator = I.moment(target, 1 - c)
+    alpha = I.div(I.moment(paid, 1 - c), denominator)
+    gamma = I.div(I.moment(paid, 1 - c + F(1, 5)), I.mul(I.power(17, F(1, 5)), denominator))
+    delta = I.div((F(11166 * 18),) * 2, I.mul(I.power(17, c), denominator))
+    L.need(alpha[1] < 1 - reserve and gamma[1] < F(31, 32) and delta[1] < F(19, 20), "Independent three compiler tails")
+    for name, interval in [("alpha", alpha), ("gamma", gamma), ("delta", delta)]:
+        other = [F(x) for x in result["tail"][name]]
+        L.need(max(interval[0], other[0]) <= min(interval[1], other[1]), "Separate rational engines agree")
+    gap, h, v = (c - uniform) / 2, F(1, 64), 1024
+    z0 = 1 - (c + uniform) / 2
+    expr = (gap * (5 + 8 * h) * v + 1 + 8 * v * (1 - z0)) / (h * gap)
+    h0 = -((-expr.numerator) // expr.denominator)
+    h1 = (h0 * (1 - z0) / gap).__floor__() + 1
+    L.need([h0, h1] == [result["tail"]["H0"], result["tail"]["H1"]], "Fresh integer compiler thresholds")
+    cover = F(1, 2 ** 36) + F(1, 10 ** 20)
+    L.need(2 ** 45 * cover > 256, "Positive cover charge")
+    c1 = uniform - cover
+    backend = F(3486609089,10**12)
+    for level in result["finite_backend_levels"]:
+        a = F(99, 100) * c1 + F(1, 100) * backend
+        b = F((a * 10 ** 12).__floor__(), 10 ** 12)
+        L.need(backend < b < a < c1 < F(1, 100) < 1 - a, "All finite acyclic backend gaps")
+        L.need([str(backend), str(a), str(b)] == [level[k] for k in ["completed_backend", "ordinary_exact", "admitted"]], "Literal backend levels")
+        backend = b
+    L.need(backend == F(3488579527,10**12), "Admitted ordinary saving")
+    L.need(result["fee_bounds"]["base_counts"]["all_owned_allocated"] == invoice["owned_allocated"] == 17, "All owned arrays in finite fees")
+    ops = glob["operation_counts"]
+    scans = sum(ops[k] for k in ["ADD", "OWNED_CLEAR", "OWNED_ZERO_HEADER", "WHOLE_ZERO_FRAME"]) + 34
+    parking = 4 * (11166 + 17) * 56799
+    fee = scans + parking + 7548 + 7248 + glob["expanded_event_count"] + 56799 * (32 * 127 ** 2 + 8 * 127 ** 3)
+    L.need(fee == result["fee_bounds"]["base_counts"]["coarse_primitive_count_with_dimension_work"] < 2 ** 64, "Recounted positive finite fees")
+    L.need(not alpha[1] < 1 - F(1, 10 ** 7) and not F(".00348857954616") < c1, "Unfunded alpha and raw-as-ordinary controls")
+    return {"admitted": str(backend), "H0": h0, "H1": h1, "positive_base_fee": fee}
+
+
+def main():
+    result = {"status": "PASS_G20_FUSION_SEPARATE_ADJOINT_STREAM_ORDINARY",
+              "adjoint_moduli": [adjoint(m) for m in [101, 101 ** 2]], "global": stream(), "ordinary": pricing()}
+    try:
+        stream(corrupt=True)
+    except ValueError:
+        result["stale_query_epoch_rejected"] = True
+    else:
+        raise ValueError("Stale query epoch accepted")
+    L.put("INDEPENDENT-RESULT.json", result)
+    print(json.dumps(result, indent=2))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/g20-refinement-admission/predecessor/native.py b/research/g20-refinement-admission/predecessor/native.py
new file mode 100644
index 0000000000..caed1cf99b
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/native.py
@@ -0,0 +1,49 @@
+"""Native replay adapted from ai-nanachi PR5512 for two extra owned banks.
+
+All source geometry and coframe checks are retained. Ali Romman with
+substantial OpenAI Codex assistance. Apache-2.0.
+"""
+from collections import Counter
+import baseline as B
+Geometry=B.SOURCE.Geometry
+need=B.need
+bitids=B.SOURCE.bitids
+N=658
+def replay(base,frames,program,owned,modulus=None):
+ geom=Geometry(frames);st=base['final']+[None]*4;rows=[1<<i for i in range(N+4)];norm=[1]*(N+4);paid=Counter();ops=Counter();peak=1;active=set();livepeak=0
+ fields=None
+ if modulus:
+  point=tuple(v%modulus for v in(1,2,4,8,16,32,64,128,3,5,7,11,13,17,19,23));fields=[{point:1<<i}for i in range(N+4)]
+ def transform(field,p):return{geom.move(p,x,modulus):v for x,v in field.items()}
+ for ix,e in enumerate(program):
+  op,d=e[:2];ops[op]+=1
+  if op=='ERASE':
+   need(d in owned,'No retained original erasure');rows[d]=norm[d]=0;st[d]=e[2];active.discard(d)
+   if fields is not None:fields[d]={}
+  elif op=='INIT':need(d in owned and rows[d]==0,'Whole zero INIT');st[d]=e[2]
+  elif op=='ADD':
+   s,f=e[2:];need(d!=s and st[d]==st[s]==f,'Actual common-frame XOR');rows[d]^=rows[s];norm[d]+=norm[s];peak=max(peak,norm[d])
+   if d in owned:active.add(d)
+   if fields is not None:
+    for x,v in fields[s].items():
+     z=fields[d].get(x,0)^v
+     if z:fields[d][x]=z
+     else:fields[d].pop(x,None)
+  elif op in('Q','ZERO_Q'):
+   s,t,k=e[2:];need(st[d]==s,'Actual current source FRAME');geom.nested(s,t,k);st[d]=t
+   if op=='ZERO_Q':need(rows[d]==0 and(fields is None or not fields[d]),'Free move only whole zero')
+   else:
+    paid[k]+=1
+    if fields is not None:fields[d]=transform(fields[d],geom.residual_mod(s,t,k,modulus))
+  else:raise ValueError('Unknown event '+op)
+  livepeak=max(livepeak,len(active))
+ need(st==base['start']+[None]*4,'All final frames')
+ expected=[0 if i in owned else (1<<i)^((1<<(i-111)) if 111<=i<222 else 0) for i in range(N+4)]
+ need(rows==expected,'All662 independent RAW and arbitrary DIRTY entry columns')
+ if fields is not None:
+  for o,row in enumerate(expected):
+   want={}
+   for i in bitids(row):
+    y=geom.move(geom.project_mod(base['start'][o],modulus),geom.move(geom.project_mod(base['final'][i],modulus),point,modulus),modulus);want[y]=want.get(y,0)^(1<<i)
+   need(fields[o]=={x:v for x,v in want.items()if v},'Full physical endpoint all662 symbols at output '+str(o))
+ return{'paid':dict(sorted(paid.items())),'operation_counts':dict(ops),'owned_allocated':len(owned),'owned_live_payload_peak':livepeak,'retained_originals':N-len(owned-{658,659,660,661}),'positive_majorant_bits':peak.bit_length(),'positive_majorant':str(peak),'native_modulus':modulus}
diff --git a/research/g20-refinement-admission/predecessor/ordinary.py b/research/g20-refinement-admission/predecessor/ordinary.py
new file mode 100644
index 0000000000..d34b178ce4
--- /dev/null
+++ b/research/g20-refinement-admission/predecessor/ordinary.py
@@ -0,0 +1,61 @@
+"""Two exact moment engines and positive-fee finite ordinary bootstrap.
+
+Adapted from ai-nanachi PR5512 ordinary.py for Dugongue PR5639 fusions and the third native window.
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+Uses the retained PR4814 finite acyclic bootstrap, with the new literal
+G20 three-fusion invoice. No multiplication-kappa update is claimed.
+"""
+from fractions import Fraction as F
+from pathlib import Path
+import importlib.util,sys,json
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import fusion as L
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def load(n,p):
+ spec=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(spec);sys.modules[n]=m;spec.loader.exec_module(m);return m
+def enc(x):
+ if isinstance(x,F):return str(x)
+ if isinstance(x,dict):return {str(k):enc(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return [enc(v)for v in x]
+ return x
+def ceil(q):return -((-q.numerator)//q.denominator)
+def fee_bounds(invoice,glob,H1,v):
+ n=invoice['originals'];M=invoice['QUERYs'];owned=invoice['owned_allocated'];ops=glob['operation_counts'];park=4*(n+owned)*M
+ routes=7548+7248;scans=ops['ADD']+ops['OWNED_CLEAR']+ops['OWNED_ZERO_HEADER']+ops['WHOLE_ZERO_FRAME']+2*owned;raw=glob['expanded_event_count'];base=scans+park+routes+raw+M*(32*127**2+8*127**3)
+ need(n==11166 and M==56799 and owned==17 and base<2**64,'Actual retained originals,17owned and positive complete finite fees')
+ need(glob['majorant_bits']==516 and 516<1024,'Fresh positive majorant and fixed matrix height')
+ need(v==1024 and 256*v>=4*v*64,'Explicit tensor count envelope')
+ return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':owned,'owned_productive_credit':0},
+ 'fixed_tensor_unit':{'v':v,'K':'2^262144','meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'},
+ 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets17distinct owned banks; C_N<=17*A(N). Denominator replication product <=A(n-1)^(n-1).'},
+ 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'},
+ 'all_in_fixed_primitive_fee':{'F':'(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=17*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'},
+ 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All17whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'},
+ 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}}
+def run():
+ invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()}
+ need(sum(T.values())==11166 and sum(P.values())==56799 and T.get(4,0)==0 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill')
+ E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py')
+ tested=F('.003488579543');uniform=F('.003488579542');cover_gap=F(1,2**36)+F(1,10**20);rho=F(1,100);reserve=F(1,2**39);v=1024;t=1-tested;u=F(1,5)
+ target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11166*18),)*2,E.mul(E.power(17,tested),target))
+ need(alpha[1]<1-reserve and gamma[1]<F(31,32)and delta[1]<F(19,20),'All three actual charged compiler tails')
+ # An independent rational-series engine certifies the raw crossing and tested margin.
+ raw_lo=F('.00348857954616');raw_hi=F('.00348857954618');cross={}
+ for label,c,sign in(('lower',raw_lo,1),('upper',raw_hi,-1),('tested',tested,1)):
+  a=I.moment(T,1-c);b=I.moment(P,1-c);margin=(a[0]-b[1],a[1]-b[0]);need(margin[0]>0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin}
+ need(F(31,32)**128<F(1,16) and F(19,20)**128<F(1,16),'Tail block decay')
+ surplus=1-F(1)/(1+v*reserve)-F(4,2**32);need(surplus>0 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient')
+ z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0=ceil((gap*(5+8*h)*v+1+8*v*(1-z0))/(h*gap));H1=(H0*(1-z0)/(z-z0)).__floor__()+1
+ need(H0>=8*v and H0*h*gap>=gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds')
+ C1=uniform-cover_gap;need(F(2**45)*cover_gap>256,'Cover/bad-prime gap')
+ backend=F(3486609089,10**12);old=backend;levels=[]
+ for j in range(1,5):
+  a=(1-rho)*C1+rho*backend;b=F((a*10**12).__floor__(),10**12);need(backend<b<a<C1<rho<1-a,'Finite acyclic backend/adapter/stock/rounding gaps');levels.append({'level':j,'completed_backend':backend,'ordinary_exact':a,'admitted':b});backend=b
+ need(backend==F(3488579527,10**12) and backend>old,'New complete ordinary component saving')
+ result={'status':'PASS_CONDITIONAL_G20_THREE_FUSIONS_ORDINARY_FOUR_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'uniform_signed_invoice_improvement':'Relative to PR5641: Pnew-Pold=-54H1-54H3+54H4; targets unchanged. Gain54*(1+3^t-4^t)>0 for0<t<1.','fee_bounds':fee_bounds(invoice,glob,H1,v),'whole_kappa':None,'assumptions':'Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed.'}
+ L.put('ORDINARY-RESULT.json',enc(result));return enc(result)
+if __name__=='__main__':
+ r=run();print(json.dumps({k:r[k]for k in('status','admitted','comparator','relative_gain_percent','tail')},indent=2))
diff --git a/research/g20-refinement-admission/source/GLOBAL-RESULT.json b/research/g20-refinement-admission/source/GLOBAL-RESULT.json
new file mode 100644
index 0000000000..8073b39c3d
--- /dev/null
+++ b/research/g20-refinement-admission/source/GLOBAL-RESULT.json
@@ -0,0 +1,11571 @@
+{
+  "status": "PASS_LITERAL_G20_OWNED_RELATIONS_11238_RETAINED_RAW",
+  "invoice": {
+    "paid": {
+      "1": 25227,
+      "2": 24156,
+      "3": 1386,
+      "4": 720,
+      "5": 1836,
+      "6": 180,
+      "7": 162,
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    },
+    "targets": {
+      "4": 72,
+      "8": 7614,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "127": 222
+    },
+    "originals": 11238,
+    "owned_allocated": 11,
+    "owned_output_credit": 0,
+    "QUERYs": 56997,
+    "rank_surplus": 753
+  },
+  "expanded_event_count": 456232,
+  "canonical_stream_sha256": "30f5f0cc16bb700465d05cafa04b6d15b86289721c84671a17cf41ecb2b86c4e",
+  "operation_counts": {
+    "OWNED_CLEAR": 2389,
+    "ADD": 389118,
+    "QUERY": 56997,
+    "WHOLE_ZERO_FRAME": 162,
+    "OWNED_ZERO_HEADER": 18,
+    "PAID_PORT_ROUTE": 7548
+  },
+  "calls": 18,
+  "owned_payload_episodes": 1845,
+  "source_descriptors": 56997,
+  "majorant_bits": 517,
+  "majorant": "350583473191863619005230532393731545919813805066884465216657040209194774903279979136259157004828133120437377491236581575073505597140324685024743252041259115",
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+    },
+    {
+      "23": 4
+    },
+    {
+      "23": 8
+    },
+    {
+      "87": 16
+    },
+    {
+      "87": 32
+    },
+    {
+      "343": 64
+    },
+    {
+      "343": 128
+    },
+    {
+      "1367": 256
+    },
+    {
+      "1367": 512
+    },
+    {
+      "5463": 1024
+    },
+    {
+      "5463": 2048
+    },
+    {
+      "21847": 4096
+    },
+    {
+      "21847": 8192
+    },
+    {
+      "12884901889": 16384
+    },
+    {
+      "12884901889": 32768
+    },
+    {
+      "13958643713": 65536
+    },
+    {
+      "13958643713": 131072
+    },
+    {
+      "14227079169": 262144
+    },
+    {
+      "14227079169": 524288
+    },
+    {
+      "14294188033": 1048576
+    },
+    {
+      "14294188033": 2097152
+    },
+    {
+      "14310965249": 4194304
+    },
+    {
+      "14310965249": 8388608
+    },
+    {
+      "14315159553": 16777216
+    },
+    {
+      "14315159553": 33554432
+    },
+    {
+      "14316208129": 67108864
+    },
+    {
+      "14316208129": 134217728
+    },
+    {
+      "14316470273": 268435456
+    },
+    {
+      "14316470273": 536870912
+    },
+    {
+      "14316557655": 1073741824
+    },
+    {
+      "14316557655": 2147483648
+    }
+  ]
+}
diff --git a/research/g20-refinement-admission/source/INVOICE.json b/research/g20-refinement-admission/source/INVOICE.json
new file mode 100644
index 0000000000..783d961bec
--- /dev/null
+++ b/research/g20-refinement-admission/source/INVOICE.json
@@ -0,0 +1,37 @@
+{
+  "paid": {
+    "1": 25227,
+    "2": 24156,
+    "3": 1386,
+    "4": 720,
+    "5": 1836,
+    "6": 180,
+    "7": 162,
+    "14": 444,
+    "21": 444,
+    "28": 444,
+    "35": 444,
+    "42": 444,
+    "49": 444,
+    "56": 444,
+    "63": 222
+  },
+  "targets": {
+    "4": 72,
+    "8": 7614,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
+    "43": 444,
+    "50": 444,
+    "57": 444,
+    "64": 222,
+    "127": 222
+  },
+  "originals": 11238,
+  "owned_allocated": 11,
+  "owned_output_credit": 0,
+  "QUERYs": 56997,
+  "rank_surplus": 753
+}
diff --git a/research/g20-refinement-admission/source/NOTICE.md b/research/g20-refinement-admission/source/NOTICE.md
new file mode 100644
index 0000000000..118750333a
--- /dev/null
+++ b/research/g20-refinement-admission/source/NOTICE.md
@@ -0,0 +1,16 @@
+New G20 nine-owned-relation application and publication packaging:
+ai-nanachi with substantial OpenAI Codex assistance, Apache-2.0.
+
+Nine owned capture relations: Ali Romman, PR5421,
+head295b00764305694b3c510d3b0bebc2ab024a7809, Apache-2.0.
+The relation rows are independently derived from the actual G20 source.
+
+Private G20 shadow-rank4 source is first published with this package. Its
+unchanged predecessor bytes, notices, provenance and cumulative source credit
+are retained in vendor/g20. Native BIT source word and helper/controller work
+retain DreamingOfClouds/eumemic and each original contributor's attribution.
+Completed ordinary composition: rohanarun PR185/199/204; PR4760/4814 application
+for ai-nanachi with OpenAI Codex assistance. See SOURCES.json and vendor notices.
+
+Independent checks included here are separate internal AI implementations;
+they do not constitute external human acceptance.
diff --git a/research/g20-refinement-admission/source/ORDINARY-RESULT.json b/research/g20-refinement-admission/source/ORDINARY-RESULT.json
new file mode 100644
index 0000000000..9925183e33
--- /dev/null
+++ b/research/g20-refinement-admission/source/ORDINARY-RESULT.json
@@ -0,0 +1,169 @@
+{
+  "status": "PASS_CONDITIONAL_G20_NINE_RELATIONS_ORDINARY_THREE_FINITE_LEVELS",
+  "invoice": {
+    "paid": {
+      "1": 25227,
+      "2": 24156,
+      "3": 1386,
+      "4": 720,
+      "5": 1836,
+      "6": 180,
+      "7": 162,
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    },
+    "targets": {
+      "4": 72,
+      "8": 7614,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "127": 222
+    },
+    "originals": 11238,
+    "owned_allocated": 11,
+    "owned_output_credit": 0,
+    "QUERYs": 56997,
+    "rank_surplus": 753
+  },
+  "params": {
+    "tested": "174199/50000000",
+    "uniform": "348397/100000000",
+    "cover_gap": "95367431706161/6553600000000000000000000",
+    "rho": "1/100",
+    "v": 1024,
+    "alpha_gap": "1/549755813888",
+    "cutoff": 17,
+    "floor": 18,
+    "u": "1/5"
+  },
+  "raw_crossing_independent_exact": {
+    "lower": {
+      "saving": "4354981663/1250000000000",
+      "margin": [
+        "11340555348878123036008909592367/1250000000000000000000000000000000000000",
+        "22681110697756246072017819395877/2500000000000000000000000000000000000000"
+      ]
+    },
+    "upper": {
+      "saving": "6967970661/2000000000000",
+      "margin": [
+        "-30952647388748809910337337099857/2500000000000000000000000000000000000000",
+        "-61905294777497619820674673780791/5000000000000000000000000000000000000000"
+      ]
+    },
+    "tested": {
+      "saving": "174199/50000000",
+      "margin": [
+        "571783310909751218729713260508338489/500000000000000000000000000000000000000",
+        "285891655454875609364856630254190381/250000000000000000000000000000000000000"
+      ]
+    }
+  },
+  "tail": {
+    "alpha": [
+      "6277101701678533736911774263191374800116154347949458842651/6277101735386680763835789423207666416102355444464034512896",
+      "3138550850839266868455887131595687400058077173974729527965/3138550867693340381917894711603833208051177722232017256448"
+    ],
+    "gamma": [
+      "6020186953171155655635684230817080731997608336956948012963/6277101735386680763835789423207666416102355444464034512896",
+      "188130842286598614238615132213033772874925260529904636669/196159429230833773869868419475239575503198607639501078528"
+    ],
+    "delta": [
+      "1476005891108099102340667660880386867002669457723736243139/1569275433846670190958947355801916604025588861116008628224",
+      "738002945554049551170333830440193433501334728861868146855/784637716923335095479473677900958302012794430558004314112"
+    ],
+    "normalized_surplus": "536870911/576460753377165312",
+    "H0": 378121592832,
+    "H1": 263473235277373441
+  },
+  "C1": "22832545696632568293839/6553600000000000000000000",
+  "finite_backend_levels": [
+    {
+      "level": 1,
+      "completed_backend": "1737729/500000000",
+      "ordinary_exact": "2283198785515424261090061/655360000000000000000000000",
+      "admitted": "696776973/200000000000"
+    },
+    {
+      "level": 2,
+      "completed_backend": "696776973/200000000000",
+      "ordinary_exact": "2283254011817888261090061/655360000000000000000000000",
+      "admitted": "1741984567/500000000000"
+    },
+    {
+      "level": 3,
+      "completed_backend": "1741984567/500000000000",
+      "ordinary_exact": "2283254564083206661090061/655360000000000000000000000",
+      "admitted": "435496247/125000000000"
+    }
+  ],
+  "admitted": "435496247/125000000000",
+  "comparator": "1737729/500000000",
+  "relative_gain": "1063997/434432250",
+  "relative_gain_percent": "2127994/8688645",
+  "qualifies_0_1_percent": true,
+  "uniform_signed_invoice_improvement": "Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8, gain162*(1+7^t-8^t)>0 for0<t<1 by strict subadditivity.",
+  "fee_bounds": {
+    "status": "PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA",
+    "base_counts": {
+      "raw_records": 456232,
+      "all_XOR_CLEAR_INIT_zeroheader_passes": 391709,
+      "parent_parking_FIELD_passes": 2564637012,
+      "internal_and_wholejob_routes": 14796,
+      "coarse_primitive_count_with_dimension_work": 965996734173,
+      "strict_upper": 18446744073709551616,
+      "all_owned_allocated": 11,
+      "owned_productive_credit": 0
+    },
+    "fixed_tensor_unit": {
+      "v": 1024,
+      "K": "2^262144",
+      "meaning": "Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting."
+    },
+    "finite_compiler": {
+      "N": "2^263473235277373441",
+      "J(n)": "(n+1)^4*K^(4*n+4)",
+      "A(1)": "K^4",
+      "A(n)": "(J(n)+2)^4*(A(n-1)+2)^(4*n+8)",
+      "counts": "Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets11distinct owned banks; C_N<=11*A(N). Denominator replication product <=A(n-1)^(n-1)."
+    },
+    "height_prime": {
+      "base_height_bits": 1024,
+      "T": "(2*N+2)^4*(A(N)+2)^2",
+      "H": "1026*4^(T+1)",
+      "q": "Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice."
+    },
+    "all_in_fixed_primitive_fee": {
+      "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8",
+      "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.",
+      "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.",
+      "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument."
+    },
+    "stock": {
+      "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend",
+      "D": "floor(log_N ceil(e/w))+1",
+      "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)",
+      "ownership": "All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed."
+    },
+    "eventual_threshold": {
+      "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.",
+      "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0",
+      "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).",
+      "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized."
+    }
+  },
+  "whole_kappa": null,
+  "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed."
+}
diff --git a/research/g20-refinement-admission/source/PROOF.md b/research/g20-refinement-admission/source/PROOF.md
new file mode 100644
index 0000000000..951ce90c64
--- /dev/null
+++ b/research/g20-refinement-admission/source/PROOF.md
@@ -0,0 +1,278 @@
+# G20 partial helpers with nine owned relations
+
+The admitted conditional ordinary BIT saving is
+
+    435496247 / 125000000000 = 0.003483969976.
+
+The comparator is the completed PR4814 supplier
+1737729/500000000 = 0.003475458.  The relative increase is exactly
+1063997/434432250, or 2127994/8688645 percent (about 0.24491667%).
+This is a BIT component result. No complete multiplication coefficient or
+selected result is changed. All native, arbitrary-function/all-column,
+ROW/spectator, mixed-target finite compiler, ordinary fallback, precision
+and fixed-tape hypotheses retained by PR4760/PR4814 remain hypotheses.
+
+## Sources, ownership and credit
+
+The two-transport source word is due to DreamingOfClouds (PR589), following
+eumemic's 111-port construction (PR555) and their credited predecessors.
+Cinna Davis / 1337isnot1337 supplies the query-thinned controller, physical
+port/ROW interface and delayed-cover bridge. The productive helper
+restriction and finite ordinary bootstrap follow our PR4760 and PR4814.
+The finite bootstrap is prior work of rohanarun (PR185/199/204), not a new
+general compiler theorem. The unchanged exact interval engine credits zxv
+and Jacob Alan Sussman's mixed-target recursion; its source notices remain.
+
+Ali Romman's PR5421, head
+295b00764305694b3c510d3b0bebc2ab024a7809, supplies the nine-owned-relation
+method. We rederive it on a different actual word: the previously private
+G20 partial436/capture-shadow producer. Its complete frozen source and
+proof are included unchanged under vendor/g20, together with its public
+predecessor source pins. It was not a previously published or externally
+approved mathematical result. The nine pivots here are 469 through 477,
+not the pivots in PR5421. Public5421 has 661 original fields; our source
+has 658 and retains its four partial-rank4 helper jobs. These contracts
+are not substituted for one another. Substantial OpenAI Codex assistance
+was used. New work is Apache-2.0; vendor notices remain unchanged.
+
+VENDOR-PINS.json records the exact immutable closure. Old absolute paths
+inside historical provenance are descriptive; no executable in the new
+scientific package reads a workspace path or network service.
+
+## 1. The actual G20 word and changed premise
+
+The source has 111 X fields, 111 Y fields, 436 arbitrary helper fields,
+one owned rank7 capture centre (658), and one owned shadow (659). Its
+productive helper targets are 432 rank8 and four rank4 jobs. Its complete
+local paid profile is
+
+    P0={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18}.
+
+G20's positive-fee shadow window replaces [1,3,3] by [3,4] at the actual
+helper464/SOURCE0 interaction. The frozen proof describes both directions,
+the fresh rank4 matcher and the paid shadow's exact lifetime. The new
+verifier does not merely trust the profile: it checks every instruction
+of the emitted inverse, every current FRAME, proper nested residual and
+common-FRAME XOR. The exact frame induction proves arbitrary-function
+correctness; finite q101 and q101^2 sparse controls exercise every one of
+the 660 distinct entry symbols. The integer majorant bounds cancellation
+free growth; it is not an integer-valued endpoint identity.
+
+This construction changes the initial-data contract by retiring nine
+independent helper targets and owning those fields. It does not reopen
+the closed unchanged-word QUERY-fusion or wrong-FRAME cache censuses.
+No surviving arbitrary original is cleared or presumed zero.
+
+## 2. Nine paid owned relations
+
+Replay the actual G20 inverse in scalar F2 symbols and record the current
+SOURCE row at every one of its nine COPY entries. Gaussian elimination
+using helper columns gives nine independent rows. Each reduced row has
+exactly its own pivot among {469,...,477}; its other terms are X fields
+0,...,110. Every term has the actual full8 entrance FRAME1, and each pivot
+has a complete full8 target (birth FRAME0, exit FRAME1). None is one of
+the four partial helpers 462,463,466,468.
+
+Own the nine pivots. At entry, erase each entire owned payload and XOR
+the other terms of its relation into it at FRAME1. These 523 pointwise
+XORs are paid. They set all nine recorded COPY forms to zero while
+preserving the 649 independent retained fields. The capture centre and
+shadow also receive paid whole-payload entry erasures; arbitrary DIRTY
+entry values in all eleven owned fields therefore have no output effect.
+
+Chronological exact replay shows nine rank1 QUERYs occur on whole zero
+fields and all nine rank7 COPY values are zero. Only these eighteen
+charged jobs disappear. A free zero FRAME change requires the entire
+symbolic function to be zero, not only its scalar bitmap. The centre is
+kept zero with paid erasure/header operations; no immutable old SOURCE
+ticket remains. The original shadow operations remain. At exit each
+pivot receives a paid whole-payload erasure, and all eleven owned fields
+return to their declared zero/end headers.
+
+The actual resulting profile and complete local operations are
+
+    P1={1:1309,2:1342,3:77,4:40,5:102,6:10,7:9},
+    19595 XORs, 39 whole ERASEs, 1 zero INIT, 9 zero FRAME changes.
+
+All 660 independent RAW/DIRTY entry columns are checked: the retained
+649-field map is (X,Y)->(X,Y+X), identity on the 427 retained helpers,
+and every owned output is zero. Native controls include the complete
+paired HEAD/TAIL function, not just the scalar rows. Missing initial
+DIRTY erasure is rejected. Independent checks also reject a changed
+relation and an unearned zero transition.
+
+## 3. Why the reverse body serves every thick caller
+
+Let P be an actual port rank1 projector, K=I-P and let D denote the
+paired ADDRESS interchange, including the source's fixed bank reversal.
+Exact rational checks give D_P^2=D_K^2=D_I^2=I and
+D_I D_P=D_P D_I=D_K. These are ADDRESS compositions. Their induced data
+permutations commute and have the same involution laws.
+
+With the two-field shear M over F2, both the original forward and inverse
+physical endpoints are
+
+    diag(D_I,D_K) M diag(D_P,I)
+      = diag(D_P,I) M diag(D_I,D_K)
+      = [[D_K,0],[D_I,D_K]].
+
+The bottom-left term in its square is zero by characteristic two and
+commutation. Each retained helper has physical endpoint D_U for its
+actual full8 or partial4 projector U; D_U is also an involution. Owning
+and restoring the nine retired helpers does not change any surviving
+physical output. Thus the new inverse implementation realizes exactly
+the previous physical thick-call operator in either direction.
+
+Every new thick core explicitly starts at base.final and ends at
+base.start. These are its internal decomposition coframes. We do not
+claim that they equal the old forward internal headers. The outer paid
+rho15 entry/return is unchanged and conjugates the same physical operator,
+so no additional unimplemented physical map is hidden in a header
+relabeling. All 111 exact rho matrices and P/K complements are checked.
+For multiplicity f tensor every projector/route with I_f and retain the
+whole ROW and spectator coordinates. The identities remain exact under
+the inherited streaming/native interface; different ports receive no
+common free physical chart.
+
+## 4. Literal global word and full target debit
+
+The p16/a7 controller has eighteen thick calls and fifteen thin stages.
+We instantiate the new body on its actual source/target banks, reuse
+nine separately owned pivot arrays between calls, and keep the centre
+and shadow separate. No erased helper remains an independent input.
+The global domain has 11238 independent retained fields and eleven
+owned arrays, with paid initialization, clear and teardown. Distinct
+owned banks are reserved again for every compiled unit instance,
+including suspended instances; they are never credited as DATA targets.
+
+The literal tape has 456232 events, canonical SHA256
+30f5f0cc16bb700465d05cafa04b6d15b86289721c84671a17cf41ecb2b86c4e.
+It checks all 11249 independent RAW/DIRTY entry columns, all eighteen
+exact mapped cores and owned returns. There are 1845 nonzero owned
+payload episodes. Exact controller group-ring evaluation gives the
+prescribed diagonal monomial on all 32 main bank inputs, including the
+real scalar boundaries. Independent orthogonal stage factors and the
+local arbitrary-function statement lift it to the complete function
+operator. Source descriptors bind every actual prefix, owner, version,
+epoch and geometric job; a RAW bitmap is only additional control data.
+
+The entire target inventory is
+
+    T={4:72,8:7614,15:444,22:444,29:444,36:444,
+       43:444,50:444,57:444,64:222,127:222}.
+
+The entire paid inventory is
+
+    P={1:25227,2:24156,3:1386,4:720,5:1836,6:180,7:162,
+       14:444,21:444,28:444,35:444,42:444,49:444,56:444,63:222}.
+
+There are 56997 paid QUERYs and rank surplus753. Relative to G20 this is
+-162 H1 -162 H7 in paid jobs and -162 H8 in targets. All four partial
+helpers per call remain credited exactly once. For any 0<t<1 the net
+concave-moment improvement is 162*(1+7^t-8^t)>0, by strict subadditivity.
+No lost target, CLEAR, normalizer or consumer cost is treated as free.
+
+Every retained target descriptor has exactly its old matcher, port,
+physical job, ROW routes and domain, with only a compact owner renaming.
+MAIN projectors are the exact central P or I8 plus disjoint coordinate
+stage projectors. All helper projectors are checked over Q. For each
+actual projector U, U^2=U=U^T and the paired D_U is a symmetric ADDRESS
+involution. Its induced FUNCTION permutation therefore satisfies
+A^-1=A=A^T=A^-T. The whole target operator is their direct sum. The SAME
+complete literal program, with eleven newly paid owned banks, supplies
+forward, inverse, transpose and inverse-transpose under the identical
+external domain. We never reverse or transpose a destructive erasure.
+This is an operator statement, not a scalar-bit-transpose inference.
+
+## 5. Complete finite fees and compiler
+
+The new literal invoice counts 389118 XOR passes, 2389 whole owned CLEARs,
+18 zero header acquisitions, 162 zero FRAME changes, and 7548 internal
+paid port routes. Separate canonical whole-job routing is still 7248
+routes, including 144 partial-helper routes. Even the known zero-centre
+header/clear steps and extra conservative initialization/teardown scans
+are charged. Before each child, charge
+
+    4*(11238+11)*56997 = 2564637012 FIELD passes
+
+for parent parking, input/output, restore and head return. No ancestor
+region is swept. Every fixed route and actual current SOURCE normalizer
+also carries its positive retained primitive constant. A 1e9 raw-record
+cap is not reused as an all-in machine coefficient.
+
+The new cancellation-free global envelope is 517 bits. The actual
+rational base geometry has at most three-bit entries, and the retained
+fixed base height bound1024 covers both. All old numerical rank/prime,
+precision and tape thresholds are regenerated rather than reused.
+
+Use tested saving0.00348398, uniform saving0.00348397, tensor power1024,
+cutoff17, floor18, and second-moment parameter1/5. Two unchanged rational
+interval engines independently check the new complete P/T, including a
+strict raw crossing in (0.0034839853304,0.0034839853305). With t=1-tested,
+
+    alpha=P_t/T_t < 1-2^-39,
+    gamma=P_(t+1/5)/(17^(1/5)*T_t) <31/32,
+    delta=11238*18/(17^tested*T_t) <19/20.
+
+Complete every small target on the SAME owner at18^1024, and split every
+paid job at17^1024 with all pieces charged. Both decay blocks raised to128
+are below1/16. The normalized contraction surplus is the positive
+536870911/576460753377165312. Separation follows from17^64<18^63;
+the minimum4 and maximum paid63 are not falsely compared directly.
+
+The fresh exact finite integer-compiler thresholds are
+
+    H0=378121592832, H1=263473235277373441, N=2^H1.
+
+The source inequalities for h=1/64, z0 halfway between t and1-uniform
+are checked exactly. They are rank-compiler thresholds, not old machine
+thresholds. With K=2^262144, use
+
+    J(n)=(n+1)^4*K^(4*n+4), A(1)=K^4,
+    A(n)=(J(n)+2)^4*(A(n-1)+2)^(4*n+8).
+
+These oversized finite integers bound productive roles, leaves, compiled
+instances and primitive descriptions, including the denominator-clearer
+product of smaller widths. Reserve C_N<=11*A(N) whole owned banks.
+Let T_arith=(2N+2)^4*(A(N)+2)^2 and H=1026*4^(T_arith+1).
+Choose an odd prime q>max(2^45*N^5,2^(2H)) avoiding all finitely compiled
+denominators and rank witnesses. These choices precede the input width.
+The positive multiplier
+
+    F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8
+
+dominates the charged fixed scans, parking, low-type/carry normalizers and
+routes in retained primitive invocations, multiplied by the positive
+maximum retained primitive/backend constant. It is not a universal unit
+machine cost. The inherited bad-class ordinary calls are charged in the
+moment/cover argument. ORDINARY-RESULT.json records the corresponding
+reserve, borrowed digits and explicit finite eventual-threshold schema.
+
+## 6. Three finite ordinary backends
+
+Use cover gap2^-36+10^-20 and atom fraction rho=1/100. The cover prime
+inequality 2^45*gap>256 is checked. Begin with the already completed
+PR4814 ordinary backend b0=1737729/500000000. At each j=1,2,3 freeze
+the completed preceding algorithm, then compile
+
+    a_j=(1-rho)*(uniform-cover_gap)+rho*b_(j-1),
+    b_j=floor(10^12*a_j)/10^12.
+
+No algorithm calls itself as its own atom backend. The adapter, stock,
+rounding and improvement gaps are all positive. Newly fixed finite
+constants and each completed all-width fallback determine a fresh
+eventual threshold; the retained proof absorbs every positive coefficient
+before taking the input-size limit. The result is b3=0.003483969976.
+The astronomical winning uniform program, prime and decimal eventual
+threshold are not expanded. This remains a conditional construction,
+not a formal or complete multiplication-theorem verification.
+
+## Open next questions
+
+An independent universal audit of the retained native/ROW, precision,
+fixed-tape and analytic recovery premises is still valuable. A feasible
+first step is one caller-bound quantified interface, with explicit all-f
+and spectator scope. The present finite checks do not close those
+framework assumptions. Further scalar savings alone do not justify a
+new exponent: any changed paid mechanism needs a fresh complete target,
+ownership, whole-program and ordinary invoice.
diff --git a/research/g20-refinement-admission/source/RECORD.json b/research/g20-refinement-admission/source/RECORD.json
new file mode 100644
index 0000000000..501cdde1cc
--- /dev/null
+++ b/research/g20-refinement-admission/source/RECORD.json
@@ -0,0 +1,20 @@
+{
+  "schema_version": 1,
+  "status": "PROPOSED_CONDITIONAL_ORDINARY_BIT_003483969976",
+  "scientific_base": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
+  "axis": "ordinary_BIT_saving",
+  "admitted": "435496247/125000000000",
+  "comparator_PR": 4814,
+  "comparator_head": "f56ae4533a7d97d782a2c596a33fe844cd051747",
+  "comparator": "1737729/500000000",
+  "relative_gain": "1063997/434432250",
+  "relative_gain_percent": "2127994/8688645",
+  "raw_paid_profile_changed": true,
+  "owned_productive_credit": 0,
+  "whole_kappa_changed": false,
+  "selected_global_kappa": "605457647/200000000000",
+  "maintainer_mathematical_review": "Pending",
+  "external_independent_reproduction": "Not claimed; separate internal AI audits.",
+  "hosted_CI": "Not yet observed for this proposed package.",
+  "publication": "Actual PR identity/head/time is recorded only after creation."
+}
diff --git a/research/g20-refinement-admission/source/WORD.json.gz b/research/g20-refinement-admission/source/WORD.json.gz
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HcmV?d00001

diff --git a/research/g20-refinement-admission/source/global_relations.py b/research/g20-refinement-admission/source/global_relations.py
new file mode 100644
index 0000000000..aed289de8b
--- /dev/null
+++ b/research/g20-refinement-admission/source/global_relations.py
@@ -0,0 +1,104 @@
+"""Literal p16/a7 caller with nine retired helper targets and shared owned work.
+
+Retains G20 native controller/geometry; uses the independently checked reverse
+physical involution at each full call. No old helper target is given to owned work.
+"""
+from pathlib import Path
+from collections import Counter
+from hashlib import sha256
+from time import process_time
+import gzip,json,importlib.util,sys
+import local_relations as L
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def read(p):return L.read(p)
+def put(n,x):L.put(n,x)
+def run():
+ clock=process_time();controller=read(S/'inputs/CONTROLLER.json');base,frames,_=L.source();local=read(R/'WORD.json.gz');owned=local['owned'];pivots=owned[:-2];need(pivots==list(range(469,478)),'Exact retired helper owners')
+ oldcalls=read(S/'provider/data/CALLS.json');retired={c['helper_owner_begin']+p-222 for c in oldcalls for p in pivots};retained=[i for i in range(11400)if i not in retired];compact={x:i for i,x in enumerate(retained)};N=len(retained);W=list(range(N,N+11));center,shadow=W[:2];pivotwork=dict(zip(pivots,W[2:]));need(N==11238,'New retained original count')
+ values=[1<<i for i in range(N+11)];norm=[1]*(N+11);versions=[0]*(N+11);epochs=[0]*(N+11);counts=Counter();paid=Counter();peak=1;events=[];source=[];calls=[];episodes=[];ticket=None;prefix=sha256()
+ def emit(e):counts[e[0]]+=1;events.append(e);prefix.update((json.dumps(e,separators=(',',':'))+'\n').encode())
+ def erase(d,why,frame=None):
+  need(d in W,'Only owned wholepayload erasure');values[d]=norm[d]=0;versions[d]+=1;epochs[d]+=1;emit(['OWNED_CLEAR',d,frame,why])
+ for d in W:erase(d,'GLOBAL_ENTRY_ARBITRARY_DIRTY')
+ def add(d,s,why):
+  nonlocal peak
+  need(d!=s,'Distinct source/destination');values[d]^=values[s];norm[d]+=norm[s];peak=max(peak,norm[d]);versions[d]+=1;emit(['ADD',d,s,why])
+ def query(d,k,detail):
+  need(k>0,'Positive rank');source.append({'event':len(events),'prefix_sha256':prefix.hexdigest(),'owner':d,'version':versions[d],'epoch':epochs[d],'rank':k,'detail':detail,'RAW_hex':hex(values[d]),'function_identity':'Exact literal program prefix plus current owner/epoch/version and actual geometric source job; RAW bitmap is extra evidence, not a claim of purity.'});paid[k]+=1;versions[d]+=1;emit(['QUERY',d,k,detail])
+ def swap(d,s,why):add(d,s,why);add(s,d,why);add(d,s,why)
+ def boundary(program,why):
+  for op,d,s in program:
+   for p in range(111):
+    if op=='ADD':add(compact[d*111+p],compact[s*111+p],why)
+    else:need(op=='SWAP','Controller opcode');swap(compact[d*111+p],compact[s*111+p],why)
+ boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY')
+ thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)}
+ for event in controller['physical_events']:
+  op=event[0]
+  if op=='LOCAL':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   helper=3552+436*stage_index[stage]
+   def owner(r):
+    if r==658:return center
+    if r==659:return shadow
+    if r in pivotwork:return pivotwork[r]
+    return compact[(x if r<111 else y)*111+r%111]if r<222 else compact[helper+r-222]
+   sx=[values[owner(i)]for i in range(111)];sy=[values[owner(111+i)]for i in range(111)];helpers=[r for r in range(222,658)if r not in pivotwork];before={r:values[owner(r)]for r in helpers}
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'ENTRY'])
+   start=len(events);lp=Counter();st=local['start'][:];livebegin={}
+   for ix,e in enumerate(local['records']):
+    typ,d=e[:2];gd=owner(d)
+    if typ=='ERASE':
+     erase(gd,['LOCAL',stage,ix],e[2]);st[d]=e[2]
+     if gd in livebegin:episodes.append({'owner':gd,'stage':stage,'begin':livebegin.pop(gd),'end':len(events)-1})
+    elif typ=='INIT':need(values[gd]==0,'Whole zero INIT');st[d]=e[2];emit(['OWNED_ZERO_HEADER',gd,e[2],stage])
+    elif typ=='ADD':
+     s,f=e[2:];need(st[d]==st[s]==f,'Actual instantiated coframe')
+     if gd in W and gd not in livebegin:livebegin[gd]=len(events)
+     add(gd,owner(s),['LOCAL',stage,f,ix])
+    elif typ in('Q','ZERO_Q'):
+     a,b,k=e[2:];need(st[d]==a,'Current instantiated query frame');st[d]=b
+     if typ=='Q':query(gd,k,['LOCAL_INVERSE',stage,a,b,ix]);lp[k]+=1
+     else:need(values[gd]==0,'Zero only free query');emit(['WHOLE_ZERO_FRAME',gd,a,b,k,stage])
+    else:raise ValueError('Local opcode '+typ)
+   need(not livebegin and st==local['final'],'No live local owned state at return')
+   need(all(values[owner(i)]==sx[i]and values[owner(111+i)]==sy[i]^sx[i]for i in range(111)),'All retained main RAW inputs')
+   need(all(values[owner(r)]==before[r]for r in helpers)and all(values[w]==0 for w in W),'All427 independent retained helper inputs and11owned returns')
+   need(lp==Counter(read(R/'LOCAL-RESULT.json')['stats']['paid'])or lp==Counter({int(k):v for k,v in read(R/'LOCAL-RESULT.json')['stats']['paid'].items()}),'Actual local query count')
+   calls.append({'stage':stage,'pair':pair,'source_bank':x,'target_bank':y,'old_direction_inverse':rev,'new_direction_inverse':True,'helper_old_owner_begin':helper,'core_begin':start,'core_end':len(events),'owned_global_indices':W,'retained_helper_count':427,'paid':dict(lp)})
+   if stage:
+    for bank in(x,y):
+     for p in range(111):emit(['PAID_PORT_ROUTE',stage,compact[bank*111+p],p,'RETURN'])
+  elif op=='QUERY_SHEAR':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   for p in range(111):
+    src,dst=compact[x*111+p],compact[y*111+p];need(values[center]==0,'Clean thin scratch');v=versions[src];begin=len(events);add(center,src,['THIN_COPY',stage,p]);query(center,1,['THIN',stage,p]);add(dst,center,['THIN_DELIVER',stage,p]);need(versions[src]==v,'Thin immutable SOURCE');erase(center,['THIN',stage,p]);episodes.append({'owner':center,'stage':stage,'kind':'THIN','begin':begin,'end':len(events)-1})
+  elif op=='IDLE':
+   _,pair,stages=event;k=7*len(stages)
+   for bank in(2*pair,2*pair+1):
+    for p in range(111):query(compact[bank*111+p],k,['WHOLE_IDLE',stages,p])
+  elif op=='ADD':
+   for p in range(111):add(compact[event[1]*111+p],compact[event[2]*111+p],'BRIDGE')
+  else:
+   need(op=='SWAP','Known controller event')
+   for p in range(111):swap(compact[event[1]*111+p],compact[event[2]*111+p],'FINAL_SWAP')
+ boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY')
+ for d in W:erase(d,'GLOBAL_EXIT_TEARDOWN')
+ need(values==[1<<i for i in range(N)]+[0]*11,'All11238 independent retained RAW and all11 arbitrary DIRTY entry columns annihilated')
+ oldtargets=read(S/'provider/data/TARGET-OWNERS.json');targets=[dict(t,original_owner=compact[t['original_owner']])for t in oldtargets if t['original_owner']not in retired];T=Counter(t['rank']for t in targets)
+ P={int(k):v for k,v in read(S/'provider/data/INVOICE.json')['paid'].items()};P[1]-=162;P[7]-=162
+ need(paid==P and sum(T.values())==N and T[4]==72 and T[8]==7614,'Literal complete changed invoice including every partial helper')
+ # Retained exact physical MAIN polynomial proof, independent of the new ledger.
+ spec=importlib.util.spec_from_file_location('old_global',S/'provider/build_global.py');mod=importlib.util.module_from_spec(spec);spec.loader.exec_module(mod);physical=mod.physical_main(controller)
+ stream=b''.join((json.dumps(e,separators=(',',':'))+'\n').encode()for e in events);need(sha256(stream).hexdigest()==prefix.hexdigest(),'Exact prefix and fullstream identity');(R/'GLOBAL.jsonl.gz').write_bytes(gzip.compress(stream,mtime=0))
+ invoice={'paid':dict(sorted(paid.items())),'targets':dict(sorted(T.items())),'originals':N,'owned_allocated':11,'owned_output_credit':0,'QUERYs':sum(paid.values()),'rank_surplus':sum(k*v for k,v in T.items())-sum(k*v for k,v in paid.items())}
+ result={'status':'PASS_LITERAL_G20_OWNED_RELATIONS_11238_RETAINED_RAW','invoice':invoice,'expanded_event_count':len(events),'canonical_stream_sha256':sha256(stream).hexdigest(),'operation_counts':dict(counts),'calls':len(calls),'owned_payload_episodes':len(episodes),'source_descriptors':len(source),'majorant_bits':peak.bit_length(),'majorant':str(peak),'retired_original_old_ids':sorted(retired),'retained_old_ids':retained,'shared_owned_ids':W,'CPU_seconds':process_time()-clock,'physical_MAIN_coefficients':physical}
+ put('GLOBAL-RESULT.json',result);put('INVOICE.json',invoice);put('CALLS.json',calls);put('PRIVATE-EPISODES.json',episodes);put('TARGET-OWNERS.json',targets);put('SOURCE-DESCRIPTORS.json.gz',source)
+ return {k:result[k]for k in('status','invoice','expanded_event_count','canonical_stream_sha256','operation_counts','majorant_bits','owned_payload_episodes','CPU_seconds')}
+if __name__=='__main__':print(json.dumps(run(),indent=2))
diff --git a/research/g20-refinement-admission/source/local_relations.py b/research/g20-refinement-admission/source/local_relations.py
new file mode 100644
index 0000000000..38e547280c
--- /dev/null
+++ b/research/g20-refinement-admission/source/local_relations.py
@@ -0,0 +1,118 @@
+"""Own nine G20 capture relations; retain 649 independent original fields.
+
+The nine-owned-relation method is Ali Romman's PR5421.  The present program
+rederives it on the distinct G20 partial436 producer, including its shadow.
+Prepared with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+from collections import Counter
+from time import process_time
+import gzip,json,hashlib,sys
+R=Path(__file__).resolve().parent
+S=R/'vendor/g20'
+sys.path.insert(0,str(S/'provider'))
+from local_ir import Geometry
+N=658
+def need(c,m):
+ if not c:raise ValueError(m)
+def read(p):return json.loads(gzip.decompress(p.read_bytes())if p.suffix=='.gz'else p.read_bytes())
+def put(name,obj):
+ p=R/name;b=(json.dumps(obj,indent=2)+'\n').encode();p.write_bytes(gzip.compress(b,mtime=0)if p.suffix=='.gz'else b)
+def bitids(row):return [i for i in range(N+2)if row>>i&1]
+def source():return read(S/'inputs/BASELINE-LOCAL.json.gz'),read(S/'inputs/FRAMES.json')['frames'],read(S/'provider/data/INVERSE.json.gz')['records']
+def relations(program):
+ rows=[1<<i for i in range(N)]+[0,0];caps=[]
+ for ix,e in enumerate(program):
+  op,d=e[:2]
+  if op=='ADD':rows[d]^=rows[e[2]]
+  elif op=='COPY':caps.append((ix,rows[e[2]]));rows[d]=rows[e[2]]
+  elif op in('CLEAR','TICKET_CLEAR'):rows[d]=0
+ basis={}
+ for _,row in caps:
+  for p,v in sorted(basis.items()):
+   if row>>p&1:row^=v
+  h=row>>222;need(h,'New helper pivot');p=222+(h&-h).bit_length()-1
+  for k in basis:
+   if basis[k]>>p&1:basis[k]^=row
+  basis[p]=row
+ need(len(basis)==9,'Nine independent relations')
+ pm=sum(1<<p for p in basis)
+ for p,row in basis.items():need(row&pm==1<<p,'Reduced pivot basis')
+ return dict(sorted(basis.items()))
+def construct(base,frames,program,basis):
+ owned=set(basis)|{658,659};rows=[1<<i for i in range(N+2)];st=base['final']+[None,None];out=[];removed=[]
+ for d in(658,659):out.append(['ERASE',d,None]);rows[d]=0
+ for p,row in basis.items():
+  need(base['start'][p]==0 and base['final'][p]==1 and frames['1']['dim']==8,'Debited full rank8 pivot')
+  need(all(st[i]==1 for i in bitids(row)),'Every relation term actual full8 entrance')
+  out.append(['ERASE',p,1]);rows[p]=0
+  for i in bitids(row):
+   if i!=p:out.append(['ADD',p,i,1]);rows[p]^=rows[i]
+ for ix,e in enumerate(program):
+  op,d=e[:2]
+  if op=='ADD':rows[d]^=rows[e[2]];out.append(e)
+  elif op=='Q':
+   need(st[d]==e[2],'Actual input frame')
+   if rows[d]:out.append(e)
+   else:out.append(['ZERO_Q',d,e[2],e[3],e[4]]);removed.append([ix,'Q',d,e[4]])
+   st[d]=e[3]
+  elif op=='COPY':
+   need(rows[e[2]]==rows[d]==0,'Zero full COPY relation')
+   out.append(['ERASE',d,0]);st[d]=0;removed.append([ix,'COPY',d,e[4]])
+  elif op=='TICKET_CLEAR':out.append(['ERASE',d,None]);rows[d]=0;st[d]=None
+  elif op=='INIT':out.append(e);st[d]=e[2];need(rows[d]==0,'Whole zero shadow INIT')
+  else:need(op=='CLEAR','Known opcode');out.append(['ERASE',d,None]);rows[d]=0;st[d]=None
+ for d in basis:out.append(['ERASE',d,base['start'][d]])
+ need(Counter(x[-1]for x in removed)=={1:9,7:9},'Exactly nine H1 and H7 removed')
+ return out,removed,owned
+def replay(base,frames,program,owned,modulus=None):
+ geom=Geometry(frames);st=base['final']+[None,None];rows=[1<<i for i in range(N+2)];norm=[1]*(N+2);paid=Counter();ops=Counter();peak=1;active=set();livepeak=0
+ fields=None
+ if modulus:
+  point=tuple(v%modulus for v in(1,2,4,8,16,32,64,128,3,5,7,11,13,17,19,23));fields=[{point:1<<i}for i in range(N+2)]
+ def transform(field,p):return{geom.move(p,x,modulus):v for x,v in field.items()}
+ for ix,e in enumerate(program):
+  op,d=e[:2];ops[op]+=1
+  if op=='ERASE':
+   need(d in owned,'No retained original erasure');rows[d]=norm[d]=0;st[d]=e[2];active.discard(d)
+   if fields is not None:fields[d]={}
+  elif op=='INIT':need(d in owned and rows[d]==0,'Whole zero INIT');st[d]=e[2]
+  elif op=='ADD':
+   s,f=e[2:];need(d!=s and st[d]==st[s]==f,'Actual common-frame XOR');rows[d]^=rows[s];norm[d]+=norm[s];peak=max(peak,norm[d])
+   if d in owned:active.add(d)
+   if fields is not None:
+    for x,v in fields[s].items():
+     z=fields[d].get(x,0)^v
+     if z:fields[d][x]=z
+     else:fields[d].pop(x,None)
+  elif op in('Q','ZERO_Q'):
+   s,t,k=e[2:];need(st[d]==s,'Actual current source FRAME');geom.nested(s,t,k);st[d]=t
+   if op=='ZERO_Q':need(rows[d]==0 and(fields is None or not fields[d]),'Free move only whole zero')
+   else:
+    paid[k]+=1
+    if fields is not None:fields[d]=transform(fields[d],geom.residual_mod(s,t,k,modulus))
+  else:raise ValueError('Unknown event '+op)
+  livepeak=max(livepeak,len(active))
+ need(st==base['start']+[None,None],'All final frames')
+ expected=[0 if i in owned else (1<<i)^((1<<(i-111)) if 111<=i<222 else 0) for i in range(N+2)]
+ need(rows==expected,'All660 independent RAW and arbitrary DIRTY entry columns')
+ if fields is not None:
+  for o,row in enumerate(expected):
+   want={}
+   for i in bitids(row):
+    y=geom.move(geom.project_mod(base['start'][o],modulus),geom.move(geom.project_mod(base['final'][i],modulus),point,modulus),modulus);want[y]=want.get(y,0)^(1<<i)
+   need(fields[o]=={x:v for x,v in want.items()if v},'Full physical endpoint all660 symbols at output '+str(o))
+ return{'paid':dict(sorted(paid.items())),'operation_counts':dict(ops),'owned_allocated':len(owned),'owned_live_payload_peak':livepeak,'retained_originals':N-len(owned-{658,659}),'positive_majorant_bits':peak.bit_length(),'positive_majorant':str(peak),'native_modulus':modulus}
+def run(write=False):
+ clock=process_time();base,frames,old=source();basis=relations(old);program,removed,owned=construct(base,frames,old,basis)
+ stats=replay(base,frames,program,owned)
+ for m in(101,101**2):replay(base,frames,program,owned,m)
+ need(stats['paid']=={1:1309,2:1342,3:77,4:40,5:102,6:10,7:9},'Changed actual local invoice')
+ bad=program[:];bad.pop(next(i for i,e in enumerate(bad)if e[0]=='ERASE'and e[1]in basis))
+ try:replay(base,frames,bad,owned)
+ except ValueError:pass
+ else:raise ValueError('Missing initial DIRTY clear accepted')
+ result={'status':'PASS_G20_NINE_OWNED_RELATIONS_ALL660_COLUMNS','basis':{str(p):bitids(row)for p,row in basis.items()},'removed':removed,'stats':stats,'CPU_seconds':process_time()-clock,'source_inverse_gzip_sha256':hashlib.sha256((S/'provider/data/INVERSE.json.gz').read_bytes()).hexdigest(),'canonical_word_sha256':hashlib.sha256(json.dumps(program,separators=(',',':')).encode()).hexdigest(),'method_credit':'Ali Romman PR5421 head295b00764305694b3c510d3b0bebc2ab024a7809; actual G20 profile differs.'}
+ if write:put('LOCAL-RESULT.json',result);put('WORD.json.gz',{'records':program,'owned':sorted(owned),'start':base['final']+[None,None],'final':base['start']+[None,None]})
+ return result
+if __name__=='__main__':print(json.dumps(run(True),indent=2))
diff --git a/research/g20-refinement-admission/source/ordinary.py b/research/g20-refinement-admission/source/ordinary.py
new file mode 100644
index 0000000000..8fa8ccede0
--- /dev/null
+++ b/research/g20-refinement-admission/source/ordinary.py
@@ -0,0 +1,57 @@
+"""Two exact moment engines and positive-fee finite ordinary bootstrap.
+
+Uses the retained PR4814 finite acyclic bootstrap, with the new literal
+G20 nine-owned-relations invoice. No multiplication-kappa update is claimed.
+"""
+from fractions import Fraction as F
+from pathlib import Path
+import importlib.util,sys,json
+import local_relations as L
+R=L.R;S=L.S
+def need(c,m):
+ if not c:raise ValueError(m)
+def load(n,p):
+ spec=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(spec);sys.modules[n]=m;spec.loader.exec_module(m);return m
+def enc(x):
+ if isinstance(x,F):return str(x)
+ if isinstance(x,dict):return {str(k):enc(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return [enc(v)for v in x]
+ return x
+def ceil(q):return -((-q.numerator)//q.denominator)
+def fee_bounds(invoice,glob,H1,v):
+ n=invoice['originals'];M=invoice['QUERYs'];owned=invoice['owned_allocated'];ops=glob['operation_counts'];park=4*(n+owned)*M
+ routes=7548+7248;scans=ops['ADD']+ops['OWNED_CLEAR']+ops['OWNED_ZERO_HEADER']+ops['WHOLE_ZERO_FRAME']+2*owned;raw=glob['expanded_event_count'];base=scans+park+routes+raw+M*(32*127**2+8*127**3)
+ need(n==11238 and M==56997 and owned==11 and base<2**64,'Actual retained originals,11owned and positive complete finite fees')
+ need(glob['majorant_bits']==517 and 517<1024,'Fresh positive majorant and fixed matrix height')
+ need(v==1024 and 256*v>=4*v*64,'Explicit tensor count envelope')
+ return{'status':'PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA','base_counts':{'raw_records':raw,'all_XOR_CLEAR_INIT_zeroheader_passes':scans,'parent_parking_FIELD_passes':park,'internal_and_wholejob_routes':routes,'coarse_primitive_count_with_dimension_work':base,'strict_upper':2**64,'all_owned_allocated':11,'owned_productive_credit':0},
+ 'fixed_tensor_unit':{'v':v,'K':'2^262144','meaning':'Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting.'},
+ 'finite_compiler':{'N':'2^'+str(H1),'J(n)':'(n+1)^4*K^(4*n+4)','A(1)':'K^4','A(n)':'(J(n)+2)^4*(A(n-1)+2)^(4*n+8)','counts':'Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets11distinct owned banks; C_N<=11*A(N). Denominator replication product <=A(n-1)^(n-1).'},
+ 'height_prime':{'base_height_bits':1024,'T':'(2*N+2)^4*(A(N)+2)^2','H':'1026*4^(T+1)','q':'Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice.'},
+ 'all_in_fixed_primitive_fee':{'F':'(q+2)^(32*(N+1)^2)*(A(N)+2)^8','actual_cost':'F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.','parking':'4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=11*A(N); F dominates their products.','bad_classes':'<=32*N^2 ordinary calls charged separately by the retained moment/cover argument.'},
+ 'stock':{'reserve':'[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend','D':'floor(log_N ceil(e/w))+1','borrowed_digits':'D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)','ownership':'All11whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed.'},
+ 'eventual_threshold':{'K_j':'At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.','eta_j':'min(rho-a_j,1-rho-a_j,a_j-b_j)>0','e_j':'Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).','scope':'Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized.'}}
+def run():
+ invoice=L.read(R/'INVOICE.json');glob=L.read(R/'GLOBAL-RESULT.json');P={int(k):v for k,v in invoice['paid'].items()};T={int(k):v for k,v in invoice['targets'].items()}
+ need(sum(T.values())==11238 and sum(P.values())==56997 and T[4]==72 and T[8]==7614 and P[7]==162,'Actual complete new target/paid bill')
+ E=load('nine_credited_interval',S/'ordinary-certificate/inputs/credited_intervals.py');I=load('nine_independent_series',S/'ordinary-certificate/inputs/separate_series.py')
+ tested=F('.00348398');uniform=F('.00348397');cover_gap=F(1,2**36)+F(1,10**20);rho=F(1,100);reserve=F(1,2**39);v=1024;t=1-tested;u=F(1,5)
+ target=E.moment(T,t);paid=E.moment(P,t);alpha=E.divide(paid,target);gamma=E.divide(E.moment(P,t+u),E.mul(E.power(17,u),target));delta=E.divide((F(11238*18),)*2,E.mul(E.power(17,tested),target))
+ need(alpha[1]<1-reserve and gamma[1]<F(31,32)and delta[1]<F(19,20),'All three actual charged compiler tails')
+ # An independent rational-series engine certifies the raw crossing and tested margin.
+ raw_lo=F('.0034839853304');raw_hi=F('.0034839853305');cross={}
+ for label,c,sign in(('lower',raw_lo,1),('upper',raw_hi,-1),('tested',tested,1)):
+  a=I.moment(T,1-c);b=I.moment(P,1-c);margin=(a[0]-b[1],a[1]-b[0]);need(margin[0]>0 if sign>0 else margin[1]<0,'Independent root sign '+label);cross[label]={'saving':c,'margin':margin}
+ need(F(31,32)**128<F(1,16) and F(19,20)**128<F(1,16),'Tail block decay')
+ surplus=1-F(1)/(1+v*reserve)-F(4,2**32);need(surplus>0 and 17**64<18**63 and max(T)<256,'Charged completion, separation and ambient')
+ z=1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64);H0=ceil((gap*(5+8*h)*v+1+8*v*(1-z0))/(h*gap));H1=(H0*(1-z0)/(z-z0)).__floor__()+1
+ need(H0>=8*v and H0*h*gap>=gap*(5+8*h)*v+1+8*v*(1-z0)and H1*(z-z0)>H0*(1-z0),'Fresh finite integer compiler thresholds')
+ C1=uniform-cover_gap;need(F(2**45)*cover_gap>256,'Cover/bad-prime gap')
+ backend=F(1737729,500000000);old=backend;levels=[]
+ for j in range(1,4):
+  a=(1-rho)*C1+rho*backend;b=F((a*10**12).__floor__(),10**12);need(backend<b<a<C1<rho<1-a,'Finite acyclic backend/adapter/stock/rounding gaps');levels.append({'level':j,'completed_backend':backend,'ordinary_exact':a,'admitted':b});backend=b
+ need(backend/old-1>F(1,1000),'New actual ordinary gain clears .1percent publication guard')
+ result={'status':'PASS_CONDITIONAL_G20_NINE_RELATIONS_ORDINARY_THREE_FINITE_LEVELS','invoice':invoice,'params':{'tested':tested,'uniform':uniform,'cover_gap':cover_gap,'rho':rho,'v':v,'alpha_gap':reserve,'cutoff':17,'floor':18,'u':u},'raw_crossing_independent_exact':cross,'tail':{'alpha':alpha,'gamma':gamma,'delta':delta,'normalized_surplus':surplus,'H0':H0,'H1':H1},'C1':C1,'finite_backend_levels':levels,'admitted':backend,'comparator':old,'relative_gain':backend/old-1,'relative_gain_percent':100*(backend/old-1),'qualifies_0_1_percent':True,'uniform_signed_invoice_improvement':'Pnew-Pold=-162H1-162H7; Tnew-Told=-162H8, gain162*(1+7^t-8^t)>0 for0<t<1 by strict subadditivity.','fee_bounds':fee_bounds(invoice,glob,H1,v),'whole_kappa':None,'assumptions':'Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed.'}
+ L.put('ORDINARY-RESULT.json',enc(result));return enc(result)
+if __name__=='__main__':
+ r=run();print(json.dumps({k:r[k]for k in('status','admitted','comparator','relative_gain_percent','qualifies_0_1_percent','tail')},indent=2))
diff --git a/research/g20-refinement-admission/source/retirement-ordinary.json b/research/g20-refinement-admission/source/retirement-ordinary.json
new file mode 100644
index 0000000000..426a7f950b
--- /dev/null
+++ b/research/g20-refinement-admission/source/retirement-ordinary.json
@@ -0,0 +1,173 @@
+{
+  "status": "PASS_CONDITIONAL_G20_RETIREMENT_ORDINARY_FOUR_FINITE_LEVELS",
+  "invoice": {
+    "paid": {
+      "1": 25155,
+      "2": 24156,
+      "3": 1314,
+      "4": 720,
+      "5": 1836,
+      "6": 180,
+      "7": 162,
+      "14": 444,
+      "21": 444,
+      "28": 444,
+      "35": 444,
+      "42": 444,
+      "49": 444,
+      "56": 444,
+      "63": 222
+    },
+    "targets": {
+      "8": 7614,
+      "15": 444,
+      "22": 444,
+      "29": 444,
+      "36": 444,
+      "43": 444,
+      "50": 444,
+      "57": 444,
+      "64": 222,
+      "127": 222
+    },
+    "originals": 11166,
+    "owned_allocated": 15,
+    "owned_output_credit": 0,
+    "QUERYs": 56853,
+    "rank_surplus": 753
+  },
+  "params": {
+    "tested": "697321821/200000000000",
+    "uniform": "217913069/62500000000",
+    "cover_gap": "95367431706161/6553600000000000000000000",
+    "rho": "1/100",
+    "v": 1024,
+    "alpha_gap": "1/549755813888",
+    "cutoff": 17,
+    "floor": 18,
+    "u": "1/5"
+  },
+  "raw_crossing_independent_exact": {
+    "lower": {
+      "saving": "348660910743/100000000000000",
+      "margin": [
+        "3899703411531877692572397192147/5000000000000000000000000000000000000000",
+        "3899703411531877692572397614301/5000000000000000000000000000000000000000"
+      ]
+    },
+    "upper": {
+      "saving": "43582613843/12500000000000",
+      "margin": [
+        "-1704720454598909454294339290709/1250000000000000000000000000000000000000",
+        "-3409440909197818908588678370119/2500000000000000000000000000000000000000"
+      ]
+    },
+    "tested": {
+      "saving": "697321821/200000000000",
+      "margin": [
+        "2608515914297433665907518069452089/5000000000000000000000000000000000000000",
+        "1304257957148716832953759034935551/2500000000000000000000000000000000000000"
+      ]
+    }
+  },
+  "tail": {
+    "alpha": [
+      "6277101735371282006259122724756662838075146806550393828579/6277101735386680763835789423207666416102355444464034512896",
+      "3138550867685641003129561362378331419037573403275197020787/3138550867693340381917894711603833208051177722232017256448"
+    ],
+    "gamma": [
+      "3011306936955720643027700092177595392868606730311123763587/3138550867693340381917894711603833208051177722232017256448",
+      "376413367119465080378462511522199424108575841288890492955/392318858461667547739736838950479151006397215279002157056"
+    ],
+    "delta": [
+      "734264011784831876719595858139286542292374669675431943507/784637716923335095479473677900958302012794430558004314112",
+      "1468528023569663753439191716278573084584749339350863937261/1569275433846670190958947355801916604025588861116008628224"
+    ],
+    "normalized_surplus": "536870911/576460753377165312",
+    "H0": 3783974628696064,
+    "H1": 26386480783217407411429377
+  },
+  "C1": "22849841328606968293839/6553600000000000000000000",
+  "finite_backend_levels": [
+    {
+      "level": 1,
+      "completed_backend": "435496247/125000000000",
+      "ordinary_exact": "2284966837166803461090061/655360000000000000000000000",
+      "admitted": "1743291349/500000000000"
+    },
+    {
+      "level": 2,
+      "completed_backend": "1743291349/500000000000",
+      "ordinary_exact": "2284983959901702661090061/655360000000000000000000000",
+      "admitted": "139464353/40000000000"
+    },
+    {
+      "level": 3,
+      "completed_backend": "139464353/40000000000",
+      "ordinary_exact": "2284984131127609861090061/655360000000000000000000000",
+      "admitted": "1743304543/500000000000"
+    },
+    {
+      "level": 4,
+      "completed_backend": "1743304543/500000000000",
+      "ordinary_exact": "2284984132838099461090061/655360000000000000000000000",
+      "admitted": "3486609089/1000000000000"
+    }
+  ],
+  "admitted": "3486609089/1000000000000",
+  "comparator": "435496247/125000000000",
+  "relative_gain": "2639113/3483969976",
+  "relative_gain_percent": "65977825/870992494",
+  "uniform_signed_invoice_improvement": "Relative to PR5512: Pnew-Pold=-72H1-72H3; Tnew-Told=-72H4. Gain72*(1+3^t-4^t)>0 for0<t<1.",
+  "fee_bounds": {
+    "status": "PASS_POSITIVE_NEW_FINITE_FEE_AND_STOCK_SCHEMA",
+    "base_counts": {
+      "raw_records": 455592,
+      "all_XOR_CLEAR_INIT_zeroheader_passes": 391221,
+      "parent_parking_FIELD_passes": 2542693572,
+      "internal_and_wholejob_routes": 14796,
+      "coarse_primitive_count_with_dimension_work": 963540729957,
+      "strict_upper": 18446744073709551616,
+      "all_owned_allocated": 15,
+      "owned_productive_credit": 0
+    },
+    "fixed_tensor_unit": {
+      "v": 1024,
+      "K": "2^262144",
+      "meaning": "Bounds fixed integer ranks, all role/round/operation inventories after tensoring, charged target completion and charged paid splitting."
+    },
+    "finite_compiler": {
+      "N": "2^26386480783217407411429377",
+      "J(n)": "(n+1)^4*K^(4*n+4)",
+      "A(1)": "K^4",
+      "A(n)": "(J(n)+2)^4*(A(n-1)+2)^(4*n+8)",
+      "counts": "Productive roles B_N, paid leaves P_N, instances and primitive descriptions <=A(N). Each compiled instance gets15distinct owned banks; C_N<=15*A(N). Denominator replication product <=A(n-1)^(n-1)."
+    },
+    "height_prime": {
+      "base_height_bits": 1024,
+      "T": "(2*N+2)^4*(A(N)+2)^2",
+      "H": "1026*4^(T+1)",
+      "q": "Choose odd prime q>max(2^45*N^5,2^(2*H)) avoiding every finitely compiled denominator/rank witness. All QQ matrices and relative SOURCE projectors compiled before choice."
+    },
+    "all_in_fixed_primitive_fee": {
+      "F": "(q+2)^(32*(N+1)^2)*(A(N)+2)^8",
+      "actual_cost": "F times positive maximum of the retained stream/route/normalizer/completed-backend constants, fixed anew at each finite level. No primitive has cost0 or a claimed universal cost1.",
+      "parking": "4*(B_N+C_N) positive FIELD passes per child plus initialization/teardown, with C_N<=15*A(N); F dominates their products.",
+      "bad_classes": "<=32*N^2 ordinary calls charged separately by the retained moment/cover argument."
+    },
+    "stock": {
+      "reserve": "[B_N*|GL_N(F_q)|*q^(N^2*(w-1))]^D*S_completed_backend",
+      "D": "floor(log_N ceil(e/w))+1",
+      "borrowed_digits": "D*(N^2*(w-1)+ceil(log_q(B_N*|GL_N(F_q)|)))+ceil(log_q S_completed_backend)+1 =O_new(w loge)",
+      "ownership": "All15whole owned banks for EVERY compiled instance, including suspended ones, get distinct tags; full entry/exit CLEAR charged. No ancestor region is swept or external zero stock assumed."
+    },
+    "eventual_threshold": {
+      "K_j": "At least16 times sum of F*positive retained primitive constants, reserve/adapter bounds and already frozen backend constant completed at all widths by finite fallback.",
+      "eta_j": "min(rho-a_j,1-rho-a_j,a_j-b_j)>0",
+      "e_j": "Fresh integer dominating E_backend^(ceil(2/rho)), borrow threshold, ceil((32*K_j/eta_j)^(ceil(8/eta_j)))+2^(ceil(8/eta_j)).",
+      "scope": "Constructive finite threshold schema under retained native/compiler/ROW/precision/tape premises. Winning uniform program and decimal threshold are not materialized."
+    }
+  },
+  "whole_kappa": null,
+  "assumptions": "Same retained native/allcolumn arbitraryinput/ROW/spectator, mixed-target finite compiler, completed ordinary fallback, precision and fixed-tape contracts as PR4760/4814; no full theorem verification claimed."
+}
diff --git a/research/g20-refinement-admission/source/retirement-proof.md b/research/g20-refinement-admission/source/retirement-proof.md
new file mode 100644
index 0000000000..3f1f05be62
--- /dev/null
+++ b/research/g20-refinement-admission/source/retirement-proof.md
@@ -0,0 +1,199 @@
+# Native G20 retirement and an ordinary BIT supplier
+
+The conditional ordinary BIT saving is `0.003486609089`. The source
+PR5512 saving is `0.003483969976`. The exact increase is `0.000002639113`.
+This result gives more BIT capacity for a future complete multiplication
+construction. It does not increase the selected multiplication coefficient.
+The complex component and its complete caller still require their own bill.
+
+## 1. Contract and attribution
+
+The native G20 word, geometry, controller, and ordinary framework are the
+PR5512 construction of ai-nanachi. Its nine owned relations use Ali Romman's
+PR5421. Dugongue's PR5629 identifies four further partial helpers that can
+retire. The exact proposal and its source commit are in `proposal/` and
+`INPUTS.json`. This package supplies an emitted word, its actual caller,
+separate replay, and a new ordinary certificate for that proposal.
+
+The fixed native, arbitrary-function, all-column, ROW, spectator, finite
+compiler, ordinary fallback, precision, and tape contracts of PR4760 and
+PR4814 remain assumptions. The finite checks here do not prove those
+contracts. Read `source/PROOF.md` and `source/NOTICE.md` for the retained
+proof and full credit. The all-input argument below is conditional on the
+same native coframe identities as that proof.
+
+## 2. Emit and retire four whole owned fields
+
+Make fields `462, 463, 466, 468` owned. Clear each complete field at entry.
+Keep every source operation through its last nonzero source read. Those
+source record indices are respectively `16202, 16206, 16160, 16139`.
+The protected rank-four reads occur before these cuts and remain paid.
+Clear each field immediately after its cut. Set its return frame at that
+clear. Omit its later destination operations and reads of the resulting
+whole zero. This removes four rank-three queries, four rank-one queries,
+four other tail ADDs, and 32 cold zero reads per local call.
+
+The source invariant represents a field in frame F by one normalized
+linear row in the independent input functions. ADD requires the same
+coframe on both operands. A native query changes the coframe and keeps
+that normalized row. Thus a zero normalized row is the zero function for
+every native input width under the retained coframe identity. It is not
+only a scalar zero at a sampled point. Specializing an owned input to
+zero and then replaying these rows proves each omitted read is zero.
+After the last nonzero read, a field has no effect on any retained output.
+Its remaining return path can therefore be replaced by whole-field CLEAR.
+No retained original input is cleared, and no live frame is renamed.
+
+The resulting local word has 645 retained original fields and 15 owned
+fields. The 15 include the source centre, its shadow, the source nine
+relations, and these four new helpers. Every owned entry can contain an
+arbitrary dirty value; the entry CLEAR removes its complete column.
+The output on each retained field is the same physical source map. The
+owned outputs are all zero. The local paid histogram is
+
+```text
+rank       1     2   3   4    5   6   7
+count   1305  1342  73  40  102  10   9
+```
+
+The source exact rational coframe checks are retained. Forward native
+replay tracks all 660 original and dirty columns over moduli 101 and
+10201. A separate adjoint implementation uses other address points at
+both moduli and checks all transpose columns. CLEAR has the total zero
+linear extension; it is not inverted. These finite tests support the
+coframe proof. They are not a substitute for its all-width assumptions.
+Missing entry CLEAR, an early retirement, and retained-input erasure all
+fail the verifier.
+
+## 3. Complete controller and target bill
+
+Install the new physical involution in all 18 G20 local calls. Share 15
+owned banks serially; all return zero between calls. Retire 234 original
+helper targets: 18 copies of the source nine helpers and the new four.
+The actual 11,166 retained originals stay independent. The caller also
+includes its thin query shears, scalar boundaries, idles, bridges, return
+routes, COPY, CLEAR, and private epochs. `GLOBAL.jsonl.gz` emits all
+455,592 events. `SOURCE-DESCRIPTORS.json.gz` binds every one of the
+56,853 queries to its chronological owner, epoch, version, normalized
+row, and prefix hash. The row is extra evidence; it does not certify a
+pure physical source without its native prefix.
+
+`independent.py` recounts these events and all targets from the source
+owner table. It verifies the full identity on 11,166 original columns
+and annihilation of all 15 dirty columns. A stale query epoch fails.
+The positive envelope has 516 bits. No owned field has output credit.
+The new bill relative to PR5512 is
+
+```text
+P_new - P_old = -72 H1 -72 H3
+T_new - T_old = -72 H4
+```
+
+For `t=1-C` in `(0,1)`, the exact target-minus-paid gain is
+`72*(1+3^t-4^t)>0`. Strict subadditivity gives the sign. This proves a
+positive gain for every such exponent, with the new target debit included.
+The full histograms, not this difference alone, feed the ordinary compiler.
+
+## 4. New finite compiler and positive costs
+
+Use tested saving `0.003486609105`, uniform saving `0.003486609104`,
+tensor power 1024, cutoff 17, floor 18, and second parameter `1/5`.
+Two separate rational interval engines verify the full bill. The raw
+crossing is in `(0.00348660910743, 0.00348660910744)`. With `t=1-tested`,
+the exact intervals satisfy
+
+```text
+alpha = P_t/T_t < 1-2^-39
+ gamma = P_(t+1/5)/(17^(1/5)*T_t) < 31/32
+ delta = 11166*18/(17^tested*T_t) < 19/20
+```
+
+Complete each small target on the same owner at `18^1024`. Split every
+paid job at `17^1024` and charge every piece. The two decay blocks to
+power 128 are less than `1/16`. The normalized contraction surplus is
+`536870911/576460753377165312`. The separation check is `17^64<18^63`.
+The new integer thresholds are
+
+```text
+H0 = 3783974628696064
+H1 = 26386480783217407411429377
+N  = 2^H1
+```
+
+These values satisfy the source inequalities with `h=1/64` and `z0`
+halfway between `t` and `1-uniform`. The base precision envelope is less
+than 1024 bits. The complete positive base count is `963540729957<2^64`.
+It includes `4*(11166+15)*56853` field passes for parent parking,
+all emitted scans, internal and whole-job routes, and dimension work.
+
+Set `K=2^262144`. Retain the source finite bounds
+
+```text
+J(n)=(n+1)^4*K^(4*n+4)
+A(1)=K^4
+A(n)=(J(n)+2)^4*(A(n-1)+2)^(4*n+8)
+T_arith=(2*N+2)^4*(A(N)+2)^2
+H=1026*4^(T_arith+1)
+```
+
+Each compiled instance gets 15 distinct owned banks. This also applies
+to suspended instances. Thus `C_N<=15*A(N)`. All entry and exit CLEAR
+passes are charged. Choose an odd prime
+`q>max(2^45*N^5,2^(2*H))` that avoids every compiled denominator and
+rank witness. Choose it after the fixed matrices and before the input
+width. The source positive multiplier
+`F=(q+2)^(32*(N+1)^2)*(A(N)+2)^8` bounds primitive counts. Multiply it
+by the positive maximum of the retained primitive and backend constants.
+No primitive has zero cost or a claimed universal unit machine cost.
+
+`ORDINARY-RESULT.json` states the complete stock, borrowed-digit, prime,
+and fresh eventual-threshold formulas. In particular, all owned banks
+have separate tags, ancestor storage is preserved, and no external zero
+stock is assumed. The retained bad-class calls are charged by the cover
+argument. These finite but large choices meet the inherited compiler
+schema. The winning uniform program and decimal threshold are not expanded.
+
+## 5. Four finite ordinary levels
+
+Let `g=2^-36+10^-20` and `rho=1/100`. The cover guard `2^45*g>256`
+holds. Start with the completed source backend `b0=0.003483969976`.
+At each level freeze the preceding completed algorithm, then set
+
+```text
+a_j=(1-rho)*(uniform-g)+rho*b_(j-1)
+b_j=floor(10^12*a_j)/10^12
+```
+
+The four new admitted values are `0.003486582698`, `0.003486608825`,
+`0.003486609086`, and **`0.003486609089`**. Every improvement, adapter,
+stock, and rounding gap is positive. Each level gets new finite constants
+and a fresh threshold from its completed all-width fallback. No level
+calls itself as its atom backend. A fifth level has the same admitted
+value on this decimal grid, so it adds no useful result here.
+
+## 6. Check the immediate extension strategy
+
+Before freezing the word, `extensions.py` checks 1,174 further cohorts.
+These include every one of the 423 possible single additions, all complete
+pure-helper supports at source reads or queries, and the whole eligible
+helper set. Each cohort contains the chosen four. The emitter constructs
+each specialized word and counts all additional removed paid queries.
+Every extra owner debits one rank-eight target per local call. For
+`0<=C<=1/100`, the sum of removed ranks is already less than the lower
+bound on that target debit. Since `r^(1-C)<=r`, none of these cohorts
+can improve the chosen bill. This is a bound for the declared finite
+census. It does not exclude other subsets or a changed reconstruction
+program. Its purpose is to test the next step in this constructive
+strategy before presenting a small local gain as the end of the search.
+
+## Open next questions
+
+Can a priced reconstruction change a later nonzero helper read and retire
+more of its return path? First emit that changed native continuation,
+then debit all lost targets and replay its complete caller. The current
+cohort census does not answer this question. A higher complete kappa also
+requires a compatible complex supplier and a complete paired bill.
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. New work
+is Apache-2.0. Credit Dugongue, ai-nanachi, DreamingOfClouds, eumemic,
+Cinna Davis, rohanarun, zxv, Jacob Alan Sussman, and all retained notices.
diff --git a/research/g20-refinement-admission/source/vendor/g20/inputs/BASELINE-LOCAL.json.gz b/research/g20-refinement-admission/source/vendor/g20/inputs/BASELINE-LOCAL.json.gz
new file mode 100644
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diff --git a/research/g20-refinement-admission/source/vendor/g20/inputs/CONTROLLER.json b/research/g20-refinement-admission/source/vendor/g20/inputs/CONTROLLER.json
new file mode 100644
index 0000000000..89c400d597
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/inputs/CONTROLLER.json
@@ -0,0 +1,2175 @@
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diff --git a/research/g20-refinement-admission/source/vendor/g20/inputs/FRAMES.json b/research/g20-refinement-admission/source/vendor/g20/inputs/FRAMES.json
new file mode 100644
index 0000000000..9edf8d95b4
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/inputs/FRAMES.json
@@ -0,0 +1,56126 @@
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+    },
+    "20006": {
+      "dim": 1,
+      "B": [
+        [
+          1,
+          0,
+          0,
+          1,
+          1,
+          0,
+          0,
+          1
+        ]
+      ],
+      "A": [
+        [
+          0,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          2,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          2,
+          0
+        ],
+        [
+          0,
+          1,
+          1,
+          0,
+          1,
+          0,
+          0,
+          -1
+        ],
+        [
+          1,
+          0,
+          1,
+          0,
+          -1,
+          0,
+          1,
+          0
+        ],
+        [
+          1,
+          1,
+          1,
+          -1,
+          0,
+          0,
+          0,
+          0
+        ]
+      ],
+      "origin": "orthogonal complement of capture frame 516"
+    },
+    "20007": {
+      "dim": 1,
+      "B": [
+        [
+          0,
+          0,
+          -1,
+          -1,
+          0,
+          0,
+          -1,
+          1
+        ]
+      ],
+      "A": [
+        [
+          2,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          2,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          2,
+          0,
+          0
+        ],
+        [
+          0,
+          1,
+          1,
+          0,
+          1,
+          0,
+          0,
+          1
+        ],
+        [
+          1,
+          0,
+          1,
+          0,
+          1,
+          0,
+          -1,
+          0
+        ],
+        [
+          1,
+          1,
+          1,
+          -1,
+          0,
+          0,
+          0,
+          0
+        ]
+      ],
+      "origin": "orthogonal complement of capture frame 517"
+    },
+    "20008": {
+      "dim": 1,
+      "B": [
+        [
+          0,
+          -1,
+          0,
+          1,
+          0,
+          1,
+          0,
+          1
+        ]
+      ],
+      "A": [
+        [
+          2,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          2,
+          0,
+          0,
+          0
+        ],
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          2,
+          0
+        ],
+        [
+          0,
+          1,
+          1,
+          0,
+          1,
+          0,
+          0,
+          1
+        ],
+        [
+          1,
+          1,
+          0,
+          0,
+          1,
+          1,
+          0,
+          0
+        ],
+        [
+          1,
+          1,
+          1,
+          1,
+          0,
+          0,
+          0,
+          0
+        ]
+      ],
+      "origin": "orthogonal complement of capture frame 518"
+    }
+  }
+}
diff --git a/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py b/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py
new file mode 100644
index 0000000000..4b24a50961
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/credited_intervals.py
@@ -0,0 +1,421 @@
+#!/usr/bin/env python3
+"""Higher-moment strictification and a polynomial-logarithm compiler bound.
+
+New arithmetic is independent of predecessor interval code. The unchanged
+invoice replay and two outer ledgers are credited, byte-pinned oracles.
+zxv with substantial OpenAI Codex assistance. Apache-2.0.
+"""
+import argparse
+import ast
+from collections import Counter
+from contextlib import redirect_stdout
+from fractions import Fraction as Q
+from functools import lru_cache
+from hashlib import sha256, sha1
+import io
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+GRID = 2**192
+C = Q('0.00268648')
+KAPPA = Q('0.00268647')
+T = {5:420, 6:270, 7:840, 8:1395, 9:3195,
+     25:448, 41:448, 57:448, 121:224}
+P = {1:37305, 2:10695, 3:3360, 4:1530, 5:300,
+     8:1464, 16:448, 32:448, 48:448}
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def down(x):
+    return Q((x*GRID).__floor__(), GRID)
+
+
+def up(x):
+    return Q(-((-x*GRID).__floor__()), GRID)
+
+
+def rounded(lo, hi):
+    return down(lo), up(hi)
+
+
+def mul(a, b):
+    products = [x*y for x in a for y in b]
+    return rounded(min(products), max(products))
+
+
+def scale(a, x):
+    return mul(a, (x, x))
+
+
+def divide(a, b):
+    need(b[0] > 0, 'positive interval denominator')
+    return mul(a, rounded(1/b[1], 1/b[0]))
+
+
+@lru_cache(None)
+def log_bounds(n):
+    """Exact atanh series, binary reduction; round only the final interval."""
+    need(isinstance(n, int) and n >= 1, 'positive integer logarithm')
+
+    def series(x):
+        u = (x-1)/(x+1)
+        term, total = u, Q(0)
+        for j in range(80):
+            total += 2*term/(2*j+1)
+            term *= u*u
+        tail = 2*term/(161*(1-u*u))
+        return total, total+tail
+
+    k = n.bit_length()-1
+    a, b = series(Q(2))
+    c, d = series(Q(n, 2**k))
+    return rounded(k*a+c, k*b+d)
+
+
+def exp_point(x):
+    """Outward fixed-point Taylor enclosure, with binary scaling/squaring."""
+    need(abs(x) < 16, 'bounded exponential argument')
+    if x < 0:
+        a, b = exp_point(-x)
+        return rounded(1/b, 1/a)
+    divisions = 0
+    while x > Q(1, 2):
+        x /= 2
+        divisions += 1
+    term = total = (Q(1), Q(1))
+    for j in range(1, 65):
+        term = scale(term, x/j)
+        total = rounded(total[0]+term[0], total[1]+term[1])
+    following = scale(term, x/65)
+    # Every remaining ratio is <= 1/132. Twice the next term is safe.
+    result = rounded(total[0], total[1]+2*following[1])
+    for _ in range(divisions):
+        result = mul(result, result)
+    return result
+
+
+def exp_interval(a):
+    return exp_point(a[0])[0], exp_point(a[1])[1]
+
+
+@lru_cache(None)
+def power(n, exponent):
+    return exp_interval(scale(log_bounds(n), exponent))
+
+
+def moment(histogram, exponent):
+    low = high = Q(0)
+    for n, count in histogram.items():
+        a, b = power(n, exponent)
+        low += count*a
+        high += count*b
+    return rounded(low, high)
+
+
+def display(a):
+    unit = 10**30
+
+    def fixed(n):
+        sign = '-' if n < 0 else ''
+        s = str(abs(n)).rjust(31, '0')
+        return sign+s[:-30]+'.'+s[-30:]
+
+    return {'lower': fixed((a[0]*unit).__floor__()),
+            'upper': fixed(-((-a[1]*unit).__floor__()))}
+
+
+def encoded(x):
+    if isinstance(x, Q):
+        return str(x)
+    if isinstance(x, dict):
+        return {str(k): encoded(v) for k, v in x.items()}
+    if isinstance(x, (list, tuple)):
+        return [encoded(v) for v in x]
+    return x
+
+
+def source_environment(path):
+    env = {'__file__': str(path), '__name__': 'pinned_source_oracle'}
+    exec(compile(path.read_bytes(), str(path), 'exec'), env)
+    return env
+
+
+def authenticate():
+    result = {}
+    for row in json.loads((HERE/'VENDOR.json').read_text())['files']:
+        path = HERE/'vendor'/Path(row['path']).relative_to(
+            'research/higher-moment-strictification/vendor')
+        digest = sha256(path.read_bytes()).hexdigest()
+        need(digest == row['sha256'], 'changed source: '+row['path'])
+        raw = path.read_bytes()
+        need(sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()
+             == row['git_blob'], 'changed Git source blob')
+        result[row['path']] = digest
+    return result
+
+
+def invoice_oracle():
+    """Run #4426 unchanged, rebinding only its two file-location globals."""
+    path = HERE/'vendor/invoice-review/verify.py'
+    env = source_environment(path)
+    env.update(ROOT=path.parent, PHASES='DATA-PHASES.json')
+    output = io.StringIO()
+    with redirect_stdout(output):
+        env['main']()
+    result = json.loads(output.getvalue())
+    need(result['status'] == 'PASS_PR4416_INVOICE_REBUILD', 'source invoice oracle')
+    need({int(k): v for k, v in result['targets'].items()} == T
+         and {int(k): v for k, v in result['paid'].items()} == P,
+         'exact literal-word invoice')
+    return result
+
+
+def tail_certificate(v=150, cutoff=10, floor=15, u=Q(3, 10)):
+    t = 1-C
+    need(v >= 1 and 1 < cutoff < floor < 121, 'strict finite ranks')
+    need(t+u >= 1, 'tail moment exponent at least one')
+    target, paid = moment(T, t), moment(P, t)
+    alpha = divide(paid, target)
+    gamma = divide(moment(P, t+u), mul(power(cutoff, u), target))
+    delta = divide((Q(sum(T.values())*floor),)*2,
+                   mul(power(cutoff, C), target))
+    limits = (1-Q(1, 10**8), Q(181, 200), Q(439, 500))
+    for name, bounds, limit in zip(('alpha', 'gamma', 'delta'),
+                                  (alpha, gamma, delta), limits):
+        need(0 < bounds[0] <= bounds[1] < limit < 1, name+' certified limit')
+    a, g, d = limits
+    bound = 1/(1+v*(1-a))+2*g**v+2*d**v
+    need(bound < 1, 'complete charged normalized moment')
+    old_gamma = divide((Q(sum(k*n for k, n in P.items())),)*2,
+                       mul(power(cutoff, C), target))
+    old_lower = alpha[0]**v+2*old_gamma[0]**v
+    need(old_lower > 1, 'rank-one-tail estimate fails at this tensor power')
+    return {'tensor_power': v, 'cutoff_base': cutoff, 'floor_base': floor,
+            'paid_moment_exponent': t+u, 'tail_offset_u': u,
+            'tested_saving': C, 'alpha': display(alpha), 'gamma': display(gamma),
+            'delta': display(delta), 'rational_upper_limits': limits,
+            'normalized_paid_upper': bound, 'strict_moment_gap': display((1-bound,)*2),
+            'old_rank_one_gamma': display(old_gamma),
+            'old_rank_one_bound_lower': display((old_lower, old_lower)),
+            'ambient': '121^'+str(v), 'minimum_target': str(floor)+'^'+str(v),
+            'maximum_paid': str(cutoff)+'^'+str(v),
+            'productive_fields_before_uniform_compiler': '7688^'+str(v),
+            'rank_one_surplus': '131723^'+str(v)+'-131115^'+str(v),
+            'materialized_product_or_uniform_word': False}
+
+
+def uniform_rank(v):
+    t, p, theta = 1-C, 13, Q(6, 7)
+    gap = (C-KAPPA)/7
+    uniform_saving = C-gap
+    need(10**7 < 15**6, 'theta upper bound')
+    need(2*(10**v)**7 <= (121**v)**6, 'shifted logarithm inequality')
+    eta = scale(exp_interval(scale(log_bounds(121), -v*C)), t)
+    need(eta[0] > theta**p, 'exit contraction below complement capacity')
+    base = exp_interval(scale(log_bounds(121), v*C))
+    need(base[1] < 2**p, 'entire ordinary base range fits')
+    # Integer grid: gap*H is integral, avoiding enormous rational powers.
+    step = gap.denominator
+    need(gap.numerator == 1, 'chosen rational gap grid')
+
+    def passes(j):
+        H = step*j
+        return (H+1)**p < 2**j
+
+    lo, hi = 1, 2
+    while not passes(hi):
+        lo, hi = hi, 2*hi
+    while hi-lo > 1:
+        mid = (lo+hi)//2
+        if passes(mid):
+            hi = mid
+        else:
+            lo = mid
+    H = step*hi
+    need(H > 7*v and passes(hi) and not passes(hi-1), 'final integer comparison')
+    need(eta[1] < theta**(p-1), 'one smaller logarithmic power fails')
+    return {'t': t, 'uniform_saving': uniform_saving, 'gap': gap,
+            'logarithm_power': p, 'theta_upper': theta, 'eta': display(eta),
+            'eta_minus_theta_to_p': display((eta[0]-theta**p, eta[1]-theta**p)),
+            'm_to_saving': display(base), 'H': H, 'N': '2^'+str(H),
+            'integer_test': {'left_base': H+1, 'left_exponent': p,
+                             'right_base': 2, 'right_exponent': hi},
+            'grid_step': step, 'previous_grid_point_rejected': True,
+            'smaller_logarithmic_power_rejected': True}
+
+
+def power_majorant_comparison(v, uniform_saving):
+    """Retain #4416's older power proof, changing only the new unit's ranks."""
+    t, z, h = 1-C, 1-uniform_saving, Q(1, 7)
+    z0 = (t+z)/2
+    delta = z0-t
+    B, debt = (4+7*h)*v, 1+7*v*(1-z0)
+    ratio = (delta*B+debt)/(h*delta)
+    H0 = -((-ratio.numerator)//ratio.denominator)
+    ratio = H0*(1-z0)/(z-z0)
+    H1 = ratio.numerator//ratio.denominator+1
+    need(H0 >= 7*v and H0*h*delta >= delta*B+debt, 'power majorant threshold')
+    need((H0-1)*h*delta < delta*B+debt, 'previous power threshold rejected')
+    need(H1*(z-z0) > H0*(1-z0) >= (H1-1)*(z-z0),
+         'strict power-majorant comparison and previous-rank control')
+    return {'H0': H0, 'H1': H1, 'N': '2^'+str(H1), 'theta_upper': 1-h,
+            'scope': 'Tail transformation alone, retaining the older power majorant.'}
+
+
+def outer_ledger(uniform_saving):
+    d = (C-KAPPA)/7
+    params = {'kappa': KAPPA, 'tested_saving': C,
+              'complex_uniform_saving': uniform_saving, 'b': KAPPA+5*d,
+              'a': KAPPA+4*d, 'q': KAPPA+3*d, 'bit_saving': Q('0.0027'),
+              'epsilon': 1-d, 'beta': 1-3*d, 'r0': d/10,
+              'stop': d, 'layout': d, 'd': d}
+    env = source_environment(HERE/'vendor/outer_endpoint.py')
+    row = env['ledger'](params)
+    need(len(row['strict_checks']) == 54 and len(row['functional_checks']) == 3,
+         'complete first outer ledger')
+    need(all(v > 0 for group in ('strict_checks', 'functional_checks')
+             for v in row[group].values()), 'all outer predicates')
+    frozen = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['outer']
+    need(encoded(row) == frozen, 'unchanged full p7 endpoint ledger')
+    parsed = ast.parse((HERE/'vendor/check_ledger.py').read_bytes())
+    function = next(n for n in parsed.body
+                    if isinstance(n, ast.FunctionDef) and n.name == 'ledger')
+    constants = [n for n in parsed.body if isinstance(n, ast.Assign)
+                 and any(isinstance(t, ast.Name) and t.id.startswith('KAPPA_')
+                         for t in n.targets)]
+    eps, beta, q, a = (params[k] for k in ('epsilon', 'beta', 'q', 'a'))
+    grid = 10**10
+    backoff = Q((eps*q*grid).__floor__(), grid)-KAPPA
+    need(backoff > 0, 'strict derived oracle grid backoff')
+    oracle = {'Q': Q, 'R0': params['r0'], 'ZETA': Q(1, 10**8),
+              'SLACK': d, 'STOP': d, 'FLOOR': grid, 'BACKOFF': backoff,
+              'EPS': eps, 'BETA': beta, 'THETA_POWER': Q(2),
+              'HALO_POWER': 48, 'CORE_POWER': 128, 'STRASSEN_TAU': Q(45, 16),
+              'b': params['b'], 'q': q, 'a': a, 'bit': params['bit_saving'],
+              'online': Q('0.001730970419199163702738'),
+              'old': Q('0.001730970419199163702738')}
+    code = ast.fix_missing_locations(ast.Module(body=constants+[function], type_ignores=[]))
+    exec(compile(code, 'pinned 63-predicate ledger', 'exec'), oracle)
+    second = oracle['ledger']('higher_moment_smaller_ranks')
+    need(second['kappa'] == KAPPA and second['margins'] == row['margins'],
+         'all nine rows match both ledgers')
+    need(len(second['strict_checks']) == 63 and
+         all(v > 0 for v in second['strict_checks'].values()), 'all 63 legacy predicates')
+    controls = {}
+    for name, updates in [('closed_epsilon', {'epsilon': Q(1)}),
+                          ('missing_layout', {'layout': Q(0)}),
+                          ('unfunded_kappa', {'kappa': C}),
+                          ('closed_uniform_gap', {'complex_uniform_saving': params['b']}),
+                          ('insufficient_BIT', {'bit_saving': Q('0.0023')})]:
+        bad = env['ledger'](dict(params, **updates))
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'outer control rejected: '+name)
+        controls[name] = failed
+    for name, options in [('old_per_axis_scan', {'old_scan': True}),
+                          ('group_equals_dimension', {'beta_': eps})]:
+        bad = oracle['ledger']('reject_'+name, **options)
+        failed = sorted(k for k, v in bad['strict_checks'].items() if v <= 0)
+        need(failed, 'legacy control rejected: '+name)
+        controls[name] = failed
+    return {'ledger': row, 'legacy_63_checks': second['strict_checks'],
+            'legacy_grid': grid, 'legacy_backoff': backoff,
+            'minimum_margin_minus_kappa': min(row['margins'].values())-KAPPA,
+            'rejected_controls': controls}
+
+
+def finite_controls():
+    def tensor(histogram):
+        out = Counter()
+        for k, n in histogram.items():
+            for h, b in histogram.items():
+                out[k*h] += n*b
+        return out
+
+    def split(histogram, cutoff):
+        out = Counter()
+        for k, n in histogram.items():
+            q, r = divmod(k, cutoff)
+            out[cutoff] += q*n
+            if r:
+                out[r] += n
+        return +out
+
+    target, paid = tensor({2:1, 5:1}), tensor({1:2, 4:1})
+    padded, completion = Counter(), Counter()
+    for k, n in target.items():
+        padded[max(k, 9)] += n
+        if k < 9:
+            completion[9-k] += n
+    final = split(paid+completion, 4)
+    mass = lambda x: sum(k*n for k, n in x.items())
+    need(mass(padded)-mass(final) == 7**2-6**2 == 13, 'exact paid padding mass')
+    need(min(padded) > max(final), 'exact toy separation')
+    need(final == Counter({1:5, 4:9}), 'literal toy expanded inventory')
+    # t=1/2, sigma=3/4, R=100, J=1 refutes a sublinear tail extension.
+    invalid = power(100, Q(1, 2))[1]+2*power(100, Q(3, 4))[1]
+    need(invalid < 100, 'sublinear upper-tail moment cannot bound splitting')
+    return {'toy_targets': padded, 'toy_paid': final, 'rank_one_surplus': 13,
+            'sublinear_tail_counterexample': {'R': 100, 'J': 1, 't': '1/2',
+                                             'sigma': '3/4', 'actual_charge': 100,
+                                             'invalid_upper': display((invalid, invalid))}}
+
+
+def verify():
+    sources = authenticate()
+    invoice = invoice_oracle()
+    tail = tail_certificate()
+    rank = uniform_rank(tail['tensor_power'])
+    endpoint = outer_ledger(rank['uniform_saving'])
+    controls = finite_controls()
+    rejected = []
+    for name, updates, expected in [
+        ('too_short_product', {'v': 100}, 'complete charged normalized moment'),
+        ('sublinear_tail', {'u': C/2}, 'tail moment exponent at least one'),
+        ('lost_separation', {'floor': 10}, 'strict finite ranks'),
+    ]:
+        try:
+            tail_certificate(**updates)
+        except ValueError as error:
+            need(str(error) == expected, 'wrong rejection: '+name)
+            rejected.append({'mutation': name, 'failed_at': str(error)})
+        else:
+            raise ValueError('accepted mutation: '+name)
+    old = json.loads((HERE/'vendor/p7-RESULT.json').read_text())['endpoint']['compiler']
+    return encoded({'schema': 'higher-moment-native-strictification/1',
+                    'status': 'PASS_HIGHER_MOMENT_STRICTIFICATION', 'kappa': KAPPA,
+                    'invoice_oracle': invoice, 'strictification': tail,
+                    'uniform_rank': rank, 'outer': endpoint,
+                    'tail_only_power_majorant': power_majorant_comparison(
+                        tail['tensor_power'], rank['uniform_saving']),
+                    'finite_controls': controls, 'rejected_mutations': rejected,
+                    'predecessor_H': old['H1'],
+                    'rank_exponent_reduction_factor': Q(old['H1'], rank['H']),
+                    'tensor_power_reduction_factor': Q(6240, tail['tensor_power']),
+                    'source_sha256': sources,
+                    'verifier_sha256': sha256(Path(__file__).read_bytes()).hexdigest(),
+                    'scope': 'Conditional charged transformation and finite compiler rank. Native all-column, physical, analytic, precision, storage, fixed-tape and recovery premises remain inherited. No new kappa, selected frontier or practical word.'})
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path)
+    args = parser.parse_args()
+    result = verify()
+    if args.out:
+        need(not args.out.exists(), 'new output path required')
+        args.out.write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+    else:
+        need(json.loads((HERE/'RESULT.json').read_text()) == result, 'changed saved receipt')
+    print(json.dumps({'status': result['status'], 'tensor_power': result['strictification']['tensor_power'],
+                      'uniform_rank': result['uniform_rank']['N'],
+                      'strict_moment_gap': result['strictification']['strict_moment_gap'],
+                      'kappa': result['kappa']}))
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/separate_series.py b/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/separate_series.py
new file mode 100644
index 0000000000..7c68264455
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/ordinary-certificate/inputs/separate_series.py
@@ -0,0 +1,32 @@
+"""Independent positive-series rational intervals, no external numeric library."""
+from fractions import Fraction as F
+from functools import lru_cache
+S=10**40
+def need(c,m):
+    if not c:raise ValueError(m)
+def floor(q):return q.numerator//q.denominator
+def ceil(q):return -((-q.numerator)//q.denominator)
+def grid(lo,hi):return F(floor(lo*S),S),F(ceil(hi*S),S)
+def logratio(z,n=60):
+    need(0<=z<=F(1,3),'Reduced log domain');s=F(0);p=z
+    for j in range(n):s+=2*p/(2*j+1);p*=z*z
+    return s,s+2*p/((2*n+1)*(1-z*z))
+LN2=logratio(F(1,3))
+@lru_cache(None)
+def logbound(x):
+    if x==1:return F(0),F(0)
+    k=x.bit_length()-1;a,b=logratio(F(x-2**k,x+2**k));return grid(a+k*LN2[0],b+k*LN2[1])
+@lru_cache(None)
+def expbound(y):
+    need(0<=y<7,'Bounded exp');s=p=F(1);n=90
+    for j in range(1,n+1):p=p*y/j;s+=p
+    return grid(s,s+(p*y/(n+1))/(1-y/(n+2)))
+@lru_cache(None)
+def power(x,t):
+    if x==1:return F(1),F(1)
+    a,b=logbound(x);a,b=grid(t*a,t*b);return expbound(a)[0],expbound(b)[1]
+def moment(profile,t):
+    vv=[(n,power(k,t))for k,n in profile.items()];return sum(n*v[0]for n,v in vv),sum(n*v[1]for n,v in vv)
+def mul(a,b):return a[0]*b[0],a[1]*b[1]
+def div(a,b):return a[0]/b[1],a[1]/b[0]
+def interval(a):return {'lower':str(a[0]),'upper':str(a[1]),'display':float(sum(a)/2)}
diff --git a/research/g20-refinement-admission/source/vendor/g20/provider/build_global.py b/research/g20-refinement-admission/source/vendor/g20/provider/build_global.py
new file mode 100644
index 0000000000..adb6e21ec7
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/provider/build_global.py
@@ -0,0 +1,125 @@
+"""Materialize the exact G23 stream and separate current-source descriptors."""
+from pathlib import Path
+from collections import Counter
+from hashlib import sha256
+from datetime import datetime,timezone
+from time import process_time
+import gzip,json
+from local_ir import N as LN,EXPECTED,need
+HERE=Path(__file__).resolve().parent;ROOT=HERE.parent;INPUT=ROOT/'inputs';DATA=HERE/'data';N=11400;V=111
+def read(p):return json.loads(gzip.decompress(p.read_bytes()))if p.suffix=='.gz'else json.loads(p.read_bytes())
+def put(p,x):p.write_text(json.dumps(x,indent=2)+'\n',encoding='utf-8')
+def xor(a,b):
+ out=a.copy()
+ for k,v in b.items():
+  out[k]=out.get(k,0)^v
+  if not out[k]:del out[k]
+ return out
+def shift(a,s):return{k^s:v for k,v in a.items()}
+def physical_main(controller):
+ rows=[{0:1<<i}for i in range(32)]
+ def boundary(program):
+  for op,d,s in program:
+   if op=='ADD':rows[d]=xor(rows[d],rows[s])
+   else:need(op=='SWAP','Boundaryopcode');rows[d],rows[s]=rows[s],rows[d]
+ boundary(controller['boundaries']['right_program'])
+ for e in controller['physical_events']:
+  op=e[0]
+  if op in('LOCAL','QUERY_SHEAR'):
+   _,stage,pair,rev=e;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   rows[y]=xor(rows[y],shift(rows[x],1))
+   if op=='LOCAL':rows[x]=shift(rows[x],1<<(stage+1));rows[y]=shift(rows[y],1<<(stage+1))
+  elif op=='IDLE':
+   _,pair,stages=e;s=sum(1<<(j+1)for j in stages)
+   for bank in(2*pair,2*pair+1):rows[bank]=shift(rows[bank],s)
+  elif op=='ADD':rows[e[1]]=xor(rows[e[1]],rows[e[2]])
+  else:need(op=='SWAP','Controlleropcode');rows[e[1]],rows[e[2]]=rows[e[2]],rows[e[1]]
+ boundary(controller['boundaries']['left_program']);need(rows==[{int(t):1<<i}for i,t in enumerate(controller['diagonal'])],'EveryphysicalMAINpolynomialcoefficient')
+ return[{str(k):v for k,v in row.items()}for row in rows]
+def main():
+ clock=process_time();DATA.mkdir(exist_ok=True);controller=read(INPUT/'CONTROLLER.json');base=read(INPUT/'BASELINE-LOCAL.json.gz');frames=read(INPUT/'FRAMES.json')['frames'];expected=read(INPUT/'G23-EXPECTED.json');thick=controller['invoice']['thick_stages'];stage_index={s:i for i,s in enumerate(thick)};programs={False:read(DATA/'FORWARD.json.gz')['records'],True:read(DATA/'INVERSE.json.gz')['records']}
+ mainrows=physical_main(controller);values=[1<<i for i in range(N)]+[0,0];versions=[0]*(N+2);norm=[1]*N+[0,0];epoch=[0]*(N+2);peak=1;privatepeak=0;counts=Counter();paid=Counter();calls=[];episodes=[];changed_requests=[];eventno=0;source_count=0;streamhash=sha256();sourcehash=sha256();tickets={}
+ raw_file=(DATA/'GLOBAL.jsonl.gz').open('wb');out=gzip.GzipFile(filename='',fileobj=raw_file,mode='wb',mtime=0);src_file=(DATA/'SOURCE-DESCRIPTORS.jsonl.gz').open('wb');srcout=gzip.GzipFile(filename='',fileobj=src_file,mode='wb',mtime=0)
+ def emit(e):
+  nonlocal eventno
+  b=(json.dumps(e,separators=(',',':'))+'\n').encode();streamhash.update(b);out.write(b);eventno+=1;counts[e[0]]+=1
+ def source(owner,rank,geometry,extra=None,arg_version=None):
+  nonlocal source_count
+  desc={'event':eventno,'prefix_sha256':streamhash.hexdigest(),'source_namespace':f'G20_CURRENT_QUERY/{source_count}','owner':owner,'owner_epoch':epoch[owner],'version':versions[owner]if arg_version is None else arg_version,'rank':rank,'geometry':geometry,'current_RAW_bitmap_sha256':sha256(values[owner].to_bytes((N+7)//8,'little')).hexdigest(),'DOMAIN':'completecurrentGLOBALunitcoverROW/HEAD/pairedTAIL/spectatorARRAY','source_history':'Frozenprefix+owner+currentversiondefinesactualFUNCTION; thisRAWbitmaphashisextraevidence,nottheonlyfunctionclaim.'}
+  if extra:desc['compound_or_context']=extra
+  b=(json.dumps(desc,separators=(',',':'))+'\n').encode();sourcehash.update(b);srcout.write(b);source_count+=1
+ def add(d,s,kind='ADD',meta=None):
+  nonlocal peak
+  need(d!=s,'DistinctDATAfields');need(not any(t[0]==d for t in tickets.values()),'ImmutableSOURCElease');values[d]^=values[s];versions[d]+=1;norm[d]+=norm[s];peak=max(peak,norm[d]);emit([kind,d,s,meta])
+ def swap(d,s,label):add(d,s,meta=label);add(s,d,meta=label);add(d,s,meta=label)
+ def boundary(program,label):
+  for op,d,s in program:
+   for p in range(V):
+    if op=='ADD':add(d*V+p,s*V+p,meta=label)
+    else:need(op=='SWAP','Fixedboundary');swap(d*V+p,s*V+p,label)
+ boundary(controller['boundaries']['right_program'],'RIGHT_BOUNDARY')
+ for event in controller['physical_events']:
+  op=event[0]
+  if op=='LOCAL':
+   _,stage,pair,rev=event;baseh=32*V+436*stage_index[stage];helpers=list(range(baseh,baseh+436));need(all(values[h]==1<<h for h in helpers),'Distinctarbitraryoriginalhelperbank');x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   sx=[values[x*V+i]for i in range(V)];sy=[values[y*V+i]for i in range(V)]
+   def owner(r):return N+r-658 if r>=658 else((x if r<V else y)*V+r%V if r<222 else baseh+r-222)
+   if stage:
+    for bank in(x,y):
+     for p in range(V):emit(['PAID_PORT_ROUTE',stage,bank*V+p,p,'ENTRY',stage_index[stage]]);versions[bank*V+p]+=1
+   begin=eventno;st=list(base['final']if rev else base['start'])+[None,None];lp=Counter();shadowlive=False;localepisode=None
+   for localno,e in enumerate(programs[rev]):
+    typ,d=e[:2];gd=owner(d)
+    if typ=='Q':
+     s,t,k=e[2:];need(st[d]==s and 0<k<8 and abs(frames[str(s)]['dim']-frames[str(t)]['dim'])==k,'Actualproperlocalcurrentframe');need(not any(v[0]==gd for v in tickets.values()),'NoimmutableSOURCEquery')
+     source(gd,k,{'kind':'LOCAL_nested_projector','stage':stage,'from':s,'to':t,'rank':k,'native_local_head':8,'future_common_head':'embedE0andtensorthecolumnI_f'},{'local_record':localno,'inverse':rev,'fresh_function':True})
+     if d==464 and {s,t}=={0,507}:changed_requests.append({'event':eventno,'stage':stage,'owner':gd,'version':versions[gd],'rank':k,'frame_from':s,'frame_to':t,'current_RAW_hex':hex(values[gd])})
+     st[d]=t;versions[gd]+=1;paid[k]+=1;lp[k]+=1;emit(['LOCAL_QUERY',stage,gd,s,t,k,rev])
+    elif typ=='ADD':
+     s,f=e[2:];need(st[d]==st[s]==f,'Actual commonFRAME LOCALADD');add(gd,owner(s),'LOCAL_ADD',[stage,f,rev])
+    elif typ=='COPY':
+     s,f,k=e[2:];gs=owner(s);need(d==658 and gd not in tickets and st[d]is None and values[gd]==0 and st[s]==f,'FreshownedwholeSOURCEcapture');values[gd]=values[gs];norm[gd]=norm[gs];epoch[gd]+=1;versions[gd]+=1
+     source(gd,k,{'kind':'LOCAL_capture_projector','stage':stage,'from':f,'to':0,'rank':k},{'local_record':localno,'copy_from':gs,'copy_source_version':versions[gs],'copy_assignment_before_query':True,'inverse':rev})
+     tickets[gd]=(gs,versions[gs],f,values[gs],eventno);st[d]=0;paid[k]+=1;lp[k]+=1;versions[gd]+=1;emit(['LOCAL_COPY_QUERY',stage,gs,gd,f,0,k,rev])
+    elif typ=='TICKET_CLEAR':
+     s,f=e[2:];gs=owner(s);need(gd in tickets and tickets[gd][:4]==(gs,versions[gs],f,values[gs])and values[gd]==values[gs]and st[s]==f,'ActualCOPYlease/version/completeRAW');episodes.append({'stage':stage,'kind':'immutable_LOCAL_COPY','owner':gd,'source':gs,'source_version':versions[gs],'begin':tickets[gd][4],'end':eventno});tickets.pop(gd);values[gd]=norm[gd]=0;st[d]=None;versions[gd]+=1;emit(['LOCAL_PAID_CLEAR',stage,gd,rev])
+    elif typ=='INIT':
+     f=e[2];need(d==659 and values[gd]==0 and st[d]is None and not shadowlive,'Newcompleteownedshadowinitializedzero');st[d]=f;shadowlive=True;shadowbegin=eventno;epoch[gd]+=1;emit(['SHADOW_PAID_INIT',stage,gd,f,rev])
+    else:
+     need(typ=='CLEAR'and d==659 and shadowlive and gd not in tickets,'PaidownedshadowwholepayloadCLEAR');episodes.append({'stage':stage,'kind':'new_sameFRAME_shadow','owner':gd,'frame':st[d],'begin':shadowbegin,'end':eventno});values[gd]=norm[gd]=0;st[d]=None;versions[gd]+=1;shadowlive=False;emit(['SHADOW_PAID_CLEAR',stage,gd,rev])
+    privatepeak=max(privatepeak,len(tickets)+int(shadowlive))
+   need(st==list(base['start']if rev else base['final'])+[None,None]and not tickets and not shadowlive and values[N:]==[0,0],'CompleteLOCALreturn')
+   need(lp==Counter(EXPECTED)and all(values[x*V+i]==sx[i]and values[y*V+i]==sy[i]^sx[i]for i in range(V))and all(values[h]==1<<h for h in helpers),'Allarbitrarycalleeinputsandunchangedhelperjobs')
+   if stage:
+    for bank in(x,y):
+     for p in range(V):emit(['PAID_PORT_ROUTE',stage,bank*V+p,p,'RETURN',stage_index[stage]]);versions[bank*V+p]+=1
+   calls.append({'stage':stage,'pair':pair,'inverse':rev,'helper_owner_begin':baseh,'source_bank':x,'target_bank':y,'core_begin':begin,'core_end':eventno,'profile':dict(lp),'owned_global_indices':[N,N+1],'original_helper_jobs':{'4':4,'8':432}})
+  elif op=='QUERY_SHEAR':
+   _,stage,pair,rev=event;x,y=2*pair,2*pair+1
+   if rev:x,y=y,x
+   for p in range(V):
+    sourcefield,dst=x*V+p,y*V+p;need(values[N:]==[0,0]and not tickets,'Noaliaswithparentownedshadow');v=versions[sourcefield];values[N]=values[sourcefield];norm[N]=norm[sourcefield];versions[N]+=1;epoch[N]+=1;begin=eventno;emit(['THIN_COPY',stage,sourcefield,N,p,v])
+    source(N,1,{'kind':'THIN_central_portline','port':p,'rank':1},{'copy_from':sourcefield,'source_version':v,'inverse':rev});paid[1]+=1;versions[N]+=1;emit(['THIN_PAID_QUERY',stage,N,p,1,rev]);add(dst,N,'THIN_ADD',[stage,p,rev]);need(versions[sourcefield]==v,'ThinSOURCEunchanged');values[N]=norm[N]=0;versions[N]+=1;emit(['THIN_PAID_CLEAR',stage,N]);episodes.append({'stage':stage,'kind':'old_THIN','owner':N,'source':sourcefield,'source_version':v,'begin':begin,'end':eventno})
+  elif op=='IDLE':
+   _,pair,stages=event;k=7*len(stages)
+   for bank in(2*pair,2*pair+1):
+    for p in range(V):
+     field=bank*V+p;source(field,k,{'kind':'WHOLE_IDLE_disjoint_stages','port':p,'stages':stages,'rank':k});paid[k]+=1;versions[field]+=1;emit(['PAID_WHOLE_IDLE',field,stages,k,p])
+  elif op=='ADD':
+   for p in range(V):add(event[1]*V+p,event[2]*V+p,meta='BRIDGE')
+  else:
+   need(op=='SWAP','Controlleropcode')
+   for p in range(V):swap(event[1]*V+p,event[2]*V+p,'FINAL_SWAP')
+ boundary(controller['boundaries']['left_program'],'LEFT_BOUNDARY');out.close();raw_file.close();srcout.close();src_file.close();need(values==[1<<i for i in range(N)]+[0,0],'All11400originalRAWandwholeownedreturn')
+ targets=Counter({8:432*18,4:4*18})
+ for term in controller['diagonal']:need(term&1,'RetainedcentralSOURCEfactor');targets[1+7*(int(term)>>1).bit_count()]+=V
+ need(streamhash.hexdigest()==expected['expanded_event_sha256']and eventno==expected['expanded_event_count'],'ExactG23literalstreamnotanewunboundvariant')
+ need(paid==Counter({int(k):v for k,v in expected['paid'].items()})and targets==Counter({int(k):v for k,v in expected['targets'].items()})and len(changed_requests)==18,'ExactG23invoiceandfreshrank4requests')
+ need(peak.bit_length()==expected['cancellation_free_majorant_bits']and str(peak)==expected['cancellation_free_majorant'],'Actual newmajorantfullyregenerated')
+ need(len(calls)==18 and len(episodes)==1845 and privatepeak==2,'Allownedepisodesandmaximumcoexistence')
+ result={'status':'MATERIALIZED_EXACT_G23_ALL11400_RAW','at_utc':datetime.now(timezone.utc).isoformat(),'originals':N,'private_allocated':2,'private_peak':privatepeak,'private_episodes':len(episodes),'calls':18,'expanded_event_count':eventno,'expanded_event_sha256':streamhash.hexdigest(),'global_gzip_sha256':sha256((DATA/'GLOBAL.jsonl.gz').read_bytes()).hexdigest(),'SOURCE_descriptor_count':source_count,'SOURCE_descriptors_sha256':sourcehash.hexdigest(),'paid':dict(sorted(paid.items())),'targets':dict(sorted(targets.items())),'rank_surplus':sum(k*v for k,v in targets.items())-sum(k*v for k,v in paid.items()),'operation_counts':dict(counts),'majorant_bits':peak.bit_length(),'majorant':str(peak),'newbound':None,'CPU_seconds':process_time()-clock}
+ put(DATA/'GLOBAL-RESULT.json',result);put(DATA/'CALLS.json',calls);put(DATA/'PRIVATE-EPISODES.json',episodes);put(DATA/'NEW-RANK4-REQUESTS.json',changed_requests);put(DATA/'MAIN-PHYSICAL-COEFFICIENTS.json',mainrows);put(DATA/'INVOICE.json',{'paid':result['paid'],'targets':result['targets'],'originals':N,'private_output_credit':0,'QUERYs':sum(paid.values()),'rawrank_surplus':result['rank_surplus'],'rawprice_reference':'inputs/G23-RAW-PRICE.json only, notordinarysaving','ordinary_tail_bootstrap_status':'Pendingseparatecertificatewithfreshfees/constants; old4760/4814unchanged'})
+ print(json.dumps({k:result[k]for k in('status','expanded_event_count','expanded_event_sha256','SOURCE_descriptor_count','private_episodes','majorant_bits','CPU_seconds')}))
+if __name__=='__main__':main()
diff --git a/research/g20-refinement-admission/source/vendor/g20/provider/data/CALLS.json b/research/g20-refinement-admission/source/vendor/g20/provider/data/CALLS.json
new file mode 100644
index 0000000000..d61a37a481
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/provider/data/CALLS.json
@@ -0,0 +1,488 @@
+[
+  {
+    "stage": 0,
+    "pair": 0,
+    "inverse": false,
+    "helper_owner_begin": 3552,
+    "source_bank": 0,
+    "target_bank": 1,
+    "core_begin": 6549,
+    "core_end": 28539,
+    "profile": {
+      "1": 1318,
+      "3": 77,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 1,
+    "pair": 0,
+    "inverse": true,
+    "helper_owner_begin": 3988,
+    "source_bank": 1,
+    "target_bank": 0,
+    "core_begin": 28761,
+    "core_end": 50973,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 3,
+    "pair": 1,
+    "inverse": true,
+    "helper_owner_begin": 4424,
+    "source_bank": 3,
+    "target_bank": 2,
+    "core_begin": 52305,
+    "core_end": 74517,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 5,
+    "pair": 2,
+    "inverse": true,
+    "helper_owner_begin": 4860,
+    "source_bank": 5,
+    "target_bank": 4,
+    "core_begin": 75849,
+    "core_end": 98061,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 7,
+    "pair": 3,
+    "inverse": true,
+    "helper_owner_begin": 5296,
+    "source_bank": 7,
+    "target_bank": 6,
+    "core_begin": 99393,
+    "core_end": 121605,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 9,
+    "pair": 4,
+    "inverse": true,
+    "helper_owner_begin": 5732,
+    "source_bank": 9,
+    "target_bank": 8,
+    "core_begin": 122937,
+    "core_end": 145149,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 11,
+    "pair": 5,
+    "inverse": true,
+    "helper_owner_begin": 6168,
+    "source_bank": 11,
+    "target_bank": 10,
+    "core_begin": 146481,
+    "core_end": 168693,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 13,
+    "pair": 6,
+    "inverse": true,
+    "helper_owner_begin": 6604,
+    "source_bank": 13,
+    "target_bank": 12,
+    "core_begin": 170025,
+    "core_end": 192237,
+    "profile": {
+      "1": 1318,
+      "2": 1342,
+      "4": 40,
+      "5": 102,
+      "7": 18,
+      "6": 10,
+      "3": 77
+    },
+    "owned_global_indices": [
+      11400,
+      11401
+    ],
+    "original_helper_jobs": {
+      "4": 4,
+      "8": 432
+    }
+  },
+  {
+    "stage": 15,
+    "pair": 7,
+    "inverse": true,
+    "helper_owner_begin": 7040,
+    "source_bank": 15,
+    "target_bank": 14,
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diff --git a/research/g20-refinement-admission/source/vendor/g20/provider/data/INVOICE.json b/research/g20-refinement-admission/source/vendor/g20/provider/data/INVOICE.json
new file mode 100644
index 0000000000..c56f56da5c
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/provider/data/INVOICE.json
@@ -0,0 +1,38 @@
+{
+  "paid": {
+    "1": 25389,
+    "2": 24156,
+    "3": 1386,
+    "4": 720,
+    "5": 1836,
+    "6": 180,
+    "7": 324,
+    "14": 444,
+    "21": 444,
+    "28": 444,
+    "35": 444,
+    "42": 444,
+    "49": 444,
+    "56": 444,
+    "63": 222
+  },
+  "targets": {
+    "4": 72,
+    "8": 7776,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
+    "43": 444,
+    "50": 444,
+    "57": 444,
+    "64": 222,
+    "127": 222
+  },
+  "originals": 11400,
+  "private_output_credit": 0,
+  "QUERYs": 57321,
+  "rawrank_surplus": 753,
+  "rawprice_reference": "inputs/G23-RAW-PRICE.json only, notordinarysaving",
+  "ordinary_tail_bootstrap_status": "Pendingseparatecertificatewithfreshfees/constants; old4760/4814unchanged"
+}
diff --git a/research/g20-refinement-admission/source/vendor/g20/provider/data/TARGET-OWNERS.json b/research/g20-refinement-admission/source/vendor/g20/provider/data/TARGET-OWNERS.json
new file mode 100644
index 0000000000..8e0887a2ee
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/provider/data/TARGET-OWNERS.json
@@ -0,0 +1,83354 @@
+[
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+    "route_pair_required_in_generic_job_matching": true
+  },
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+    "operator": "D_(P_line+selectedorthogonalstageblocks)",
+    "route_pair_required_in_generic_job_matching": true
+  },
+  {
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+    "operator": "D_(P_line+selectedorthogonalstageblocks)",
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+    "operator": "D_(P_line+selectedorthogonalstageblocks)",
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+    "route_pair_required_in_generic_job_matching": true
+  },
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+  },
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11302,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11303,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11304,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11305,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11306,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11308,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11309,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11310,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11311,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11312,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11313,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11314,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11315,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11316,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11317,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11318,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11319,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11320,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11321,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11322,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11323,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11324,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11325,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11326,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11328,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11329,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11363,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11365,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11366,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11367,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11371,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
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+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11374,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11375,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11376,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11377,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11378,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11379,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11380,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11381,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11382,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11383,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11384,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11385,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11386,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11387,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11388,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11389,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11390,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11391,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11392,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11393,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11394,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11395,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11396,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11397,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11398,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  },
+  {
+    "original_owner": 11399,
+    "rank": 8,
+    "matcher": "IDENTITY_FULL8",
+    "native_frame": 1,
+    "route_pair_required_in_generic_job_matching": false
+  }
+]
diff --git a/research/g20-refinement-admission/source/vendor/g20/provider/local_ir.py b/research/g20-refinement-admission/source/vendor/g20/provider/local_ir.py
new file mode 100644
index 0000000000..2edfa7018d
--- /dev/null
+++ b/research/g20-refinement-admission/source/vendor/g20/provider/local_ir.py
@@ -0,0 +1,130 @@
+"""Local physical ARRAY IR and exact types; portable standard library only."""
+from collections import Counter
+from fractions import Fraction as F
+from functools import lru_cache
+from math import gcd
+
+N=658;OWNED=(658,659);EXPECTED={1:1318,2:1342,3:77,4:40,5:102,6:10,7:18}
+def need(c,m):
+ if not c:raise ValueError(m)
+def transpose_rows(a,n=N):return [sum(((r>>j)&1)<<i for i,r in enumerate(a))for j in range(n)]
+def combo(a,mask):
+ x=0
+ while mask:b=mask&-mask;x^=a[b.bit_length()-1];mask^=b
+ return x
+def rowproduct(a,b):return [combo(b,r)for r in a]
+def baseline_program(word,reverse=False):
+ out=[]
+ for op,d,s,c,f,z in reversed(word['records'])if reverse else word['records']:
+  if op==0:out.append(['Q',d,c if reverse else s,s if reverse else c,f])
+  elif op==1:out.append(['ADD',d,s,f])
+  elif op==(3 if reverse else 2):out.append(['COPY',s,d,c,7])
+  else:out.append(['TICKET_CLEAR',s,d,c])
+ return out
+def ad_inverse(program,birth,exit):
+ source=[]
+ for e in program:
+  op=e[0]
+  if op=='ADD':source.append(['ADD',e[1],e[2]])
+  elif op=='Q':source.append(e)
+  elif op=='COPY':source.extend([['COPY',e[1],e[2]],['Q',e[1],e[3],0,e[4]]])
+  else:need(op in('INIT','CLEAR','TICKET_CLEAR'),'Known local inverse operation');source.append(['CLEAR',e[1]])
+ raw=[]
+ for e in reversed(source):
+  if e[0]=='ADD':raw.append(['ADD',e[2],e[1]])
+  elif e[0]=='Q':raw.append(['Q',e[1],e[3],e[2],e[4]])
+  elif e[0]=='COPY':raw.extend([['ADD',e[2],e[1]],['CLEAR',e[1]]])
+  else:raw.append(e)
+ raw.extend(['CLEAR',d]for d in OWNED)
+ st=birth[:]+[None,None];zero=[False]*N+[True,True];out=[];retags=[]
+ def header(d,f,k):
+  need(d in OWNED and zero[d],'Only known entire-functionzero can be reheadered')
+  if st[d]!=f:out.append(['INIT',d,f]);retags.append({'raw_instruction':k,'owner':d,'from':st[d],'to':f});st[d]=f
+ for k,e in enumerate(raw):
+  op,d=e[:2]
+  if op=='CLEAR':need(d in OWNED,'No original CLEAR');out.append(e);zero[d]=True;st[d]=None
+  elif op=='Q':
+   if d in OWNED and zero[d]:header(d,e[2],k)
+   need(st[d]==e[2],'AD actual QUERY inputframe');out.append(e);st[d]=e[3]
+  else:
+   s=e[2]
+   if d in OWNED and zero[d]and st[s]is not None:header(d,st[s],k)
+   if s in OWNED and zero[s]and st[d]is not None:header(s,st[d],k)
+   if st[d]is None and st[s]is None:header(d,0,k);header(s,0,k)
+   need(st[d]==st[s]and st[d]is not None,'AD commonactualFRAME');out.append(['ADD',d,s,st[d]]);zero[d]=zero[d]and zero[s]
+ need(st==exit+[None,None]and all(zero[d]for d in OWNED),'AD originalflags/ownedreturn')
+ return out,retags
+
+class Geometry:
+ def __init__(self,frames):self.frames=frames;self.dims={int(k):v['dim']for k,v in frames.items()}
+ @lru_cache(None)
+ def nested(self,s,t,k):
+  lo,hi=(s,t)if self.dims[s]<self.dims[t]else(t,s)
+  need(0<k<8 and self.dims[hi]-self.dims[lo]==k,'Proper actual residual rank, not FRAME id')
+  need(all(sum(F(v)*F(w)for v,w in zip(a,b))==0 for a in self.frames[str(lo)]['B']for b in self.frames[str(hi)]['A']),'ExactQQ nested residual')
+  return lo,hi
+ @lru_cache(None)
+ def project_mod(self,f,m):
+  b=[[F(v).numerator*pow(F(v).denominator,-1,m)%m for v in row]for row in self.frames[str(f)]['B']]
+  if not b:return tuple(tuple(0 for _ in range(8))for _ in range(8))
+  def mm(a,b):return [[sum(x*y for x,y in zip(r,c))%m for c in zip(*b)]for r in a]
+  size=len(b);bt=list(map(list,zip(*b)));gram=mm(b,bt);a=[r[:]+[int(i==j)for j in range(size)]for i,r in enumerate(gram)]
+  for j in range(size):
+   p=next(i for i in range(j,size)if gcd(a[i][j],m)==1);a[j],a[p]=a[p],a[j];v=pow(a[j][j],-1,m);a[j]=[x*v%m for x in a[j]]
+   for i in range(size):
+    if i!=j:
+     v=a[i][j];a[i]=[(x-v*y)%m for x,y in zip(a[i],a[j])]
+  return tuple(map(tuple,mm(mm(bt,[r[size:]for r in a]),b)))
+ @lru_cache(None)
+ def residual_mod(self,s,t,k,m):
+  lo,hi=self.nested(s,t,k);return tuple(tuple((x-y)%m for x,y in zip(a,b))for a,b in zip(self.project_mod(hi,m),self.project_mod(lo,m)))
+ @staticmethod
+ @lru_cache(None)
+ def move(p,x,m):
+  diff=[(x[i]-x[15-i])%m for i in range(8)];z=[sum(v*w for v,w in zip(r,diff))%m for r in p];out=list(x)
+  for i in range(8):out[i]=(out[i]-z[i])%m;out[15-i]=(out[15-i]+z[i])%m
+  return tuple(out)
+
+def replay(program,birth,exit,geometry,modulus=None,mutant=None):
+ st=birth[:]+[None,None];rows=[1<<i for i in range(N)]+[0,0];norm=[1]*N+[0,0];versions=[0]*660;knownzero=[False]*N+[True,True];tickets={};counts=Counter();paid=Counter();peak=1;privatepeak=0;epochs=[0]*660;retag_count=0;changed=False
+ fields=None
+ if modulus:
+  point=tuple(v%modulus for v in(1,2,4,8,16,32,64,128,3,5,7,11,13,17,19,23));fields=[{point:1<<i}for i in range(N)]+[{},{}]
+ def transform(field,p):return {geometry.move(p,x,modulus):v for x,v in field.items()}
+ for ix,orig in enumerate(program):
+  e=orig[:];op,d=e[:2]
+  if mutant=='wrong_rank4'and op=='Q'and d==464 and set(e[2:4])=={0,507}and not changed:e[4]=3;changed=True
+  if mutant=='omit_shadow_clear'and op=='CLEAR'and d==659 and not changed:changed=True;continue
+  if mutant=='wrong_shadow_frame'and op=='INIT'and d==659 and not changed:e[2]=0;changed=True
+  counts[op]+=1
+  if op=='Q':
+   s,t,k=e[2:];need(st[d]==s,'Actual currentSOURCE frame');geometry.nested(s,t,k);need(not any(v[0]==d for v in tickets.values()),'SOURCE notmoved during immutableCOPYlease');st[d]=t;versions[d]+=1;paid[k]+=1
+   if fields is not None:fields[d]=transform(fields[d],geometry.residual_mod(s,t,k,modulus))
+  elif op=='ADD':
+   s,f=e[2:];need(d!=s and st[d]==st[s]==f,'Actualaligned commonFRAME ADD');need(not any(v[0]==d for v in tickets.values()),'ImmutableSOURCE notVALUEwritten');rows[d]^=rows[s];norm[d]+=norm[s];peak=max(peak,norm[d]);knownzero[d]=knownzero[d]and knownzero[s];versions[d]+=1
+   if fields is not None:
+    for x,v in fields[s].items():
+     z=fields[d].get(x,0)^v
+     if z:fields[d][x]=z
+     else:fields[d].pop(x,None)
+  elif op=='COPY':
+   s,f,k=e[2:];need(d in OWNED and knownzero[d]and not rows[d]and st[d]is None and d not in tickets,'WholeownedfreshzeroCOPY');need(st[s]==f and k==geometry.dims[f]==7,'Actualrank7capture SOURCE');rows[d]=rows[s];norm[d]=norm[s];st[d]=0;knownzero[d]=False;tickets[d]=(s,versions[s],f,rows[s]);paid[k]+=1;versions[d]+=1;epochs[d]+=1
+   if fields is not None:fields[d]=transform(fields[s],geometry.project_mod(f,modulus))
+  elif op=='TICKET_CLEAR':
+   s,f=e[2:];need(tickets[d]==(s,versions[s],f,rows[s])and st[s]==f and rows[d]==rows[s]and st[d]==0,'FreshcurrentimmutableSOURCE guard');tickets.pop(d);rows[d]=norm[d]=0;knownzero[d]=True;st[d]=None;versions[d]+=1
+   if fields is not None:need(fields[d]==transform(fields[s],geometry.project_mod(f,modulus)),'Wholefunction COPYguard');fields[d]={}
+  elif op=='INIT':
+   f=e[2];need(d in OWNED and knownzero[d]and rows[d]==0 and d not in tickets,'Only wholeknownzero ownedreheader');st[d]=f;epochs[d]+=1;retag_count+=1
+  else:
+   need(op=='CLEAR'and d in OWNED and d not in tickets,'Paid fullownedpayloadCLEAR, notoriginal/inverseSOURCE');rows[d]=norm[d]=0;knownzero[d]=True;st[d]=None;versions[d]+=1
+   if fields is not None:fields[d]={}
+  privatepeak=max(privatepeak,sum(st[p]is not None for p in OWNED))
+ need(st==exit+[None,None]and not tickets and rows[N:]==[0,0]and all(knownzero[p]for p in OWNED),'All658originalFLAGs and ownedwholepayloadreturn')
+ if fields is not None:
+  for out in range(N):
+   expected={};mask=rows[out]
+   while mask:
+    b=mask&-mask;raw=b.bit_length()-1;y=geometry.move(geometry.project_mod(exit[out],modulus),geometry.move(geometry.project_mod(birth[raw],modulus),point,modulus),modulus);expected[y]=expected.get(y,0)^b;mask^=b
+   need(fields[out]=={x:v for x,v in expected.items()if v},'ALL658symbol fullphysicalFUNCTION endpoint factor')
+  need(all(not fields[p]for p in OWNED),'EveryownednativeFUNCTIONzero')
+ return rows[:N],{'paid':dict(sorted(paid.items())),'rankmass':sum(k*v for k,v in paid.items()),'operation_counts':dict(counts),'private_allocated':2,'private_peak':privatepeak,'owned_header_acquisitions':retag_count,'majorant_bits':peak.bit_length(),'majorant':str(peak),'epochs':{str(p):epochs[p]for p in OWNED},'native_all658_symbols':modulus},fields
diff --git a/research/g20-refinement-admission/strict_margins.py b/research/g20-refinement-admission/strict_margins.py
new file mode 100644
index 0000000000..d62d56f888
--- /dev/null
+++ b/research/g20-refinement-admission/strict_margins.py
@@ -0,0 +1,51 @@
+"""Choose finite strict compiler margins for the retained G20 framework.
+
+The caller supplies a certified positive first-moment reserve. The tail bounds
+are checked separately on the complete profile. Ali Romman with substantial
+OpenAI Codex assistance. Apache-2.0.
+"""
+from fractions import Fraction as F
+
+
+def need(ok,message):
+    if not ok:raise ValueError(message)
+
+
+def tensor_degree(reserve):
+    need(F(0)<reserve<1,'positive certified reserve')
+    need(F(31,32)**128<F(1,16) and F(19,20)**128<F(1,16),'retained tail blocks')
+    v=1024
+    while 1-F(1)/(1+v*reserve)-F(4,2**(v//32))<=0:
+        v*=2
+    return v
+
+
+def compiler_cutoffs(tested,uniform,v):
+    need(0<uniform<tested<F(1,100) and v>=1024 and v%1024==0,'strict compiler inputs')
+    t,z=1-tested,1-uniform;z0=(t+z)/2;gap=z0-t;h=F(1,64)
+    rhs=gap*(5+8*h)*v+1+8*v*(1-z0)
+    h0=(rhs/(h*gap)).__floor__()+1
+    h1=(h0*(1-z0)/(z-z0)).__floor__()+1
+    need(h0>=8*v and h0*h*gap>rhs and h1*(z-z0)>h0*(1-z0),'strict finite cutoffs')
+    return h0,h1
+
+
+def below_grid(value,denominator):
+    need(isinstance(denominator,int) and denominator>0,'positive grid denominator')
+    out=F(-((-value.numerator*denominator)//value.denominator)-1,denominator)
+    need(0<value-out<=F(1,denominator),'strict lower grid')
+    return out
+
+
+def controls():
+    degrees={}
+    for k in (8,39,48,96,192,384):
+        reserve=F(1,2**k);v=tensor_degree(reserve)
+        need(v%1024==0 and 1-F(1)/(1+v*reserve)>F(4,2**(v//32)),'positive exact contraction')
+        degrees[str(k)]=v
+    for value in (F(7,1000),F(701,100000),F(699,100000)):
+        need(below_grid(value,1000)<value,'strict grid includes exact-grid inputs')
+    try:tensor_degree(F(0))
+    except ValueError:pass
+    else:raise ValueError('zero reserve accepted')
+    return degrees
diff --git a/research/g20-refinement-admission/verify.py b/research/g20-refinement-admission/verify.py
new file mode 100644
index 0000000000..2a848fc156
--- /dev/null
+++ b/research/g20-refinement-admission/verify.py
@@ -0,0 +1,50 @@
+"""Rebuild the complete G20 admission from authenticated inputs in a fresh copy."""
+from hashlib import sha256
+from pathlib import Path
+import gzip,json,shutil,subprocess,sys,tempfile
+R=Path(__file__).resolve().parent
+OUTPUTS=['WORD.json.gz','MATCHER.json','LOCAL-RESULT.json','GLOBAL.jsonl.gz','GLOBAL-RESULT.json',
+         'INVOICE.json','CALLS.json','PRIVATE-EPISODES.json','TARGET-OWNERS.json','SOURCE-DESCRIPTORS.json.gz',
+         'ORDINARY-RESULT.json','INDEPENDENT-RESULT.json']
+
+
+def need(ok,message):
+    if not ok:raise ValueError(message)
+
+
+def snapshot(root):
+    return {str(f.relative_to(root)):sha256(f.read_bytes()).hexdigest() for f in root.rglob('*')
+            if f.is_file() and '__pycache__' not in f.parts and f.suffix!='.pyc'}
+
+
+def payload(path):
+    raw=path.read_bytes()
+    if path.suffix=='.gz':raw=gzip.decompress(raw)
+    if path.name=='GLOBAL.jsonl.gz':return raw
+    x=json.loads(raw)
+    if path.name=='GLOBAL-RESULT.json':x.pop('CPU_seconds')
+    return x
+
+
+def main():
+    before=snapshot(R)
+    inputs=json.loads((R/'INPUTS.json').read_text())
+    for item in inputs:need(before[item['local']]==item['sha256'],'Frozen input '+item['local'])
+    need((R/'WORD.json.gz').read_bytes()==(R/'audited/WORD.json.gz').read_bytes(),'Exact audited word bytes')
+    with tempfile.TemporaryDirectory(prefix='g20-refinement-admission-') as name:
+        root=Path(name)/'package';shutil.copytree(R,root,ignore=shutil.ignore_patterns('__pycache__','*.pyc'))
+        for name in OUTPUTS:(root/name).unlink()
+        for name in ['integration.py','global_retirement.py','ordinary.py','independent.py']:
+            args=[sys.executable,'-I','-B','-W','error','-X','pycache_prefix='+str(Path(name).name+'.fresh-cache')]
+            if sys.flags.optimize:args.append('-O')
+            completed=subprocess.run(args+[str(root/name)],cwd=root,text=True,capture_output=True,timeout=130)
+            need(completed.returncode==0,name+' failed:\n'+completed.stdout[-2000:]+completed.stderr[-3000:])
+            print('PASS_REBUILT',name,flush=True)
+        for name in OUTPUTS:need(payload(root/name)==payload(R/name),'Exact rebuilt output '+name)
+        need((root/'WORD.json.gz').read_bytes()==(root/'audited/WORD.json.gz').read_bytes(),'Exact rebuilt word bytes')
+        for item in inputs:need(sha256((root/item['local']).read_bytes()).hexdigest()==item['sha256'],'Frozen input changed')
+    need(snapshot(R)==before,'Replay changed source or result files')
+    print('PASS_G20_REFINEMENT_COMPLETE_ORDINARY_003497804579519',flush=True)
+
+
+if __name__=='__main__':main()