From c79df8e3c61676445f8e1782814450199d8221e6 Mon Sep 17 00:00:00 2001
From: rohanarun <rohanarun@gmail.com>
Date: Tue, 13 Oct 2026 15:27:41 -0400
Subject: [PATCH 1/4] Draft conditional T37 composition of PR1148 local
 interfaces

---
 .../CANDIDATE.json                            |     11 +
 .../GEOMETRY-CHECK.json                       |     10 +
 .../MANIFEST.json                             |     13 +
 .../OWNERS.json.gz                            |    Bin 0 -> 1864063 bytes
 .../PATTERN-FLOW.json                         |      1 +
 .../three-demotions-t37-composition/PLAN.json | 230829 +++++++++++++++
 .../PRICE.json                                |    123 +
 .../PROFILE.json                              |      9 +
 .../three-demotions-t37-composition/README.md |     17 +
 .../SEARCH.json                               |     53 +
 .../UPSTREAM-NOTICE.md                        |     45 +
 .../construct.py                              |    108 +
 12 files changed, 231219 insertions(+)
 create mode 100644 research/three-demotions-t37-composition/CANDIDATE.json
 create mode 100644 research/three-demotions-t37-composition/GEOMETRY-CHECK.json
 create mode 100644 research/three-demotions-t37-composition/MANIFEST.json
 create mode 100644 research/three-demotions-t37-composition/OWNERS.json.gz
 create mode 100644 research/three-demotions-t37-composition/PATTERN-FLOW.json
 create mode 100644 research/three-demotions-t37-composition/PLAN.json
 create mode 100644 research/three-demotions-t37-composition/PRICE.json
 create mode 100644 research/three-demotions-t37-composition/PROFILE.json
 create mode 100644 research/three-demotions-t37-composition/README.md
 create mode 100644 research/three-demotions-t37-composition/SEARCH.json
 create mode 100644 research/three-demotions-t37-composition/UPSTREAM-NOTICE.md
 create mode 100644 research/three-demotions-t37-composition/construct.py

diff --git a/research/three-demotions-t37-composition/CANDIDATE.json b/research/three-demotions-t37-composition/CANDIDATE.json
new file mode 100644
index 0000000000..62bf49bbce
--- /dev/null
+++ b/research/three-demotions-t37-composition/CANDIDATE.json
@@ -0,0 +1,11 @@
+{
+  "status": "DRAFT_EXACT_PRICE_AND_LITERAL_OWNERS_FULL_ADMISSION_PENDING",
+  "kappa": "1675129371412064/1000000000000000000",
+  "kappa_decimal": "0.001675129371412064",
+  "previous_kappa": "0.001675121647789207",
+  "gain_percent": "0.00046107832629310757",
+  "pr1148_head": "98235a9cf4ce355ec5cf3fac2eca7b3b98a20838",
+  "pr1129_head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21",
+  "pr1131_head": "fcdc42737b703323d8ed550a528141a482e68e96",
+  "scope": "Conditional finite candidate. Full T37 provider/controller/invoice admission pending. Native provider separately reproduced from exact PR1148 head. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions retained. No unconditional theorem, full Lean certification, or general packing optimality claim."
+}
diff --git a/research/three-demotions-t37-composition/GEOMETRY-CHECK.json b/research/three-demotions-t37-composition/GEOMETRY-CHECK.json
new file mode 100644
index 0000000000..2b1bd1cbcf
--- /dev/null
+++ b/research/three-demotions-t37-composition/GEOMETRY-CHECK.json
@@ -0,0 +1,10 @@
+{
+  "roles": 159840,
+  "idle": {
+    "0": 62384,
+    "1": 834,
+    "48": 11374
+  },
+  "owner_content_sha256": "6aac44c27ee80dbcbfcc48ab358c8e79887ea34c5064bc0ba5955dd19df12a6f",
+  "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY"
+}
diff --git a/research/three-demotions-t37-composition/MANIFEST.json b/research/three-demotions-t37-composition/MANIFEST.json
new file mode 100644
index 0000000000..f1ea5b41ca
--- /dev/null
+++ b/research/three-demotions-t37-composition/MANIFEST.json
@@ -0,0 +1,13 @@
+{
+  "CANDIDATE.json": "43cc85370e98160f870484754240cd08a70cbdbc5ee3f75f705b7725693ff6c0",
+  "GEOMETRY-CHECK.json": "497c71976c01378b84552a245c1359fc53a6b6474b0c46c00546a419710ca826",
+  "OWNERS.json.gz": "449d230ae8ea9b5adf2f4a06da0dd89473e6e259b986e46ebf7407e169ac1d4b",
+  "PATTERN-FLOW.json": "d7accd36895a218d0db8e1434ea013c18d924059e4b32f25a21e3529539d7352",
+  "PLAN.json": "2c5e493cfdc4c424ebf20c91be089408dc04f183c979a9b76efb867b6f357424",
+  "PRICE.json": "dae64ef8026dd50ffce655f3094ca263e680a25db29669ab70a40fabf5db11d2",
+  "PROFILE.json": "440912ba08baa19af76194a7bcd8640b73926f5182c97bc6b73c3587b0256858",
+  "README.md": "b895d31ff6ebfec43b94a37981c9249f922999cbfc1ca1a50b05756e34ec2d3d",
+  "SEARCH.json": "c42084bbadd361f90dc21ffbd300c03b3739a57e9bf978e4272e0c822bca27bd",
+  "UPSTREAM-NOTICE.md": "b97fb4731e84aef736c58a9c126334eb5b8d3a057a8d9d45b4ffff24af65c38b",
+  "construct.py": "eee2edff41871b929e4c85289a2bd80842f5a5ae6130b8c7b0574178d4de9562"
+}
diff --git a/research/three-demotions-t37-composition/OWNERS.json.gz b/research/three-demotions-t37-composition/OWNERS.json.gz
new file mode 100644
index 0000000000000000000000000000000000000000..a49281b64f6f963bc217db8b2af04a1d40f6dad2
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diff --git a/research/three-demotions-t37-composition/PATTERN-FLOW.json b/research/three-demotions-t37-composition/PATTERN-FLOW.json
new file mode 100644
index 0000000000..63e8408b05
--- /dev/null
+++ b/research/three-demotions-t37-composition/PATTERN-FLOW.json
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diff --git a/research/three-demotions-t37-composition/PLAN.json b/research/three-demotions-t37-composition/PLAN.json
new file mode 100644
index 0000000000..518ea50eae
--- /dev/null
+++ b/research/three-demotions-t37-composition/PLAN.json
@@ -0,0 +1,230829 @@
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+        4,
+        8,
+        4,
+        4,
+        4,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5,
+        8,
+        8,
+        8,
+        5,
+        8,
+        5,
+        5,
+        5
+      ],
+      "actual_paid_profile": {
+        "1": 2372,
+        "2": 494,
+        "3": 412,
+        "4": 130,
+        "5": 82,
+        "8": 8
+      },
+      "orientation_program_sha256": {
+        "forward": "551a1211d208774f826eea0e7f0bf1c71b2a6668fc6d5e663a154baed2b2c405",
+        "backward": "d8a1b20df928953caf4dbdc5d4ace9e94c8c26db07cc026805bb63300a4e6b22"
+      },
+      "artifact_semantic_sha256": {
+        "CANONICAL-WORD.json.gz": "01c5f60fb0cb2ae522ec926168281023f4315d2be76d75b0c5d5b341014a8c9e",
+        "LOCAL-PROGRAMS.json.gz": "0b74225d802107084e08cff09a658af6cb0399daab495db6e42b6d088730c0c4",
+        "LOCAL-CHECKS.json": "f5acbca2609d813e77c7de46deb406a0b381cf81d242d6536125a7106b90659d",
+        "INDEPENDENT-LOCAL-REPLAY.json": "ae1c832371024ab7c42ed2d02f0bea552df52f84f184959a47a236484b7c2dc2",
+        "CLIFFORD-RECIPES.json": "803271ac4098ce1bca6d3dcc20dd9e6eb650843ad2c07d98c93e1c78f0873463",
+        "CLIFFORD-REVIEW.json": "046e89ed60e9745cfc27c8d98e269d0bece9271b9f99f9aa00ee916c945ccff3",
+        "RESIDUAL-ADAPTERS.json": "f96536a306c4202865667b2a213b7dacb0292fe5354dc412c1d6022c8d68b4cd"
+      }
+    }
+  },
+  "source_plan_sha256": "c5da66a8061a86ca7d3eab975829488f6c086a59966150b193d614ff0d0c4847",
+  "assignment_sha256": "449d230ae8ea9b5adf2f4a06da0dd89473e6e259b986e46ebf7407e169ac1d4b",
+  "source_owners_sha256": "c41fdf51541ecc91af914f264967f3633570500994f8866daf642440a5d843dd",
+  "assignment_content_sha256": "6aac44c27ee80dbcbfcc48ab358c8e79887ea34c5064bc0ba5955dd19df12a6f",
+  "replica_lift": {
+    "groups": [
+      8,
+      8,
+      8,
+      8,
+      5
+    ],
+    "source_replicas": 8,
+    "replicas": 37,
+    "parent_template_content_sha256": "514e59314c8e2fa3c22d0a48083816f6686211090835e8f8775318c1c3e992d8",
+    "owners_file_sha256": "449d230ae8ea9b5adf2f4a06da0dd89473e6e259b986e46ebf7407e169ac1d4b",
+    "schedule_content_sha256": "fb86346be60ae00c88ff41f77906aae3c9d8fc488d63cd4abbfa03c4785c2d2d",
+    "window_semantics": "Strict physical source-event intervals, including bridges"
+  }
+}
diff --git a/research/three-demotions-t37-composition/PRICE.json b/research/three-demotions-t37-composition/PRICE.json
new file mode 100644
index 0000000000..38c4a28b5f
--- /dev/null
+++ b/research/three-demotions-t37-composition/PRICE.json
@@ -0,0 +1,123 @@
+{
+  "status": "PASS_EXACT_ARITHMETIC_ONLY_PENDING_FULL_ADMISSION",
+  "prices": {
+    "native": {
+      "root": {
+        "lower": "0.001677940138221069351902",
+        "upper": "0.001677940138221069351903",
+        "lower_endpoint_residual_upper": "-2.219467388917781341720488603388561940263345730698966853233093397624555E-25",
+        "upper_endpoint_residual_lower": "2.702681579032767449762188399953727879223826848446522506447128412881375E-24",
+        "strict_rational_signs": true,
+        "moment_minus_one_at_current_k_required_rate": [
+          "-0.002868813741415620663117559115513815454438327519310983613745378749471557",
+          "-0.002868813741415620663117559115513815454438327519310983613745378749397373"
+        ],
+        "nominal_k_ceiling_interval": [
+          "0.001675129371412064020180623220648693264150464440679712853735888668107748",
+          "0.001675129371412064020181619873196008850989800805481882651702771099159474"
+        ]
+      },
+      "moments": [
+        {
+          "endpoint": "838970069110534675951/500000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-2991836121735173596624439273317349489678723/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-1495918060867586798312219636658674744839361/6739986666787659948666753771754907668409286105635143120275902562304"
+          ],
+          "base_two_residual": [
+            "-221947/1000000000000000000000000000000",
+            "-110973/500000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "1677940138221069351903/1000000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "72864151229013887289118021292465544517640617/26959946667150639794667015087019630673637144422540572481103610249216",
+            "72864151229013887289118021292465544517640619/26959946667150639794667015087019630673637144422540572481103610249216"
+          ],
+          "base_two_residual": [
+            "2702681/1000000000000000000000000000000",
+            "1351341/500000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer": {
+        "complex_b": "838970069110534675951/500000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "52347792856627/31250000000000000",
+        "kappa_decimal": "0.001675129371412064",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    },
+    "conservative": {
+      "root": {
+        "lower": "0.001677940135364722601859",
+        "upper": "0.00167794013536472260186",
+        "lower_endpoint_residual_upper": "-2.537684038701087314457453203479807752970516421584737526885940585245438E-24",
+        "upper_endpoint_residual_lower": "3.869442792288328893531898607068556558869356594553008616456167924995620E-25",
+        "strict_rational_signs": true,
+        "moment_minus_one_at_current_k_required_rate": [
+          "-0.002868813733097014390224864250502200284017811987276035412218507990982309",
+          "-0.002868813733097014390224864250502200284017811987276035412218507990908125"
+        ],
+        "nominal_k_ceiling_interval": [
+          "0.001675129368565278755725551683551476317245438813313468183642728441961422",
+          "0.001675129368565278755726548336098797588117836875179397673233565303574340"
+        ]
+      },
+      "moments": [
+        {
+          "endpoint": "1677940135364722601859/1000000000000000000000000",
+          "accept": true,
+          "mercator_residual": [
+            "-8551978292682594269400361220874041671630055/3369993333393829974333376885877453834204643052817571560137951281152",
+            "-34207913170730377077601444883496166686520219/13479973333575319897333507543509815336818572211270286240551805124608"
+          ],
+          "base_two_residual": [
+            "-25376843020393068796399/10000000000000000000000000000000000000000000000",
+            "-25376833020393068796257/10000000000000000000000000000000000000000000000"
+          ]
+        },
+        {
+          "endpoint": "83897006768236130093/50000000000000000000000",
+          "accept": false,
+          "mercator_residual": [
+            "2607999282792094948097029577094036239325135/6739986666787659948666753771754907668409286105635143120275902562304",
+            "5215998565584189896194059154188072478650271/13479973333575319897333507543509815336818572211270286240551805124608"
+          ],
+          "base_two_residual": [
+            "386943697996534557033/1000000000000000000000000000000000000000000000",
+            "3869446979965345570471/10000000000000000000000000000000000000000000000"
+          ]
+        }
+      ],
+      "outer": {
+        "complex_b": "1677940135364722601859/1000000000000000000000000",
+        "bit_c": "1733427039589844234749/1000000000000000000000000",
+        "kappa": "837564684282639/500000000000000000",
+        "kappa_decimal": "0.001675129368565278",
+        "binding": "complex",
+        "strict_constraints_passed": 47,
+        "controls_rejected": [
+          "next_grid",
+          "zero_eta",
+          "zero_beta",
+          "unit_beta"
+        ]
+      }
+    }
+  },
+  "gain_over_pr1061": "7723622857/1000000000000000000",
+  "gain_percent": "0.000461078326293107569960974573946156603765550637178292686874000598160875303838",
+  "profile_sha256": "440912ba08baa19af76194a7bcd8640b73926f5182c97bc6b73c3587b0256858",
+  "scope": "Conditional PR645 framework and PR589 bit assumptions retained. Owner, native and global admission are separate."
+}
diff --git a/research/three-demotions-t37-composition/PROFILE.json b/research/three-demotions-t37-composition/PROFILE.json
new file mode 100644
index 0000000000..7c35d9f51f
--- /dev/null
+++ b/research/three-demotions-t37-composition/PROFILE.json
@@ -0,0 +1,9 @@
+{
+  "1": 790710,
+  "2": 164502,
+  "3": 137196,
+  "4": 43290,
+  "5": 27306,
+  "8": 2664,
+  "48": 11374
+}
diff --git a/research/three-demotions-t37-composition/README.md b/research/three-demotions-t37-composition/README.md
new file mode 100644
index 0000000000..4d9b74ce13
--- /dev/null
+++ b/research/three-demotions-t37-composition/README.md
@@ -0,0 +1,17 @@
+# Three-demotion provider with T37 whole-owner packing
+
+DRAFT: exact arithmetic and literal owner construction pass; full global admission is pending.
+
+The candidate conditional price is κ = 0.001675129371412064, 0.0004610783% above PR1148 at 0.001675121647789207. It combines PR1148's unchanged local word with a new integer flow on PR1131's T37 wave order. It has 159,840 whole-helper roles in 333 calls and idle profile {1:834,48:11374}. Exact equations and bipartite matching pass. Two independent rational moment engines and 47 strict outer inequalities price the explicit profile. This does not yet assert complete physical admission.
+
+The 37-replica root equals the fixed-family grid upper value proved in PR1148; that upper bound alone is not a construction. The frozen assignment here supplies the candidate construction; provider, controller, charts and finite invoice must still be replayed before this draft is marked ready.
+
+Rebuild the owner map using Python 3.11+:
+
+    python -B construct.py --flow PATTERN-FLOW.json --plan PLAN.json --out NEW_OUTPUT
+
+The resulting OWNERS.json.gz must match the frozen map. Full verification receipts and a standalone replay wrapper will be added after verification.
+
+Credit: Thomas DiFiore and Codex for PR1148's demotions and endpoints; Ali Romman and Codex for PR1129's pattern-flow/matching construction and T37 audit; PR1131 for the wave order and independent T37 construction; PR1074/1018 and their full local ancestry, Chafik Boukhalfa's PR795 dual prices, PR890/942, Hao Yan's owner/source-event machinery, PR1091, and the unchanged PR589 bit supplier. New composition by Rohan Arun with substantial OpenAI Codex assistance. Derived construction code retains Apache-2.0 licensing and original notices.
+
+All inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 obligations remain. PR559 recurrence correction is retained. This is not an unconditional multiplication theorem, full formalization, or runtime benchmark.
diff --git a/research/three-demotions-t37-composition/SEARCH.json b/research/three-demotions-t37-composition/SEARCH.json
new file mode 100644
index 0000000000..0747d3f3a6
--- /dev/null
+++ b/research/three-demotions-t37-composition/SEARCH.json
@@ -0,0 +1,53 @@
+{
+  "status": 0,
+  "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)",
+  "seconds": 116.19498995799222,
+  "variables": 122712,
+  "constraints": 61441,
+  "inventory": {
+    "9": 240,
+    "4": 44,
+    "8": 114,
+    "7": 38,
+    "5": 44
+  },
+  "active_patterns": [
+    [
+      8,
+      0
+    ],
+    [
+      16,
+      0
+    ],
+    [
+      16,
+      1
+    ],
+    [
+      16,
+      2
+    ],
+    [
+      32,
+      3
+    ],
+    [
+      32,
+      4
+    ],
+    [
+      32,
+      5
+    ],
+    [
+      48,
+      0
+    ],
+    [
+      48,
+      1
+    ]
+  ],
+  "exact_integer_equations": "PASS"
+}
\ No newline at end of file
diff --git a/research/three-demotions-t37-composition/UPSTREAM-NOTICE.md b/research/three-demotions-t37-composition/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..1e3b40de32
--- /dev/null
+++ b/research/three-demotions-t37-composition/UPSTREAM-NOTICE.md
@@ -0,0 +1,45 @@
+# Attribution and license
+
+New owner theorem, exact flow construction, checker, and package by
+Ali Romman <226877337+aliromman@users.noreply.github.com>, with substantial
+OpenAI Codex assistance. New work is under Apache-2.0.
+
+The fixed local supplier is Jeremy Kothe's seven-slot k8 word in PR1074,
+commit `052afc128954f7b6a2b3c409eb4d72248e4020f2`. The seven-slot step comes
+from PR1018 and credits Rohan Arun's PR987 search. The earlier local word and
+its scalar, frame, phase, and source-access construction retain all notices
+in `vendor/pr1074/NOTICE.md` and `vendor/pr1074/UPSTREAM-NOTICE.md`.
+This package does not claim authorship of those local changes.
+
+The signed bin prices come from Chafik Boukhalfa's PR795. The proof method
+builds on the PR890/PR942 owner bounds and the prior all-replica T37 theorem.
+The new right-hand side, exact attaining flow, and complete R480 owner map
+are specific to the changed seven-slot inventory. The old theorem did not
+cover this word.
+
+The T16 source-event routines are by Hao Yan (@FanPUYen). Their source notice
+is kept in `vendor/pr1074/t16/NOTICE.md` and their source headers. The derived
+independent owner checker comes from `research/complex-t21-owners` at the
+exact repository base. `INDEPENDENT-DERIVATION.patch` records its changes.
+
+The global admission code comes from the exact PR1074 package. Its sources
+and notices are retained. `CODE-DERIVATION.patch` records all changes needed
+for 37 replicas and the 1024-bit complex prefix allowance. The arithmetic
+engines and full PR589 bit supplier are unchanged and source-pinned.
+
+PR1034 proved a mixed bound for 71 older catalogue entries and excluded
+R480. PR1069 independently checked the rank-mass identity for recent claims.
+These contributions informed the scope and cost audit. Neither admits the
+new physical owner map by itself.
+
+The concurrent mutable-leaver sprint worker rebuilt the unchanged local k8
+and seven-slot chains, including their scalar and phase checks. This package
+retains that source-bound evidence. It does not use the worker's new local
+word experiments. No predecessor notice, license, or AI disclosure is replaced
+by this notice.
+
+Josie Elliston's PR1091 independently checked fifteen T16 owner maps and
+made the disjoint-pending-axis obligation explicit. The independent T37
+audit includes that check and a targeted negative control. Rohan Arun's
+PR1094 gives a later same-word T16 repack. Jeremy Kothe's PR1117 changes
+the local word; it is a concurrent comparison outside the proved inventory.
diff --git a/research/three-demotions-t37-composition/construct.py b/research/three-demotions-t37-composition/construct.py
new file mode 100644
index 0000000000..de52d33831
--- /dev/null
+++ b/research/three-demotions-t37-composition/construct.py
@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Rebuild literal owners from the exact pattern-flow certificate."""
+import argparse,json,gzip,hashlib
+from collections import Counter,defaultdict
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+parser=argparse.ArgumentParser(description=__doc__)
+parser.add_argument('--out',type=Path,required=True)
+parser.add_argument('--flow',type=Path,required=True)
+parser.add_argument('--plan',type=Path,required=True)
+args=parser.parse_args()
+if not __debug__:raise ValueError('Construction checks require assertions')
+if args.out.exists():raise ValueError('Choose a new construction directory')
+D=json.loads(args.flow.read_text())
+assert D['T']==37 and sorted(D['order'])==[[s,r] for s in range(9) for r in range(37)]
+P=json.loads(gzip.decompress(args.plan.read_bytes()) if args.plan.suffix=='.gz' else args.plan.read_bytes())
+widths=P['provider_registry']['gauge44']['widths'];ws=(4,5,7,8,9)
+xs={};ys=defaultdict(Counter)
+for entry,n in D['entries']:
+ assert type(n) is int and n>0
+ if entry[0]=='x':_,g,p=entry;xs[g,p]=n
+ else:_,g,p,t,w=entry;ys[g,p][t,w]+=n
+assign=defaultdict(list);global_count=Counter();idle=Counter();offsets=defaultdict(int)
+for gi,(r,cap,ts,children) in enumerate(D['groups']):
+ port_index=0
+ for pi,pat in enumerate(D['patterns'][str(cap)]):
+  N=xs.get((gi,pi),0)
+  if not N:continue
+  v=ys[gi,pi]
+  assert all(t in ts for t,w in v)
+  assert Counter({w:sum(n for (t,ww),n in v.items() if w==ww) for w,num in enumerate(pat) if num})==Counter({w:N*num for w,num in enumerate(pat) if num})
+  assert all(sum(n for (tt,w),n in v.items() if tt==t)<=N for t in ts)
+  slot_width=[w for w,n in enumerate(pat) for _ in range(n)]
+  graph=[Counter() for _ in slot_width]
+  # Split each width vertex into vertices of degree N.
+  for w in set(slot_width):
+   slots=[s for s,ww in enumerate(slot_width) if ww==w];j=0;used=0
+   for (t,ww),n in sorted(v.items()):
+    if ww!=w:continue
+    while n:
+     count=min(n,N-used);graph[slots[j]][t]+=count;used+=count;n-=count
+     if used==N:used=0;j+=1
+   assert j==len(slots) and used==0
+  assert all(sum(a.values())==N for a in graph)
+  for remaining in range(N,0,-1):
+   degree=Counter()
+   for adj in graph:degree.update(adj)
+   assert max(degree.values(),default=0)<=remaining
+   required=sorted(t for t,n in degree.items() if n==remaining)
+   st={};tt={}
+   def match_time(t,seen):
+    for s,adj in enumerate(graph):
+     if adj[t]==0 or s in seen:continue
+     seen.add(s)
+     if s not in st or match_time(st[s],seen):
+      st[s]=t;tt[t]=s;return True
+    return False
+   for t in required:assert match_time(t,set())
+   def match_slot(s,seen):
+    for t,n in sorted(graph[s].items()):
+     if not n or t in seen:continue
+     seen.add(t)
+     if t not in tt or match_slot(tt[t],seen):
+      tt[t]=s;st[s]=t;return True
+    return False
+   for s in range(len(graph)):
+    if s not in st:assert match_slot(s,set())
+   assert len(st)==len(tt)==len(graph) and all(t in tt for t in required)
+   child=children[port_index//112];port=port_index%112;port_index+=1
+   offset=0
+   for s,t in sorted(st.items(),key=lambda it:(it[1],it[0])):
+    w=ws[slot_width[s]];graph[s][t]-=1
+    assign[t,w].append((r,child,port,offset))
+    offset+=w;global_count[w]+=1
+   assert offset<=cap
+   idle[cap-offset]+=1
+  assert all(not any(adj.values()) for adj in graph)
+ assert port_index==112*len(children)
+roles=[]
+for t,(stage,replica) in enumerate(D['order']):
+ for h,w in enumerate(widths):
+  owner,child,port,offset=assign[t,w].pop()
+  family=896*owner+112*(2*P['pairs'][str(child)]+P['sides'][str(child)])+port
+  roles.append(dict(time=t,stage=stage,replica=replica,helper=h,width=w,owner_replica=owner,child=child,port=port,offset=offset,copy=112*owner+port,family=family))
+assert not any(assign.values());assert len(roles)==37*9*480
+print('literal roles',len(roles),'idle',dict(sorted(idle.items())))
+# Separate direct check from the aggregate model.
+used=defaultdict(set);seen=defaultdict(set);coverage=defaultdict(set)
+windows={(r,ch):(cap,set(ts)) for r,cap,ts,chs in D['groups'] for ch in chs}
+for z in roles:
+ t=z['time'];key=z['owner_replica'],z['child'];cap,ts=windows[key]
+ assert t in ts and z['family'] not in seen[t];seen[t].add(z['family'])
+ g=key+(z['port'],);cells=set(range(z['offset'],z['offset']+z['width']))
+ assert not cells&used[g] and all(0<=x<cap for x in cells);used[g]|=cells;coverage[t].add(z['helper'])
+for t,hh in coverage.items():assert hh==set(range(480))
+left=Counter()
+for key,(cap,ts) in windows.items():
+ for port in range(112):
+  cell=used[key+(port,)];assert cell==set(range(len(cell)));left[cap-len(cell)]+=1
+assert left==idle
+raw=json.dumps(roles,sort_keys=True,separators=(',',':')).encode()
+# Discovery constructor: freeze the derived map for a later strict replay.
+out=args.out;out.mkdir(parents=True)
+(out/'OWNERS.json.gz').write_bytes(gzip.compress(raw,mtime=0))
+(out/'ORDER.json').write_text(json.dumps(D['order'])+'\n')
+(out/'GEOMETRY-CHECK.json').write_text(json.dumps({'roles':len(roles),'idle':dict(sorted(idle.items())),'owner_content_sha256':hashlib.sha256(raw).hexdigest(),'status':'PASS_LITERAL_WHOLE_HELPER_GEOMETRY'},indent=2)+'\n')
+print('PASS_LITERAL_WHOLE_HELPER_GEOMETRY',hashlib.sha256(raw).hexdigest())

From 45ea73bd21667e444d65a6a148e95a24266852f6 Mon Sep 17 00:00:00 2001
From: rohanarun <rohanarun@gmail.com>
Date: Tue, 13 Oct 2026 15:34:04 -0400
Subject: [PATCH 2/4] Draft stronger joint-entrance T37 composition

---
 .../CANDIDATE.json                            |   14 +-
 .../GEOMETRY-CHECK.json                       |    2 +-
 .../MANIFEST.json                             |   14 +-
 .../OWNERS.json.gz                            |  Bin 1864063 -> 1864483 bytes
 .../three-demotions-t37-composition/PLAN.json | 6056 ++++++++---------
 .../PRICE.json                                |   90 +-
 .../PROFILE.json                              |    4 +-
 .../three-demotions-t37-composition/README.md |   20 +-
 8 files changed, 3101 insertions(+), 3099 deletions(-)

diff --git a/research/three-demotions-t37-composition/CANDIDATE.json b/research/three-demotions-t37-composition/CANDIDATE.json
index 62bf49bbce..d1a67e2dae 100644
--- a/research/three-demotions-t37-composition/CANDIDATE.json
+++ b/research/three-demotions-t37-composition/CANDIDATE.json
@@ -1,11 +1,11 @@
 {
-  "status": "DRAFT_EXACT_PRICE_AND_LITERAL_OWNERS_FULL_ADMISSION_PENDING",
-  "kappa": "1675129371412064/1000000000000000000",
-  "kappa_decimal": "0.001675129371412064",
-  "previous_kappa": "0.001675121647789207",
-  "gain_percent": "0.00046107832629310757",
-  "pr1148_head": "98235a9cf4ce355ec5cf3fac2eca7b3b98a20838",
+  "status": "DRAFT_JOINT_ENTRANCES_T37_FULL_ADMISSION_PENDING",
+  "kappa": "1675568675201533/1000000000000000000",
+  "kappa_decimal": "0.001675568675201533",
+  "previous_kappa": "0.001675560947524449",
+  "gain_percent": "0.00046119940282788438",
+  "pr1148_head": "f1d8dc59288dcab77cae713c450d14069e7eec05",
   "pr1129_head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21",
   "pr1131_head": "fcdc42737b703323d8ed550a528141a482e68e96",
-  "scope": "Conditional finite candidate. Full T37 provider/controller/invoice admission pending. Native provider separately reproduced from exact PR1148 head. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions retained. No unconditional theorem, full Lean certification, or general packing optimality claim."
+  "scope": "Conditional finite candidate. Full new native and T37 provider/controller/invoice admission pending. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions retained. No unconditional theorem or full Lean certification."
 }
diff --git a/research/three-demotions-t37-composition/GEOMETRY-CHECK.json b/research/three-demotions-t37-composition/GEOMETRY-CHECK.json
index 2b1bd1cbcf..314abd9c82 100644
--- a/research/three-demotions-t37-composition/GEOMETRY-CHECK.json
+++ b/research/three-demotions-t37-composition/GEOMETRY-CHECK.json
@@ -5,6 +5,6 @@
     "1": 834,
     "48": 11374
   },
-  "owner_content_sha256": "6aac44c27ee80dbcbfcc48ab358c8e79887ea34c5064bc0ba5955dd19df12a6f",
+  "owner_content_sha256": "a838473dc255952abebc6fb4f44a41800a812d3f5d27b461146be09b20e82447",
   "status": "PASS_LITERAL_WHOLE_HELPER_GEOMETRY"
 }
diff --git a/research/three-demotions-t37-composition/MANIFEST.json b/research/three-demotions-t37-composition/MANIFEST.json
index f1ea5b41ca..07591da758 100644
--- a/research/three-demotions-t37-composition/MANIFEST.json
+++ b/research/three-demotions-t37-composition/MANIFEST.json
@@ -1,12 +1,12 @@
 {
-  "CANDIDATE.json": "43cc85370e98160f870484754240cd08a70cbdbc5ee3f75f705b7725693ff6c0",
-  "GEOMETRY-CHECK.json": "497c71976c01378b84552a245c1359fc53a6b6474b0c46c00546a419710ca826",
-  "OWNERS.json.gz": "449d230ae8ea9b5adf2f4a06da0dd89473e6e259b986e46ebf7407e169ac1d4b",
+  "CANDIDATE.json": "f2edef3b48bddb93d5ffebc55e742f090322ecf34918a878bbd345a9701cc2ea",
+  "GEOMETRY-CHECK.json": "c26f1998b20c70c3f5a46f7eb08a89953555881fbffcb1e9f79985e00131594f",
+  "OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6",
   "PATTERN-FLOW.json": "d7accd36895a218d0db8e1434ea013c18d924059e4b32f25a21e3529539d7352",
-  "PLAN.json": "2c5e493cfdc4c424ebf20c91be089408dc04f183c979a9b76efb867b6f357424",
-  "PRICE.json": "dae64ef8026dd50ffce655f3094ca263e680a25db29669ab70a40fabf5db11d2",
-  "PROFILE.json": "440912ba08baa19af76194a7bcd8640b73926f5182c97bc6b73c3587b0256858",
-  "README.md": "b895d31ff6ebfec43b94a37981c9249f922999cbfc1ca1a50b05756e34ec2d3d",
+  "PLAN.json": "f9b2592c5af1953c4c893e18be1e3444e7a07257e3054eceb99c42fd40351597",
+  "PRICE.json": "2712af0e3a1719f09666f0029c59e3e5e441b4fca342b08b32f63ed78afbf428",
+  "PROFILE.json": "3e1be872303172ad7ce286bd5525c64cec13d70198c72496de2f0cdb729247c2",
+  "README.md": "acedee1d3e0752dd405b89e3fc392f968b227fc7ace3dde57d9bc45c0f374191",
   "SEARCH.json": "c42084bbadd361f90dc21ffbd300c03b3739a57e9bf978e4272e0c822bca27bd",
   "UPSTREAM-NOTICE.md": "b97fb4731e84aef736c58a9c126334eb5b8d3a057a8d9d45b4ffff24af65c38b",
   "construct.py": "eee2edff41871b929e4c85289a2bd80842f5a5ae6130b8c7b0574178d4de9562"
diff --git a/research/three-demotions-t37-composition/OWNERS.json.gz b/research/three-demotions-t37-composition/OWNERS.json.gz
index a49281b64f6f963bc217db8b2af04a1d40f6dad2..078f621724cbaf30bcc24815898a878b1470cc3d 100644
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diff --git a/research/three-demotions-t37-composition/PLAN.json b/research/three-demotions-t37-composition/PLAN.json
index 518ea50eae..418c700ab5 100644
--- a/research/three-demotions-t37-composition/PLAN.json
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@@ -66043,7 +66043,7 @@
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@@ -66051,7 +66051,7 @@
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@@ -66059,7 +66059,7 @@
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@@ -66067,7 +66067,7 @@
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@@ -66075,7 +66075,7 @@
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@@ -66083,7 +66083,7 @@
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@@ -66091,7 +66091,7 @@
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@@ -66099,7 +66099,7 @@
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@@ -66107,7 +66107,7 @@
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@@ -66115,7 +66115,7 @@
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@@ -66123,7 +66123,7 @@
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@@ -66131,7 +66131,7 @@
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@@ -66139,7 +66139,7 @@
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@@ -66147,7 +66147,7 @@
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@@ -66155,7 +66155,7 @@
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@@ -66163,7 +66163,7 @@
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@@ -66171,7 +66171,7 @@
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@@ -66179,7 +66179,7 @@
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@@ -66187,7 +66187,7 @@
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@@ -66195,7 +66195,7 @@
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@@ -66203,7 +66203,7 @@
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@@ -66211,7 +66211,7 @@
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@@ -66219,7 +66219,7 @@
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@@ -66227,7 +66227,7 @@
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@@ -66235,7 +66235,7 @@
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@@ -66243,7 +66243,7 @@
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@@ -66251,7 +66251,7 @@
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@@ -66259,7 +66259,7 @@
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@@ -66267,7 +66267,7 @@
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@@ -66275,7 +66275,7 @@
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@@ -66283,7 +66283,7 @@
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@@ -66291,7 +66291,7 @@
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@@ -66299,7 +66299,7 @@
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@@ -66307,7 +66307,7 @@
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@@ -66315,7 +66315,7 @@
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@@ -66323,7 +66323,7 @@
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@@ -66331,7 +66331,7 @@
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@@ -66339,7 +66339,7 @@
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@@ -66347,7 +66347,7 @@
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@@ -66355,7 +66355,7 @@
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@@ -66363,7 +66363,7 @@
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@@ -66371,7 +66371,7 @@
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@@ -66379,7 +66379,7 @@
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@@ -66387,7 +66387,7 @@
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@@ -66395,7 +66395,7 @@
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@@ -66403,7 +66403,7 @@
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@@ -66411,7 +66411,7 @@
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@@ -66419,7 +66419,7 @@
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@@ -66427,7 +66427,7 @@
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@@ -66435,7 +66435,7 @@
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@@ -66443,7 +66443,7 @@
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@@ -66451,7 +66451,7 @@
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@@ -66459,7 +66459,7 @@
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@@ -66467,7 +66467,7 @@
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@@ -66475,7 +66475,7 @@
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@@ -66483,7 +66483,7 @@
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@@ -66491,7 +66491,7 @@
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@@ -66499,7 +66499,7 @@
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@@ -66507,7 +66507,7 @@
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@@ -66515,7 +66515,7 @@
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@@ -66523,7 +66523,7 @@
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@@ -66531,7 +66531,7 @@
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@@ -66539,7 +66539,7 @@
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@@ -66547,7 +66547,7 @@
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@@ -66555,7 +66555,7 @@
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@@ -66563,7 +66563,7 @@
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@@ -66571,7 +66571,7 @@
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@@ -66579,7 +66579,7 @@
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@@ -66587,7 +66587,7 @@
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@@ -66595,7 +66595,7 @@
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@@ -66603,7 +66603,7 @@
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@@ -66611,7 +66611,7 @@
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@@ -66619,7 +66619,7 @@
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@@ -66627,7 +66627,7 @@
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@@ -66635,7 +66635,7 @@
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@@ -66643,7 +66643,7 @@
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@@ -66651,7 +66651,7 @@
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@@ -66659,7 +66659,7 @@
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@@ -66667,7 +66667,7 @@
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@@ -66675,7 +66675,7 @@
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@@ -66683,7 +66683,7 @@
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@@ -66691,7 +66691,7 @@
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@@ -66699,7 +66699,7 @@
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@@ -66707,7 +66707,7 @@
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@@ -66715,7 +66715,7 @@
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@@ -66723,7 +66723,7 @@
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@@ -66731,7 +66731,7 @@
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@@ -66739,7 +66739,7 @@
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@@ -66747,7 +66747,7 @@
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@@ -66755,7 +66755,7 @@
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@@ -66763,7 +66763,7 @@
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@@ -66771,7 +66771,7 @@
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@@ -66779,7 +66779,7 @@
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@@ -66787,7 +66787,7 @@
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@@ -66795,7 +66795,7 @@
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@@ -66803,7 +66803,7 @@
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@@ -66811,7 +66811,7 @@
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@@ -66819,7 +66819,7 @@
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@@ -66827,7 +66827,7 @@
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@@ -66835,7 +66835,7 @@
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@@ -66843,7 +66843,7 @@
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@@ -66851,7 +66851,7 @@
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@@ -66859,7 +66859,7 @@
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@@ -66867,7 +66867,7 @@
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@@ -66875,7 +66875,7 @@
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@@ -66883,7 +66883,7 @@
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@@ -66891,7 +66891,7 @@
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@@ -66899,7 +66899,7 @@
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@@ -66907,7 +66907,7 @@
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@@ -66915,7 +66915,7 @@
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@@ -66923,7 +66923,7 @@
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@@ -66931,7 +66931,7 @@
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@@ -66939,7 +66939,7 @@
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@@ -66947,7 +66947,7 @@
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@@ -66955,7 +66955,7 @@
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@@ -66963,7 +66963,7 @@
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@@ -66971,7 +66971,7 @@
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@@ -66979,7 +66979,7 @@
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@@ -66987,7 +66987,7 @@
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@@ -66995,7 +66995,7 @@
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@@ -67003,7 +67003,7 @@
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@@ -67011,7 +67011,7 @@
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@@ -67019,7 +67019,7 @@
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@@ -67027,7 +67027,7 @@
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@@ -67035,7 +67035,7 @@
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@@ -67043,7 +67043,7 @@
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@@ -67051,7 +67051,7 @@
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@@ -67059,7 +67059,7 @@
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@@ -67067,7 +67067,7 @@
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@@ -67075,7 +67075,7 @@
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@@ -67083,7 +67083,7 @@
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@@ -67091,7 +67091,7 @@
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@@ -67099,7 +67099,7 @@
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@@ -67107,7 +67107,7 @@
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@@ -67115,7 +67115,7 @@
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@@ -67123,7 +67123,7 @@
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@@ -67131,7 +67131,7 @@
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@@ -67139,7 +67139,7 @@
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@@ -67147,7 +67147,7 @@
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@@ -67155,7 +67155,7 @@
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@@ -67163,7 +67163,7 @@
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@@ -67171,7 +67171,7 @@
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@@ -67179,7 +67179,7 @@
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@@ -67187,7 +67187,7 @@
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@@ -67195,7 +67195,7 @@
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@@ -67203,7 +67203,7 @@
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@@ -67211,7 +67211,7 @@
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@@ -67219,7 +67219,7 @@
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@@ -67227,7 +67227,7 @@
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@@ -67235,7 +67235,7 @@
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@@ -67243,7 +67243,7 @@
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@@ -67251,7 +67251,7 @@
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@@ -67259,7 +67259,7 @@
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@@ -67267,7 +67267,7 @@
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@@ -67275,7 +67275,7 @@
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@@ -67283,7 +67283,7 @@
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@@ -67291,7 +67291,7 @@
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@@ -67299,7 +67299,7 @@
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@@ -67307,7 +67307,7 @@
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@@ -67315,7 +67315,7 @@
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@@ -67323,7 +67323,7 @@
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@@ -67331,7 +67331,7 @@
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@@ -67339,7 +67339,7 @@
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@@ -67347,7 +67347,7 @@
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@@ -67355,7 +67355,7 @@
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@@ -67363,7 +67363,7 @@
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@@ -67371,7 +67371,7 @@
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@@ -67379,7 +67379,7 @@
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@@ -67387,7 +67387,7 @@
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@@ -67395,7 +67395,7 @@
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@@ -67403,7 +67403,7 @@
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@@ -67411,7 +67411,7 @@
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@@ -67419,7 +67419,7 @@
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@@ -67427,7 +67427,7 @@
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@@ -67435,7 +67435,7 @@
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@@ -67443,7 +67443,7 @@
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@@ -67451,7 +67451,7 @@
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@@ -67459,7 +67459,7 @@
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@@ -67467,7 +67467,7 @@
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@@ -67475,7 +67475,7 @@
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@@ -67483,7 +67483,7 @@
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@@ -67491,7 +67491,7 @@
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@@ -67499,7 +67499,7 @@
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@@ -67507,7 +67507,7 @@
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@@ -67515,7 +67515,7 @@
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@@ -67523,7 +67523,7 @@
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@@ -67531,7 +67531,7 @@
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@@ -67539,7 +67539,7 @@
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@@ -67547,7 +67547,7 @@
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@@ -67555,7 +67555,7 @@
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@@ -67563,7 +67563,7 @@
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@@ -67571,7 +67571,7 @@
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@@ -67579,7 +67579,7 @@
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@@ -67587,7 +67587,7 @@
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@@ -67595,7 +67595,7 @@
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@@ -67603,7 +67603,7 @@
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@@ -67611,7 +67611,7 @@
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@@ -67619,7 +67619,7 @@
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@@ -67627,7 +67627,7 @@
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@@ -67635,7 +67635,7 @@
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@@ -67643,7 +67643,7 @@
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@@ -67651,7 +67651,7 @@
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@@ -67659,7 +67659,7 @@
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@@ -67667,7 +67667,7 @@
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@@ -67675,7 +67675,7 @@
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@@ -67683,7 +67683,7 @@
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@@ -67691,7 +67691,7 @@
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@@ -67699,7 +67699,7 @@
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@@ -67707,7 +67707,7 @@
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@@ -67715,7 +67715,7 @@
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@@ -67723,7 +67723,7 @@
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@@ -67731,7 +67731,7 @@
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@@ -67739,7 +67739,7 @@
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@@ -67747,7 +67747,7 @@
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@@ -67755,7 +67755,7 @@
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@@ -67763,7 +67763,7 @@
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@@ -67771,7 +67771,7 @@
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@@ -67779,7 +67779,7 @@
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@@ -67787,7 +67787,7 @@
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@@ -67795,7 +67795,7 @@
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@@ -67803,7 +67803,7 @@
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@@ -67811,7 +67811,7 @@
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@@ -67819,7 +67819,7 @@
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@@ -67827,7 +67827,7 @@
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@@ -67835,7 +67835,7 @@
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@@ -67843,7 +67843,7 @@
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@@ -67851,7 +67851,7 @@
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@@ -67859,7 +67859,7 @@
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@@ -67867,7 +67867,7 @@
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@@ -67875,7 +67875,7 @@
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@@ -67883,7 +67883,7 @@
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@@ -67891,7 +67891,7 @@
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@@ -67899,7 +67899,7 @@
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@@ -67907,7 +67907,7 @@
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@@ -67915,7 +67915,7 @@
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@@ -67923,7 +67923,7 @@
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@@ -67931,7 +67931,7 @@
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@@ -67939,7 +67939,7 @@
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@@ -67947,7 +67947,7 @@
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@@ -67955,7 +67955,7 @@
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@@ -67963,7 +67963,7 @@
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@@ -67971,7 +67971,7 @@
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diff --git a/research/three-demotions-t37-composition/PRICE.json b/research/three-demotions-t37-composition/PRICE.json
index 38c4a28b5f..372d75fca6 100644
--- a/research/three-demotions-t37-composition/PRICE.json
+++ b/research/three-demotions-t37-composition/PRICE.json
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+            "37461531782114767321903500131065006272770531/26959946667150639794667015087019630673637144422540572481103610249216",
+            "37461531782114767321903500131065006272770533/26959946667150639794667015087019630673637144422540572481103610249216"
           ],
           "base_two_residual": [
-            "2702681/1000000000000000000000000000000",
-            "1351341/500000000000000000000000000000"
+            "55581/40000000000000000000000000000",
+            "694763/500000000000000000000000000000"
           ]
         }
       ],
       "outer": {
-        "complex_b": "838970069110534675951/500000000000000000000000",
+        "complex_b": "419595229423068636473/250000000000000000000000",
         "bit_c": "1733427039589844234749/1000000000000000000000000",
-        "kappa": "52347792856627/31250000000000000",
-        "kappa_decimal": "0.001675129371412064",
+        "kappa": "1675568675201533/1000000000000000000",
+        "kappa_decimal": "0.001675568675201533",
         "binding": "complex",
         "strict_constraints_passed": 47,
         "controls_rejected": [
@@ -60,51 +60,51 @@
     },
     "conservative": {
       "root": {
-        "lower": "0.001677940135364722601859",
-        "upper": "0.00167794013536472260186",
-        "lower_endpoint_residual_upper": "-2.537684038701087314457453203479807752970516421584737526885940585245438E-24",
-        "upper_endpoint_residual_lower": "3.869442792288328893531898607068556558869356594553008616456167924995620E-25",
+        "lower": "0.001678380914838404923495",
+        "upper": "0.001678380914838404923496",
+        "lower_endpoint_residual_upper": "-7.373438247627208114426179987119846674716538356778287803616927660661386E-25",
+        "upper_endpoint_residual_lower": "2.186516038601431405266956334852026282750074329971903664663050079917329E-24",
         "strict_rational_signs": true,
         "moment_minus_one_at_current_k_required_rate": [
-          "-0.002868813733097014390224864250502200284017811987276035412218507990982309",
-          "-0.002868813733097014390224864250502200284017811987276035412218507990908125"
+          "-0.002869345680643086696099167937682876067035635932619535662516135289940493",
+          "-0.002869345680643086696099167937682876067035635932619535662516135289866309"
         ],
         "nominal_k_ceiling_interval": [
-          "0.001675129368565278755725551683551476317245438813313468183642728441961422",
-          "0.001675129368565278755726548336098797588117836875179397673233565303574340"
+          "0.001675568672357219441968931341767446218766139998551852430602350180685324",
+          "0.001675568672357219441969927993437631880112191055806719620729577589987502"
         ]
       },
       "moments": [
         {
-          "endpoint": "1677940135364722601859/1000000000000000000000000",
+          "endpoint": "335676182967680984699/200000000000000000000000",
           "accept": true,
           "mercator_residual": [
-            "-8551978292682594269400361220874041671630055/3369993333393829974333376885877453834204643052817571560137951281152",
-            "-34207913170730377077601444883496166686520219/13479973333575319897333507543509815336818572211270286240551805124608"
+            "-9939375095477910164332596196741051839643787/13479973333575319897333507543509815336818572211270286240551805124608",
+            "-4969687547738955082166298098370525919821893/6739986666787659948666753771754907668409286105635143120275902562304"
           ],
           "base_two_residual": [
-            "-25376843020393068796399/10000000000000000000000000000000000000000000000",
-            "-25376833020393068796257/10000000000000000000000000000000000000000000000"
+            "-7373445190321096725251/10000000000000000000000000000000000000000000000",
+            "-737343519032109672511/1000000000000000000000000000000000000000000000"
           ]
         },
         {
-          "endpoint": "83897006768236130093/50000000000000000000000",
+          "endpoint": "209797614354800615437/125000000000000000000000",
           "accept": false,
           "mercator_residual": [
-            "2607999282792094948097029577094036239325135/6739986666787659948666753771754907668409286105635143120275902562304",
-            "5215998565584189896194059154188072478650271/13479973333575319897333507543509815336818572211270286240551805124608"
+            "1842136118361377508842095642055641207718069/842498333348457493583344221469363458551160763204392890034487820288",
+            "29474177893782040141473530272890259323489105/13479973333575319897333507543509815336818572211270286240551805124608"
           ],
           "base_two_residual": [
-            "386943697996534557033/1000000000000000000000000000000000000000000000",
-            "3869446979965345570471/10000000000000000000000000000000000000000000000"
+            "21865154810036912718779/10000000000000000000000000000000000000000000000",
+            "546629120250922817973/250000000000000000000000000000000000000000000"
           ]
         }
       ],
       "outer": {
-        "complex_b": "1677940135364722601859/1000000000000000000000000",
+        "complex_b": "335676182967680984699/200000000000000000000000",
         "bit_c": "1733427039589844234749/1000000000000000000000000",
-        "kappa": "837564684282639/500000000000000000",
-        "kappa_decimal": "0.001675129368565278",
+        "kappa": "1675568672357219/1000000000000000000",
+        "kappa_decimal": "0.001675568672357219",
         "binding": "complex",
         "strict_constraints_passed": 47,
         "controls_rejected": [
@@ -116,8 +116,8 @@
       }
     }
   },
-  "gain_over_pr1061": "7723622857/1000000000000000000",
-  "gain_percent": "0.000461078326293107569960974573946156603765550637178292686874000598160875303838",
-  "profile_sha256": "440912ba08baa19af76194a7bcd8640b73926f5182c97bc6b73c3587b0256858",
+  "gain_over_pr1061": "1931919271/250000000000000000",
+  "gain_percent": "0.000461199402827884382761469829927427825855379287589693499822822519932735429315",
+  "profile_sha256": "3e1be872303172ad7ce286bd5525c64cec13d70198c72496de2f0cdb729247c2",
   "scope": "Conditional PR645 framework and PR589 bit assumptions retained. Owner, native and global admission are separate."
 }
diff --git a/research/three-demotions-t37-composition/PROFILE.json b/research/three-demotions-t37-composition/PROFILE.json
index 7c35d9f51f..b219d01e58 100644
--- a/research/three-demotions-t37-composition/PROFILE.json
+++ b/research/three-demotions-t37-composition/PROFILE.json
@@ -1,6 +1,6 @@
 {
-  "1": 790710,
-  "2": 164502,
+  "1": 788046,
+  "2": 165834,
   "3": 137196,
   "4": 43290,
   "5": 27306,
diff --git a/research/three-demotions-t37-composition/README.md b/research/three-demotions-t37-composition/README.md
index 4d9b74ce13..ba2a766740 100644
--- a/research/three-demotions-t37-composition/README.md
+++ b/research/three-demotions-t37-composition/README.md
@@ -1,17 +1,19 @@
-# Three-demotion provider with T37 whole-owner packing
+# Joint entrance choices with T37 whole-owner packing
 
-DRAFT: exact arithmetic and literal owner construction pass; full global admission is pending.
+The updated draft composes PR1148's joint entrance choices (head f1d8dc59288dcab77cae713c450d14069e7eec05) with a new exact T37 owner flow on PR1131's wave order. The candidate conditional price is **κ = 0.001675568675201533**, **0.0004611994%** above that PR1148 head at 0.001675560947524449.
 
-The candidate conditional price is κ = 0.001675129371412064, 0.0004610783% above PR1148 at 0.001675121647789207. It combines PR1148's unchanged local word with a new integer flow on PR1131's T37 wave order. It has 159,840 whole-helper roles in 333 calls and idle profile {1:834,48:11374}. Exact equations and bipartite matching pass. Two independent rational moment engines and 47 strict outer inequalities price the explicit profile. This does not yet assert complete physical admission.
+**Verification pending:** the 159,840 literal whole-helper roles in 333 calls, exact integer flow equations, bipartite matching decomposition, and two-engine rational profile price pass. Full native replay and strict T37 admission are in progress. This draft is not yet a verified new frontier.
 
-The 37-replica root equals the fixed-family grid upper value proved in PR1148; that upper bound alone is not a construction. The frozen assignment here supplies the candidate construction; provider, controller, charts and finite invoice must still be replayed before this draft is marked ready.
+The local paid profile is `{1:2364,2:498,3:412,4:130,5:82,8:8}`. The new flow has idle profile `{1:834,48:11374}` and targets the fixed-word grid upper value from PR1148. An upper relaxation alone does not establish physical realization; the draft supplies a concrete owner map for full admission.
 
-Rebuild the owner map using Python 3.11+:
+Package: `research/three-demotions-t37-composition/`. Reconstruct the owner map without an optimizer using:
 
-    python -B construct.py --flow PATTERN-FLOW.json --plan PLAN.json --out NEW_OUTPUT
+```sh
+python -B construct.py --flow PATTERN-FLOW.json --plan PLAN.json --out NEW_OUTPUT
+```
 
-The resulting OWNERS.json.gz must match the frozen map. Full verification receipts and a standalone replay wrapper will be added after verification.
+A standalone full verification wrapper and receipts will be added after verification. The package directory name is retained from the initial three-demotion composition; its latest payload uses joint entrance groups 603, 611 and 635.
 
-Credit: Thomas DiFiore and Codex for PR1148's demotions and endpoints; Ali Romman and Codex for PR1129's pattern-flow/matching construction and T37 audit; PR1131 for the wave order and independent T37 construction; PR1074/1018 and their full local ancestry, Chafik Boukhalfa's PR795 dual prices, PR890/942, Hao Yan's owner/source-event machinery, PR1091, and the unchanged PR589 bit supplier. New composition by Rohan Arun with substantial OpenAI Codex assistance. Derived construction code retains Apache-2.0 licensing and original notices.
+Credit: Thomas DiFiore/Codex and PR1148's full local ancestry; seslly/shipstuff PR1111's group-635 lead; Ali Romman/Codex PR1129's integer flow, matching decomposition and T37 audit; PR1131's wave order; PR1074/1018, Rohan Arun's PR987, PR1030, PR864, Hao Yan/FanPUYen's PR858, PR870, Chafik Boukhalfa's PR795/890 duals, PR942, PR1091, and the unchanged PR589 bit supplier. New composition by Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0. Original notices retained.
 
-All inherited all-size/compiler, common-label/mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 obligations remain. PR559 recurrence correction is retained. This is not an unconditional multiplication theorem, full formalization, or runtime benchmark.
+All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and bit H1-H5 obligations remain. No unconditional multiplication theorem, full formalization, general sphere-packing optimality or runtime improvement is claimed.

From 13d02293a7af67d7e3bd2e4d7f1a2943ac20537e Mon Sep 17 00:00:00 2001
From: rohanarun <rohanarun@gmail.com>
Date: Tue, 13 Oct 2026 15:40:04 -0400
Subject: [PATCH 3/4] Verify joint-entrance T37 composition and package
 portable replay

---
 .../CANDIDATE.json                            |    4 +-
 .../GLOBAL-TEMPLATE.json.gz                   |  Bin 0 -> 1124331 bytes
 .../INDEPENDENT-DERIVATION.patch              |   30 +
 .../MANIFEST.json                             |   13 +-
 .../NATIVE-VALIDATION.json                    |   93 +
 .../three-demotions-t37-composition/README.md |   19 +-
 .../three-demotions-t37-composition/SPEC.json | 3670 +++++++++++++++++
 .../VALIDATION.json                           |   58 +
 .../upstream-layout.tar.gz                    |  Bin 0 -> 13397097 bytes
 .../three-demotions-t37-composition/verify.py |   43 +
 10 files changed, 3918 insertions(+), 12 deletions(-)
 create mode 100644 research/three-demotions-t37-composition/GLOBAL-TEMPLATE.json.gz
 create mode 100644 research/three-demotions-t37-composition/INDEPENDENT-DERIVATION.patch
 create mode 100644 research/three-demotions-t37-composition/NATIVE-VALIDATION.json
 create mode 100644 research/three-demotions-t37-composition/SPEC.json
 create mode 100644 research/three-demotions-t37-composition/VALIDATION.json
 create mode 100644 research/three-demotions-t37-composition/upstream-layout.tar.gz
 create mode 100644 research/three-demotions-t37-composition/verify.py

diff --git a/research/three-demotions-t37-composition/CANDIDATE.json b/research/three-demotions-t37-composition/CANDIDATE.json
index d1a67e2dae..e1079cdcd6 100644
--- a/research/three-demotions-t37-composition/CANDIDATE.json
+++ b/research/three-demotions-t37-composition/CANDIDATE.json
@@ -1,5 +1,5 @@
 {
-  "status": "DRAFT_JOINT_ENTRANCES_T37_FULL_ADMISSION_PENDING",
+  "status": "PASS_T37_JOINT_ENTRANCES_NATIVE_AND_STRICT_ADMISSION",
   "kappa": "1675568675201533/1000000000000000000",
   "kappa_decimal": "0.001675568675201533",
   "previous_kappa": "0.001675560947524449",
@@ -7,5 +7,5 @@
   "pr1148_head": "f1d8dc59288dcab77cae713c450d14069e7eec05",
   "pr1129_head": "a007dc2e1cc7ae7e8f7ec1343e8883fe43259f21",
   "pr1131_head": "fcdc42737b703323d8ed550a528141a482e68e96",
-  "scope": "Conditional finite candidate. Full new native and T37 provider/controller/invoice admission pending. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions retained. No unconditional theorem or full Lean certification."
+  "scope": "Conditional finite construction. Fresh native replay from pinned PR1148 word and strict T37 admission passed. Parent geometry is reused with pinned exact artifacts and independently reconstructed source-event windows. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global sphere-packing claim."
 }
diff --git a/research/three-demotions-t37-composition/GLOBAL-TEMPLATE.json.gz b/research/three-demotions-t37-composition/GLOBAL-TEMPLATE.json.gz
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HcmV?d00001

diff --git a/research/three-demotions-t37-composition/INDEPENDENT-DERIVATION.patch b/research/three-demotions-t37-composition/INDEPENDENT-DERIVATION.patch
new file mode 100644
index 0000000000..0d78f7f4e1
--- /dev/null
+++ b/research/three-demotions-t37-composition/INDEPENDENT-DERIVATION.patch
@@ -0,0 +1,30 @@
+--- PR1129/independent_owner.py
++++ candidate/independent_owner.py
+@@ -94,7 +94,7 @@
+     for orientation in ('forward', 'backward'):
+         require(dict(paid) == {int(r): count for r, count in replay['paid_profiles'][orientation].items()}, 'local replay profile binding')
+     widths = [len(frames[word['final'][q]]) - len(frames[word['start'][q]]) for q in range(2 * V, n)]
+-    require(Counter(widths) == {4: 56, 5: 32, 7: 30, 8: 122, 9: 240}, 'current supplier width inventory')
++    require(Counter(widths) == EXPECTED_WIDTHS, 'current supplier width inventory')
+     return widths, paid
+ 
+ 
+@@ -305,7 +305,7 @@
+ 
+ 
+ def main():
+-    global T, EXPECTED_IDLE
++    global T, EXPECTED_IDLE, EXPECTED_WIDTHS
+     parser = argparse.ArgumentParser(description=__doc__)
+     parser.add_argument('--baseline-parent', type=Path, required=True)
+     parser.add_argument('--owners', type=Path, required=True)
+@@ -315,7 +315,9 @@
+     parser.add_argument('--out', type=Path, required=True)
+     parser.add_argument("--replicas", type=int, required=True)
+     parser.add_argument("--expected-idle", required=True)
++    parser.add_argument("--expected-widths", required=True)
+     args = parser.parse_args()
++    EXPECTED_WIDTHS = {int(k):v for k,v in json.loads(args.expected_widths).items()}
+     T = args.replicas
+     require(T == 37, "replica range")
+     EXPECTED_IDLE = {int(k): v for k,v in json.loads(args.expected_idle).items()}
diff --git a/research/three-demotions-t37-composition/MANIFEST.json b/research/three-demotions-t37-composition/MANIFEST.json
index 07591da758..cfe306c7f6 100644
--- a/research/three-demotions-t37-composition/MANIFEST.json
+++ b/research/three-demotions-t37-composition/MANIFEST.json
@@ -1,13 +1,20 @@
 {
-  "CANDIDATE.json": "f2edef3b48bddb93d5ffebc55e742f090322ecf34918a878bbd345a9701cc2ea",
+  "CANDIDATE.json": "2e8cf81a2c3a1560f57dfab2a330c38de8b9aa2c339507c98c5174291c4dceab",
   "GEOMETRY-CHECK.json": "c26f1998b20c70c3f5a46f7eb08a89953555881fbffcb1e9f79985e00131594f",
+  "GLOBAL-TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "INDEPENDENT-DERIVATION.patch": "ca48fe7dc8d7e905a45dca7972e2b97590f44482ffb2b8b0883c7b0ce07335ed",
+  "NATIVE-VALIDATION.json": "7e7bec3ac530a42b8e8fc6f446e3f3104c840591915f978ad1ccbef3aea65e09",
   "OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6",
   "PATTERN-FLOW.json": "d7accd36895a218d0db8e1434ea013c18d924059e4b32f25a21e3529539d7352",
   "PLAN.json": "f9b2592c5af1953c4c893e18be1e3444e7a07257e3054eceb99c42fd40351597",
   "PRICE.json": "2712af0e3a1719f09666f0029c59e3e5e441b4fca342b08b32f63ed78afbf428",
   "PROFILE.json": "3e1be872303172ad7ce286bd5525c64cec13d70198c72496de2f0cdb729247c2",
-  "README.md": "acedee1d3e0752dd405b89e3fc392f968b227fc7ace3dde57d9bc45c0f374191",
+  "README.md": "8c4244fe1727fbce4c29ff206855439498aa42880a5b15ad3e7816748a667114",
   "SEARCH.json": "c42084bbadd361f90dc21ffbd300c03b3739a57e9bf978e4272e0c822bca27bd",
+  "SPEC.json": "f7bc164032a7d98c94f1dbd1f54e1eb8e444ec68519824d9ce4c94973685c89d",
   "UPSTREAM-NOTICE.md": "b97fb4731e84aef736c58a9c126334eb5b8d3a057a8d9d45b4ffff24af65c38b",
-  "construct.py": "eee2edff41871b929e4c85289a2bd80842f5a5ae6130b8c7b0574178d4de9562"
+  "VALIDATION.json": "5e8ec5535f69f3c215ca21ef8c1af52545e74cdc5330386826dc5eae5456e1e3",
+  "construct.py": "eee2edff41871b929e4c85289a2bd80842f5a5ae6130b8c7b0574178d4de9562",
+  "upstream-layout.tar.gz": "a0cc229bb0fc9ab8ee5c14d5de87b3de31d1fcb793e99192c9cdc63781e794a0",
+  "verify.py": "c317259af90ef4881bad5ce18844f4cd55b55e925bba35d433c20c901ed00da1"
 }
diff --git a/research/three-demotions-t37-composition/NATIVE-VALIDATION.json b/research/three-demotions-t37-composition/NATIVE-VALIDATION.json
new file mode 100644
index 0000000000..76c0441969
--- /dev/null
+++ b/research/three-demotions-t37-composition/NATIVE-VALIDATION.json
@@ -0,0 +1,93 @@
+{
+  "status": "PASS_JOINT_ENTRANCES_COMPLETE_ADMISSION",
+  "kappa": "1675560947524449/1000000000000000000",
+  "kappa_decimal": "0.001675560947524449",
+  "complex_lower": "41959329101337756331/25000000000000000000000",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "controls": {
+    "admission": 69,
+    "bit_supplier": 12,
+    "independent_t16": 6,
+    "controller": 15
+  },
+  "entrance_controls": 27,
+  "outer_strict_inequalities": 47,
+  "native_steps": [
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 0.835344624996651
+    },
+    {
+      "step": "ledgers",
+      "exit_code": 0,
+      "seconds": 0.5655130000086501
+    },
+    {
+      "step": "local-replay",
+      "exit_code": 0,
+      "seconds": 3.576863082998898
+    },
+    {
+      "step": "wrappers",
+      "exit_code": 0,
+      "seconds": 1.4976038750028238
+    },
+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 98.2167668339971
+    }
+  ],
+  "native_semantic_artifacts": {
+    "CANONICAL-WORD.json.gz": "9885ff29b54f8d2de67d58d68e40a48b7897530d565f932fe63534caa3b405c9",
+    "LOCAL-PROGRAMS.json.gz": "1c81387e144fe92eadc6296d44d3fd80e6f9573e0269cadaf591f75de0661eed",
+    "LOCAL-CHECKS.json": "36c5685b24037dcf3767fc7d8d48c308da50f754fc50a05d760e399dd275b045",
+    "INDEPENDENT-LOCAL-REPLAY.json": "4ffe4b6ea3a1e027ef67a519e92253286d5cb794155eea1d1bef940521521a5f",
+    "CLIFFORD-RECIPES.json": "c58d2bd3492a031820aec434661c9297fa41d810ad661c651f139e9b592c6a4a",
+    "CLIFFORD-REVIEW.json": "3ca5c207027b17a305206541c9792b73cd6e4c92dbb7ada0cb765882af9f4f9e",
+    "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"
+  },
+  "native_reuse": false,
+  "parent_reuse": true,
+  "previous_kappa": "0.001675121647789207",
+  "scope": "Conditional native exact-complex witness replacing the third demoted entrance group 619 with group 635 and its different four-dimensional subspace, jointly refitting local recursive frames. Groups 603 and 611 remain demoted. Whole-helper T16 hosting and the unchanged PR589 bit supplier are retained. Scalar operations and their order are unchanged. PR559 exact-cover recurrence correction, bit bad-residue surcharge, and H1-H5 retained. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.",
+  "steps": [
+    {
+      "step": "build",
+      "exit_code": 0,
+      "seconds": 0.0711659169755876,
+      "log_sha256": "9a6250d812a76ece46c01f94bb2c8f9b1dba2b28a864be7c6713c4c9ffd8b4e3"
+    },
+    {
+      "step": "independent-local",
+      "exit_code": 0,
+      "seconds": 0.6289189170056488,
+      "log_sha256": "a6af87f7f1b51d2748b8f3b0b3f71fe05e5f528bab9ddb3eb59cbfe329d4bdac"
+    },
+    {
+      "step": "entrance-controls",
+      "exit_code": 0,
+      "seconds": 12.947597292019054,
+      "log_sha256": "ffd5989ea8b71b6b5660895a458d3a6db372deb1fb9aca6722da5f870c97aa32"
+    },
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 104.71991537499707,
+      "log_sha256": "5ca9f310247cb601c905ff30597baa4634847395d7826e9ab926a9876ced2514"
+    },
+    {
+      "step": "strict-global",
+      "exit_code": 0,
+      "seconds": 18.757017916999757,
+      "log_sha256": "7e150d52477f9263bc138fef7ead516fe8f41582664e3ce71d452549e54d4673"
+    },
+    {
+      "step": "all-replica-bound",
+      "exit_code": 0,
+      "seconds": 0.3606735000212211,
+      "log_sha256": "da1012ae7c38da9d5e6ec2315e58abbb011583ff2a5fef5c484adf851f413e2e"
+    }
+  ]
+}
diff --git a/research/three-demotions-t37-composition/README.md b/research/three-demotions-t37-composition/README.md
index ba2a766740..b2d33b3ebe 100644
--- a/research/three-demotions-t37-composition/README.md
+++ b/research/three-demotions-t37-composition/README.md
@@ -1,19 +1,24 @@
 # Joint entrance choices with T37 whole-owner packing
 
-The updated draft composes PR1148's joint entrance choices (head f1d8dc59288dcab77cae713c450d14069e7eec05) with a new exact T37 owner flow on PR1131's wave order. The candidate conditional price is **κ = 0.001675568675201533**, **0.0004611994%** above that PR1148 head at 0.001675560947524449.
+This composes PR1148's joint entrance choices (head `f1d8dc59288dcab77cae713c450d14069e7eec05`) with a new exact T37 owner flow on PR1131's wave order. The verified conditional value is **κ = 0.001675568675201533**, **0.0004611994%** above PR1148's T16 value `0.001675560947524449`.
 
-**Verification pending:** the 159,840 literal whole-helper roles in 333 calls, exact integer flow equations, bipartite matching decomposition, and two-engine rational profile price pass. Full native replay and strict T37 admission are in progress. This draft is not yet a verified new frontier.
+The construction has **159,840 whole-helper roles in 333 calls**, local profile `{1:2364,2:498,3:412,4:130,5:82,8:8}`, and idle profile `{1:834,48:11374}`. It attains PR1148's exact grid upper value for this fixed local word, helper inventory, whole-helper bin family and outer recipe. This scoped packing ceiling does not cover changed local words, mixed suppliers or other recursion geometries.
 
-The local paid profile is `{1:2364,2:498,3:412,4:130,5:82,8:8}`. The new flow has idle profile `{1:834,48:11374}` and targets the fixed-word grid upper value from PR1148. An upper relaxation alone does not establish physical realization; the draft supplies a concrete owner map for full admission.
+Validation passed:
+- Exact integer flow equations and literal bipartite matching reconstruction; every role is included and every capacity/window is checked.
+- Fresh native five-stage replay of the pinned joint-entrance word, including all 704 columns and 2,904 phase edges; independent local audit and 27 entrance controls.
+- Strict T37 provider binding, controller, invoice and assembly using the retained PR1129 admission engines: 69 admission, 12 bit, 15 controller and 7 independent owner controls; all 47 outer inequalities.
+- Independent checks of 2,016 disjoint pending-child axis relations. Prefix bound 775 < 1024 and physical row coefficient 17,495 < 20,161.
+- Portable package replay, using the explicitly supplied fresh native replay above and pinned parent geometry, returns `PASS_T37_JOINT_ENTRANCES_NATIVE_AND_STRICT_ADMISSION` at the stated κ. The fixed-family upper bound is separately recomputed with two exact engines.
 
-Package: `research/three-demotions-t37-composition/`. Reconstruct the owner map without an optimizer using:
+Package: `research/three-demotions-t37-composition/` (directory retained from the initial three-demotion draft; latest payload uses joint entrance groups 603, 611 and 635).
 
 ```sh
-python -B construct.py --flow PATTERN-FLOW.json --plan PLAN.json --out NEW_OUTPUT
+python -B research/three-demotions-t37-composition/verify.py --work /absolute/new/output-directory
 ```
 
-A standalone full verification wrapper and receipts will be added after verification. The package directory name is retained from the initial three-demotion composition; its latest payload uses joint entrance groups 603, 611 and 635.
+Python 3.11+, a C++ compiler and Boost headers are required. This default rebuilds the native provider. `--native-from /path/to/completed/native-replay` explicitly reuses a completed five-stage replay with word and semantic bindings checked; local controls and all T37 admission stages still rerun. Parent geometry is reused from archived pinned inputs and its actual windows are independently reconstructed. The package requires no network or optimization solver. Repository-wide hosted CI is separate from these focused local passes.
 
-Credit: Thomas DiFiore/Codex and PR1148's full local ancestry; seslly/shipstuff PR1111's group-635 lead; Ali Romman/Codex PR1129's integer flow, matching decomposition and T37 audit; PR1131's wave order; PR1074/1018, Rohan Arun's PR987, PR1030, PR864, Hao Yan/FanPUYen's PR858, PR870, Chafik Boukhalfa's PR795/890 duals, PR942, PR1091, and the unchanged PR589 bit supplier. New composition by Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0. Original notices retained.
+Credit: Thomas DiFiore/Codex and PR1148's full local ancestry; seslly/shipstuff PR1111's group-635 lead; Ali Romman/Codex PR1129's integer flow, matching decomposition and T37 audit; PR1131's wave order; PR1074/1018, Rohan Arun's PR987, PR1030, PR864, Hao Yan/FanPUYen's PR858, PR870, Chafik Boukhalfa's PR795/890 duals, PR942, PR1091, and the unchanged PR589 bit supplier. New composition by Rohan Arun with substantial OpenAI Codex assistance, Apache-2.0. Original notices and source pins are retained. `INDEPENDENT-DERIVATION.patch` shows the sole checker adaptation: the same inventory predicate now receives the new frozen width inventory as an input.
 
 All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and bit H1-H5 obligations remain. No unconditional multiplication theorem, full formalization, general sphere-packing optimality or runtime improvement is claimed.
diff --git a/research/three-demotions-t37-composition/SPEC.json b/research/three-demotions-t37-composition/SPEC.json
new file mode 100644
index 0000000000..e632a59929
--- /dev/null
+++ b/research/three-demotions-t37-composition/SPEC.json
@@ -0,0 +1,3670 @@
+{
+  "schema": "witness-spec/1",
+  "name": "three-demotions-t37",
+  "data": {
+    "plan_sha256": "f9b2592c5af1953c4c893e18be1e3444e7a07257e3054eceb99c42fd40351597",
+    "owners_sha256": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6"
+  },
+  "dispatch": [
+    [
+      0,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      2,
+      "gauge44"
+    ],
+    [
+      0,
+      3,
+      "gauge44"
+    ],
+    [
+      0,
+      4,
+      "gauge44"
+    ],
+    [
+      1,
+      0,
+      "gauge44"
+    ],
+    [
+      0,
+      5,
+      "gauge44"
+    ],
+    [
+      1,
+      1,
+      "gauge44"
+    ],
+    [
+      0,
+      6,
+      "gauge44"
+    ],
+    [
+      1,
+      2,
+      "gauge44"
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+}
diff --git a/research/three-demotions-t37-composition/VALIDATION.json b/research/three-demotions-t37-composition/VALIDATION.json
new file mode 100644
index 0000000000..820af708b6
--- /dev/null
+++ b/research/three-demotions-t37-composition/VALIDATION.json
@@ -0,0 +1,58 @@
+{
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+  "kappa": "1675568675201533/1000000000000000000",
+  "kappa_decimal": "0.001675568675201533",
+  "parent_geometry_reuse": true,
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+  "bit_controls": 12,
+  "controller_controls": 15,
+  "independent_owner_controls": 7,
+  "outer_inequalities": 47,
+  "stages": [
+    {
+      "name": "literal-construct",
+      "exit_code": 0,
+      "seconds": 1.7327544580039103,
+      "log_sha256": "ce4fc0163d16cf2b08abaaefea3ec34976569cd766bb86a61f9412053b4a742c"
+    },
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+      "exit_code": 0,
+      "seconds": 2.33080987498397,
+      "log_sha256": "f11fa04b34e62e5137a8228266ee1955f963128ffb783ef5ade370e8b135b0cd"
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+      "exit_code": 0,
+      "seconds": 0.643390792014543,
+      "log_sha256": "d7c4a4a1d066429336f6fdd6545082406e621138ce0297d580cb3ab23b68a27a"
+    },
+    {
+      "name": "demotion-controls",
+      "exit_code": 0,
+      "seconds": 13.084083583002212,
+      "log_sha256": "ffd5989ea8b71b6b5660895a458d3a6db372deb1fb9aca6722da5f870c97aa32"
+    },
+    {
+      "name": "strict-global",
+      "exit_code": 0,
+      "seconds": 36.06323958397843,
+      "log_sha256": "064dc71c00000a51bf79bb8dbad226c0deb529752e72a1c4acbe1c2845a28b7c"
+    },
+    {
+      "name": "fixed-family-upper",
+      "exit_code": 0,
+      "seconds": 0.37118070901487954,
+      "log_sha256": "da1012ae7c38da9d5e6ec2315e58abbb011583ff2a5fef5c484adf851f413e2e"
+    }
+  ],
+  "scope": "Conditional finite construction. Fresh native replay from pinned PR1148 word and strict T37 admission passed. Parent geometry is reused with pinned exact artifacts and independently reconstructed source-event windows. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global sphere-packing claim."
+}
diff --git a/research/three-demotions-t37-composition/upstream-layout.tar.gz b/research/three-demotions-t37-composition/upstream-layout.tar.gz
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diff --git a/research/three-demotions-t37-composition/verify.py b/research/three-demotions-t37-composition/verify.py
new file mode 100644
index 0000000000..6d1086191e
--- /dev/null
+++ b/research/three-demotions-t37-composition/verify.py
@@ -0,0 +1,43 @@
+"""Strict finite replay with fresh PR1148 native replay and a pinned parent geometry.
+Requires Python 3.11+, C++ and Boost. No network or optimization solver is used.
+"""
+import argparse,gzip,hashlib,importlib.util,json,os,shutil,subprocess,sys,tarfile,time
+from pathlib import Path
+P=Path(__file__).resolve().parent
+ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);ap.add_argument('--native-from',type=Path);a=ap.parse_args();work=a.work.resolve();assert __debug__ and not work.exists() and not work.is_relative_to(P)
+def rd(p):return json.loads(p.read_text())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+pins=rd(P/'MANIFEST.json');actual={str(x.relative_to(P)) for x in P.rglob('*') if x.is_file() and '__pycache__' not in x.parts and x.name!='MANIFEST.json'};assert actual==set(pins)
+for rel,h in pins.items():assert sha(P/rel)==h,rel
+work.mkdir();layout=work/'layout';layout.mkdir();tmp=work/'tmp';tmp.mkdir();env=dict(os.environ,TMPDIR=str(tmp),PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0')
+for k in ('PYTHONOPTIMIZE','WITNESS_SPEC','WITNESS_DISCOVER','WITNESS_RECORD'):env.pop(k,None)
+with tarfile.open(P/'upstream-layout.tar.gz') as t:
+ for m in t.getmembers():assert m.isfile() and not Path(m.name).is_absolute() and '..' not in Path(m.name).parts
+ t.extractall(layout,filter='data')
+R=layout/'owner37-round44';N=layout/'joint1148-round45';SRC=N/'source';tools=R/'candidate-tools-joint';data=R/'candidate-data';data.mkdir()
+for name in ['PLAN.json','OWNERS.json.gz','SPEC.json','PROFILE.json','GLOBAL-TEMPLATE.json.gz']:shutil.copy2(P/name,data/name)
+stages=[]
+def run(name,script,*args):
+ start=time.monotonic();log=work/(name+'.log')
+ with log.open('w') as f:r=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],cwd=layout,env=env,stdout=f,stderr=subprocess.STDOUT)
+ stages.append(dict(name=name,exit_code=r.returncode,seconds=time.monotonic()-start,log_sha256=sha(log)));(work/'STAGES.json').write_text(json.dumps(stages,indent=2));assert r.returncode==0,(name,log.read_text()[-5000:]);print('PASS',name,flush=True)
+run('literal-construct',P/'construct.py','--flow',P/'PATTERN-FLOW.json','--plan',P/'PLAN.json','--out',work/'constructed')
+assert gzip.decompress((work/'constructed/OWNERS.json.gz').read_bytes())==gzip.decompress((P/'OWNERS.json.gz').read_bytes())
+run('parent-and-plan',tools/'prepare.py','--construction',work/'constructed','--flow',P/'PATTERN-FLOW.json','--out',work/'reconstructed-data')
+assert rd(work/'reconstructed-data/PLAN.json')==rd(P/'PLAN.json')
+assert gzip.decompress((work/'reconstructed-data/GLOBAL-TEMPLATE.json.gz').read_bytes())==gzip.decompress((P/'GLOBAL-TEMPLATE.json.gz').read_bytes())
+word=SRC/'research/k8-joint-entrances/FULL-WORD.json.gz'
+run('local-recipe',SRC/'research/k8-joint-entrances/build_word.py','--out',work/'rebuilt-word.json.gz')
+assert gzip.decompress(word.read_bytes())==gzip.decompress((work/'rebuilt-word.json.gz').read_bytes())
+run('independent-local',SRC/'research/gauge44-slots/independent/audit_local.py','--word',word,'--main',SRC,'--output',work/'INDEPENDENT-LOCAL.json')
+run('demotion-controls',SRC/'research/k8-joint-entrances/controls.py','--out',work/'DEMOTION-CONTROLS.json')
+assert len(rd(work/'DEMOTION-CONTROLS.json')['rejected'])==27
+native=a.native_from.resolve() if a.native_from else work/'native'
+if not a.native_from:run('fresh-native',SRC/'research/k8-eight-ends/replay_native.py',word,native)
+assert gzip.decompress((native/'local/FULL-WORD.json.gz').read_bytes())==gzip.decompress(word.read_bytes())
+steps=rd(native/'STEPS.json');assert [x['step'] for x in steps]==['native','ledgers','local-replay','wrappers','phases'] and all(x['exit_code']==0 for x in steps)
+run('strict-global',tools/'replay.py','--data',data,'--work',work/'strict','--local',native/'local')
+r=rd(work/'strict/RESULT.json');assert r['status']=='PASS_STRICT_T37_THREE_DEMOTIONS' and r['kappa']==rd(P/'CANDIDATE.json')['kappa']
+run('fixed-family-upper',SRC/'research/k8-joint-entrances/independent/all_t_bound.py','--out',work/'UPPER.json')
+assert rd(work/'UPPER.json')['all_T_grid_upper']==r['kappa']
+result=dict(status='PASS_T37_JOINT_ENTRANCES_NATIVE_AND_STRICT_ADMISSION',kappa=r['kappa'],kappa_decimal=r['kappa_decimal'],parent_geometry_reuse=True,native_reuse=bool(a.native_from),local_controls=27,admission_controls=69,bit_controls=12,controller_controls=15,independent_owner_controls=7,outer_inequalities=47,stages=stages,scope=rd(P/'CANDIDATE.json')['scope']);(work/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n');print(result['status'],result['kappa_decimal'])

From aac9ce7d83e02989eed76e08815cfd2399214e90 Mon Sep 17 00:00:00 2001
From: rohanarun <rohan@getsupers.com>
Date: Tue, 13 Oct 2026 16:04:15 -0400
Subject: [PATCH 4/4] Conditional kappa 0.001675608585476885: X54 slot on the
 joint-entrance k8 word with exact T37 owners

Applies jeremykothe2's width-neutral X54 triangle-hybrid slot (#1130 recipe, identical edits
and frames) to tomdif's joint-entrance k8 word (#1148, groups 603/611/635). The helper width
inventory is unchanged, so #1169's exact T37 owner flow, owner map, windows and parent
geometry are reused as-is; only the provider identity is rebound to a fresh native replay of
the new word and the SPEC is re-frozen through the unchanged discovery/freeze path.
Local profile {3:+2,4:-4,5:+2}; strict T37 admission passes; the all-T fixed-family
signed-dual ceiling for the new word equals the attained value.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01TGoMCHAqctZe4wTb4Qr7VV
---
 research/joint-x54-t37/CANDIDATE.json         |     55 +
 research/joint-x54-t37/MANIFEST.json          |     59 +
 research/joint-x54-t37/NOTICE.md              |     28 +
 .../joint-x54-t37/PLAN-SOURCE-X54.json.gz     |    Bin 0 -> 6751 bytes
 research/joint-x54-t37/PLAN.json              | 230829 +++++++++++++++
 research/joint-x54-t37/PROFILE.json           |      9 +
 research/joint-x54-t37/README.md              |     85 +
 research/joint-x54-t37/RECIPE-X54-joint.json  |    163 +
 research/joint-x54-t37/SOURCE-PINS.json       |      7 +
 research/joint-x54-t37/SPEC.json              |   3670 +
 research/joint-x54-t37/all_t_bound_x54.py     |    182 +
 research/joint-x54-t37/build_word.py          |     12 +
 research/joint-x54-t37/evidence/UPPER.json    |    320 +
 .../evidence/discovery/RESULT.json            |    169 +
 .../evidence/discovery/STAGES.json            |     44 +
 .../evidence/discovery/WITNESS-RECORD.jsonl   |     35 +
 .../evidence/discovery/assembly.txt           |      1 +
 .../evidence/discovery/audit.txt              |     74 +
 .../joint-x54-t37/evidence/discovery/bind.txt |      1 +
 .../joint-x54-t37/evidence/discovery/emit.txt |     50 +
 .../evidence/discovery/freeze.txt             |      1 +
 .../evidence/discovery/independent.txt        |      1 +
 .../evidence/discovery/invoice.txt            |     35 +
 .../local/INDEPENDENT-LOCAL-BASE-JOINT.json   |    137 +
 .../evidence/local/INDEPENDENT-LOCAL.json     |    137 +
 .../evidence/local/X54-CONTROLS.json          |     78 +
 .../evidence/native/ARTIFACT-SHA256.json      |     12 +
 .../evidence/native/CLIFFORD-REVIEW.json      |     19 +
 .../native/INDEPENDENT-LOCAL-REPLAY.json      |     71 +
 .../evidence/native/LOCAL-CHECKS.json         |     36 +
 .../evidence/native/SCALAR-FRAME-AUDIT.json   |    712 +
 .../joint-x54-t37/evidence/native/STEPS.json  |     27 +
 .../evidence/native/WRAPPER-CHECKS.json       |    421 +
 .../joint-x54-t37/evidence/native/ledgers.txt |      2 +
 .../evidence/native/local-replay.txt          |      3 +
 .../joint-x54-t37/evidence/native/native.txt  |    230 +
 .../joint-x54-t37/evidence/native/phases.txt  |     16 +
 .../evidence/native/wrappers.txt              |      1 +
 .../evidence/strict/ADMISSION-CONTROLS.json   |    102 +
 .../evidence/strict/ASSEMBLY.json             |    344 +
 .../evidence/strict/BIT-CONTROLS.json         |     49 +
 .../evidence/strict/INDEPENDENT.json          |    119 +
 .../joint-x54-t37/evidence/strict/RESULT.json |    175 +
 .../joint-x54-t37/evidence/strict/STAGES.json |     50 +
 .../evidence/strict/admission.txt             |      1 +
 .../evidence/strict/assembly.txt              |      1 +
 .../joint-x54-t37/evidence/strict/audit.txt   |     74 +
 .../joint-x54-t37/evidence/strict/bind.txt    |      1 +
 .../joint-x54-t37/evidence/strict/bit.txt     |      1 +
 .../joint-x54-t37/evidence/strict/emit.txt    |     50 +
 .../evidence/strict/independent.txt           |      1 +
 .../joint-x54-t37/evidence/strict/invoice.txt |     35 +
 research/joint-x54-t37/prepare_x54.py         |     41 +
 research/joint-x54-t37/rebind_plan.py         |     27 +
 .../joint-x54-t37/vendor/barch/build_tri.py   |     87 +
 .../vendor/barch/run_controls.py              |     33 +
 research/joint-x54-t37/verify.py              |     61 +
 research/joint-x54-t37/x54_controls.py        |     10 +
 58 files changed, 238994 insertions(+)
 create mode 100644 research/joint-x54-t37/CANDIDATE.json
 create mode 100644 research/joint-x54-t37/MANIFEST.json
 create mode 100644 research/joint-x54-t37/NOTICE.md
 create mode 100644 research/joint-x54-t37/PLAN-SOURCE-X54.json.gz
 create mode 100644 research/joint-x54-t37/PLAN.json
 create mode 100644 research/joint-x54-t37/PROFILE.json
 create mode 100644 research/joint-x54-t37/README.md
 create mode 100644 research/joint-x54-t37/RECIPE-X54-joint.json
 create mode 100644 research/joint-x54-t37/SOURCE-PINS.json
 create mode 100644 research/joint-x54-t37/SPEC.json
 create mode 100644 research/joint-x54-t37/all_t_bound_x54.py
 create mode 100644 research/joint-x54-t37/build_word.py
 create mode 100644 research/joint-x54-t37/evidence/UPPER.json
 create mode 100644 research/joint-x54-t37/evidence/discovery/RESULT.json
 create mode 100644 research/joint-x54-t37/evidence/discovery/STAGES.json
 create mode 100644 research/joint-x54-t37/evidence/discovery/WITNESS-RECORD.jsonl
 create mode 100644 research/joint-x54-t37/evidence/discovery/assembly.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/audit.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/bind.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/emit.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/freeze.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/independent.txt
 create mode 100644 research/joint-x54-t37/evidence/discovery/invoice.txt
 create mode 100644 research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL-BASE-JOINT.json
 create mode 100644 research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL.json
 create mode 100644 research/joint-x54-t37/evidence/local/X54-CONTROLS.json
 create mode 100644 research/joint-x54-t37/evidence/native/ARTIFACT-SHA256.json
 create mode 100644 research/joint-x54-t37/evidence/native/CLIFFORD-REVIEW.json
 create mode 100644 research/joint-x54-t37/evidence/native/INDEPENDENT-LOCAL-REPLAY.json
 create mode 100644 research/joint-x54-t37/evidence/native/LOCAL-CHECKS.json
 create mode 100644 research/joint-x54-t37/evidence/native/SCALAR-FRAME-AUDIT.json
 create mode 100644 research/joint-x54-t37/evidence/native/STEPS.json
 create mode 100644 research/joint-x54-t37/evidence/native/WRAPPER-CHECKS.json
 create mode 100644 research/joint-x54-t37/evidence/native/ledgers.txt
 create mode 100644 research/joint-x54-t37/evidence/native/local-replay.txt
 create mode 100644 research/joint-x54-t37/evidence/native/native.txt
 create mode 100644 research/joint-x54-t37/evidence/native/phases.txt
 create mode 100644 research/joint-x54-t37/evidence/native/wrappers.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/ADMISSION-CONTROLS.json
 create mode 100644 research/joint-x54-t37/evidence/strict/ASSEMBLY.json
 create mode 100644 research/joint-x54-t37/evidence/strict/BIT-CONTROLS.json
 create mode 100644 research/joint-x54-t37/evidence/strict/INDEPENDENT.json
 create mode 100644 research/joint-x54-t37/evidence/strict/RESULT.json
 create mode 100644 research/joint-x54-t37/evidence/strict/STAGES.json
 create mode 100644 research/joint-x54-t37/evidence/strict/admission.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/assembly.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/audit.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/bind.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/bit.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/emit.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/independent.txt
 create mode 100644 research/joint-x54-t37/evidence/strict/invoice.txt
 create mode 100644 research/joint-x54-t37/prepare_x54.py
 create mode 100644 research/joint-x54-t37/rebind_plan.py
 create mode 100644 research/joint-x54-t37/vendor/barch/build_tri.py
 create mode 100644 research/joint-x54-t37/vendor/barch/run_controls.py
 create mode 100644 research/joint-x54-t37/verify.py
 create mode 100644 research/joint-x54-t37/x54_controls.py

diff --git a/research/joint-x54-t37/CANDIDATE.json b/research/joint-x54-t37/CANDIDATE.json
new file mode 100644
index 0000000000..79190f04e1
--- /dev/null
+++ b/research/joint-x54-t37/CANDIDATE.json
@@ -0,0 +1,55 @@
+{
+  "status": "PASS_X54_JOINT_ENTRANCES_T37_NATIVE_AND_STRICT_ADMISSION",
+  "kappa": "335121717095377/200000000000000000",
+  "kappa_decimal": "0.001675608585476885",
+  "conservative_kappa_decimal": "0.001675608582632503",
+  "previous_kappa": "0.001675568675201533",
+  "previous_pr": 1169,
+  "gain": "0.000000039910275352",
+  "gain_percent": "0.0023818943349009",
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 414,
+    "4": 126,
+    "5": 84,
+    "8": 8
+  },
+  "base_local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 412,
+    "4": 130,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 44,
+    "5": 44,
+    "7": 38,
+    "8": 114,
+    "9": 240
+  },
+  "idle_profile": {
+    "1": 834,
+    "48": 11374
+  },
+  "calls": 333,
+  "live": 33152,
+  "deficit": 11840,
+  "global_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "word_content_sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20",
+  "base_word_content_sha256": "1f66640293bde6c7e1df2d4ee0004c2de2327887a98575c5d975d6a14a8b7e74",
+  "pr1148_head": "f1d8dc59288dcab77cae713c450d14069e7eec05",
+  "pr1169_head": "13d02293a7af67d7e3bd2e4d7f1a2943ac20537e",
+  "pr1130_recipe": "RECIPE-X54-ends7.json",
+  "scope": "Conditional finite construction. Fresh native replay of the X54 joint-entrance word and strict T37 admission passed; PR1169 owner map and parent geometry reused with pinned exact artifacts and independently reconstructed source-event windows. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery, analytic transfer, PR559 recurrence correction and PR589 bit H1-H5 assumptions remain. No unconditional theorem, full Lean certification, or global sphere-packing claim."
+}
diff --git a/research/joint-x54-t37/MANIFEST.json b/research/joint-x54-t37/MANIFEST.json
new file mode 100644
index 0000000000..faec5032a6
--- /dev/null
+++ b/research/joint-x54-t37/MANIFEST.json
@@ -0,0 +1,59 @@
+{
+  "CANDIDATE.json": "5f28fa2a491d100f266f1ab15e7acc7186a1a671afe4e631dca589f739da4ff3",
+  "NOTICE.md": "cd16c4d21c2eddbeab9745b4097e7a8d258b4b69b067e73f415126e7ff9f0b18",
+  "PLAN-SOURCE-X54.json.gz": "d6b0609e9329ba9dbfe5f0cc64210ca8199308cccf8addccd79b19b6bf370ff1",
+  "PLAN.json": "0cace33792b458810f68c3995753235c4e48f24100aa1f5764385e67328b8f0e",
+  "PROFILE.json": "63bacd4fd794b6cd2d153462f643778a6dce829fc9e27d9c41013eadf6ee0e77",
+  "README.md": "6e5f545308b1d3af1bab65e26470895454060b344aac13b6d018e5c92aa8d786",
+  "RECIPE-X54-joint.json": "04f2331988fe04144642e8e2df144923e789f28c79ec2e83eb001fb1cb72b220",
+  "SOURCE-PINS.json": "47b4b0a91832deccf4fde1b31f7a12518cd9a9fe37df64f88bfaa04cd4b46a13",
+  "SPEC.json": "061569adc2122077e9b5c710c2abff4c3f1947b72672af7868347cccb3b2af5b",
+  "all_t_bound_x54.py": "9bd071ccfe11994c8b523b8967db45bbe312f413066f67bee19087e3afb3d7c2",
+  "build_word.py": "0a1d7deef536177982d056a2208876d2d8d1f22cf4463433ef424e7b9244c36b",
+  "evidence/UPPER.json": "b3f49f64c576aa87a058952e13a7c93d51e2f7138792bf3fa3ce7e55677d7a60",
+  "evidence/discovery/RESULT.json": "f1785512b1efc30e57b4e2421cb4092719499d2e77aef9c274eff3a5d75c850f",
+  "evidence/discovery/STAGES.json": "956f97630a5fc9aa79a679fa289205477e1ed468414b48ffeaf86245f4956c92",
+  "evidence/discovery/WITNESS-RECORD.jsonl": "177ae7c571dde3f4b527b5fca767428081d5c223761e803beca79c8ae06a8699",
+  "evidence/discovery/assembly.txt": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35",
+  "evidence/discovery/audit.txt": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4",
+  "evidence/discovery/bind.txt": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a",
+  "evidence/discovery/emit.txt": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9",
+  "evidence/discovery/freeze.txt": "a5849b5fcba6eed03e132b72b3e4efe7da0451456a0643a09f715ac44713ff5e",
+  "evidence/discovery/independent.txt": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e",
+  "evidence/discovery/invoice.txt": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca",
+  "evidence/local/INDEPENDENT-LOCAL-BASE-JOINT.json": "fb29e71acf17c3540bb2b5b4a1bcb04dd102e22b6b57aaed018ae224377c317f",
+  "evidence/local/INDEPENDENT-LOCAL.json": "45e6b19bfa554bbef2646fc2bd23586d4e8420828ef82000452aa9726d229117",
+  "evidence/local/X54-CONTROLS.json": "c82bf8be977a7b162164fcf0254dd7a404c2029479e92c035c15b1b97f4853dc",
+  "evidence/native/ARTIFACT-SHA256.json": "f23c8009992a970c357e53c947046f31e4000df2ee97c54607c129d3d1c6954d",
+  "evidence/native/CLIFFORD-REVIEW.json": "8106db62ba73e6b666762eecf51b419986ff21fac5a1b3507be55a0ab8037799",
+  "evidence/native/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+  "evidence/native/LOCAL-CHECKS.json": "658c80d13dc992e18186740f71e88aa4d9a76010bf8da2de77722970d83710e9",
+  "evidence/native/SCALAR-FRAME-AUDIT.json": "f931c64dab59e3a531e19ac63270125201858a6dd5bc0de76231d5129cf6647e",
+  "evidence/native/STEPS.json": "73b159231a6f4542eea6759e661b1aea0bf403ed40975cc1b1555cbb36f943f9",
+  "evidence/native/WRAPPER-CHECKS.json": "f2a005b54bea64d66633d8a82d0454348172da3b88361081a72126bf1d51744d",
+  "evidence/native/ledgers.txt": "c143c5a3825f6ffc475306281f800d30531826872b2f7857d088658f44e3f900",
+  "evidence/native/local-replay.txt": "dd643a58258431c3b07d3b06d9060c49677fa23b4fafc9f10988ed1f6867bd9a",
+  "evidence/native/native.txt": "c4c1c39f8d8de90d2ae7ec1042f6f605677f2a10dc5581b78e27ba47796a912e",
+  "evidence/native/phases.txt": "26aa98cff3975ab264c4e611a534193239a1fef2ba6e20ea4bd35a4e7d2f2923",
+  "evidence/native/wrappers.txt": "74b13cf8570ca2f32ce0018575b1b73e95af77a28e59d09556fec59260bdbba5",
+  "evidence/strict/ADMISSION-CONTROLS.json": "bf25c348fca6dd5b9faae7873c76af4489670c2ae6c2e5e5e3265747951b7b68",
+  "evidence/strict/ASSEMBLY.json": "5cb1346fe9c50314c6340f2ce7963a7fd3dbc73e3a4698e85c6c4f634c8c89ad",
+  "evidence/strict/BIT-CONTROLS.json": "d39e57c8e5f521c52cd20b313c0497649ec5d94b63c5f3b3f1ec1b65a02a63f0",
+  "evidence/strict/INDEPENDENT.json": "7ddeef8fc6af7b76b4d8e6dc0853ec53361a449841b117be962a97be1dfc3001",
+  "evidence/strict/RESULT.json": "be3370748c1a81de83b9b50a2b45b4df10156c9e1a912601cc94c25916f496f8",
+  "evidence/strict/STAGES.json": "0ed23dd723bc6f357e254ba1955b3a44cd697b17f18ed199294b2052d1ce9d32",
+  "evidence/strict/admission.txt": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3",
+  "evidence/strict/assembly.txt": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35",
+  "evidence/strict/audit.txt": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4",
+  "evidence/strict/bind.txt": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a",
+  "evidence/strict/bit.txt": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67",
+  "evidence/strict/emit.txt": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9",
+  "evidence/strict/independent.txt": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e",
+  "evidence/strict/invoice.txt": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca",
+  "prepare_x54.py": "6b8e079db07ca19df37063bb2a985740462edada7072b594196699575ecdfefb",
+  "rebind_plan.py": "9e11a46882984ca9c561c1a8c3ce18f7642b33cfedc90262fdf2d3a7f4aa54b0",
+  "vendor/barch/build_tri.py": "0fba65b31c2fd71864c291358bb0ad8d5f7e1be07e21df23f0ae73d7b966002e",
+  "vendor/barch/run_controls.py": "42639bf62bf57795e3ea615c1944c67efed00f28591333daeb3139bf63d04476",
+  "verify.py": "080608b066f3c797a7ff396e4b9e4a4586fbf43ddf8ad5563766744e8b24008e",
+  "x54_controls.py": "9764b36fda16801d3134f0f67b61870c6b28a1ae82f7809a0838fa2b6e975353"
+}
diff --git a/research/joint-x54-t37/NOTICE.md b/research/joint-x54-t37/NOTICE.md
new file mode 100644
index 0000000000..625e153b7b
--- /dev/null
+++ b/research/joint-x54-t37/NOTICE.md
@@ -0,0 +1,28 @@
+# Attribution and license
+
+New composition, provider rebind, adapted preparation and upper-bound scripts, and packaging by
+Rohan Arun, with substantial AI assistance (Claude). New work is under Apache-2.0.
+
+- **X54 slot.** The width-neutral eighth triangle-hybrid slot X54/E589 (holders 335, 367) is Jeremy Kothe's
+  (jeremykothe2) `RECIPE-X54-ends7.json` from PR1130. The edits and frames are unchanged; only the base-word
+  binding is new.
+- **Builder and controls.** `vendor/barch/build_tri.py` and `vendor/barch/run_controls.py` are NewBArch's
+  standard-library triangle-hybrid builder and controls, copied byte-for-byte from
+  `research/gauge44-slots/construction/barch` (sha256 `0fba65b3…` and `42639bf6…`).
+- **Base word.** The joint-entrance k8 word, its 27 entrance controls, native replay and local audit are from
+  PR1148 (Thomas DiFiore/Codex) and its full local ancestry. They are used unchanged from PR1169's pinned
+  `upstream-layout.tar.gz`.
+- **T37 owner map and admission.** The T37 owner map, pattern flow, parent geometry, literal construction and
+  strict admission tools are PR1169's (Rohan Arun/Codex), building on Ali Romman/Codex PR1129 (integer flow,
+  matching decomposition and T37 audit) and PR1131's wave order. They are reused unchanged from the sibling
+  package `research/three-demotions-t37-composition` (pinned in `SOURCE-PINS.json`).
+- **Adapted scripts.**
+  - `prepare_x54.py` adapts PR1169's `prepare.py`: the provider plan becomes an input, and the baseline label
+    changes.
+  - `all_t_bound_x54.py` adapts PR1148's `k8-joint-entrances/independent/all_t_bound.py`, itself from
+    jon314159's PR942 with Chafik Boukhalfa's PR795/890 dual prices. Only the pinned plan and the source-root
+    argument change.
+- **Bit supplier.** The PR589 bit supplier is unchanged.
+
+All original notices, licenses and AI disclosures in the cited packages are retained. This package does not
+claim authorship of any of those components.
diff --git a/research/joint-x54-t37/PLAN-SOURCE-X54.json.gz b/research/joint-x54-t37/PLAN-SOURCE-X54.json.gz
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new file mode 100644
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diff --git a/research/joint-x54-t37/PROFILE.json b/research/joint-x54-t37/PROFILE.json
new file mode 100644
index 0000000000..6d982012ab
--- /dev/null
+++ b/research/joint-x54-t37/PROFILE.json
@@ -0,0 +1,9 @@
+{
+  "1": 788046,
+  "2": 165834,
+  "3": 137862,
+  "4": 41958,
+  "5": 27972,
+  "8": 2664,
+  "48": 11374
+}
diff --git a/research/joint-x54-t37/README.md b/research/joint-x54-t37/README.md
new file mode 100644
index 0000000000..8c72b74c4f
--- /dev/null
+++ b/research/joint-x54-t37/README.md
@@ -0,0 +1,85 @@
+# X54 slot on the joint-entrance k8 word with exact T37 owner packing
+
+Conditional **κ = 0.001675608585476885** (exact `335121717095377/200000000000000000`).
+That is **+3.9910275352e-8**, or **0.0023819%**, above PR1169's `0.001675568675201533`.
+The conservative endpoint is 0.001675608582632503.
+
+## What changes
+
+This package adds one ingredient to PR1169: the width-neutral eighth triangle-hybrid slot **X54/E589** from PR1130 (jeremykothe2), with holders 335 and 367.
+PR1169 itself is PR1148's joint entrance choices (groups 603, 611, 635) with an exact T37 owner flow.
+
+- **Recipe.** The edits and frames are identical to `RECIPE-X54-ends7.json`. The recipe is rebased onto PR1148's joint-entrance word (`k8-joint-entrances/FULL-WORD.json.gz`, content sha `1f666402…`).
+- **Why the indices carry over.** The joint-entrance recipe changes only frames, so the gate indices are those of the eight-end word. None of the 39 changed B frames lies on an X54 position.
+- **Local profile.** `{1:2364, 2:498, 3:412, 4:130, 5:82, 8:8}` becomes `{1:2364, 2:498, 3:414, 4:126, 5:84, 8:8}`. The target merges a (4,1) climb pair into one 5, and the holder splits a 4 into (3,1).
+- **Helper widths.** The width inventory `{4:44, 5:44, 7:38, 8:114, 9:240}` is unchanged.
+- **Owners and geometry.** PR1169's 159,840 whole-helper roles in 333 calls are reused unchanged: owner map, pattern flow, windows, parent geometry, and idle `{1:834, 48:11374}`. Only the provider identity is new; it is rebound to a fresh native replay of the new word.
+- **Fixed-family ceiling.** The construction attains the all-T signed-dual grid ceiling for this fixed local word and inventory, again `0.001675608585476885`. That ceiling comes from `all_t_bound_x54.py`, PR1148's all-T bound with the X54 plan pinned.
+
+Global profile: `{1:788046, 2:165834, 3:137862, 4:41958, 5:27972, 8:2664, 48:11374}`. Live stock is 33,152 and the deficit is 11,840.
+
+## Validation (all passed)
+
+- **Words and local audit:**
+  - Rebuilt PR1148's joint-entrance word from its frozen recipe.
+  - Built the X54 word (content sha `ac95ff95…`).
+  - Independent exact local audit on all 704 columns in both orientations: `PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES`.
+- **Local controls:**
+  - PR1148's 27 entrance controls are rejected.
+  - NewBArch's slot controls: C0 identity, the recipe, and four mutants (dropped restore, FULL restore, dropped pre-read, late donation), run globally and for X=54. All 10 outcomes are as pinned.
+- **Native replay and rebind:**
+  - Fresh native five-stage replay of the X54 word: native, ledgers, local replay, wrappers, phases.
+  - The provider plan is rebound from that replay (15 identities) and must equal the shipped `PLAN-SOURCE-X54.json.gz`.
+- **Owners and plan:**
+  - PR1169's literal owner construction rebuilds the identical owner table.
+  - The plan, profile and template are reconstructed with independently recomputed source-event windows.
+- **Strict T37 admission** with the retained PR1129 engines:
+  - bind, emit, audit, invoice and assembly;
+  - 69 admission and 12 bit controls;
+  - the independent owner checker with 7 controls;
+  - all 47 outer inequalities.
+
+  Result: `PASS_STRICT_T37_THREE_DEMOTIONS` at the stated κ.
+- **Fixed-family all-T upper bound** equals κ.
+
+```sh
+python -B research/joint-x54-t37/verify.py --work /absolute/new/output-directory
+```
+
+Requirements:
+
+- Python 3.11+, a C++ compiler and Boost headers.
+- No network and no optimization solver.
+
+`--native-from DIR` reuses a completed five-stage native replay; its word binding is checked. The run reuses PR1169's `upstream-layout.tar.gz`, `construct.py`, `PATTERN-FLOW.json`, `OWNERS.json.gz` and `GLOBAL-TEMPLATE.json.gz` from the sibling package. `SOURCE-PINS.json` pins them.
+
+`evidence/` holds the receipts from a full run.
+
+## Scope
+
+This is a conditional finite construction. The following obligations remain:
+
+- all-size compiler;
+- common-label and mutable-source realization;
+- whole-call hosting;
+- precision/tape;
+- exact recovery;
+- analytic transfer;
+- the PR559 recurrence correction;
+- PR589 bit H1–H5.
+
+No unconditional multiplication theorem, full formalization, global packing optimality or runtime improvement is claimed.
+
+## Credit
+
+- PR1130 (jeremykothe2): the X54 slot recipe.
+- PR869: NewBArch triangle-hybrid builder and controls (vendored unchanged in `vendor/barch/`).
+- PR1148 (Thomas DiFiore/Codex) and its full local ancestry: the joint-entrance word.
+- PR1169: the T37 owner flow and packaging.
+- PR1129 (Ali Romman/Codex): integer flow, matching and T37 audit.
+- PR1131: wave order.
+- PR942, PR795 and PR890: the dual all-T bound.
+- PR589: the unchanged bit supplier.
+- PR987 (Rohan Arun): the slot method lineage.
+
+New composition by Rohan Arun with substantial AI assistance (Claude). Apache-2.0. Original notices are retained; see `NOTICE.md`.
diff --git a/research/joint-x54-t37/RECIPE-X54-joint.json b/research/joint-x54-t37/RECIPE-X54-joint.json
new file mode 100644
index 0000000000..ea77fe8ac3
--- /dev/null
+++ b/research/joint-x54-t37/RECIPE-X54-joint.json
@@ -0,0 +1,163 @@
+{
+ "base_sha256": "1f66640293bde6c7e1df2d4ee0004c2de2327887a98575c5d975d6a14a8b7e74",
+ "B_delete": [
+  44,
+  922,
+  933,
+  1196,
+  1212
+ ],
+ "B_insert": [
+  [
+   44,
+   [
+    "add",
+    219,
+    589,
+    -1,
+    1,
+    [
+     30
+    ]
+   ]
+  ],
+  [
+   898,
+   [
+    "add",
+    367,
+    589,
+    1,
+    1,
+    [
+     288,
+     166,
+     96,
+     20,
+     10,
+     1
+    ]
+   ]
+  ],
+  [
+   898,
+   [
+    "add",
+    335,
+    54,
+    1,
+    1,
+    [
+     267,
+     138,
+     75,
+     42,
+     25,
+     7
+    ]
+   ]
+  ],
+  [
+   1196,
+   [
+    "add",
+    219,
+    589,
+    1,
+    1,
+    [
+     256,
+     134,
+     64,
+     32,
+     20,
+     10,
+     1
+    ]
+   ]
+  ],
+  [
+   1212,
+   [
+    "add",
+    155,
+    54,
+    1,
+    1,
+    [
+     257,
+     128,
+     65,
+     32,
+     19,
+     10,
+     7
+    ]
+   ]
+  ]
+ ],
+ "B_frames": {},
+ "tail_insert": [
+  [
+   0,
+   [
+    "add",
+    367,
+    589,
+    -1,
+    1,
+    [
+     256,
+     128,
+     64,
+     32,
+     18,
+     10,
+     6,
+     1
+    ]
+   ]
+  ]
+ ],
+ "cleanup_prepend": [
+  [
+   "add",
+   335,
+   54,
+   -1,
+   1,
+   [
+    256,
+    128,
+    64,
+    32,
+    16,
+    8,
+    4,
+    2,
+    1
+   ]
+  ]
+ ],
+ "local_profile": {
+  "1": 2364,
+  "2": 498,
+  "3": 414,
+  "4": 126,
+  "5": 84,
+  "8": 8
+ },
+ "expect_sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20",
+ "variants": [
+  {
+   "X": 54,
+   "E": 589,
+   "hold": [
+    335,
+    367
+   ]
+  }
+ ],
+ "source": "Eighth triangle-hybrid slot X54/E589 (holders 335, 367) from jeremykothe2 #1130 (RECIPE-X54-ends7.json), identical edits and frames, rebased onto tomdif's #1148 joint-entrance k8 word (k8-joint-entrances, head f1d8dc59).",
+ "note": "early-cleanup gate frames in cleanup are kept as in base (package T-frame convention)"
+}
\ No newline at end of file
diff --git a/research/joint-x54-t37/SOURCE-PINS.json b/research/joint-x54-t37/SOURCE-PINS.json
new file mode 100644
index 0000000000..6a96f4b229
--- /dev/null
+++ b/research/joint-x54-t37/SOURCE-PINS.json
@@ -0,0 +1,7 @@
+{
+  "three-demotions-t37-composition/upstream-layout.tar.gz": "a0cc229bb0fc9ab8ee5c14d5de87b3de31d1fcb793e99192c9cdc63781e794a0",
+  "three-demotions-t37-composition/construct.py": "eee2edff41871b929e4c85289a2bd80842f5a5ae6130b8c7b0574178d4de9562",
+  "three-demotions-t37-composition/PATTERN-FLOW.json": "d7accd36895a218d0db8e1434ea013c18d924059e4b32f25a21e3529539d7352",
+  "three-demotions-t37-composition/OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6",
+  "three-demotions-t37-composition/GLOBAL-TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e"
+}
diff --git a/research/joint-x54-t37/SPEC.json b/research/joint-x54-t37/SPEC.json
new file mode 100644
index 0000000000..9734e95b40
--- /dev/null
+++ b/research/joint-x54-t37/SPEC.json
@@ -0,0 +1,3670 @@
+{
+  "schema": "witness-spec/1",
+  "name": "joint-x54-t37",
+  "data": {
+    "plan_sha256": "0cace33792b458810f68c3995753235c4e48f24100aa1f5764385e67328b8f0e",
+    "owners_sha256": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6"
+  },
+  "dispatch": [
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+      0,
+      0,
+      "gauge44"
+    ],
+    [
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+          5
+        ],
+        "local_adapters": 387088,
+        "local_primitive_bound": 10038870452398,
+        "compiler": 25934336,
+        "children": 3494,
+        "paid_profile": {
+          "1": 2364,
+          "2": 498,
+          "3": 414,
+          "4": 126,
+          "5": 84,
+          "8": 8
+        },
+        "program_hashes": {
+          "backward": "1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb",
+          "forward": "12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e"
+        },
+        "semantic_artifact_sha256": {
+          "CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af",
+          "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b",
+          "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec",
+          "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff",
+          "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+          "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d",
+          "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"
+        }
+      },
+      "semantic_phase_sha256": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d",
+      "expected_local": {
+        "forward": {
+          "events": 24769,
+          "macros": 19695,
+          "real_component_primitives": 198782,
+          "prefix_l1": "2765345371136269591/1024",
+          "coefficient_work_primitive_count": 98341
+        },
+        "backward": {
+          "events": 24769,
+          "macros": 19695,
+          "real_component_primitives": 198830,
+          "prefix_l1": "14824960514781440791821/64",
+          "coefficient_work_primitive_count": 98373
+        }
+      },
+      "wrappers": 240
+    }
+  },
+  "expected": {
+    "gain_baseline_kappa": "0.001675568675201533",
+    "hosted_residuals": 159840,
+    "rank_mass": 2408256,
+    "actual_73column_sigmas": 10803,
+    "cross_replica_helper_roles": 149072,
+    "idle_remainders": 12208,
+    "idle_remainder_profile": {
+      "1": 834,
+      "48": 11374
+    },
+    "global_profile": {
+      "1": 788046,
+      "2": 165834,
+      "3": 137862,
+      "4": 41958,
+      "5": 27972,
+      "8": 2664,
+      "48": 11374
+    },
+    "live": 33152,
+    "physical": 33642,
+    "conservative_kappa_decimal": "0.001675608582632503",
+    "kappa_decimal": "0.001675608585476885",
+    "complex_lower": "1678420962050942454559/1000000000000000000000000",
+    "conservative_complex_lower": "839210479598502224499/500000000000000000000000",
+    "kappa": "335121717095377/200000000000000000",
+    "assembly_controls_rejected": 69,
+    "provider_counts": {
+      "gauge44": 333
+    },
+    "mutations_rejected": 15
+  },
+  "pivot_swap": {
+    "recipe": "construction/leaver/PIVOT-SWAP-k8.json",
+    "sha256": "3ef7acf0cf67442a532f25b53d5fbeda76d3a84524118df8e003ca69b5cac0bb"
+  }
+}
diff --git a/research/joint-x54-t37/all_t_bound_x54.py b/research/joint-x54-t37/all_t_bound_x54.py
new file mode 100644
index 0000000000..e7c63e1e3c
--- /dev/null
+++ b/research/joint-x54-t37/all_t_bound_x54.py
@@ -0,0 +1,182 @@
+"""All-replica signed-dual bound for the X54 joint-entrance k8 whole-owner family.
+
+Adapted from k8-joint-entrances/independent/all_t_bound.py (tomdif/Codex, PR1148): the only changes are
+the pinned provider plan (the rebound X54 plan, local profile {3:+2,4:-4,5:+2}) and the source root argument.
+
+Adapted from jon314159's PR942 all_t_bound.py, with the joint-entrance k8 inventory.
+Dual prices: chafreaky's PR795/890. See ../NOTICE.md. Apache-2.0.
+Two exact rational engines certify the inequalities and endpoint signs.
+This is an upper relaxation only: it does not establish physical feasibility.
+"""
+import argparse
+import gzip
+from collections import Counter
+from fractions import Fraction as Q
+import hashlib
+import importlib.util
+import itertools
+import json
+from pathlib import Path
+import sys
+
+if sys.flags.optimize:
+    raise RuntimeError('Retained arithmetic assertions must stay enabled; do not use Python -O')
+
+HERE = Path(__file__).resolve().parent
+ROOT = None
+ENGINE = 'research/complex-k492-owner-repair/vendor/multicold/engines/'
+PINS = {'research/complex-k492-owner-repair/vendor/multicold/engines/moment.py': '81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482', 'research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py': 'aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098', }
+PLAN_SHA256 = 'd6b0609e9329ba9dbfe5f0cc64210ca8199308cccf8addccd79b19b6bf370ff1'
+WIDTHS = (4, 5, 7, 8, 9)
+PRICES = (-1, -20, -8, -2, 4)
+CAPACITIES = {8: (672, 2), 16: (448, 4), 32: (448, 8), 48: (448, -13)}
+INVENTORY = {4: 44, 5: 44, 7: 38, 8: 114, 9: 240}
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def load(relative, name):
+    spec = importlib.util.spec_from_file_location(name, ROOT/relative)
+    obj = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(obj)
+    return obj
+
+
+def dual_tables():
+    """Cartesian product enumeration and independently programmed recurrence."""
+    upper, count = {}, 0
+    for cap, (_, bonus) in CAPACITIES.items():
+        for vector in itertools.product(*(range(cap//w+1) for w in WIDTHS)):
+            used = sum(w*n for w, n in zip(WIDTHS, vector))
+            if used > cap:
+                continue
+            count += 1
+            r = cap-used
+            value = bonus+sum(p*n for p, n in zip(PRICES, vector))
+            upper[r] = max(upper.get(r, -10**6), value)
+    alt = {}
+    for cap, (_, bonus) in CAPACITIES.items():
+        scores = [None]*(cap+1)
+        scores[0] = 0
+        for fill in range(cap+1):
+            if scores[fill] is None:
+                continue
+            for width, price in zip(WIDTHS, PRICES):
+                nxt = fill+width
+                if nxt <= cap:
+                    proposal = scores[fill]+price
+                    if scores[nxt] is None or proposal > scores[nxt]:
+                        scores[nxt] = proposal
+        for fill, value in enumerate(scores):
+            if value is not None:
+                alt[cap-fill] = max(alt.get(cap-fill, -10**6), value+bonus)
+    need(upper == alt and count == 1163, 'two independently structured dual enumerations')
+    return upper, count
+
+
+def phi_pair(engine, kind, r, z):
+    if kind == 'mercator':
+        a, b = engine.logarithm(Q(73, r))
+        a, b = engine.exponential(z*a, z*b)
+    else:
+        a, b = engine.log_bounds(Q(73, r))
+        a, b = engine.exp_bounds(z*a)[0], engine.exp_bounds(z*b)[1]
+    return r*a, r*b
+
+
+def ratio_certificate(engine, kind, upper, z):
+    phi = {r: phi_pair(engine, kind, r, z) for r in upper if r}
+    cost = {r: (48*lo-r*phi[48][1], 48*hi-r*phi[48][0])
+            for r, (lo, hi) in phi.items() if r < 48}
+    credit = {r: 48*upper[r]+13*r for r in cost}
+    need(credit[1] == 925, 'rank-one credit')
+    need(all(a > 0 for a, b in cost.values()), 'positive non48 costs')
+    # c(r)-v(r)*c(1)/925 > 0 at every r != 1, so a single
+    # multiplier gives a supporting inequality for every count vector.
+    margins = {}
+    for r, (lo, hi) in cost.items():
+        if r == 1:
+            continue
+        c = credit[r]
+        rhs = c*cost[1][1 if c >= 0 else 0]/925
+        margins[r] = lo-rhs
+        need(margins[r] > 0, 'rank-one strictly optimal cost/credit ratio: '+str(r))
+    return dict(credit=credit, multiplier_interval=[str(cost[1][0]/925), str(cost[1][1]/925)],
+                strict_margin_by_rank={r: str(x) for r, x in margins.items()},
+                minimum_strict_margin=str(min(margins.values())))
+
+
+def main(out, root, plan_path):
+    global ROOT
+    ROOT = root.resolve()
+    for relative, expected in PINS.items():
+        need(hashlib.sha256((ROOT/relative).read_bytes()).hexdigest() == expected, 'source drift: '+relative)
+    need(hashlib.sha256(plan_path.read_bytes()).hexdigest() == PLAN_SHA256, 'source drift: X54 provider plan')
+    M = load(ENGINE+'moment.py', 'retained_mercator')
+    B = load(ENGINE+'base_two_moment.py', 'retained_atanh')
+    plan = json.loads(gzip.decompress(plan_path.read_bytes()))
+    provider = plan['provider_registry']['gauge44']
+    local = {int(r): n for r, n in provider['actual_paid_profile'].items()}
+    need(Counter(provider['widths']) == INVENTORY, 'fixed helper inventory')
+    actual_caps = Counter(v[0] for v in plan['windows'].values())
+    need({c: n*112//plan['T'] for c, n in actual_caps.items()} ==
+         {c: n for c, (n, _) in CAPACITIES.items()}, 'fixed bin inventory per replica')
+    upper, vectors = dual_tables()
+    mass = sum(c*n for c, (n, _) in CAPACITIES.items())-9*sum(r*n for r, n in INVENTORY.items())
+    signed = sum(n*p for n, p in CAPACITIES.values())+9*sum(INVENTORY[r]*p for r, p in zip(WIDTHS, PRICES))
+    need((mass, signed, upper[0], upper[48]) == (14778, -3568, 0, -13), 'fixed-family coefficients')
+    credit = 48*signed+13*mass
+    need(credit == 20850 and Q(credit, 925) == Q(834, 37), 'dual credit demand')
+    T = 37
+    idle = {1: 834, 48: 11374}
+    need(sum(r*n for r, n in idle.items()) == mass*T, 'formal relaxed idle mass')
+    need(sum(upper[r]*n for r, n in idle.items()) == signed*T, 'dual equality')
+    profile = Counter({r: 9*T*n for r, n in local.items()})
+    profile.update(idle)
+    live = 896*T
+    need(73*live-sum(r*n for r, n in profile.items()) == 320*T, 'rank deficit')
+    root = M.certify(profile, 73, live, False)
+    lo, hi = Q(root['lower']), Q(root['upper'])
+    signs = {}
+    for name, z in [('lower', lo), ('upper', hi)]:
+        first = M.moment(profile, 73, live, z)
+        second = B.moment(73, live, list(profile.items()), z)
+        need(first[1] < 1 and second[1] < 1 if name == 'lower' else first[0] > 1 and second[0] > 1,
+             'two exact moment signs at '+name)
+        signs[name] = dict(endpoint=str(z), mercator=[str(x-1) for x in first],
+                           atanh=[str(x-1) for x in second])
+    certs = {kind: ratio_certificate(engine, kind, upper, hi)
+             for kind, engine in [('mercator', M), ('atanh', B)]}
+    # The retained outer recipe always has a < b and kappa < a/(1+a).
+    # Therefore b < hi implies kappa < hi/(1+hi), without assuming that
+    # this formal relaxed profile can pass any finite or physical admission.
+    ceiling = hi/(1+hi)
+    ticks = ceiling*10**18
+    grid = Q((ticks.numerator-1)//ticks.denominator, 10**18)
+    result = dict(status='PASS_ALL_T_K8_JOINT_X54_SIGNED_DUAL_UPPER_RELAXATION',
+                  scope='All positive integer replica counts, fixed X54 joint-entrance local word and widths, nine calls and 896 live wires per replica, whole helpers and fixed 8/16/32/48 bin inventory. Geometry, time windows, finite invoice and physical realization are relaxed. This does not construct a supplier at the upper bound and does not cover different circuits, split helpers, banks or recursion geometries.',
+                  dual_bin_vectors=vectors, upper=upper, mass_per_replica=mass,
+                  signed_price_per_replica=signed, credit_per_replica=credit,
+                  normalized_idle={'1': '834/37', '48': '11374/37'},
+                  equality_requires_replica_count_multiple_of=37,
+                  formal_profile=dict(replicas=T, idle=idle, profile=dict(sorted(profile.items())),
+                                      live=live, deficit=320*T),
+                  root=root, two_engine_signs=signs, supporting_inequalities=certs,
+                  kappa_strict_rational_upper=str(ceiling), kappa_strict_upper_decimal=M.decimal(ceiling),
+                  all_T_grid_upper=str(grid), all_T_grid_upper_decimal=M.decimal(grid),
+                  source_sha256=dict(PINS, x54_provider_plan=PLAN_SHA256))
+    need(not out.exists(), 'output preservation: choose a new file')
+    out.write_text(json.dumps(result, indent=2)+'\n')
+    print(result['status'], result['all_T_grid_upper_decimal'])
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--out', type=Path, required=True)
+    parser.add_argument('--root', type=Path, required=True)
+    parser.add_argument('--plan', type=Path, required=True)
+    a = parser.parse_args()
+    main(a.out, a.root, a.plan)
diff --git a/research/joint-x54-t37/build_word.py b/research/joint-x54-t37/build_word.py
new file mode 100644
index 0000000000..66482acc52
--- /dev/null
+++ b/research/joint-x54-t37/build_word.py
@@ -0,0 +1,12 @@
+"""Apply the X54 triangle-hybrid slot (NewBArch builder, vendored unchanged) to PR1148's joint-entrance k8 word."""
+import argparse,gzip,hashlib,json,subprocess,sys
+from pathlib import Path
+P=Path(__file__).resolve().parent
+def main():
+ assert __debug__
+ ap=argparse.ArgumentParser();ap.add_argument('--base',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists()
+ r=json.loads((P/'RECIPE-X54-joint.json').read_text())
+ assert hashlib.sha256(gzip.decompress(a.base.read_bytes())).hexdigest()==r['base_sha256']
+ subprocess.run([sys.executable,'-B',str(P/'vendor/barch/build_tri.py'),str(a.base),str(P/'RECIPE-X54-joint.json'),str(a.out)],check=True)
+ assert hashlib.sha256(gzip.decompress(a.out.read_bytes())).hexdigest()==r['expect_sha256'];print('PASS_X54_ON_JOINT_ENTRANCES')
+if __name__=='__main__':main()
diff --git a/research/joint-x54-t37/evidence/UPPER.json b/research/joint-x54-t37/evidence/UPPER.json
new file mode 100644
index 0000000000..fa50e709a0
--- /dev/null
+++ b/research/joint-x54-t37/evidence/UPPER.json
@@ -0,0 +1,320 @@
+{
+  "status": "PASS_ALL_T_K8_JOINT_X54_SIGNED_DUAL_UPPER_RELAXATION",
+  "scope": "All positive integer replica counts, fixed X54 joint-entrance local word and widths, nine calls and 896 live wires per replica, whole helpers and fixed 8/16/32/48 bin inventory. Geometry, time windows, finite invoice and physical realization are relaxed. This does not construct a supplier at the upper bound and does not cover different circuits, split helpers, banks or recursion geometries.",
+  "dual_bin_vectors": 1163,
+  "upper": {
+    "8": 2,
+    "0": 0,
+    "1": 19,
+    "3": 7,
+    "4": 1,
+    "16": 4,
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+    "6": 14,
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+    "5": 20,
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+    "24": 6,
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+    "25": 0,
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+    "10": 15,
+    "27": -12,
+    "19": 11,
+    "20": 5,
+    "13": -3,
+    "22": -7,
+    "28": 7,
+    "21": -1,
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+    "39": -9,
+    "30": -5,
+    "40": -15,
+    "31": -11,
+    "41": -21,
+    "33": -23,
+    "34": -29,
+    "26": -6,
+    "43": -33,
+    "35": -10,
+    "36": -16,
+    "29": -24,
+    "38": -53,
+    "44": -14,
+    "37": -22
+  },
+  "mass_per_replica": 14778,
+  "signed_price_per_replica": -3568,
+  "credit_per_replica": 20850,
+  "normalized_idle": {
+    "1": "834/37",
+    "48": "11374/37"
+  },
+  "equality_requires_replica_count_multiple_of": 37,
+  "formal_profile": {
+    "replicas": 37,
+    "idle": {
+      "1": 834,
+      "48": 11374
+    },
+    "profile": {
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+      "2": 165834,
+      "3": 137862,
+      "4": 41958,
+      "5": 27972,
+      "8": 2664,
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+    },
+    "live": 33152,
+    "deficit": 11840
+  },
+  "root": {
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+    "upper": "0.00167842096205094245456",
+    "lower_endpoint_residual_upper": "-1.395869827269782001007075657441464084488161253145914279705909012552929E-24",
+    "upper_endpoint_residual_lower": "1.527920479861650159380141111064834089527067959147150898331046035891388E-24",
+    "strict_rational_signs": true,
+    "moment_minus_one_at_current_k_required_rate": [
+      "-0.002869394098219711473543233022576194051639332345674203209307759051476693",
+      "-0.002869394098219711473543233022576194051639332345674203209307759051402509"
+    ],
+    "nominal_k_ceiling_interval": [
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+      "0.001675608585476885521519980560408966729436722106042019405746302230008139"
+    ]
+  },
+  "two_engine_signs": {
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+      "mercator": [
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+      "atanh": [
+        "-139587/100000000000000000000000000000",
+        "-1395869/1000000000000000000000000000000"
+      ]
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+    "upper": {
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+      ],
+      "atanh": [
+        "19099/12500000000000000000000000000",
+        "1527921/1000000000000000000000000000000"
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+      },
+      "minimum_strict_margin": "6985145833163862727316472971208295762155506177610375553192654194133976195789296937365350093992432394703587682973310684543281757142262260655984707113691498039810676450644697815191013513441265882247922906497201586134069801481691420182236157848942312478199210352204680678767381403379736961006612909101393224628219797344596874456590424610089975519172190004787375365112997102984916715899297642800047160837227437458376930571616172599349500658406312202229300709422827788778651319071544860440146940598434825007733739743752003458277157195518213043286113545185861234253138811369135396152509760603968811817706154265962906148670866657054631774778192720170783967947074136701401329263775539811464930219627984623533527228233605510852329018073274501/23777037278974163391545008148113942932537746680334422241259680847600689095126676887136631678347534306730929544926311791641637682914733886718750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
+    }
+  },
+  "kappa_strict_rational_upper": "10490131012818390341/6260490131012818390341",
+  "kappa_strict_upper_decimal": "0.001675608585476885521519980560408966729436722106042019405746302230008139",
+  "all_T_grid_upper": "335121717095377/200000000000000000",
+  "all_T_grid_upper_decimal": "0.001675608585476885",
+  "source_sha256": {
+    "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "x54_provider_plan": "d6b0609e9329ba9dbfe5f0cc64210ca8199308cccf8addccd79b19b6bf370ff1"
+  }
+}
diff --git a/research/joint-x54-t37/evidence/discovery/RESULT.json b/research/joint-x54-t37/evidence/discovery/RESULT.json
new file mode 100644
index 0000000000..580a3306bd
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/RESULT.json
@@ -0,0 +1,169 @@
+{
+  "status": "DISCOVERY",
+  "kappa": "335121717095377/200000000000000000",
+  "kappa_decimal": "0.001675608585476885",
+  "steps": [
+    {
+      "name": "bind",
+      "seconds": 0.9055078659985156,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 26.194827993000217,
+      "exit_code": 0,
+      "log_sha256": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9"
+    },
+    {
+      "name": "audit",
+      "seconds": 94.56764901200222,
+      "exit_code": 0,
+      "log_sha256": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.2193918939992727,
+      "exit_code": 0,
+      "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.9823604740013252,
+      "exit_code": 0,
+      "log_sha256": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35"
+    },
+    {
+      "name": "freeze",
+      "seconds": 0.0655146210010571,
+      "exit_code": 0,
+      "log_sha256": "a5849b5fcba6eed03e132b72b3e4efe7da0451456a0643a09f715ac44713ff5e"
+    },
+    {
+      "name": "independent",
+      "seconds": 3.3540156460003345,
+      "exit_code": 0,
+      "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+    }
+  ],
+  "independent": {
+    "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+    "roles": 159840,
+    "calls": 333,
+    "source_events_per_replica": 30,
+    "expanded_replica_events": 1110,
+    "bridge_events": 333,
+    "literal_windows": 666,
+    "checked_whole_helper_widths": 159840,
+    "checked_busy_family_windows": 159840,
+    "orthogonal_port_bases": 112,
+    "actual_73_axis_charts": 10803,
+    "checked_slice_prefixes": 74592,
+    "local_profile": {
+      "1": 2364,
+      "2": 498,
+      "3": 414,
+      "4": 126,
+      "5": 84,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 44,
+      "5": 44,
+      "7": 38,
+      "8": 114,
+      "9": 240
+    },
+    "idle": {
+      "1": 834,
+      "48": 11374
+    },
+    "profile": {
+      "1": 788046,
+      "2": 165834,
+      "3": 137862,
+      "4": 41958,
+      "5": 27972,
+      "8": 2664,
+      "48": 11374
+    },
+    "live": 33152,
+    "physical": 33642,
+    "rank_mass": 2408256,
+    "deficit": 11840,
+    "namespace": {
+      "data": [
+        0,
+        33152
+      ],
+      "centres": [
+        33152,
+        33160
+      ],
+      "tableau": [
+        33160,
+        33640
+      ],
+      "coefficient": [
+        33640,
+        33642
+      ]
+    },
+    "local_prefix_bits": 68,
+    "local_prefix_from_native_receipt": true,
+    "local_profile_recounted": true,
+    "prefix_formula": {
+      "local_scalar": 68,
+      "input_l2": 37,
+      "invocations": 333,
+      "bridges": 333,
+      "margin": 4
+    },
+    "prefix_bits": 775,
+    "charged_prefix_bits": 1024,
+    "physical_stock_bits": 2643,
+    "physical_row_coefficient": 17495,
+    "row_limit": 20161,
+    "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+    "disjoint_pending_child_axis_checks": 2016,
+    "controls_rejected": [
+      {
+        "name": "private_namespace_collision",
+        "reason": "private-namespace collision"
+      },
+      {
+        "name": "copy_replica_alias",
+        "reason": "role invocation time"
+      },
+      {
+        "name": "missing_whole_helper",
+        "reason": "complete helper role count"
+      },
+      {
+        "name": "split_whole_helper",
+        "reason": "complete helper role count"
+      },
+      {
+        "name": "truncated_helper_width",
+        "reason": "whole-helper residual width"
+      },
+      {
+        "name": "cross_idle_boundary",
+        "reason": "strict bridge-aware idle window"
+      },
+      {
+        "name": "cross_child_pending_axis_alias",
+        "reason": "overlapping pending children on one family"
+      }
+    ],
+    "input_sha256": {
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "/tmp/jx/native/local/CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+      "/tmp/jx/native/local/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+      "/tmp/jx/ddisc/OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6"
+    }
+  },
+  "scope": "Conditional finite construction only; unchanged native provider independently replayed from PR1148; all inherited theorem obligations retained."
+}
\ No newline at end of file
diff --git a/research/joint-x54-t37/evidence/discovery/STAGES.json b/research/joint-x54-t37/evidence/discovery/STAGES.json
new file mode 100644
index 0000000000..7b60c1e33c
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/STAGES.json
@@ -0,0 +1,44 @@
+[
+  {
+    "name": "bind",
+    "seconds": 0.9055078659985156,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 26.194827993000217,
+    "exit_code": 0,
+    "log_sha256": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9"
+  },
+  {
+    "name": "audit",
+    "seconds": 94.56764901200222,
+    "exit_code": 0,
+    "log_sha256": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4"
+  },
+  {
+    "name": "invoice",
+    "seconds": 3.2193918939992727,
+    "exit_code": 0,
+    "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.9823604740013252,
+    "exit_code": 0,
+    "log_sha256": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35"
+  },
+  {
+    "name": "freeze",
+    "seconds": 0.0655146210010571,
+    "exit_code": 0,
+    "log_sha256": "a5849b5fcba6eed03e132b72b3e4efe7da0451456a0643a09f715ac44713ff5e"
+  },
+  {
+    "name": "independent",
+    "seconds": 3.3540156460003345,
+    "exit_code": 0,
+    "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+  }
+]
\ No newline at end of file
diff --git a/research/joint-x54-t37/evidence/discovery/WITNESS-RECORD.jsonl b/research/joint-x54-t37/evidence/discovery/WITNESS-RECORD.jsonl
new file mode 100644
index 0000000000..34c13075d8
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/WITNESS-RECORD.jsonl
@@ -0,0 +1,35 @@
+["data.plan_sha256", "0cace33792b458810f68c3995753235c4e48f24100aa1f5764385e67328b8f0e"]
+["providers.gauge44.inventory", {"4": 44, "5": 44, "7": 38, "8": 114, "9": 240}]
+["providers.gauge44.native_negative_controls", 25]
+["providers.gauge44.phase_edges", 2900]
+["providers.gauge44.expected_profile", {"1": 2364, "2": 498, "3": 414, "4": 126, "5": 84, "8": 8}]
+["providers.gauge44.artifact_semantic_sha256", {"CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af", "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b", "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec", "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff", "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c", "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d", "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"}]
+["providers.gauge44.inventory", {"4": 44, "5": 44, "7": 38, "8": 114, "9": 240}]
+["providers.gauge44.artifact_semantic_sha256", {"CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af", "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b", "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec", "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff", "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c", "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d", "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"}]
+["expected.hosted_residuals", 159840]
+["expected.rank_mass", 2408256]
+["expected.actual_73column_sigmas", 10803]
+["expected.cross_replica_helper_roles", 149072]
+["expected.idle_remainders", 12208]
+["providers.gauge44.entering", 192]
+["providers.gauge44.entrance", 372]
+["providers.gauge44.inventory", {"4": 44, "5": 44, "7": 38, "8": 114, "9": 240}]
+["providers.gauge44.width_digest", "3e2624964db4f881ad1404d94ec595b3d1baba07bef90cf9037d802cc6299d11"]
+["providers.gauge44.expected_profile", {"1": 2364, "2": 498, "3": 414, "4": 126, "5": 84, "8": 8}]
+["providers.gauge44.program_hashes", {"backward": "1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb", "forward": "12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e"}]
+["providers.gauge44.artifacts.LOCAL-CHECKS.json", "658c80d13dc992e18186740f71e88aa4d9a76010bf8da2de77722970d83710e9"]
+["providers.gauge44.artifacts.CLIFFORD-RECIPES.json", "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c"]
+["providers.gauge44.artifacts.RESIDUAL-ADAPTERS.json", "c099207d60ab49392bcadcaf7e9cbcfe01178e732f14e2591a8c3463162460d7"]
+["providers.gauge44.artifact_semantic_sha256", {"CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af", "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b", "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec", "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff", "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c", "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d", "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"}]
+["providers.gauge44.complete_contract", {"local": {"backward": {"events": 24769, "macros": 19695, "real_component_primitives": 198830, "prefix_l1": "14824960514781440791821/64", "prefix_bits": 68, "coefficient_work_primitive_count": 98373, "all_exact_columns": 704, "dirty_helper_columns": 480, "all_dirty_helper_columns_restored": true, "private_centres_and_coefficient_work_cleared": true, "pre_wrappers": 240, "post_wrappers": 240, "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"}, "forward": {"events": 24769, "macros": 19695, "real_component_primitives": 198782, "prefix_l1": "2765345371136269591/1024", "prefix_bits": 52, "coefficient_work_primitive_count": 98341, "all_exact_columns": 704, "dirty_helper_columns": 480, "all_dirty_helper_columns_restored": true, "private_centres_and_coefficient_work_cleared": true, "pre_wrappers": 240, "post_wrappers": 240, "endpoint_evidence": "Hash-bound fresh INDEPENDENT-LOCAL-REPLAY.json"}}, "helpers": 480, "centres": 8, "v": 112, "h": 9, "n": 704, "entering_helpers": 192, "entrance_rank": 372, "terminal_codimension": 214, "hyperplane_ended_helpers": 78, "cold_hyperplane_ended_helpers": 48, "width_inventory": {"4": 44, "5": 44, "7": 38, "8": 114, "9": 240}, "widths": [9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 8, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 8, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 4, 9, 4, 9, 4, 9, 9, 9, 9, 4, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 8, 8, 8, 9, 8, 8, 9, 9, 9, 9, 8, 9, 7, 7, 8, 9, 8, 8, 9, 9, 9, 9, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 7, 8, 8, 9, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 9, 8, 9, 8, 8, 8, 8, 8, 7, 7, 9, 8, 9, 8, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 4, 8, 4, 4, 4, 8, 8, 8, 4, 8, 4, 4, 4, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 4, 8, 4, 4, 4, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5, 8, 8, 8, 5, 8, 5, 5, 5], "local_adapters": 387088, "local_primitive_bound": 10038870452398, "compiler": 25934336, "children": 3494, "paid_profile": {"1": 2364, "2": 498, "3": 414, "4": 126, "5": 84, "8": 8}, "program_hashes": {"backward": "1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb", "forward": "12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e"}, "semantic_artifact_sha256": {"CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af", "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b", "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec", "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff", "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c", "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d", "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"}}]
+["providers.gauge44.semantic_phase_sha256", "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d"]
+["providers.gauge44.expected_local.forward", {"events": 24769, "macros": 19695, "real_component_primitives": 198782, "prefix_l1": "2765345371136269591/1024", "coefficient_work_primitive_count": 98341}]
+["providers.gauge44.wrappers", 240]
+["providers.gauge44.expected_local.backward", {"events": 24769, "macros": 19695, "real_component_primitives": 198830, "prefix_l1": "14824960514781440791821/64", "coefficient_work_primitive_count": 98373}]
+["providers.gauge44.wrappers", 240]
+["expected.idle_remainder_profile", {"1": 834, "48": 11374}]
+["expected.global_profile", {"1": 788046, "2": 165834, "3": 137862, "4": 41958, "5": 27972, "8": 2664, "48": 11374}]
+["expected.live", 33152]
+["expected.physical", 33642]
+["expected.conservative_kappa_decimal", "0.001675608582632503"]
+["expected.kappa_decimal", "0.001675608585476885"]
diff --git a/research/joint-x54-t37/evidence/discovery/assembly.txt b/research/joint-x54-t37/evidence/discovery/assembly.txt
new file mode 100644
index 0000000000..c08f883a47
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/assembly.txt
@@ -0,0 +1 @@
+PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001675608585476885
diff --git a/research/joint-x54-t37/evidence/discovery/audit.txt b/research/joint-x54-t37/evidence/discovery/audit.txt
new file mode 100644
index 0000000000..080ac0b54b
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/audit.txt
@@ -0,0 +1,74 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "complex_template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "complex_live": 33152,
+  "complex_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "complex_hosted_residuals": 159840,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "entering_helper_roles": 79920,
+  "cross_replica_helper_roles": 149072,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 159840,
+  "complete_invocations": 333,
+  "actual_orthogonal_73column_maps": 10803,
+  "actual_sigma_stream_sha256": "084c91aec13cba8adf58d7680c54253433734ac10ad67cc6a5b3d20789320f07",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 12208,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af",
+      "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b",
+      "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec",
+      "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff",
+      "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+      "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d",
+      "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 44,
+      "5": 44,
+      "7": 38,
+      "8": 114,
+      "9": 240
+    }
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/joint-x54-t37/evidence/discovery/bind.txt b/research/joint-x54-t37/evidence/discovery/bind.txt
new file mode 100644
index 0000000000..a964929571
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/bind.txt
@@ -0,0 +1 @@
+PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING
diff --git a/research/joint-x54-t37/evidence/discovery/emit.txt b/research/joint-x54-t37/evidence/discovery/emit.txt
new file mode 100644
index 0000000000..43d882a654
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/emit.txt
@@ -0,0 +1,50 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "parent_template_sha256": "514e59314c8e2fa3c22d0a48083816f6686211090835e8f8775318c1c3e992d8",
+  "live": 33152,
+  "physical": 33642,
+  "global_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "maxchild": 48,
+  "hosted_residuals": 159840,
+  "banks_per_stage": [
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "entering_helper_roles": 79920,
+  "unique_actual_73column_sigmas": 10803,
+  "sigma_stream_sha256": "084c91aec13cba8adf58d7680c54253433734ac10ad67cc6a5b3d20789320f07",
+  "cross_replica_helper_roles": 149072,
+  "asynchronous_order_sha256": "84f030a59dde4fa4635988ef0931ebae66964b3a202df79d38247fbe8a5592dc",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "cf20b3bfdfc2c92fabfbec492ae441d4fbf670ed5d2fc42e4f89d6011695f315",
+    "providers/gauge44/LOCAL-CHECKS.json": "658c80d13dc992e18186740f71e88aa4d9a76010bf8da2de77722970d83710e9",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "c099207d60ab49392bcadcaf7e9cbcfe01178e732f14e2591a8c3463162460d7",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "8106db62ba73e6b666762eecf51b419986ff21fac5a1b3507be55a0ab8037799"
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/joint-x54-t37/evidence/discovery/freeze.txt b/research/joint-x54-t37/evidence/discovery/freeze.txt
new file mode 100644
index 0000000000..db0523941d
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/freeze.txt
@@ -0,0 +1 @@
+Frozen exact witness for strict replay: 0.001675608585476885
diff --git a/research/joint-x54-t37/evidence/discovery/independent.txt b/research/joint-x54-t37/evidence/discovery/independent.txt
new file mode 100644
index 0000000000..3bffc24f17
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/independent.txt
@@ -0,0 +1 @@
+PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW roles=159840 controls=7
diff --git a/research/joint-x54-t37/evidence/discovery/invoice.txt b/research/joint-x54-t37/evidence/discovery/invoice.txt
new file mode 100644
index 0000000000..81de5dd3c2
--- /dev/null
+++ b/research/joint-x54-t37/evidence/discovery/invoice.txt
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "selected_real_component_primitives": 66201510,
+  "selected_coefficient_work_primitive_count": 32752289,
+  "global_prefix_bits": 775,
+  "finite": {
+    "physical_stock_bits": 2643,
+    "router_bits": 7991,
+    "literal_bits": 35286,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  }
+}
diff --git a/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL-BASE-JOINT.json b/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL-BASE-JOINT.json
new file mode 100644
index 0000000000..ee395965e7
--- /dev/null
+++ b/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL-BASE-JOINT.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "FULL-WORD.json.gz",
+  "content_sha256": "1f66640293bde6c7e1df2d4ee0004c2de2327887a98575c5d975d6a14a8b7e74",
+  "compressed_sha256": "a0622d86259c4163e58cf0677ce575b6039a8ae4c95aa6d8b82a8163cbd42718",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 412,
+    "4": 130,
+    "5": 82,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 44,
+    "5": 44,
+    "7": 38,
+    "8": 114,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 1.7030117719987174,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL.json b/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL.json
new file mode 100644
index 0000000000..4be97cb0b2
--- /dev/null
+++ b/research/joint-x54-t37/evidence/local/INDEPENDENT-LOCAL.json
@@ -0,0 +1,137 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES",
+  "input_file": "JX54.json.gz",
+  "content_sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20",
+  "compressed_sha256": "fcef92874411635a91464bd3851b3704be96be5f0ae7d51ac7e2ef16eed6efa9",
+  "parent_center_interface": {
+    "parent_path": "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz",
+    "parent_file_sha256": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "transport_tau": 43,
+    "ordered_frame_bases_match": true,
+    "all_ports_match": true,
+    "transported_centers": [
+      92,
+      57,
+      81,
+      224,
+      11,
+      240,
+      9,
+      256
+    ],
+    "source_centers": [
+      92,
+      57,
+      81,
+      11,
+      9
+    ],
+    "ordered_frame_bases": [
+      [
+        256,
+        128,
+        64,
+        34,
+        16,
+        10,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ],
+      [
+        256,
+        128,
+        66,
+        32,
+        18,
+        8,
+        4,
+        1
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        5,
+        3
+      ],
+      [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        4,
+        2
+      ],
+      [
+        256,
+        128,
+        68,
+        32,
+        16,
+        12,
+        2,
+        1
+      ]
+    ]
+  },
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "entering": 192,
+  "lowends": 78,
+  "coldends": 48,
+  "compensation_gates": 7208,
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 414,
+    "4": 126,
+    "5": 84,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 44,
+    "5": 44,
+    "7": 38,
+    "8": 114,
+    "9": 240
+  },
+  "checked_columns": 704,
+  "elapsed_seconds": 1.5735924869986775,
+  "scope": "Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing."
+}
diff --git a/research/joint-x54-t37/evidence/local/X54-CONTROLS.json b/research/joint-x54-t37/evidence/local/X54-CONTROLS.json
new file mode 100644
index 0000000000..9bb8f99589
--- /dev/null
+++ b/research/joint-x54-t37/evidence/local/X54-CONTROLS.json
@@ -0,0 +1,78 @@
+{
+ "C0_identity": {
+  "ok": true,
+  "out": "{\"control\": null, \"sha256\": \"1f66640293bde6c7e1df2d4ee0004c2de2327887a98575c5d975d6a14a8b7e74\"}"
+ },
+ "recipe": {
+  "ok": true,
+  "build": {
+   "control": null,
+   "sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20"
+  },
+  "audit_tail": "}"
+ },
+ "drop_restore": {
+  "ok": true,
+  "build": {
+   "control": "drop_restore",
+   "sha256": "dfd02eed9ef1b7c57646af57507f9e89292d7f1ec279f3be563c9e2e50bc8738"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [108, 111, 328, 334, 335, 511, 519])"
+ },
+ "restore_full": {
+  "ok": true,
+  "build": {
+   "control": "restore_full",
+   "sha256": "55399440fc646fd786bd429f27b8398df60bba8fbe594d7530822b3657ec72ac"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [44, 47, 359, 360, 366, 367, 519, 543])"
+ },
+ "drop_preread": {
+  "ok": true,
+  "build": {
+   "control": "drop_preread",
+   "sha256": "a425d0c0517d41637828917ccfe0f79a63effd8d47287fbf7764bf01ea82df21"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "donation_after": {
+  "ok": true,
+  "build": {
+   "control": "donation_after",
+   "sha256": "4df4df7f74d18e14ee58ab0196aafe58286a5f1c85043f4132501da02aa33f6c"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "drop_restore@54": {
+  "ok": true,
+  "build": {
+   "control": "drop_restore@54",
+   "sha256": "dfd02eed9ef1b7c57646af57507f9e89292d7f1ec279f3be563c9e2e50bc8738"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [108, 111, 328, 334, 335, 511, 519])"
+ },
+ "restore_full@54": {
+  "ok": true,
+  "build": {
+   "control": "restore_full@54",
+   "sha256": "55399440fc646fd786bd429f27b8398df60bba8fbe594d7530822b3657ec72ac"
+  },
+  "audit_tail": "RuntimeError: all-column endpoint failure (False, [44, 47, 359, 360, 366, 367, 519, 543])"
+ },
+ "drop_preread@54": {
+  "ok": true,
+  "build": {
+   "control": "drop_preread@54",
+   "sha256": "a425d0c0517d41637828917ccfe0f79a63effd8d47287fbf7764bf01ea82df21"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ },
+ "donation_after@54": {
+  "ok": true,
+  "build": {
+   "control": "donation_after@54",
+   "sha256": "4df4df7f74d18e14ee58ab0196aafe58286a5f1c85043f4132501da02aa33f6c"
+  },
+  "audit_tail": "RuntimeError: nonzero entrance response"
+ }
+}
\ No newline at end of file
diff --git a/research/joint-x54-t37/evidence/native/ARTIFACT-SHA256.json b/research/joint-x54-t37/evidence/native/ARTIFACT-SHA256.json
new file mode 100644
index 0000000000..2ad60b76a4
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/ARTIFACT-SHA256.json
@@ -0,0 +1,12 @@
+{
+  "CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+  "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+  "CLIFFORD-REVIEW.json": "8106db62ba73e6b666762eecf51b419986ff21fac5a1b3507be55a0ab8037799",
+  "FULL-WORD.json.gz": "fcef92874411635a91464bd3851b3704be96be5f0ae7d51ac7e2ef16eed6efa9",
+  "INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+  "LOCAL-CHECKS.json": "658c80d13dc992e18186740f71e88aa4d9a76010bf8da2de77722970d83710e9",
+  "LOCAL-PROGRAMS.json.gz": "cf20b3bfdfc2c92fabfbec492ae441d4fbf670ed5d2fc42e4f89d6011695f315",
+  "RESIDUAL-ADAPTERS.json": "c099207d60ab49392bcadcaf7e9cbcfe01178e732f14e2591a8c3463162460d7",
+  "SCALAR-FRAME-AUDIT.json": "f931c64dab59e3a531e19ac63270125201858a6dd5bc0de76231d5129cf6647e",
+  "WRAPPER-CHECKS.json": "f2a005b54bea64d66633d8a82d0454348172da3b88361081a72126bf1d51744d"
+}
diff --git a/research/joint-x54-t37/evidence/native/CLIFFORD-REVIEW.json b/research/joint-x54-t37/evidence/native/CLIFFORD-REVIEW.json
new file mode 100644
index 0000000000..43c6cd803d
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/CLIFFORD-REVIEW.json
@@ -0,0 +1,19 @@
+{
+  "status": "PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES",
+  "canonical_word_sha256": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+  "frames": 1008,
+  "directed_edges": 2900,
+  "ranks": {
+    "1": 1888,
+    "2": 456,
+    "3": 381,
+    "8": 16,
+    "4": 117,
+    "5": 42
+  },
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true,
+  "recipe_sha256": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+  "seconds": 240.98286681099853,
+  "scope": "Every local frame and center transition. Expanded scalar-interface integration and global emitted program are separate obligations."
+}
diff --git a/research/joint-x54-t37/evidence/native/INDEPENDENT-LOCAL-REPLAY.json b/research/joint-x54-t37/evidence/native/INDEPENDENT-LOCAL-REPLAY.json
new file mode 100644
index 0000000000..09147df2a5
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/INDEPENDENT-LOCAL-REPLAY.json
@@ -0,0 +1,71 @@
+{
+  "status": "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY",
+  "canonical_word_sha256": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+  "local_programs_sha256": "cf20b3bfdfc2c92fabfbec492ae441d4fbf670ed5d2fc42e4f89d6011695f315",
+  "v": 112,
+  "helpers": 480,
+  "local": {
+    "forward": {
+      "all_exact_columns": 704,
+      "prefix_l1_upper": "2765345371136269591/1024",
+      "prefix_bits_upper": 52,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    },
+    "backward": {
+      "all_exact_columns": 704,
+      "prefix_l1_upper": "14824960514781440791821/64",
+      "prefix_bits_upper": 68,
+      "charged_payload_bits": 192,
+      "private_work_erased": true
+    }
+  },
+  "paid_profiles": {
+    "forward": {
+      "1": 2364,
+      "4": 126,
+      "8": 8,
+      "3": 414,
+      "2": 498,
+      "5": 84
+    },
+    "backward": {
+      "1": 2364,
+      "4": 126,
+      "8": 8,
+      "3": 414,
+      "2": 498,
+      "5": 84
+    }
+  },
+  "entering_helpers": 192,
+  "cold_hyperplane_ended_helpers": 48,
+  "negative_controls_rejected": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper"
+  ],
+  "scope": "Literal forward and inverse-transpose replay on every arbitrary data/helper column, physical frame incidence, ordered paid wrappers, cleared private work and prefix coefficients. Global hosting and outer exponent are separate."
+}
diff --git a/research/joint-x54-t37/evidence/native/LOCAL-CHECKS.json b/research/joint-x54-t37/evidence/native/LOCAL-CHECKS.json
new file mode 100644
index 0000000000..871b4fcd82
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/LOCAL-CHECKS.json
@@ -0,0 +1,36 @@
+{
+  "forward": {
+    "sha256": "12960a48d39ca4e4187dbcafa0cd8ecfc43fd7a9479c1a2fb3ba8438c3ddfb5e",
+    "events": 24769,
+    "scalar_macros": 19695,
+    "real_component_primitive_bound": 198782,
+    "paid_profile": {
+      "1": 2364,
+      "2": 498,
+      "3": 414,
+      "4": 126,
+      "5": 84,
+      "8": 8
+    },
+    "all_columns": 704,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  },
+  "backward": {
+    "sha256": "1e1f4ada65568b65479452e89569a7c9ec1c1900a10684ebfe3ec835800dfddb",
+    "events": 24769,
+    "scalar_macros": 19695,
+    "real_component_primitive_bound": 198830,
+    "paid_profile": {
+      "1": 2364,
+      "2": 498,
+      "3": 414,
+      "4": 126,
+      "5": 84,
+      "8": 8
+    },
+    "all_columns": 704,
+    "private_centers_cleared": true,
+    "private_coefficient_stream_cleared_after_each_macro": true
+  }
+}
diff --git a/research/joint-x54-t37/evidence/native/SCALAR-FRAME-AUDIT.json b/research/joint-x54-t37/evidence/native/SCALAR-FRAME-AUDIT.json
new file mode 100644
index 0000000000..a0f873523e
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/SCALAR-FRAME-AUDIT.json
@@ -0,0 +1,712 @@
+{
+  "status": "PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES",
+  "input_content_sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20",
+  "routing_content_sha256": "7c84ac65c8b37173aa4293934f041915895e8ec30595844cc1534e2a19ae0d25",
+  "canonical_content_sha256": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af",
+  "live_columns_each_orientation": 704,
+  "helpers": 480,
+  "compensation_additions": 7208,
+  "scalar_operations": 19671,
+  "center_rank_sum": 64,
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 414,
+    "4": 126,
+    "5": 84,
+    "8": 8
+  },
+  "local_rank_mass": 5590,
+  "widths": [
+    9,
+    9,
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+    8,
+    4,
+    4,
+    4,
+    8,
+    8,
+    8,
+    5,
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+    5,
+    8,
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+    5,
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+    5,
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+    5,
+    5,
+    8,
+    8,
+    8,
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+    5,
+    5,
+    5,
+    8,
+    8,
+    8,
+    5,
+    8,
+    5,
+    5,
+    5
+  ],
+  "frames": 1008,
+  "directed_edges": 2900,
+  "tau": 43,
+  "target_port_order_matches_baseline": true,
+  "seconds": 2.560973265000939,
+  "scope": "Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.",
+  "hyperplane_ended_helpers": [
+    273,
+    275,
+    277,
+    282,
+    289,
+    291,
+    293,
+    298,
+    305,
+    307,
+    309,
+    311,
+    314,
+    321,
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+    339,
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+    346,
+    353,
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+    357,
+    362,
+    369,
+    371,
+    373,
+    378,
+    385,
+    387,
+    389,
+    394,
+    448,
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+    584,
+    585,
+    586,
+    587,
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+    589,
+    590,
+    591
+  ],
+  "early_cleanup_gates": 117,
+  "cold_hyperplane_ended_helpers": [
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+    275,
+    277,
+    282,
+    289,
+    291,
+    293,
+    298,
+    305,
+    307,
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+    311,
+    314,
+    321,
+    323,
+    325,
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+    330,
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+    341,
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+    353,
+    355,
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+    362,
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+    371,
+    373,
+    378,
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+    498,
+    500,
+    501,
+    510,
+    512,
+    513,
+    572,
+    573,
+    574,
+    575,
+    580,
+    581,
+    582,
+    583
+  ],
+  "refactored_cleanup_gates": 6798,
+  "refactored_cleanup": {
+    "cold_low_frame_ended_helpers": [
+      273,
+      275,
+      277,
+      282,
+      289,
+      291,
+      293,
+      298,
+      305,
+      307,
+      309,
+      311,
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+      321,
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+      512,
+      513,
+      572,
+      573,
+      574,
+      575,
+      580,
+      581,
+      582,
+      583
+    ],
+    "construction": "; G44Stack premix-only factored entering ends 554,555,566,567 (start frame [24]); G44Stack premix-only factored entering ends 586,588,531,543 (start frame [30]); CarrierBypass premix-only factored cold ends 513,574,575,573,581,582; CarrierBypass premix-only factored cold ends 572,583,580,512; CarrierBypass premix-only factored cold ends 500,501,311,498,510,327",
+    "entering_low_frame_ended_helpers": [
+      531,
+      543,
+      554,
+      555,
+      566,
+      567,
+      586,
+      588
+    ],
+    "exact_non_target_isolation_checked": true,
+    "forward_absorption_A_indices": [],
+    "forward_absorptions": 0,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "lower_frame_gates": 81,
+    "new_cold_ends": 32,
+    "premix_gates": 1190,
+    "premix_target_writes": 0
+  }
+}
diff --git a/research/joint-x54-t37/evidence/native/STEPS.json b/research/joint-x54-t37/evidence/native/STEPS.json
new file mode 100644
index 0000000000..4c87b44944
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/STEPS.json
@@ -0,0 +1,27 @@
+[
+  {
+    "step": "native",
+    "exit_code": 0,
+    "seconds": 2.65219212699958
+  },
+  {
+    "step": "ledgers",
+    "exit_code": 0,
+    "seconds": 1.5769466940000711
+  },
+  {
+    "step": "local-replay",
+    "exit_code": 0,
+    "seconds": 13.877292221000971
+  },
+  {
+    "step": "wrappers",
+    "exit_code": 0,
+    "seconds": 3.8568169139980455
+  },
+  {
+    "step": "phases",
+    "exit_code": 0,
+    "seconds": 241.091522722003
+  }
+]
diff --git a/research/joint-x54-t37/evidence/native/WRAPPER-CHECKS.json b/research/joint-x54-t37/evidence/native/WRAPPER-CHECKS.json
new file mode 100644
index 0000000000..31af707df8
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/WRAPPER-CHECKS.json
@@ -0,0 +1,421 @@
+{
+ "status": "PASS_RESIDUAL_WRAPPERS_ARE_EXACT",
+ "frames": 22,
+ "hyperplane_end_pairs": [
+  {
+   "frame": 0,
+   "terminal": 129,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 158,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 187,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 215,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 243,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 271,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 299,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 327,
+   "entrance_rank": 0,
+   "terminal_rank": 4,
+   "residual_width": 4
+  },
+  {
+   "frame": 0,
+   "terminal": 1000,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1001,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1002,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1003,
+   "entrance_rank": 0,
+   "terminal_rank": 8,
+   "residual_width": 8
+  },
+  {
+   "frame": 0,
+   "terminal": 1004,
+   "entrance_rank": 0,
+   "terminal_rank": 7,
+   "residual_width": 7
+  },
+  {
+   "frame": 0,
+   "terminal": 1005,
+   "entrance_rank": 0,
+   "terminal_rank": 7,
+   "residual_width": 7
+  },
+  {
+   "frame": 0,
+   "terminal": 1006,
+   "entrance_rank": 0,
+   "terminal_rank": 7,
+   "residual_width": 7
+  },
+  {
+   "frame": 0,
+   "terminal": 1007,
+   "entrance_rank": 0,
+   "terminal_rank": 7,
+   "residual_width": 7
+  },
+  {
+   "frame": 2,
+   "terminal": 999,
+   "entrance_rank": 1,
+   "terminal_rank": 8,
+   "residual_width": 7
+  },
+  {
+   "frame": 3,
+   "terminal": 998,
+   "entrance_rank": 1,
+   "terminal_rank": 8,
+   "residual_width": 7
+  }
+ ],
+ "cold_hyperplane_end_pairs": 16,
+ "wrappers_reject": [
+  "wrong global phase",
+  "wrong translation",
+  "wrong quadratic form",
+  "sides swapped",
+  "wrong width",
+  "hpe: U-wrapper decoded against a FULL ending",
+  "hpe: width misreported as 9 - dim E",
+  "hpe: wrong terminal hyperplane",
+  "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+  "hpe: wrong global phase",
+  "cold hpe: identity pre wrapper instead of R_{0,U}",
+  "cold hpe: identity post wrapper instead of L_{0,U}",
+  "cold hpe: no wrappers (cold FULL convention L = R = I)",
+  "cold hpe: U-wrapper decoded against a FULL ending",
+  "cold hpe: width misreported as 9",
+  "cold hpe: wrong terminal hyperplane",
+  "cold hpe: wrong global phase"
+ ],
+ "all_even_weight": false,
+ "all_totally_isotropic": false,
+ "detail": [
+  {
+   "frame": 2,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    30
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 3,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    51
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 9,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    459
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 10,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    75
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 11,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    102
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 12,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    120
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 13,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    85
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 423,
+   "entrance_rank": 1,
+   "residual_width": 8,
+   "vectors": [
+    45
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": true
+  },
+  {
+   "frame": 424,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
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+    72,
+    48,
+    3
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 425,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
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+    36,
+    9
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 426,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
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+    33,
+    18,
+    12
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 427,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    258,
+    130,
+    85,
+    45
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 428,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    264,
+    136,
+    85,
+    51
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 429,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    427,
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+    24,
+    6
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 430,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    423,
+    65,
+    20,
+    10
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 431,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    257,
+    129,
+    102,
+    30
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 432,
+   "entrance_rank": 5,
+   "residual_width": 4,
+   "vectors": [
+    391,
+    68,
+    34,
+    17,
+    8
+   ],
+   "all_even_weight": false,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 433,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    80,
+    40,
+    5,
+    2
+   ],
+   "all_even_weight": false,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 434,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    144,
+    75,
+    42,
+    7
+   ],
+   "all_even_weight": false,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 435,
+   "entrance_rank": 4,
+   "residual_width": 5,
+   "vectors": [
+    320,
+    192,
+    45,
+    30
+   ],
+   "all_even_weight": true,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 436,
+   "entrance_rank": 5,
+   "residual_width": 4,
+   "vectors": [
+    288,
+    160,
+    75,
+    25,
+    7
+   ],
+   "all_even_weight": false,
+   "totally_isotropic": false
+  },
+  {
+   "frame": 437,
+   "entrance_rank": 5,
+   "residual_width": 4,
+   "vectors": [
+    260,
+    132,
+    75,
+    42,
+    25
+   ],
+   "all_even_weight": false,
+   "totally_isotropic": false
+  }
+ ]
+}
diff --git a/research/joint-x54-t37/evidence/native/ledgers.txt b/research/joint-x54-t37/evidence/native/ledgers.txt
new file mode 100644
index 0000000000..6c00328cef
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/ledgers.txt
@@ -0,0 +1,2 @@
+PASS emitted forward 24769 events
+PASS emitted backward 24769 events
diff --git a/research/joint-x54-t37/evidence/native/local-replay.txt b/research/joint-x54-t37/evidence/native/local-replay.txt
new file mode 100644
index 0000000000..dafef87e13
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/local-replay.txt
@@ -0,0 +1,3 @@
+independent emitted replay PASS forward
+independent emitted replay PASS backward
+PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY 25 controls rejected
diff --git a/research/joint-x54-t37/evidence/native/native.txt b/research/joint-x54-t37/evidence/native/native.txt
new file mode 100644
index 0000000000..a575dd7da7
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/native.txt
@@ -0,0 +1,230 @@
+{
+  "status": "PASS_CHANGED_WORD_ALL_COLUMNS_AND_NATIVE_FRAMES",
+  "input_content_sha256": "ac95ff95d5b1360e040e50f480dd7edc80f50f76160c30e73d6f0b04276ace20",
+  "routing_content_sha256": "7c84ac65c8b37173aa4293934f041915895e8ec30595844cc1534e2a19ae0d25",
+  "canonical_content_sha256": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af",
+  "live_columns_each_orientation": 704,
+  "helpers": 480,
+  "compensation_additions": 7208,
+  "scalar_operations": 19671,
+  "center_rank_sum": 64,
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 414,
+    "4": 126,
+    "5": 84,
+    "8": 8
+  },
+  "local_rank_mass": 5590,
+  "frames": 1008,
+  "directed_edges": 2900,
+  "tau": 43,
+  "target_port_order_matches_baseline": true,
+  "seconds": 2.560973265000939,
+  "scope": "Fresh exact forward and inverse-transpose scalar replay on every arbitrary input; all native frame chains and dyadic primitives. Phase lowering, wrappers, global owners and global assembly are separate.",
+  "hyperplane_ended_helpers": [
+    273,
+    275,
+    277,
+    282,
+    289,
+    291,
+    293,
+    298,
+    305,
+    307,
+    309,
+    311,
+    314,
+    321,
+    323,
+    325,
+    327,
+    330,
+    337,
+    339,
+    341,
+    346,
+    353,
+    355,
+    357,
+    362,
+    369,
+    371,
+    373,
+    378,
+    385,
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+    448,
+    449,
+    450,
+    451,
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+    453,
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+    508,
+    509,
+    510,
+    512,
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+    532,
+    533,
+    543,
+    554,
+    555,
+    556,
+    557,
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+    572,
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+    575,
+    580,
+    581,
+    582,
+    583,
+    584,
+    585,
+    586,
+    587,
+    588,
+    589,
+    590,
+    591
+  ],
+  "early_cleanup_gates": 117,
+  "cold_hyperplane_ended_helpers": [
+    273,
+    275,
+    277,
+    282,
+    289,
+    291,
+    293,
+    298,
+    305,
+    307,
+    309,
+    311,
+    314,
+    321,
+    323,
+    325,
+    327,
+    330,
+    337,
+    339,
+    341,
+    346,
+    353,
+    355,
+    357,
+    362,
+    369,
+    371,
+    373,
+    378,
+    385,
+    387,
+    389,
+    394,
+    498,
+    500,
+    501,
+    510,
+    512,
+    513,
+    572,
+    573,
+    574,
+    575,
+    580,
+    581,
+    582,
+    583
+  ],
+  "refactored_cleanup_gates": 6798,
+  "refactored_cleanup": {
+    "cold_low_frame_ended_helpers": [
+      273,
+      275,
+      277,
+      282,
+      289,
+      291,
+      293,
+      298,
+      305,
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+      311,
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+      500,
+      501,
+      510,
+      512,
+      513,
+      572,
+      573,
+      574,
+      575,
+      580,
+      581,
+      582,
+      583
+    ],
+    "construction": "; G44Stack premix-only factored entering ends 554,555,566,567 (start frame [24]); G44Stack premix-only factored entering ends 586,588,531,543 (start frame [30]); CarrierBypass premix-only factored cold ends 513,574,575,573,581,582; CarrierBypass premix-only factored cold ends 572,583,580,512; CarrierBypass premix-only factored cold ends 500,501,311,498,510,327",
+    "entering_low_frame_ended_helpers": [
+      531,
+      543,
+      554,
+      555,
+      566,
+      567,
+      586,
+      588
+    ],
+    "exact_non_target_isolation_checked": true,
+    "forward_absorption_A_indices": [],
+    "forward_absorptions": 0,
+    "high_inverse": "dyadic_sparse_Gauss_Jordan",
+    "kind": "source_branch_gauge_and_retired_completion_cold44",
+    "lower_frame_gates": 81,
+    "new_cold_ends": 32,
+    "premix_gates": 1190,
+    "premix_target_writes": 0
+  }
+}
diff --git a/research/joint-x54-t37/evidence/native/phases.txt b/research/joint-x54-t37/evidence/native/phases.txt
new file mode 100644
index 0000000000..2f893cca4d
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/phases.txt
@@ -0,0 +1,16 @@
+exact phase edges 0 / 2900 seconds 1.1237920620005752
+exact phase edges 200 / 2900 seconds 14.515241378998326
+exact phase edges 400 / 2900 seconds 30.35943063599916
+exact phase edges 600 / 2900 seconds 46.476484628001344
+exact phase edges 800 / 2900 seconds 62.93078726699969
+exact phase edges 1000 / 2900 seconds 79.32307197900082
+exact phase edges 1200 / 2900 seconds 95.42457229399952
+exact phase edges 1400 / 2900 seconds 111.6591454599984
+exact phase edges 1600 / 2900 seconds 128.06466108500172
+exact phase edges 1800 / 2900 seconds 145.22705223600133
+exact phase edges 2000 / 2900 seconds 162.5422218749991
+exact phase edges 2200 / 2900 seconds 180.0553406600011
+exact phase edges 2400 / 2900 seconds 196.4074065729983
+exact phase edges 2600 / 2900 seconds 212.4056936929992
+exact phase edges 2800 / 2900 seconds 228.87994474600055
+PASS exact local phases 240.98286681099853 seconds
diff --git a/research/joint-x54-t37/evidence/native/wrappers.txt b/research/joint-x54-t37/evidence/native/wrappers.txt
new file mode 100644
index 0000000000..bd2962079c
--- /dev/null
+++ b/research/joint-x54-t37/evidence/native/wrappers.txt
@@ -0,0 +1 @@
+Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for 22 entrance frames, global phase included; 17 wrapper mutations rejected; all-even-weight: False
diff --git a/research/joint-x54-t37/evidence/strict/ADMISSION-CONTROLS.json b/research/joint-x54-t37/evidence/strict/ADMISSION-CONTROLS.json
new file mode 100644
index 0000000000..b12b52937b
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/ADMISSION-CONTROLS.json
@@ -0,0 +1,102 @@
+{
+  "status": "PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS",
+  "valid_receipt_kappa": "335121717095377/200000000000000000",
+  "input_sha256": {
+    "owner_audit": "3bafe472661a37798858d8dee547851d195edd82e7163009243f074dab4ced44",
+    "fresh_invoice": "15ff60de78ecd2fa8646759cb0b2bec96a8ed6b77dbab2590f7dba77700a5b64",
+    "package:inputs/PR589-EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482",
+    "engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098",
+    "engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c"
+  },
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
+  "rejected_controls": [
+    "empty_certification_maps",
+    "failed_invoice_status",
+    "nonboolean_precision_check",
+    "wrong_owner_role_count",
+    "understated_physical_stock",
+    "changed_profile_same_rank_mass",
+    "insufficient_finite_C0",
+    "missing_finite_check",
+    "wrong_reflected_orientation_selfconsistent_totals",
+    "missing_selected_call",
+    "wrong_selected_primitive_sum",
+    "wrong_selected_coefficient_work_sum",
+    "unpaid_wrapper_factors",
+    "wrong_global_compiler",
+    "wrong_global_adapter_maximum",
+    "understated_exact_prefix_and_global_sum",
+    "wrong_global_prefix_sum",
+    "wrong_row_prefix_reserve",
+    "wrong_parent_geometry_charge",
+    "wrong_rebased_geometry_charge",
+    "wrong_complete_pervertex_envelope",
+    "wrong_prior_added_complete_invoice",
+    "wrong_finite_router_bits",
+    "wrong_finite_literal_bits",
+    "wrong_finite_physical_stock_bits",
+    "wrong_finite_row_coefficient",
+    "reordered_complete_calls",
+    "understated_explicit_idle_remainders",
+    "understated_actual_chart_types",
+    "wrong_cross_replica_role_count",
+    "old_no_cold_wrapper_counts_selfconsistent",
+    "gauge44:missing_provider",
+    "gauge44:missing_backward_orientation",
+    "gauge44:unpaid_scalar_primitive",
+    "gauge44:wrong_local_artifact_binding",
+    "gauge44:false_dirty_restoration",
+    "gauge44:wrong_declared_provider_count",
+    "gauge44:wrong_local_compiler",
+    "gauge44:wrong_local_adapter_charge",
+    "gauge44:wrong_local_primitive_bound",
+    "gauge44:forged_provider_and_call_program_hash",
+    "gauge44:provider_at_wrong_call",
+    "gauge44:synchronized_forged_source_recipe_hash",
+    "gauge44:synchronized_forged_phase_review_semantics",
+    "gauge44:width_order_swap_4_5",
+    "gauge44:width_inventory_shift_4_5",
+    "gauge44:width_order_swap_4_7",
+    "gauge44:width_inventory_shift_4_7",
+    "gauge44:width_order_swap_4_8",
+    "gauge44:width_inventory_shift_4_8",
+    "gauge44:width_order_swap_4_9",
+    "gauge44:width_inventory_shift_4_9",
+    "gauge44:width_order_swap_5_7",
+    "gauge44:width_inventory_shift_5_7",
+    "gauge44:width_order_swap_5_8",
+    "gauge44:width_inventory_shift_5_8",
+    "gauge44:width_order_swap_5_9",
+    "gauge44:width_inventory_shift_5_9",
+    "gauge44:width_order_swap_7_8",
+    "gauge44:width_inventory_shift_7_8",
+    "gauge44:width_order_swap_7_9",
+    "gauge44:width_inventory_shift_7_9",
+    "gauge44:width_order_swap_8_9",
+    "gauge44:width_inventory_shift_8_9",
+    "gauge44:cold_helper_width_swap_258",
+    "gauge44:cold_helper_width_swap_270",
+    "gauge44:cold_helper_width_swap_282",
+    "gauge44:cold_helper_width_swap_294",
+    "wrong_owner_receipt_hash"
+  ],
+  "discovery_accepted_controls": [],
+  "exact_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "conservative_outer_controls": [
+    "next_grid",
+    "zero_eta",
+    "zero_beta",
+    "unit_beta"
+  ],
+  "recurrence_model_controls": [
+    "native_complex_endpoint_rejected_with_old_surcharge",
+    "omitting_bit_surcharge_would_fail_next_endpoint_rejection"
+  ],
+  "scope": "Complete receipt schema; ordered widths and both reflected providers; exact program, work and paid-profile binding; independently recounted compiler, conservative envelope and finite inequalities. Does not replace fresh physical replay."
+}
diff --git a/research/joint-x54-t37/evidence/strict/ASSEMBLY.json b/research/joint-x54-t37/evidence/strict/ASSEMBLY.json
new file mode 100644
index 0000000000..5b3cdd2785
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/ASSEMBLY.json
@@ -0,0 +1,344 @@
+{
+  "status": "PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY",
+  "kappa": "335121717095377/200000000000000000",
+  "kappa_decimal": "0.001675608585476885",
+  "complex_lower": "1678420962050942454559/1000000000000000000000000",
+  "complex_decimal": "0.001678420962050942454559",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "gain_over_pr635_percent": "0.002381894334900937252843073956740553636977133153840493839565879778118178",
+  "complex_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "surcharge_model": {
+    "complex": false,
+    "bit": true
+  },
+  "conservative_complex_lower": "839210479598502224499/500000000000000000000000",
+  "conservative_complex_decimal": "0.001678420959197004448998",
+  "conservative_kappa": "1675608582632503/1000000000000000000",
+  "conservative_kappa_decimal": "0.001675608582632503",
+  "conservative_moments": [
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "839210479598502224499/500000000000000000000000",
+      "accept": true,
+      "mercator": [
+        "-16395414739811759606584219125693061318574415/6739986666787659948666753771754907668409286105635143120275902562304",
+        "-32790829479623519213168438251386122637148829/13479973333575319897333507543509815336818572211270286240551805124608"
+      ],
+      "base_two": [
+        "-1216279859800321471321/500000000000000000000000000000000000000000000",
+        "-24325587196006429426279/10000000000000000000000000000000000000000000000"
+      ]
+    },
+    {
+      "side": "conservative_complex",
+      "surcharge": true,
+      "endpoint": "1678420959197004448999/1000000000000000000000000",
+      "accept": false,
+      "mercator": [
+        "13243571787093348984402704266866464103349981/26959946667150639794667015087019630673637144422540572481103610249216",
+        "13243571787093348984402704266866464103349983/26959946667150639794667015087019630673637144422540572481103610249216"
+      ],
+      "base_two": [
+        "2456156402175790039559/5000000000000000000000000000000000000000000000",
+        "4912322804351580079259/10000000000000000000000000000000000000000000000"
+      ]
+    }
+  ],
+  "conservative_bootstrap": [
+    {
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+      "cutoff_log2": "4751531807065"
+    },
+    {
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+      "cutoff_log2": "9506549446506315542685726469083581975818034257"
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+  ],
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+    "complex_below_one_over32": "14785789520401497775501/500000000000000000000000",
+    "beta_positive": "1/1000000000000000000000000",
+    "beta_below_one": "999999999999999999999999/1000000000000000000000000",
+    "leaf_saving_above_bit": "240384735671027585101053614581434954387568401430554906866767239578855800342041939914257806506597864542122818221579102554481066190748460389500150814615336066999698045049715655539622277621186417709637009963907234896791488218003442419894282426007770550710075489502743298167563970731276544028447761050662963499041601675377057639206589829352749334987282199189204001/3906250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+    "unit_beta"
+  ],
+  "scope": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain."
+}
diff --git a/research/joint-x54-t37/evidence/strict/BIT-CONTROLS.json b/research/joint-x54-t37/evidence/strict/BIT-CONTROLS.json
new file mode 100644
index 0000000000..179e62b7af
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/BIT-CONTROLS.json
@@ -0,0 +1,49 @@
+{
+  "status": "PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS",
+  "kappa": "0.001675608585476885",
+  "bit_lower": "1733427039589844234749/1000000000000000000000000",
+  "bit_decimal": "0.001733427039589844234749",
+  "binding": "complex",
+  "bit_supplier": {
+    "pr": 589,
+    "repository": "CrocSwap/integer-mult-bounds",
+    "commit": "a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46",
+    "merged_as": "b3eb785ac5b4b1ca2beea0f80db078a505626a90",
+    "path": "research/e8-bit-p111-tuned/tune/EXPECTED.json",
+    "git_blob_sha1": "e293ddc557742637f9f679f083a1a282d87b1b13",
+    "word": {
+      "v": 111,
+      "decoder_constant": 63,
+      "copy_ranks": [
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7,
+        7
+      ]
+    },
+    "derived_deficit": 10272,
+    "deficit_formula": "T(2Kv-L*cst), L=9 T=32 K=4 M=64",
+    "replay_scope": "Cited unchanged supplier; this assembly reprices its full profile and does not rebuild its bit circuit."
+  },
+  "derived_deficit": 10272,
+  "rejected_controls": [
+    "revert_hardcoded_9984",
+    "ports_112",
+    "decoder_constant_64_copy_ranks_unchanged",
+    "decoder_constant_64_with_one_copy_rank_8",
+    "eight_retained_totals",
+    "live_minus_one",
+    "profile_rank_mass_plus_one",
+    "profile_rank_mass_receipt_mismatch",
+    "bit_lower_next_grid",
+    "not_nine_stage_record",
+    "tampered_bytes_next_grid",
+    "pr543_file_under_pr589_pin"
+  ],
+  "assembler_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a"
+}
diff --git a/research/joint-x54-t37/evidence/strict/INDEPENDENT.json b/research/joint-x54-t37/evidence/strict/INDEPENDENT.json
new file mode 100644
index 0000000000..13caf247b0
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/INDEPENDENT.json
@@ -0,0 +1,119 @@
+{
+  "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+  "roles": 159840,
+  "calls": 333,
+  "source_events_per_replica": 30,
+  "expanded_replica_events": 1110,
+  "bridge_events": 333,
+  "literal_windows": 666,
+  "checked_whole_helper_widths": 159840,
+  "checked_busy_family_windows": 159840,
+  "orthogonal_port_bases": 112,
+  "actual_73_axis_charts": 10803,
+  "checked_slice_prefixes": 74592,
+  "local_profile": {
+    "1": 2364,
+    "2": 498,
+    "3": 414,
+    "4": 126,
+    "5": 84,
+    "8": 8
+  },
+  "width_inventory": {
+    "4": 44,
+    "5": 44,
+    "7": 38,
+    "8": 114,
+    "9": 240
+  },
+  "idle": {
+    "1": 834,
+    "48": 11374
+  },
+  "profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "live": 33152,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "namespace": {
+    "data": [
+      0,
+      33152
+    ],
+    "centres": [
+      33152,
+      33160
+    ],
+    "tableau": [
+      33160,
+      33640
+    ],
+    "coefficient": [
+      33640,
+      33642
+    ]
+  },
+  "local_prefix_bits": 68,
+  "local_prefix_from_native_receipt": true,
+  "local_profile_recounted": true,
+  "prefix_formula": {
+    "local_scalar": 68,
+    "input_l2": 37,
+    "invocations": 333,
+    "bridges": 333,
+    "margin": 4
+  },
+  "prefix_bits": 775,
+  "charged_prefix_bits": 1024,
+  "physical_stock_bits": 2643,
+  "physical_row_coefficient": 17495,
+  "row_limit": 20161,
+  "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+  "disjoint_pending_child_axis_checks": 2016,
+  "controls_rejected": [
+    {
+      "name": "private_namespace_collision",
+      "reason": "private-namespace collision"
+    },
+    {
+      "name": "copy_replica_alias",
+      "reason": "role invocation time"
+    },
+    {
+      "name": "missing_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "split_whole_helper",
+      "reason": "complete helper role count"
+    },
+    {
+      "name": "truncated_helper_width",
+      "reason": "whole-helper residual width"
+    },
+    {
+      "name": "cross_idle_boundary",
+      "reason": "strict bridge-aware idle window"
+    },
+    {
+      "name": "cross_child_pending_axis_alias",
+      "reason": "overlapping pending children on one family"
+    }
+  ],
+  "input_sha256": {
+    "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+    "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+    "/tmp/jx/native/local/CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+    "/tmp/jx/native/local/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+    "/tmp/jx/ddisc/OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6"
+  }
+}
diff --git a/research/joint-x54-t37/evidence/strict/RESULT.json b/research/joint-x54-t37/evidence/strict/RESULT.json
new file mode 100644
index 0000000000..553ee8053b
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/RESULT.json
@@ -0,0 +1,175 @@
+{
+  "status": "PASS_STRICT_T37_THREE_DEMOTIONS",
+  "kappa": "335121717095377/200000000000000000",
+  "kappa_decimal": "0.001675608585476885",
+  "steps": [
+    {
+      "name": "bind",
+      "seconds": 0.892671141999017,
+      "exit_code": 0,
+      "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+    },
+    {
+      "name": "emit",
+      "seconds": 26.574940623999282,
+      "exit_code": 0,
+      "log_sha256": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9"
+    },
+    {
+      "name": "audit",
+      "seconds": 95.02617165799893,
+      "exit_code": 0,
+      "log_sha256": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4"
+    },
+    {
+      "name": "invoice",
+      "seconds": 3.495417272002669,
+      "exit_code": 0,
+      "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+    },
+    {
+      "name": "assembly",
+      "seconds": 0.7114261240021733,
+      "exit_code": 0,
+      "log_sha256": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35"
+    },
+    {
+      "name": "admission",
+      "seconds": 1.2020302760029153,
+      "exit_code": 0,
+      "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+    },
+    {
+      "name": "bit",
+      "seconds": 1.209536433001631,
+      "exit_code": 0,
+      "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+    },
+    {
+      "name": "independent",
+      "seconds": 3.269724977999431,
+      "exit_code": 0,
+      "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+    }
+  ],
+  "independent": {
+    "status": "PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW",
+    "roles": 159840,
+    "calls": 333,
+    "source_events_per_replica": 30,
+    "expanded_replica_events": 1110,
+    "bridge_events": 333,
+    "literal_windows": 666,
+    "checked_whole_helper_widths": 159840,
+    "checked_busy_family_windows": 159840,
+    "orthogonal_port_bases": 112,
+    "actual_73_axis_charts": 10803,
+    "checked_slice_prefixes": 74592,
+    "local_profile": {
+      "1": 2364,
+      "2": 498,
+      "3": 414,
+      "4": 126,
+      "5": 84,
+      "8": 8
+    },
+    "width_inventory": {
+      "4": 44,
+      "5": 44,
+      "7": 38,
+      "8": 114,
+      "9": 240
+    },
+    "idle": {
+      "1": 834,
+      "48": 11374
+    },
+    "profile": {
+      "1": 788046,
+      "2": 165834,
+      "3": 137862,
+      "4": 41958,
+      "5": 27972,
+      "8": 2664,
+      "48": 11374
+    },
+    "live": 33152,
+    "physical": 33642,
+    "rank_mass": 2408256,
+    "deficit": 11840,
+    "namespace": {
+      "data": [
+        0,
+        33152
+      ],
+      "centres": [
+        33152,
+        33160
+      ],
+      "tableau": [
+        33160,
+        33640
+      ],
+      "coefficient": [
+        33640,
+        33642
+      ]
+    },
+    "local_prefix_bits": 68,
+    "local_prefix_from_native_receipt": true,
+    "local_profile_recounted": true,
+    "prefix_formula": {
+      "local_scalar": 68,
+      "input_l2": 37,
+      "invocations": 333,
+      "bridges": 333,
+      "margin": 4
+    },
+    "prefix_bits": 775,
+    "charged_prefix_bits": 1024,
+    "physical_stock_bits": 2643,
+    "physical_row_coefficient": 17495,
+    "row_limit": 20161,
+    "scope": "Finite role/window/chart and inherited prefix/row obligations. Requires separately admitted local supplier and emitted controller, complete finite invoice, exact moments and outer assembly; no all-size theorem is asserted.",
+    "disjoint_pending_child_axis_checks": 2016,
+    "controls_rejected": [
+      {
+        "name": "private_namespace_collision",
+        "reason": "private-namespace collision"
+      },
+      {
+        "name": "copy_replica_alias",
+        "reason": "role invocation time"
+      },
+      {
+        "name": "missing_whole_helper",
+        "reason": "complete helper role count"
+      },
+      {
+        "name": "split_whole_helper",
+        "reason": "complete helper role count"
+      },
+      {
+        "name": "truncated_helper_width",
+        "reason": "whole-helper residual width"
+      },
+      {
+        "name": "cross_idle_boundary",
+        "reason": "strict bridge-aware idle window"
+      },
+      {
+        "name": "cross_child_pending_axis_alias",
+        "reason": "overlapping pending children on one family"
+      }
+    ],
+    "input_sha256": {
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/GLOBAL-TEMPLATE.json.gz": "ab8448de2036a23d9b55a196a8846512dc24fdf09855c1e0f0caa5b7a6965f7b",
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+      "/tmp/jx/layout/demotions1148-round43/baseline-replay/parent/t16/global8/base/split-centres/CANONICAL-WORD.json.gz": "66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",
+      "/tmp/jx/native/local/CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+      "/tmp/jx/native/local/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+      "/tmp/jx/ddisc/OWNERS.json.gz": "7fd6f69e806aaa5a6094d52b1400d8bde25aaa8ea26216eb4ffc989151ad0ab6"
+    }
+  },
+  "scope": "Conditional finite construction only; unchanged native provider independently replayed from PR1148; all inherited theorem obligations retained."
+}
\ No newline at end of file
diff --git a/research/joint-x54-t37/evidence/strict/STAGES.json b/research/joint-x54-t37/evidence/strict/STAGES.json
new file mode 100644
index 0000000000..ca38daf48b
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/STAGES.json
@@ -0,0 +1,50 @@
+[
+  {
+    "name": "bind",
+    "seconds": 0.892671141999017,
+    "exit_code": 0,
+    "log_sha256": "71f679ce5a123fb58397fd6852ba64ce3832fd20e81a096bfda9a1cf3237237a"
+  },
+  {
+    "name": "emit",
+    "seconds": 26.574940623999282,
+    "exit_code": 0,
+    "log_sha256": "e416caf8ef99d649454b104e787c64f60d46d9fe6068ce69a6887ca5811a0fe9"
+  },
+  {
+    "name": "audit",
+    "seconds": 95.02617165799893,
+    "exit_code": 0,
+    "log_sha256": "933c5cd8be4b7d01da46030daf7ee036a7af1b9278ef0b2b6fed4963d72805f4"
+  },
+  {
+    "name": "invoice",
+    "seconds": 3.495417272002669,
+    "exit_code": 0,
+    "log_sha256": "19571dcad21b6e4ad414138545569eece71c693db6fc515ca7c9c485226d25ca"
+  },
+  {
+    "name": "assembly",
+    "seconds": 0.7114261240021733,
+    "exit_code": 0,
+    "log_sha256": "3af38e9ab6f816c1ad4cf678004c04262816366357ade69ffcda5a59735edc35"
+  },
+  {
+    "name": "admission",
+    "seconds": 1.2020302760029153,
+    "exit_code": 0,
+    "log_sha256": "051d242318154827c1672ffbb63ad2bdc8ecc4033be650b791dd69cd57d716b3"
+  },
+  {
+    "name": "bit",
+    "seconds": 1.209536433001631,
+    "exit_code": 0,
+    "log_sha256": "d54d260bf95bd8ae4ab8846314082b93b2e3d8f427eb35376691f2ce543a6b67"
+  },
+  {
+    "name": "independent",
+    "seconds": 3.269724977999431,
+    "exit_code": 0,
+    "log_sha256": "b5006d0b4f13b4eb42470ed87dd8f0a52c220763fe703a0c2cd6a4bd37ca7e9e"
+  }
+]
\ No newline at end of file
diff --git a/research/joint-x54-t37/evidence/strict/admission.txt b/research/joint-x54-t37/evidence/strict/admission.txt
new file mode 100644
index 0000000000..5a8d19dd96
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/admission.txt
@@ -0,0 +1 @@
+PASS_EXACT_MIXED_048_ALLCOLD_NATIVE_ASSEMBLY_ADMISSION_NEGATIVE_CONTROLS 69
diff --git a/research/joint-x54-t37/evidence/strict/assembly.txt b/research/joint-x54-t37/evidence/strict/assembly.txt
new file mode 100644
index 0000000000..c08f883a47
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/assembly.txt
@@ -0,0 +1 @@
+PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001675608585476885
diff --git a/research/joint-x54-t37/evidence/strict/audit.txt b/research/joint-x54-t37/evidence/strict/audit.txt
new file mode 100644
index 0000000000..080ac0b54b
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/audit.txt
@@ -0,0 +1,74 @@
+{
+  "status": "PASS_INDEPENDENT_ASYNC_WHOLE_OWNER_CONTROLLER_PHASES_AND_SPECTATORS",
+  "template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "complex_template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "complex_live": 33152,
+  "complex_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "complex_hosted_residuals": 159840,
+  "physical": 33642,
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "entering_helper_roles": 79920,
+  "cross_replica_helper_roles": 149072,
+  "one_owner_per_complete_invocation": true,
+  "helper_busy_family_window_checks": 159840,
+  "complete_invocations": 333,
+  "actual_orthogonal_73column_maps": 10803,
+  "actual_sigma_stream_sha256": "084c91aec13cba8adf58d7680c54253433734ac10ad67cc6a5b3d20789320f07",
+  "all_actual_residual_and_spectator_charts": true,
+  "idle_remainders": 12208,
+  "mutations_rejected": [
+    "alias two whole owners",
+    "helper on active data family",
+    "owner in private namespace",
+    "wrong residual width",
+    "wrong spectator coordinate",
+    "omit idle remainder",
+    "understate physical reserve",
+    "gauge44: wrong provider at its invocation",
+    "gauge44: stale per-call local program hash",
+    "gauge44: stale serialized provider program",
+    "gauge44: unbound residual adapter hash",
+    "gauge44: wrong provider width registry",
+    "gauge44: wrong per-call residual width",
+    "gauge44: wrong sweep provider",
+    "gauge44: entering helper width silently restored to nine"
+  ],
+  "mutation_controls_run": true,
+  "provider_phase_semantic_sha256": {
+    "gauge44": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d"
+  },
+  "provider_artifact_semantic_sha256": {
+    "gauge44": {
+      "CANONICAL-WORD.json.gz": "2b34a781ec6a0b6249bc116afbf60c926474a84c7ef613e76f17dca1f26178af",
+      "LOCAL-PROGRAMS.json.gz": "b6e6d496eefc02532f91e833561b8cb676062c57d3943afc2ae0932810a5a36b",
+      "LOCAL-CHECKS.json": "5d843a435c5dd0e8276d637ec29ed99f3e601cbc50e26ed7c0f80795ccb71aec",
+      "INDEPENDENT-LOCAL-REPLAY.json": "41ed1ee4c0842c9da8bc1c88ad3f16feea9d83392341687361c26943c4d662ff",
+      "CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+      "CLIFFORD-REVIEW.json": "5cc8cecb1562863e7105564eb15b13f7d0d1b180a83bf05237b2301f1895ae5d",
+      "RESIDUAL-ADAPTERS.json": "d77ab0c3689e5c10f7129487a85d1497dd721e31138372b4a35913691fe5bc69"
+    }
+  },
+  "widths_by_provider": {
+    "gauge44": {
+      "4": 44,
+      "5": 44,
+      "7": 38,
+      "8": 114,
+      "9": 240
+    }
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "all_provider_program_phase_and_wrapper_bindings": true,
+  "scope": "Independent exact asynchronous chronology, per-replica phase projection, owner/chart/paid-profile audit. Uses per-invocation local providers bound by exact scalar, phase and residual-wrapper receipts; all-size compilation and complete coefficient invoice are separate inherited obligations."
+}
diff --git a/research/joint-x54-t37/evidence/strict/bind.txt b/research/joint-x54-t37/evidence/strict/bind.txt
new file mode 100644
index 0000000000..a964929571
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/bind.txt
@@ -0,0 +1 @@
+PASS_FROZEN_048_ALLCOLD_DISPATCH_FRESH_PROVIDER_BINDING
diff --git a/research/joint-x54-t37/evidence/strict/bit.txt b/research/joint-x54-t37/evidence/strict/bit.txt
new file mode 100644
index 0000000000..434ec86a59
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/bit.txt
@@ -0,0 +1 @@
+PASS_PR589_BIT_SUPPLIER_DERIVED_DEFICIT_NEGATIVE_CONTROLS 12
diff --git a/research/joint-x54-t37/evidence/strict/emit.txt b/research/joint-x54-t37/evidence/strict/emit.txt
new file mode 100644
index 0000000000..43d882a654
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/emit.txt
@@ -0,0 +1,50 @@
+{
+  "status": "EMITTED_MIXED_PROVIDER_ASYNCHRONOUS_WHOLE_OWNER_COMPLEX_TEMPLATE",
+  "template_sha256": "5741848d12921344fff40fa573431e5f086cfcda31c11a658b95c67cb3a32eb6",
+  "parent_template_sha256": "514e59314c8e2fa3c22d0a48083816f6686211090835e8f8775318c1c3e992d8",
+  "live": 33152,
+  "physical": 33642,
+  "global_profile": {
+    "1": 788046,
+    "2": 165834,
+    "3": 137862,
+    "4": 41958,
+    "5": 27972,
+    "8": 2664,
+    "48": 11374
+  },
+  "rank_mass": 2408256,
+  "deficit": 11840,
+  "maxchild": 48,
+  "hosted_residuals": 159840,
+  "banks_per_stage": [
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "entering_helper_roles": 79920,
+  "unique_actual_73column_sigmas": 10803,
+  "sigma_stream_sha256": "084c91aec13cba8adf58d7680c54253433734ac10ad67cc6a5b3d20789320f07",
+  "cross_replica_helper_roles": 149072,
+  "asynchronous_order_sha256": "84f030a59dde4fa4635988ef0931ebae66964b3a202df79d38247fbe8a5592dc",
+  "source_artifacts": {
+    "work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "providers/gauge44/CANONICAL-WORD.json.gz": "cec996f812022db4a6bc6f95d778b04b85938b82e1de0d2dca0825dc395e03cf",
+    "providers/gauge44/LOCAL-PROGRAMS.json.gz": "cf20b3bfdfc2c92fabfbec492ae441d4fbf670ed5d2fc42e4f89d6011695f315",
+    "providers/gauge44/LOCAL-CHECKS.json": "658c80d13dc992e18186740f71e88aa4d9a76010bf8da2de77722970d83710e9",
+    "providers/gauge44/INDEPENDENT-LOCAL-REPLAY.json": "29831c94af90faa41efbb81c1e276535109821c34378acb2b252e396b96ed590",
+    "providers/gauge44/RESIDUAL-ADAPTERS.json": "c099207d60ab49392bcadcaf7e9cbcfe01178e732f14e2591a8c3463162460d7",
+    "providers/gauge44/CLIFFORD-RECIPES.json": "40520ee10efd4ed228b0105e76541f288fa9b1b027740b77cafc50b3ae5f6a7c",
+    "providers/gauge44/CLIFFORD-REVIEW.json": "8106db62ba73e6b666762eecf51b419986ff21fac5a1b3507be55a0ab8037799"
+  },
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "scope": "Two actual verified plain/width-seven providers dispatched per complete invocation; independent controller/spectator/normalization and complete finite invoice admission required."
+}
diff --git a/research/joint-x54-t37/evidence/strict/independent.txt b/research/joint-x54-t37/evidence/strict/independent.txt
new file mode 100644
index 0000000000..3bffc24f17
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/independent.txt
@@ -0,0 +1 @@
+PASS_INDEPENDENT_VARIABLE_T_LITERAL_WINDOWS_CHARTS_PREFIX_ROW roles=159840 controls=7
diff --git a/research/joint-x54-t37/evidence/strict/invoice.txt b/research/joint-x54-t37/evidence/strict/invoice.txt
new file mode 100644
index 0000000000..81de5dd3c2
--- /dev/null
+++ b/research/joint-x54-t37/evidence/strict/invoice.txt
@@ -0,0 +1,35 @@
+{
+  "status": "PASS_INDEPENDENT_MIXED_ASYNC_SCALAR_PREFIX_AND_FINITE_INVOICE",
+  "provider_counts": {
+    "gauge44": 333
+  },
+  "selected_real_component_primitives": 66201510,
+  "selected_coefficient_work_primitive_count": 32752289,
+  "global_prefix_bits": 775,
+  "finite": {
+    "physical_stock_bits": 2643,
+    "router_bits": 7991,
+    "literal_bits": 35286,
+    "physical_row_coefficient": 17495,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  }
+}
diff --git a/research/joint-x54-t37/prepare_x54.py b/research/joint-x54-t37/prepare_x54.py
new file mode 100644
index 0000000000..3c5f227ab9
--- /dev/null
+++ b/research/joint-x54-t37/prepare_x54.py
@@ -0,0 +1,41 @@
+"""Rebuild the T37 PLAN/SPEC/PROFILE for the X54 joint-entrance word.
+
+Adapted from PR1169's candidate-tools-joint/prepare.py (Rohan Arun/Codex, Apache-2.0).
+Sole changes: the provider plan is the rebound X54 plan supplied by --source-plan (instead of
+research/k8-joint-entrances/PLAN.json.gz), the expected idle/windows/owners are unchanged, and the
+SPEC records PR1169's value as the comparison baseline.
+"""
+import argparse,collections,copy,gzip,hashlib,importlib.util,json,shutil
+from pathlib import Path
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_bytes())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def identity(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def load(n,p):
+ s=importlib.util.spec_from_file_location(n,p);m=importlib.util.module_from_spec(s);s.loader.exec_module(m);return m
+ap=argparse.ArgumentParser();ap.add_argument('--layout',type=Path,required=True);ap.add_argument('--construction',type=Path,required=True);ap.add_argument('--flow',type=Path,required=True);ap.add_argument('--source-plan',type=Path,required=True);ap.add_argument('--baseline-kappa',required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert __debug__ and not a.out.exists();a.out.mkdir();out=a.out
+F=a.layout.resolve();R=F/'owner37-round44';S=R/'source/research/r480-owner-optimum';B=F/'demotions1148-round43/baseline-replay'
+assert rd(B/'RESULT.json')['status']=='PASS_THREE_DEMOTIONS_COMPLETE_ADMISSION'
+L=load('lift',S/'lift.py');W=load('windows',S/'vendor/pr1074/t16/build_parent.py');base=B/'parent/t16/global8/base';parent=L.lift(rd(base/'split-centres/GLOBAL-TEMPLATE.json.gz'));flow=rd(a.flow);order=flow['order'];windows,schedule=W.actual_windows(parent,order)
+expected={f'{r},{ch}':[cap,ts] for r,cap,ts,chs in flow['groups'] for ch in chs};assert windows==expected
+roles=rd(a.construction/'OWNERS.json.gz');plan=rd(a.source_plan);used=collections.Counter();seen=set()
+for z in roles:
+ assert order[z['time']]==[z['stage'],z['replica']];k=z['owner_replica'],z['child'],z['port'];cap,ts=windows[f'{k[0]},{k[1]}'];assert z['time'] in ts;key=z['time'],z['family'];assert key not in seen;seen.add(key);used[k]+=z['width'];assert used[k]<=cap
+idle=collections.Counter()
+for key,(cap,ts) in windows.items():
+ r,ch=map(int,key.split(','))
+ for port in range(112):
+  rem=cap-used[r,ch,port]
+  if rem:idle[rem]+=1
+assert idle=={1:834,48:11374}
+profile=collections.Counter({int(r):len(order)*n for r,n in plan['provider_registry']['gauge44']['actual_paid_profile'].items()});profile.update(idle)
+plan.update(T=37,live=896*37,deficit=320*37,order=order,windows=windows,profile={str(r):n for r,n in sorted(profile.items())},status='EXPLICIT_T37_THREE_DEMOTIONS_OWNER_NOMINATION',mode='three-demotions-t37',solver_status='exact integer flow and matching',gap=None)
+for field in ('provider_calls','per_call_widths'):
+ old={(z['stage'],z['replica']):z for z in plan[field]};plan[field]=[]
+ for t,(s,r) in enumerate(order):
+  z=copy.deepcopy(old[s,r%16]);z['replica']=r
+  if 'time' in z:z['time']=t
+  plan[field].append(z)
+shutil.copy2(a.construction/'OWNERS.json.gz',out/'OWNERS.json.gz');plan.update(assignment_sha256=sha(out/'OWNERS.json.gz'),assignment_content_sha256=identity(roles));plan['replica_lift']=dict(groups=[8,8,8,8,5],source_replicas=8,replicas=37,parent_template_content_sha256=identity(parent),owners_file_sha256=sha(out/'OWNERS.json.gz'),schedule_content_sha256=identity(schedule),window_semantics='Strict physical source-event intervals, including bridges')
+assert sum(r*n for r,n in profile.items())==73*plan['live']-plan['deficit']
+(out/'PLAN.json').write_text(json.dumps(plan,indent=2)+'\n');L.write_gzip(out/'GLOBAL-TEMPLATE.json.gz',parent)
+spec=rd(S/'data/SPEC.json');spec.update(name='joint-x54-t37',call_order=order,dispatch=[[s,r,'gauge44'] for s,r in order],providers={},expected={'gain_baseline_kappa':a.baseline_kappa},data={'plan_sha256':sha(out/'PLAN.json'),'owners_sha256':sha(out/'OWNERS.json.gz')});(out/'SPEC.json').write_text(json.dumps(spec,indent=2)+'\n');(out/'PROFILE.json').write_text(json.dumps(dict(profile),indent=2)+'\n');print('PREPARED',len(roles),dict(idle))
diff --git a/research/joint-x54-t37/rebind_plan.py b/research/joint-x54-t37/rebind_plan.py
new file mode 100644
index 0000000000..32dc28ddac
--- /dev/null
+++ b/research/joint-x54-t37/rebind_plan.py
@@ -0,0 +1,27 @@
+"""Rebind PR1148's k8-joint-entrances provider plan to a fresh native replay of the X54 word.
+
+Every old provider identity (file sha256, semantic sha256 and orientation program sha256) is replaced by the
+identity of the same-named artifact in the supplied native replay; the paid profile is read from its LOCAL-CHECKS.
+No other plan field changes. Standard library only.
+"""
+import argparse,gzip,hashlib,importlib.util,json
+from pathlib import Path
+def sha(p):return hashlib.sha256(Path(p).read_bytes()).hexdigest()
+def main():
+ assert __debug__
+ ap=argparse.ArgumentParser();ap.add_argument('--layout',type=Path,required=True);ap.add_argument('--native-local',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists()
+ L=a.layout.resolve();new=a.native_local.resolve()
+ spec=importlib.util.spec_from_file_location('gi',L/'owner37-round44/source/research/r480-owner-optimum/code/generated_identity.py');gi=importlib.util.module_from_spec(spec);spec.loader.exec_module(gi)
+ plan=json.loads(gzip.decompress((L/'joint1148-round45/source/research/k8-joint-entrances/PLAN.json.gz').read_bytes()));reg=plan['provider_registry']['gauge44']
+ inew=gi.artifact_identities(new);cn=json.loads((new/'LOCAL-CHECKS.json').read_text());mp={}
+ assert set(inew)==set(reg['artifact_semantic_sha256'])==set(reg['artifact_sha256'])
+ for n,old in reg['artifact_semantic_sha256'].items():mp[old]=inew[n]
+ for n,old in reg['artifact_sha256'].items():mp[old]=sha(new/n)
+ for o,old in reg['orientation_program_sha256'].items():mp[old]=cn[o]['sha256']
+ txt=json.dumps(plan,sort_keys=True)
+ for x,y in mp.items():assert txt.count(x)>0,x;txt=txt.replace(x,y)
+ plan=json.loads(txt);assert cn['backward']['paid_profile']==cn['forward']['paid_profile']
+ plan['provider_registry']['gauge44']['actual_paid_profile']={str(k):v for k,v in cn['forward']['paid_profile'].items()}
+ a.out.write_bytes(gzip.compress(json.dumps(plan,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+ print('PASS_X54_PROVIDER_PLAN_REBOUND',len(mp),plan['provider_registry']['gauge44']['actual_paid_profile'])
+if __name__=='__main__':main()
diff --git a/research/joint-x54-t37/vendor/barch/build_tri.py b/research/joint-x54-t37/vendor/barch/build_tri.py
new file mode 100644
index 0000000000..11c4371114
--- /dev/null
+++ b/research/joint-x54-t37/vendor/barch/build_tri.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""build_tri.py BASE_WORD RECIPE OUT_WORD [--control NAME]
+
+Standard library only. Applies a NewBArch triangle-hybrid recipe to the X4 word (1e1d99ba) and writes a FULL-WORD.json.gz.
+Recipe keys (all indices refer to the BASE word):
+  base_sha256      sha256 of the decompressed base JSON (checked)
+  B_delete         list of B indices removed
+  B_insert         list of [pos, gate]: gate (with frame) inserted before base B gate pos (list order kept)
+  B_frames         {index: frame}: explicit re-chosen frame of a kept base B gate
+  tail_insert      list of [early_index, gate]: gates appended to cleanup in list order, then registered as early cleanup at early_index (ascending)
+  cleanup_prepend  list of gates prepended to the full cleanup (early indices are shifted)
+  local_profile    report.local_profile of the result
+  expect_sha256    sha256 of the decompressed result (checked unless a control is requested)
+Controls (each must be REJECTED by audit_local; see controls.json):
+  drop_restore     omit cleanup_prepend (end value of the holder not restored)
+  restore_full     move tail_insert gates into the full cleanup (FULL frame) instead of early cleanup
+  drop_preread     omit the inserted entrance pre-reads (inserted target += E gates at pos < first donation)
+  donation_after   insert each donation after its reading target's read instead of before it
+  NAME@X           the same control restricted to the instance whose packet register is X (recipe 'variants')
+"""
+import sys, json, gzip, hashlib, copy
+
+FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+
+def load(p):
+    raw = gzip.decompress(open(p, 'rb').read()); return json.loads(raw), hashlib.sha256(raw).hexdigest()
+
+def apply(w, rc, control=None):
+    w = copy.deepcopy(w); B = w['B']
+    S = None
+    if control and '@' in control:                     # per-instance control: name@X mutates only instance X's gates
+        control, x = control.split('@'); x = int(x)
+        vv = [s for s in rc['variants'] if s['X'] == x][0]; S = {vv['X'], vv['E'], *vv['hold']}
+    sel = lambda g: S is None or bool({g[1], g[2]} & S)
+    dele = set(rc['B_delete']); fr = {int(k): f for k, f in rc['B_frames'].items()}
+    ins = [list(x) for x in rc['B_insert']]
+    don = [x for x in ins if not (112 <= x[1][1] < 224)]           # donations: destination is not a target
+    first_don = min(p for p, _ in don) if don else 0
+    if control == 'drop_preread':
+        ins = [x for x in ins if not (x[0] < first_don and 112 <= x[1][1] < 224 and sel(x[1]))]
+    if control == 'donation_after':
+        new = []
+        for p, g in ins:
+            if g in [d[1] for d in don] and sel(g):
+                rd = [i for i, e in enumerate(B) if i >= p and e[0] == 'add' and e[2] == g[1] and 112 <= e[1] < 224]
+                p = rd[0] + 1
+            new.append([p, g])
+        ins = new
+    at = {}
+    for p, g in ins: at.setdefault(p, []).append(list(g))
+    out = []
+    for i, e in enumerate(B):
+        out.extend(at.get(i, []))
+        if i in dele: continue
+        e = list(e)
+        if i in fr: e = e[:-1] + [list(fr[i])]
+        out.append(e)
+    out.extend(at.get(len(B), []))
+    w['B'] = out
+    pre = [list(g) for g in rc['cleanup_prepend'] if not (control == 'drop_restore' and sel(g))]
+    tails = [list(x) for x in rc['tail_insert']]
+    if control == 'restore_full':
+        pre = pre + [g[1][:-1] + [FULL] for g in tails if sel(g[1])]; tails = [g for g in tails if not sel(g[1])]
+    C = pre + w['cleanup']; sh = len(pre)
+    early = [[i + sh, U] for i, U in w['early_cleanup']]
+    idx = []
+    for j, g in tails: C.append(list(g)); idx.append((j, len(C) - 1, list(g[-1])))   # appended in recipe order
+    for j, ci, U in sorted(idx): early.insert(j, [ci, U])                               # then registered at their early index
+    w['cleanup'] = C; w['early_cleanup'] = early
+    w['report'] = dict(w['report']); w['report']['local_profile'] = rc['local_profile']
+    return w
+
+def main():
+    a = sys.argv[1:]; control = None
+    if '--control' in a: k = a.index('--control'); control = a[k + 1]; del a[k:k + 2]
+    base, out = a[0], a[2]
+    w, sha = load(base); rc = json.load(open(a[1]))
+    if sha != rc['base_sha256']: raise SystemExit('base sha mismatch ' + sha)
+    w2 = apply(w, rc, control)
+    raw = json.dumps(w2, separators=(',', ':')).encode()
+    open(out, 'wb').write(gzip.compress(raw, mtime=0))
+    s = hashlib.sha256(raw).hexdigest()
+    if control is None and s != rc['expect_sha256']: raise SystemExit('result sha mismatch ' + s)
+    print(json.dumps(dict(control=control, sha256=s)))
+
+if __name__ == '__main__':
+    main()
diff --git a/research/joint-x54-t37/vendor/barch/run_controls.py b/research/joint-x54-t37/vendor/barch/run_controls.py
new file mode 100644
index 0000000000..f1ce999bfb
--- /dev/null
+++ b/research/joint-x54-t37/vendor/barch/run_controls.py
@@ -0,0 +1,33 @@
+#!/usr/bin/env python3
+"""run_controls.py BASE_WORD RECIPE AUDIT_LOCAL_PY OUTDIR : C0 identity, the recipe word (must PASS) and the four negative
+controls (each must FAIL audit_local with its pinned message prefix). Standard library only; writes OUTDIR/controls.json."""
+import sys, json, subprocess, os, gzip, hashlib
+base, recipe, audit, out = sys.argv[1:5]
+here = os.path.dirname(os.path.abspath(__file__)); os.makedirs(out, exist_ok=True)
+# pinned rejection sites (observed on RECIPE-V1 and RECIPE-B0; the failing rows are recorded in controls.json): the holder 485 is not restored; the low-end restore 497-=451 moved to the
+# FULL cleanup runs after 451's own tail and leaves 497 wrong; without the pre-read (or with the donation after the read)
+# the entering helper's start value reaches a target.
+EXPECT = {None: 'PASS', 'drop_restore': 'all-column endpoint failure (False, ',
+          'restore_full': 'all-column endpoint failure (False, ',
+          'drop_preread': 'nonzero entrance response', 'donation_after': 'nonzero entrance response'}
+res = {}
+ident = os.path.join(out, 'C0.json')
+json.dump(dict(json.load(open(recipe)), B_delete=[], B_insert=[], B_frames={}, tail_insert=[], cleanup_prepend=[],
+               local_profile=json.loads(gzip.decompress(open(base, 'rb').read()))['report']['local_profile'],
+               expect_sha256=hashlib.sha256(gzip.decompress(open(base, 'rb').read())).hexdigest()), open(ident, 'w'))
+r = subprocess.run([sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, ident, os.path.join(out, 'C0.json.gz')], capture_output=True, text=True)
+res['C0_identity'] = dict(ok=r.returncode == 0, out=r.stdout.strip() or r.stderr.strip()[-200:])
+ctls = list(EXPECT) + [c + '@' + str(s['X']) for s in json.load(open(recipe)).get('variants', []) for c in EXPECT if c]
+for ctl in ctls:
+    name = ctl or 'recipe'; wp = os.path.join(out, name + '.json.gz')
+    cmd = [sys.executable, '-B', os.path.join(here, 'build_tri.py'), base, recipe, wp] + (['--control', ctl] if ctl else [])
+    b = subprocess.run(cmd, capture_output=True, text=True)
+    if b.returncode: res[name] = dict(ok=False, build=b.stderr[-300:]); continue
+    a = subprocess.run([sys.executable, '-B', audit, '--word', wp, '--output', os.path.join(out, name + '.audit.json')], capture_output=True, text=True)
+    txt = a.stdout + a.stderr
+    if ctl is None: ok = a.returncode == 0 and 'PASS_INDEPENDENT' in txt
+    else: ok = a.returncode != 0 and EXPECT[ctl.split('@')[0]] in txt
+    res[name] = dict(ok=ok, build=json.loads(b.stdout), audit_tail=txt.strip().splitlines()[-1][:200])
+json.dump(res, open(os.path.join(out, 'controls.json'), 'w'), indent=1)
+print(json.dumps({k: x['ok'] for k, x in res.items()}))
+sys.exit(0 if all(x['ok'] for x in res.values()) else 1)
diff --git a/research/joint-x54-t37/verify.py b/research/joint-x54-t37/verify.py
new file mode 100644
index 0000000000..4b8371ec61
--- /dev/null
+++ b/research/joint-x54-t37/verify.py
@@ -0,0 +1,61 @@
+"""Strict finite replay of the X54 slot on PR1148's joint-entrance k8 word with PR1169's exact T37 owner packing.
+Requires Python 3.11+, a C++ compiler and Boost headers. No network or optimization solver is used.
+
+Stages: sibling-pin check, literal owner construction (PR1169, unchanged), plan/geometry reconstruction with the
+rebound X54 provider plan, joint-entrance word rebuild (PR1148), X54 word build, independent local audit, PR1148's
+27 entrance controls, X54's 10 slot controls, fresh native five-stage replay, provider rebind from that replay,
+strict T37 admission (bind, emit, audit, invoice, assembly, 69 admission + 12 bit controls, independent owner
+checker) and the fixed-family all-T upper bound.
+"""
+import argparse,gzip,hashlib,json,os,shutil,subprocess,sys,tarfile,time
+from pathlib import Path
+P=Path(__file__).resolve().parent;Q=P.parent/'three-demotions-t37-composition'
+ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);ap.add_argument('--native-from',type=Path);a=ap.parse_args();work=a.work.resolve();assert __debug__ and not work.exists() and not work.is_relative_to(P)
+def rd(p):return json.loads(gzip.decompress(p.read_bytes()) if p.suffix=='.gz' else p.read_text())
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def raw(p):return gzip.decompress(p.read_bytes())
+pins=rd(P/'MANIFEST.json');actual={str(x.relative_to(P)) for x in P.rglob('*') if x.is_file() and '__pycache__' not in x.parts and x.name!='MANIFEST.json'};assert actual==set(pins),sorted(actual^set(pins))
+for rel,h in pins.items():assert sha(P/rel)==h,rel
+for rel,h in rd(P/'SOURCE-PINS.json').items():assert sha(P.parent/rel)==h,rel
+claim=rd(P/'CANDIDATE.json')
+work.mkdir();layout=work/'layout';layout.mkdir();tmp=work/'tmp';tmp.mkdir();env=dict(os.environ,TMPDIR=str(tmp),PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0')
+for k in ('PYTHONOPTIMIZE','WITNESS_SPEC','WITNESS_DISCOVER','WITNESS_RECORD'):env.pop(k,None)
+with tarfile.open(Q/'upstream-layout.tar.gz') as t:
+ for m in t.getmembers():assert m.isfile() and not Path(m.name).is_absolute() and '..' not in Path(m.name).parts
+ t.extractall(layout,filter='data')
+R=layout/'owner37-round44';N=layout/'joint1148-round45';SRC=N/'source';tools=R/'candidate-tools-joint';data=work/'data';data.mkdir()
+for name in ['PLAN.json','SPEC.json','PROFILE.json']:shutil.copy2(P/name,data/name)
+for name in ['OWNERS.json.gz','GLOBAL-TEMPLATE.json.gz']:shutil.copy2(Q/name,data/name)
+stages=[]
+def run(name,script,*args):
+ start=time.monotonic();log=work/(name+'.log')
+ with log.open('w') as f:r=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],cwd=layout,env=env,stdout=f,stderr=subprocess.STDOUT)
+ stages.append(dict(name=name,exit_code=r.returncode,seconds=time.monotonic()-start,log_sha256=sha(log)));(work/'STAGES.json').write_text(json.dumps(stages,indent=2));assert r.returncode==0,(name,log.read_text()[-5000:]);print('PASS',name,flush=True)
+run('literal-construct',Q/'construct.py','--flow',Q/'PATTERN-FLOW.json','--plan',P/'PLAN.json','--out',work/'constructed')
+assert raw(work/'constructed/OWNERS.json.gz')==raw(Q/'OWNERS.json.gz')
+run('parent-and-plan',P/'prepare_x54.py','--layout',layout,'--construction',work/'constructed','--flow',Q/'PATTERN-FLOW.json','--source-plan',P/'PLAN-SOURCE-X54.json.gz','--baseline-kappa',claim['previous_kappa'],'--out',work/'reconstructed-data')
+assert rd(work/'reconstructed-data/PLAN.json')==rd(P/'PLAN.json') and rd(work/'reconstructed-data/PROFILE.json')==rd(P/'PROFILE.json')
+assert raw(work/'reconstructed-data/GLOBAL-TEMPLATE.json.gz')==raw(Q/'GLOBAL-TEMPLATE.json.gz')
+base=SRC/'research/k8-joint-entrances/FULL-WORD.json.gz'
+run('joint-entrance-recipe',SRC/'research/k8-joint-entrances/build_word.py','--out',work/'rebuilt-joint-word.json.gz')
+assert raw(base)==raw(work/'rebuilt-joint-word.json.gz')
+word=work/'X54-JOINT-WORD.json.gz'
+run('x54-recipe',P/'build_word.py','--base',base,'--out',word)
+run('independent-local',SRC/'research/gauge44-slots/independent/audit_local.py','--word',word,'--main',SRC,'--output',work/'INDEPENDENT-LOCAL.json')
+loc=rd(work/'INDEPENDENT-LOCAL.json');plan=rd(P/'PLAN.json');reg=plan['provider_registry']['gauge44']
+assert loc['status']=='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES' and loc['local_profile']==reg['actual_paid_profile']=={'1':2364,'2':498,'3':414,'4':126,'5':84,'8':8}
+assert loc['width_inventory']=={'4':44,'5':44,'7':38,'8':114,'9':240}
+run('demotion-controls',SRC/'research/k8-joint-entrances/controls.py','--out',work/'DEMOTION-CONTROLS.json')
+assert len(rd(work/'DEMOTION-CONTROLS.json')['rejected'])==27
+run('x54-controls',P/'x54_controls.py','--base',base,'--audit',SRC/'research/gauge44-slots/independent/audit_local.py','--out',work/'x54-controls')
+native=a.native_from.resolve() if a.native_from else work/'native'
+if not a.native_from:run('fresh-native',SRC/'research/k8-eight-ends/replay_native.py',word,native)
+assert raw(native/'local/FULL-WORD.json.gz')==raw(word)
+steps=rd(native/'STEPS.json');assert [x['step'] for x in steps]==['native','ledgers','local-replay','wrappers','phases'] and all(x['exit_code']==0 for x in steps)
+run('provider-rebind',P/'rebind_plan.py','--layout',layout,'--native-local',native/'local','--out',work/'PLAN-SOURCE-X54.json.gz')
+assert raw(work/'PLAN-SOURCE-X54.json.gz')==raw(P/'PLAN-SOURCE-X54.json.gz')
+run('strict-global',tools/'replay.py','--data',data,'--work',work/'strict','--local',native/'local')
+r=rd(work/'strict/RESULT.json');assert r['status']=='PASS_STRICT_T37_THREE_DEMOTIONS' and r['kappa']==claim['kappa'] and r['kappa_decimal']==claim['kappa_decimal']
+run('fixed-family-upper',P/'all_t_bound_x54.py','--root',SRC,'--plan',P/'PLAN-SOURCE-X54.json.gz','--out',work/'UPPER.json')
+assert rd(work/'UPPER.json')['all_T_grid_upper']==r['kappa']
+result=dict(status='PASS_X54_JOINT_ENTRANCES_T37_NATIVE_AND_STRICT_ADMISSION',kappa=r['kappa'],kappa_decimal=r['kappa_decimal'],previous_kappa=claim['previous_kappa'],word_content_sha256=hashlib.sha256(raw(word)).hexdigest(),parent_geometry_reuse=True,native_reuse=bool(a.native_from),local_controls=27,x54_controls=10,admission_controls=69,bit_controls=12,independent_owner_controls=7,outer_inequalities=47,stages=stages,scope=claim['scope']);(work/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n');print(result['status'],result['kappa_decimal'])
diff --git a/research/joint-x54-t37/x54_controls.py b/research/joint-x54-t37/x54_controls.py
new file mode 100644
index 0000000000..27e2bc4a4d
--- /dev/null
+++ b/research/joint-x54-t37/x54_controls.py
@@ -0,0 +1,10 @@
+"""NewBArch's unchanged run_controls.py on the X54 joint-entrance recipe: C0, recipe, and four mutants globally and for X=54 (10 outcomes)."""
+import argparse,json,subprocess,sys
+from pathlib import Path
+P=Path(__file__).resolve().parent
+def main():
+ assert __debug__
+ ap=argparse.ArgumentParser();ap.add_argument('--base',type=Path,required=True);ap.add_argument('--audit',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();assert not a.out.exists()
+ subprocess.run([sys.executable,'-B',str(P/'vendor/barch/run_controls.py'),str(a.base),str(P/'RECIPE-X54-joint.json'),str(a.audit),str(a.out)],check=True)
+ res=json.loads((a.out/'controls.json').read_text());assert len(res)==10 and all(x['ok'] for x in res.values());print('PASS_X54_CONTROLS',len(res))
+if __name__=='__main__':main()