From a6e6ad3936f67b8f63b5b68c5e75d540610a65e7 Mon Sep 17 00:00:00 2001
From: Ali Romman <226877337+aliromman@users.noreply.github.com>
Date: Wed, 14 Oct 2026 10:14:01 -0500
Subject: [PATCH] Add verified joint centre-query transfers on sixteen data
 ports

---
 research/joint-query/NOTICE.md                |  45 ++
 research/joint-query/README.md                | 153 ++++++
 research/joint-query/SOURCES.json             | 165 +++++++
 research/joint-query/certificate.json.gz      | Bin 0 -> 725120 bytes
 .../evidence/BRIDGE-OPERATOR-REVIEW.json      |  73 +++
 .../joint-query/evidence/BRIDGE-REVIEW.md     | 235 +++++++++
 .../joint-query/evidence/CLEAN-J-CHECKS.json  |  67 +++
 .../joint-query/evidence/CONSERVED-QQ16.json  | 428 +++++++++++++++++
 .../joint-query/evidence/CONSERVED-QQ16.md    | 338 +++++++++++++
 .../evidence/JOINT-QUERY-TRANSFER-REVIEW.json |  23 +
 .../evidence/JOINT-QUERY-TRANSFER.json        |  77 +++
 .../evidence/JOINT-QUERY-TRANSFER.md          | 303 ++++++++++++
 .../joint-query/evidence/NATIVE-CHECKS.json   | 450 ++++++++++++++++++
 .../joint-query/evidence/NATIVE-REVIEW.json   | 397 +++++++++++++++
 .../joint-query/evidence/NATIVE-REVIEW.md     | 203 ++++++++
 .../joint-query/evidence/ORDERED-CHECKS.json  |  74 +++
 .../evidence/PACKAGE-COLD-REVIEW.json         | 128 +++++
 .../evidence/PACKAGE-MUTATION-REVIEW.json     |  20 +
 .../joint-query/evidence/PACKAGE-REVIEW.json  |  29 ++
 .../joint-query/evidence/PACKAGE-REVIEW.md    | 133 ++++++
 .../evidence/QQ16-COVER-ACTION-ADDENDUM.md    |  76 +++
 .../QQ16-RATIONAL-OBSERVATION-REVIEW.json     | 410 ++++++++++++++++
 .../QQ16-RATIONAL-OBSERVATION-REVIEW.md       |  95 ++++
 .../evidence/QQ16-SELECTED-WITNESS.json       | 410 ++++++++++++++++
 .../evidence/QQ16-SELECTED-WITNESS.md         | 124 +++++
 research/joint-query/evidence/REPLAY.json     |  35 ++
 .../joint-query/evidence/SCALAR-CHECKS.json   |  46 ++
 .../joint-query/evidence/SCALAR-REVIEW.json   |  92 ++++
 .../joint-query/evidence/SCALAR-REVIEW.md     | 142 ++++++
 research/joint-query/notices/LICENSE          | 201 ++++++++
 .../research/gauge44-slots-t16/NOTICE.md      |  24 +
 .../gauge44-slots-t16/UPSTREAM-NOTICE.md      |  34 ++
 .../gauge44-slots-t16/construction/NOTICE.md  |   9 +
 .../research/gauge44-slots-t16/t16/NOTICE.md  |  39 ++
 research/joint-query/replay.py                |  89 ++++
 research/joint-query/source_data.py           | 348 ++++++++++++++
 research/joint-query/verify_native.py         | 423 ++++++++++++++++
 research/joint-query/verify_ordered.py        | 238 +++++++++
 research/joint-query/verify_scalar.py         | 267 +++++++++++
 39 files changed, 6443 insertions(+)
 create mode 100644 research/joint-query/NOTICE.md
 create mode 100644 research/joint-query/README.md
 create mode 100644 research/joint-query/SOURCES.json
 create mode 100644 research/joint-query/certificate.json.gz
 create mode 100644 research/joint-query/evidence/BRIDGE-OPERATOR-REVIEW.json
 create mode 100644 research/joint-query/evidence/BRIDGE-REVIEW.md
 create mode 100644 research/joint-query/evidence/CLEAN-J-CHECKS.json
 create mode 100644 research/joint-query/evidence/CONSERVED-QQ16.json
 create mode 100644 research/joint-query/evidence/CONSERVED-QQ16.md
 create mode 100644 research/joint-query/evidence/JOINT-QUERY-TRANSFER-REVIEW.json
 create mode 100644 research/joint-query/evidence/JOINT-QUERY-TRANSFER.json
 create mode 100644 research/joint-query/evidence/JOINT-QUERY-TRANSFER.md
 create mode 100644 research/joint-query/evidence/NATIVE-CHECKS.json
 create mode 100644 research/joint-query/evidence/NATIVE-REVIEW.json
 create mode 100644 research/joint-query/evidence/NATIVE-REVIEW.md
 create mode 100644 research/joint-query/evidence/ORDERED-CHECKS.json
 create mode 100644 research/joint-query/evidence/PACKAGE-COLD-REVIEW.json
 create mode 100644 research/joint-query/evidence/PACKAGE-MUTATION-REVIEW.json
 create mode 100644 research/joint-query/evidence/PACKAGE-REVIEW.json
 create mode 100644 research/joint-query/evidence/PACKAGE-REVIEW.md
 create mode 100644 research/joint-query/evidence/QQ16-COVER-ACTION-ADDENDUM.md
 create mode 100644 research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json
 create mode 100644 research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md
 create mode 100644 research/joint-query/evidence/QQ16-SELECTED-WITNESS.json
 create mode 100644 research/joint-query/evidence/QQ16-SELECTED-WITNESS.md
 create mode 100644 research/joint-query/evidence/REPLAY.json
 create mode 100644 research/joint-query/evidence/SCALAR-CHECKS.json
 create mode 100644 research/joint-query/evidence/SCALAR-REVIEW.json
 create mode 100644 research/joint-query/evidence/SCALAR-REVIEW.md
 create mode 100644 research/joint-query/notices/LICENSE
 create mode 100644 research/joint-query/notices/research/gauge44-slots-t16/NOTICE.md
 create mode 100644 research/joint-query/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md
 create mode 100644 research/joint-query/notices/research/gauge44-slots-t16/construction/NOTICE.md
 create mode 100644 research/joint-query/notices/research/gauge44-slots-t16/t16/NOTICE.md
 create mode 100644 research/joint-query/replay.py
 create mode 100644 research/joint-query/source_data.py
 create mode 100644 research/joint-query/verify_native.py
 create mode 100644 research/joint-query/verify_ordered.py
 create mode 100644 research/joint-query/verify_scalar.py

diff --git a/research/joint-query/NOTICE.md b/research/joint-query/NOTICE.md
new file mode 100644
index 0000000000..297ac2775c
--- /dev/null
+++ b/research/joint-query/NOTICE.md
@@ -0,0 +1,45 @@
+# Source attribution and license
+
+New research, code, and verification used substantial OpenAI Codex
+assistance under the user's direction. Separate agents developed and
+reviewed the algebra, scalar words, owner maps, and native phases.
+The recorded independent reviews are agent reviews. No independent
+human review is claimed. New material uses the repository's Apache-2.0
+license, retained in [notices/LICENSE](notices/LICENSE).
+
+The local word and phase data come from the gauge44 and t16 source
+lineage at commit bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Their original
+notices are copied without changes:
+
+- [Gauge44 notice](notices/research/gauge44-slots-t16/NOTICE.md).
+- [Construction notice](notices/research/gauge44-slots-t16/construction/NOTICE.md).
+- [T16 integration notice](notices/research/gauge44-slots-t16/t16/NOTICE.md).
+- [Complete upstream notice](notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md).
+
+Those notices preserve the credited contributors, predecessor results,
+licenses, source pins, and earlier AI disclosures. This package does not
+claim those results as new work.
+
+The source loader is unchanged from research/native-source-codes at
+commit 7649d9ceecec949541bec4bbde5929344166ba59. The new package does not
+change that package or depend on its four example programs. It reads the
+same immutable source archive directly.
+
+The centre-encoding campaign first supplied the selected-section and
+source-code constructions. The cover-algebra lane supplied the ordered
+joint-query theorem and inverses. The residual-syndrome lane supplied the
+short scalar words and independent scalar review. The coherent-port lane
+supplied the native component lowering and proof review. The
+circuit-interface lane supplied the frozen full-cover words. The
+residual-syndrome independent reviewer supplied the full native review.
+The interface-proof lane supplied the inherited bridge proof and the
+independent controller witness review. The encoded-controller lane
+supplied the selected-observation witness. These source files and their
+exact hashes are recorded in [SOURCES.json](SOURCES.json).
+
+The portable scalar, native, and ordered checkers adapt those proof and
+independent review methods. They do not import the exploratory emitters.
+The sixteen-port construction follows the earlier source-only logger;
+its use of joint X and Y state is a separate local construction. No
+controller closure, complete supplier gain, or official frontier change
+is claimed.
diff --git a/research/joint-query/README.md b/research/joint-query/README.md
new file mode 100644
index 0000000000..2bf4fc0aa2
--- /dev/null
+++ b/research/joint-query/README.md
@@ -0,0 +1,153 @@
+# Local joint-query transfer through sixteen existing ports
+
+This package gives invertible local forward and backward words that use
+sixteen existing data ports to carry centre queries. They change the
+selected source baseline and use joint X and Y state. The ordered proof
+does not require an inverse of the ordinary response matrix M. This
+removes the Schur-unit requirement of the earlier fixed-baseline model
+for this local construction family.
+
+The [ordered proof](evidence/JOINT-QUERY-TRANSFER.md) gives the precise
+hypotheses, maps, and inverses. The [native contract](evidence/CONSERVED-QQ16.md)
+gives the full-cover action and sweep order. The frozen words passed
+[independent scalar review](evidence/SCALAR-REVIEW.md) and
+[independent native review](evidence/NATIVE-REVIEW.md). The native review
+supersedes the older pending-review sentence in the frozen native note.
+The [independent package audit](evidence/PACKAGE-REVIEW.md) also passed.
+It checks the portable adaptation and a copied-directory cold replay.
+
+The construction does not close the changing-chart controller. It does
+not establish a complete supplier or a new kappa bound.
+
+## Query contract
+
+The two disjoint selected sets are
+
+```text
+A = [0, 7, 20, 27, 36, 46, 57, 111]
+T = [21, 37, 47, 76, 81, 87, 92, 110].
+```
+
+Use the actual 8 by 112 centre matrix R, K=R^T/4, and J=I-KR.
+The A and T minors have dyadic inverses. The ordinary set U has 96 ports,
+and R K_U=12I. Each current chart s has the routed operators R_s, K_s,
+and selected query ell_s. A future chart t has the A logger E_t.
+
+The backward word has u=E_t y, a=ell_s x, and b=R_s u. It returns
+
+```text
+R_s y' = a,
+ell_(t,A) y' = R_t y,
+ell_s x' = b + 12a.
+```
+
+These are different records. The selected X result is not b alone.
+The forward word returns the full current X query in T and moves the
+old T query into A. Both words preserve X_p+Y_p for all p in A union T.
+Their displayed data inverses work in both orders. The forward and
+backward words are companions; they are not inverse circuits.
+
+The general ordered theorem replaces 12I by M=R K_U. It uses only the
+stated selected sections and support conditions. M may be singular.
+The portable tests include the actual R, a noncentral matrix M, and M=0.
+The ring proof, not these finite examples, establishes the general claim.
+
+## Native and workspace contract
+
+The certificate contains all 28 B_s_t words for 1 <= s < t <= 8 and all
+nine F_s words for 0 <= s <= 8. A cover map changes the owner and applies
+its separate payload translation on every tensor layer. It is not a
+payload permutation of one fixed owner array.
+
+Each cover sweep must finish before the next event. Each private sweep
+executes its whole row body at one owner before it moves to the next
+owner. The new wrappers use one existing owned C0 field, with a clear
+before and after each row. They allocate no new field. All 480 arbitrary
+ordinary helpers are restored. The eight owned private inputs may be
+arbitrary; the complete word discards them and returns zero. They are
+not claimed to be borrowed inputs that must be restored.
+
+| Complete local word | Real scalar primitive bound | Added rank-one children | Native rank mass | Added full-cover maps | Native wrapper maps |
+|---|---:|---:|---:|---:|---:|
+| B_s_t | 214986 | 24 | 5546 | 528 | 48 |
+| F_s, s > 0 | 211210 | 8 | 5530 | 288 | 16 |
+| F_0 | 211210 | 8 | 5530 | 0 | 16 |
+
+These counts include the retained core. Each core costs 202138 scalar
+primitives and has native mass 5522. The map columns count operations;
+they are not a physical stream or address implementation cost. The
+formal scalar prefix guards are 73 bits for B and 55 bits for F. They
+are not a recursive precision proof.
+
+## Reproduce
+
+Use Python 3.10 or later, its standard library, and Git. The repository
+must contain commit bce54fb3f895cbe5cd4c0eb477c3afeed100190f and its
+selected-replay archive. No network, package installation, scratch lane,
+or predecessor Python package is used at runtime. Run one process.
+
+From a checkout that contains this package at research/joint-query:
+
+```sh
+python3 -I -O -B research/joint-query/replay.py --repo . --out /tmp/qq16-replay
+```
+
+Expected first line:
+
+```text
+PASS_PORTABLE_QQ16_LOCAL_JOINT_QUERY
+```
+
+The entrypoint rebuilds R and both clean-J cores from the immutable Git
+archive. It then rebuilds every added scalar coefficient and all 1008
+chart routes from the actual source phase data. It checks:
+
+- both 712-column scalar maps, all helper outputs, both data inverse
+  orders, two algebraic compositions, and sixteen conserved sums;
+- all 37 literal owner paths, private lifetimes, exact frame polynomials,
+  and the complete local scalar and native invoices;
+- all 16384 Gaussian basis columns of the 32 signed native line recipes;
+- timing, private-clear, scalar-phase, inverse-sign, translation,
+  owner-action, and odd-denominator controls.
+
+All validation remains active under -O. The output JSON files record
+the source and code hashes. [SOURCES.json](SOURCES.json) records the
+original proof and review dependencies and their exact hash modes.
+
+## Scope and open obligations
+
+The retained core bytes, scalar maps, and local frame ledger are checked
+again. The [bridge proof](evidence/BRIDGE-REVIEW.md) supplies the inherited
+owner embedding and endpoint adapters. The old recursive child kernels
+are not rerun by this package. The algebraic inverse formulas do not give
+free legal reads from the native output frames.
+
+The [selected-observation witness](evidence/QQ16-SELECTED-WITNESS.md)
+blocks the current conserved controller with its fixed first F0/B1 pair
+and retained ordinary bank schedule. It still blocks later homogeneous
+selected-only linear controls when all five F query histories are given.
+It does not exclude a changed first pair, ordinary-to-selected reads,
+affine helper state, or paid query operations. Its
+[independent review](evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md) is
+retained evidence; this entrypoint does not rerun that global witness.
+
+New child and helper hosting, controller closure, endpoint recovery,
+stream and address costs, recursive precision, and the complete supplier
+invoice remain open. The separately reviewed map-fusion follow-up is not
+included in this base certificate. Source credits and AI assistance are
+recorded in [NOTICE.md](NOTICE.md).
+
+## Open next questions
+
+Can a changed local interface retain the old chart queries through the
+whole controller? The first step is an ordered inverse calculation with
+explicit selected records. The fixed first-pair witness blocks the
+current conserved interface and its stated observation set.
+
+Can new children use the actual owner and helper schedule? Bind each
+child to an owner, prove each private lifetime, and check each complete
+cover sweep. The local certificate does not supply that global layout.
+
+Does a complete construction reduce the supplier cost? After controller
+closure, count all storage, address maps, scalar work, precision and
+recursive children. The local count alone does not settle this question.
diff --git a/research/joint-query/SOURCES.json b/research/joint-query/SOURCES.json
new file mode 100644
index 0000000000..3e66629292
--- /dev/null
+++ b/research/joint-query/SOURCES.json
@@ -0,0 +1,165 @@
+{
+  "AI_assistance": "Research, implementation, and verification used substantial OpenAI Codex assistance. Separate agents supplied the recorded reviews; no independent human review is claimed.",
+  "adapted_checkers": {
+    "verify_native.py": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/native/verify_native_review.py",
+      "source_sha256": "a4029bc65ac4149adc7043dc6da254e03630dc0037d32c903058162c46003c16"
+    },
+    "verify_ordered.py": {
+      "campaign_source": "lanes/cover-algebra/check_joint_query_transfer.py",
+      "source_sha256": "fb60403444aa0a7cea8c1a3774a4aa85fb238013dd94796f8ffd4020c68f4073"
+    },
+    "verify_scalar.py": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/verify_conserved_review.py",
+      "source_sha256": "4bbbefd65cc06a3120bc30072979e6597dd002460a952385bde7e98196ea9fb9"
+    }
+  },
+  "chart_reconstruction": "The 112 local chart bases and all 1008 routes are rebuilt from the pinned single-layer DATA-PHASES source. The frozen packet consumed doubled chart payload 498d85807dd3032de01b5da72a67717f02ee0ecf068e8c47f67d4f21034cd896. Both supply the same local bases.",
+  "evidence": {
+    "evidence/BRIDGE-OPERATOR-REVIEW.json": {
+      "campaign_source": "lanes/interface-proof/BRIDGE-OPERATOR-REVIEW.json",
+      "role": "Inherited exact bridge and source binding receipt",
+      "sha256": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc"
+    },
+    "evidence/BRIDGE-REVIEW.md": {
+      "campaign_source": "lanes/interface-proof/BRIDGE-REVIEW.md",
+      "role": "Inherited owner and core embedding proof",
+      "sha256": "d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3"
+    },
+    "evidence/CONSERVED-QQ16.json": {
+      "campaign_source": "lanes/circuit-interface/qq16/CONSERVED-QQ16.json",
+      "role": "Original full native producer receipt",
+      "sha256": "b91eb8599c403db55c889bb225a1cd93f46fdb83eb339f101d18843d52b1c920"
+    },
+    "evidence/CONSERVED-QQ16.md": {
+      "campaign_source": "lanes/circuit-interface/qq16/CONSERVED-QQ16.md",
+      "role": "Frozen native contract; later independent review supersedes its pending status",
+      "sha256": "60f0de3a7205ba5046b5ae7ffa8bf2b1ea42ea46b498face0a77966b59e7f3fb"
+    },
+    "evidence/JOINT-QUERY-TRANSFER-REVIEW.json": {
+      "campaign_source": "lanes/coherent-port/JOINT-QUERY-TRANSFER-REVIEW.json",
+      "role": "Independent ordered proof review",
+      "sha256": "28d9d525c9eec07c91cb51edfdb5a0cf01ff75fddd39046b3d2fda03456e9153"
+    },
+    "evidence/JOINT-QUERY-TRANSFER.json": {
+      "campaign_source": "lanes/cover-algebra/JOINT-QUERY-TRANSFER.json",
+      "role": "Original ordered regression receipt",
+      "sha256": "1f32819591103ab323c69cf50cf6579b0e881e105ca4a93b48125d5b89214c31"
+    },
+    "evidence/JOINT-QUERY-TRANSFER.md": {
+      "campaign_source": "lanes/cover-algebra/JOINT-QUERY-TRANSFER.md",
+      "role": "Ordered ring proof and exact maps",
+      "sha256": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75"
+    },
+    "evidence/NATIVE-REVIEW.json": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/native/REVIEW.json",
+      "role": "Independent full native receipt",
+      "sha256": "e9e9287a4a4d1be3c802899a42f70ff5dd5efd1e144a48bd585386fe234832e5"
+    },
+    "evidence/NATIVE-REVIEW.md": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/native/REVIEW.md",
+      "role": "Independent full native review",
+      "sha256": "2247e3cbe73f3f0da55c647ffae15f98dd9445b2366ba9e255b9bebc9f742b70"
+    },
+    "evidence/QQ16-COVER-ACTION-ADDENDUM.md": {
+      "campaign_source": "lanes/coherent-port/QQ16-COVER-ACTION-ADDENDUM.md",
+      "role": "Exact distinction between owner routes and payload permutations",
+      "sha256": "4bb4a68d8b4811b6d8364150612056bc124d38f1974d6f603dae68a99c4682fb"
+    },
+    "evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json": {
+      "campaign_source": "lanes/interface-proof/rational-decoder/QQ16-RATIONAL-OBSERVATION-REVIEW.json",
+      "role": "Independent controller witness receipt",
+      "sha256": "588a3ce4593576ae921e97c6ced6a050f88736f29708cfee117385b254cd358f"
+    },
+    "evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md": {
+      "campaign_source": "lanes/interface-proof/rational-decoder/QQ16-RATIONAL-OBSERVATION-REVIEW.md",
+      "role": "Independent controller witness proof review",
+      "sha256": "9a06ff40830ef80d3566fce77c78639cb64d519d487a0a7f57d543c3146e2c49"
+    },
+    "evidence/QQ16-SELECTED-WITNESS.json": {
+      "campaign_source": "lanes/encoded-controller/QQ16-SELECTED-WITNESS.json",
+      "role": "Controller witness receipt",
+      "sha256": "e35e5868a1322e406191079c0675975b139692ba50b1e2e5fb8a40b6480519f4"
+    },
+    "evidence/QQ16-SELECTED-WITNESS.md": {
+      "campaign_source": "lanes/encoded-controller/QQ16-SELECTED-WITNESS.md",
+      "role": "Current controller obstruction and exact scope",
+      "sha256": "52f2ee565320f05282c637aa79eee100606c24240b1b5866f0c8d62e7913c9fc"
+    },
+    "evidence/SCALAR-REVIEW.json": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/REVIEW.json",
+      "role": "Independent scalar receipt",
+      "sha256": "171bdbec200359c82aba79e4153d73bfcbf14ac3ae4e07b15476b79b7fcbf091"
+    },
+    "evidence/SCALAR-REVIEW.md": {
+      "campaign_source": "lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/REVIEW.md",
+      "role": "Independent scalar proof review",
+      "sha256": "aa7b9f74430b56c42e1099029a501a9b6be9ab56b81bfdc681e4c2e6ff5bc97d"
+    },
+    "notices/LICENSE": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:LICENSE",
+      "role": "Unchanged source notice or license",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    "notices/research/gauge44-slots-t16/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/NOTICE.md",
+      "role": "Unchanged source notice or license",
+      "sha256": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf"
+    },
+    "notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/UPSTREAM-NOTICE.md",
+      "role": "Unchanged source notice or license",
+      "sha256": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610"
+    },
+    "notices/research/gauge44-slots-t16/construction/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/construction/NOTICE.md",
+      "role": "Unchanged source notice or license",
+      "sha256": "defe7e44af610e25a6c50c1c3b2efd0972d0690574995c0c872fc50eebf4c816"
+    },
+    "notices/research/gauge44-slots-t16/t16/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/t16/NOTICE.md",
+      "role": "Unchanged source notice or license",
+      "sha256": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5"
+    }
+  },
+  "native_certificate": {
+    "campaign_source": "lanes/circuit-interface/qq16/CONSERVED-QQ16-PROGRAMS.json.gz",
+    "decompressed_sha256": "2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef",
+    "file_sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7"
+  },
+  "original_source_audit": {
+    "campaign_source": "lanes/circuit-interface/qq16/SOURCE-BUNDLE.json",
+    "scope": "All 31 direct source files and their hash modes were checked before packaging. Absolute workspace paths are omitted from this portable package.",
+    "sha256": "6654c7a2cf68c20963c2eb36da4dda039a6afa16a6f894e170dd58dfa5cc63cf"
+  },
+  "portable_loader": {
+    "sha256": "d23924511e3aed41e5e64511ca70126a636d91c8aa02e656cb61d6ceca1fe0a0",
+    "source_commit": "7649d9ceecec949541bec4bbde5929344166ba59",
+    "source_path": "research/native-source-codes/source_data.py"
+  },
+  "review_boundary": "Original independent receipts are preserved. The new portable adaptation needs its own independent review.",
+  "schema": "portable-qq16-source-manifest-v1",
+  "source": {
+    "archive_path": "research/community-frontier1042-audit/selected-replay.tar.gz",
+    "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754",
+    "base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+    "credit_sources": {
+      "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+      "research/gauge44-slots-t16/NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+      "research/gauge44-slots-t16/UPSTREAM-NOTICE.md": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+      "research/gauge44-slots-t16/construction/NOTICE.md": "defe7e44af610e25a6c50c1c3b2efd0972d0690574995c0c872fc50eebf4c816",
+      "research/gauge44-slots-t16/t16/NOTICE.md": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5"
+    },
+    "decompressed_payloads": {
+      "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+      "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3"
+    },
+    "members": {
+      "slots/local/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+      "slots/local/CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+      "slots/local/LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+      "slots/local/RESIDUAL-ADAPTERS.json": "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+      "t16/global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa"
+    }
+  }
+}
diff --git a/research/joint-query/certificate.json.gz b/research/joint-query/certificate.json.gz
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diff --git a/research/joint-query/evidence/BRIDGE-OPERATOR-REVIEW.json b/research/joint-query/evidence/BRIDGE-OPERATOR-REVIEW.json
new file mode 100644
index 0000000000..bdd8781819
--- /dev/null
+++ b/research/joint-query/evidence/BRIDGE-OPERATOR-REVIEW.json
@@ -0,0 +1,73 @@
+{
+  "actual_data_owner_routes_checked": 32256,
+  "actual_local_shear": "D L(J) D or D U(-J^T) D in the pinned boundary gauges",
+  "actual_stage_entry_exit_gauges_checked": 1008,
+  "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754",
+  "complete_phase_identity_character_checks": 51744,
+  "divide13_finite_bit_circuit": {
+    "divisor": 13,
+    "exactness_condition": "Input numerator is divisible by 13 under the common odd-grid invariant",
+    "excluded_costs": [
+      "stream reads and writes",
+      "address routing",
+      "root common-grid conversions"
+    ],
+    "extra_finite_control_bits_upper_bound": 32,
+    "nondivisible_inputs_with_nonzero_remainder": 15123,
+    "scan_order": "Conditional negation from low to high; unsigned division from high to low; conditional negation from low to high",
+    "signed_14_bit_inputs_checked": 16384,
+    "signed_AND_OR_NOT_gates_per_numerator_bit": 179,
+    "unsigned_AND_OR_NOT_gates_per_numerator_bit": 161,
+    "valid_state_transitions": 26
+  },
+  "interface_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+  "logical_bridge": "A^-1 J A T_boundary=T_boundary D J D; the same identity holds for J^-1",
+  "maximum_resident_bytes": 182386688,
+  "operator_alignment": "A=Z_delta D; A T_boundary=T_common D",
+  "phase_controls": {
+    "omitted_X_translation_rejected": 112,
+    "omitted_Y_translation_rejected": 112,
+    "reversed_Y_route_translation_order_rejected": 112
+  },
+  "phase_method": "Exact Fourier-character evaluation on all weight-zero, one, and two inputs in the active 17-dimensional space",
+  "scalar_programs": {
+    "forward": {
+      "additional_real_divide_by_13_streams": 0,
+      "dyadic_real_primitive_bound": 7232,
+      "events": 920,
+      "full_input_columns_checked": 113,
+      "macros": {
+        "add": 896,
+        "clear": 16,
+        "quarter": 8
+      },
+      "maximum_live_private_arrays": 1,
+      "native_children": 0,
+      "private_input_and_output_zero": true
+    },
+    "inverse": {
+      "additional_real_divide_by_13_streams": 16,
+      "dyadic_real_primitive_bound": 7232,
+      "events": 928,
+      "full_input_columns_checked": 113,
+      "macros": {
+        "add": 896,
+        "clear": 16,
+        "divide13": 8,
+        "quarter": 8
+      },
+      "maximum_live_private_arrays": 1,
+      "native_children": 0,
+      "private_input_and_output_zero": true
+    }
+  },
+  "scope": "Exact native operator and finite scalar macro invoice. Address routing, bit division cost, and a complete controller invoice remain separate.",
+  "seconds": 4.192791291999583,
+  "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "source_pins": {
+    "t16/global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+    "t16/global/hosted/GLOBAL-TEMPLATE.json.gz": "73f47a1e60b1e4ea66dbca9a497c411c8e6adc7984e276a437a10a9a7a13b47a"
+  },
+  "status": "PASS_EXACT_BRIDGE_OPERATORS_AND_ACTUAL_LOCAL_GAUGE",
+  "two_factor_phase_checks": 17248
+}
diff --git a/research/joint-query/evidence/BRIDGE-REVIEW.md b/research/joint-query/evidence/BRIDGE-REVIEW.md
new file mode 100644
index 0000000000..86139908c4
--- /dev/null
+++ b/research/joint-query/evidence/BRIDGE-REVIEW.md
@@ -0,0 +1,235 @@
+# Exact operators for the phase-aware bridges
+
+The bridge construction in `../cover-algebra/BRIDGES.md` implements the same
+logical operator K_t as the centre-free local word. It does not leave a Pauli
+conjugation in the logical content. This conclusion requires both listed
+translation corrections in the stated order. A bare cover permutation does
+not give the result.
+
+`BRIDGE-OPERATOR-REVIEW.json` records an independent check. The checker imports
+none of the route, bridge, or Clifford checkers. It reads the actual phase
+recipes and hosted template from the
+[pinned replay archive](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/community-frontier1042-audit/selected-replay.tar.gz).
+The archive hash is `22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754`.
+The receipt also records the hashes of both source members and the centre
+matrix. This note is an operator review and a finite scalar invoice. It does
+not admit a complete recursive supplier.
+
+## 1. Native conventions
+
+Let T_a be address translation by a. The native line operator is
+
+    C_a = (1+i) I/2 + (1-i) T_a/2.
+
+On the Fourier character indexed by u, its multiplier is i^(a dot u), where
+the binary dot product is read as the integer zero or one. Hence a signed
+product of line operators has multiplier i^phi(u), with
+
+    phi(u) = sum_j epsilon_j (a_j dot u) modulo 4.
+
+All operators here fix the constant character. There is no undetermined
+global phase. A translation T_delta has multiplier (-1)^(delta dot u).
+
+For an orthonormal coordinate space U, let F_U be the product of its
+coordinate line operators. At a completed stage s, the boundary gauges are
+
+    X at port q and cover d:  F_(d U_s),
+    Y at port q and cover d:  F_(d U_s) C_(d q)^-1.
+
+Here U_s=L+E_1+...+E_s, dim(L)=9, and dim(E_t)=8. The initial gauges are
+C_(d q) on X and I on Y. These are the selected controller conventions.
+The source check below binds the local entry and exit adapters to them.
+It does not independently repeat the entire idle-child schedule proof.
+
+Write B_q for the eight orthonormal chart columns in q-perp. The actual
+involution rho_t(q) fixes q, swaps these columns with E_t, and fixes the
+other external blocks. Let
+
+    beta_q[i] = (weight(B_q[i])-1)/2 modulo 2.
+
+The review checks the following complete operator identities:
+
+    rho_t(F_(U_s) C_q^-1) = T_(q+lift_t(beta_q)) F_(E_1+...+E_s+E_t), s<t,
+    rho_t(F_(U_s)) = T_(B_q beta_q+lift_t(beta_q)) F_(U_s),             s>=t.
+
+The notation rho_t(F) means transport of every axis of F by rho_t. The
+other external blocks are fixed, so their identical factors cancel from
+each equation. It is enough to check the 17 coordinates in L+E_t.
+
+The checker evaluates the full phase at zero, at every unit vector, and at
+every sum of two distinct unit vectors. This determines the complete phase:
+the integer expansion of a binary parity modulo four has degree at most two.
+It gives 51,744 exact character checks for the two bridge identities and the
+source entrance identity. Omission of either correction is rejected for all
+112 ports. Reversal of the Y route and correction order is also rejected
+for every port. There are 17,248 additional two-factor phase checks.
+
+## 2. Which logical operator the bridge performs
+
+Let T be one of the boundary gauges above, as a block diagonal operator on
+all port-cover positions. Define D by
+
+    (D v)_(d,q) = v_(d rho_t(q),q).
+
+This operation only changes the selected cover position. It does not apply
+rho_t to the payload address. These are independent input arrays, and their
+contents must remain distinct.
+
+Let Z be the block translation whose component at (d,q) is T_(d delta_q),
+with delta from section 1. Put A=ZD. The exact phase identities give
+
+    A T = T_common D.
+
+At each fixed cover d, T_common is independent of q. Therefore every scalar
+port matrix M commutes with it. In particular,
+
+    (A^-1 M A) T = T D M D.
+
+Since D is an involution and translations are involutions, the physical
+sequence is D, then Z, then M, then Z, then D. On logical content its result
+is exactly D M D. For M=J or M=J^-1 this is K_t or K_t^-1. The result holds
+on Y before stage t and on X at or after stage t. It is valid at all cover
+positions and on arbitrary payloads.
+
+This proof also gives the general construction: any port matrix that has a
+finite scalar implementation can be applied after alignment. Only its
+coefficient and workspace costs change. Inverses and products use the same
+logical gauges; each individual bridge returns to the original gauge.
+
+## 3. Binding to the actual local shear
+
+For t>0, the exact `DATA-PHASES.json` entries in owner coordinates are
+
+    entry_X = entry_Y = q + B_q beta_q,
+    exit_X  = exit_Y  = B_q beta_q + lift_t(beta_q).
+
+The stage-zero entries are all zero. The independent check verifies all
+1,008 port-stage recipes against these formulas. It also checks all 32,256
+data owner routes in the hosted template. The source template refers to
+this exact phase file and uses physical cover position d rho_t(q).
+
+An owner-coordinate translation a is a translation by d rho_t(q) a in the
+local cover sweep at d. Thus the entry correction is physically
+T_(d(q+lift_t(beta_q))). The exit vector is rho_t-invariant, so its physical
+correction is T_(d(B_q beta_q+lift_t(beta_q))).
+
+After routing and the entry correction, X has native frame C_(d q) times
+the common exterior factor, and Y has just that common exterior factor.
+The local word thus receives its exact native entry gauges. Its scalar
+forward map is L(J), and its backward map is U(-J^T). The exact local review
+in `PROOF.md` proves these maps on arbitrary data and helper values. At exit,
+both words have their prescribed full local frames. The exit correction
+converts these frames to the routed global boundary frames. Routing back
+therefore gives
+
+    D L(J) D, or D U(-J^T) D.
+
+Their off-diagonal coefficient is exactly K_t=D J D, or its transpose with
+the backward sign. This is the same K_t as section 2. No payload permutation
+or leftover translation has been removed by assumption.
+
+## 4. Tensor powers and legal access
+
+Replace every native frame and translation by its lambda-th tensor power.
+Every operator equality above remains an equality. The scalar port matrix
+acts on the port coordinate and commutes with the tensor address operators.
+Its coefficients stay unchanged; they are not raised to power lambda.
+Identity spectator factors can be added throughout. This proves the result
+for every positive integer lambda and arbitrary spectator contents.
+
+The cover route and translation can also define a view of the data array.
+For each fixed port they are bijections. Distinct routed cover blocks thus
+do not overlap, and gathering one block before its update is legal. A direct
+implementation can use these views for its source reads and target writes;
+it need not materialize a full additional data bank. This statement does not
+make address computation free. The supplier must price the route, the
+repeated tensor translation, stream access, and any physical realization.
+
+One private accumulator suffices for the scalar step below. Its physical
+contents are cleared before use, so it can carry the common frame without
+a native preparation child. The final clear restores it to zero. No
+assumption is made about its initial contents. No other borrowed register
+is changed by the scalar step.
+
+## 5. A one-accumulator scalar implementation
+
+Let r_k be row k of R. The exact relation R R^T=56I gives r_j r_k^T=0 for
+j different from k. Consequently the following eight row updates commute:
+
+    v <- v - r_k^T (r_k v)/4.
+
+An earlier row update does not change a later row sum. Their product is
+J=I-R^T R/4. Replacing 4 by 52 gives J^-1, since
+
+    (I-R^T R/4)(I-R^T R/52)=I.
+
+For each row, clear one private accumulator, gather r_k v, divide the
+accumulator by 4, scatter its signed value by -r_k^T, and clear it. For the
+inverse, also divide the accumulator by 13 before the scatter. The source
+matrix has 448 nonzero entries, all plus or minus one.
+
+| Item per port-cover block | J | J^-1 |
+|---|---:|---:|
+| Signed ADD macros | 896 | 896 |
+| Divide-by-four SCALE macros | 8 | 8 |
+| CLEAR macros | 16 | 16 |
+| Complex divide-by-13 scans | 0 | 8 |
+| Maximum live private arrays | 1 | 1 |
+| Added native children | 0 | 0 |
+
+Under the retained primitive bounds, each signed ADD costs at most four
+real primitives, each divide-by-four SCALE costs two, and each CLEAR costs
+one. Including both real components gives 7,232 real primitives. The inverse
+adds 16 real constant-division scans. Both emitted abstract scalar programs
+were replayed on all 113 input columns. This includes the arbitrary private
+input. The output private row and its input column are zero. Omitting the
+first clear or the first inverse division fails the full map check.
+
+The current dyadic compiler does not admit division by 13. Section 3 of
+`COEFFICIENTS.md` identifies the repository's common odd-grid construction.
+It applies with a fixed factor 13. This is an extension that must be included
+in the changed compiler and recursive precision proof.
+
+There is a concrete finite bit circuit for that division. In unsigned binary
+long division, the state is a remainder r in {0,...,12}. On input bit b,
+emit floor((2r+b)/13) and keep (2r+b) modulo 13. A truth-table circuit for
+these 26 cases uses 161 two-input AND/OR or one-input NOT gates per bit.
+Two conditional-negation scans handle a signed two's-complement numerator.
+Each uses at most nine such gates per bit. Thus a signed ell-bit division
+uses at most 179 ell Boolean gates, three linear scans, and at most 32 bits
+of extra finite control. Stream reads, writes, and addressing are separate.
+The checker verifies all 26 transitions and all 16,384 signed 14-bit inputs.
+Nondivisible inputs have a nonzero remainder; they are not silently accepted.
+
+Exactness on the supplier follows from the common-grid invariant, not from
+arbitrary integer divisibility. Choose enough root factors of 13 for the
+maximum unfinished recursion chain. Completed native children are Gaussian
+dyadic and do not consume this reserve. Every division input numerator is
+then divisible by 13. Root scaling and final unscaling remain part of the
+complete assembly bill. The bridge alone does not prove this recursive
+invariant for a proposed whole controller.
+
+## 6. Review result and remaining work
+
+No material phase or logical-operator defect was found in this bridge
+construction. Its exact scope is a finite, reusable bridge on an allowed
+side of a stage, with the scalar and native endpoints stated above. It does
+not by itself cancel the full controller residual. The full compiler must
+still lower the new routed accesses and odd division, bind the available
+private array, prove all lifetime and recursive precision bounds, and add
+the complete finite bill. A favourable rank count alone does not settle
+those obligations.
+
+Reproduce from the workspace root:
+
+```sh
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/interface-proof/verify_bridge_operators.py --repo worktrees/k5-centre-sharing --interface work/centre-encoding-campaign-20261014/lanes/circuit-interface/INTERFACE.json --out work/centre-encoding-campaign-20261014/lanes/interface-proof/BRIDGE-OPERATOR-REVIEW.json
+```
+
+Expected status: `PASS_EXACT_BRIDGE_OPERATORS_AND_ACTUAL_LOCAL_GAUGE`.
+All validation checks remain active under `-O`. The cover-algebra lane
+supplied the bridge construction and phase formulas. This lane supplied
+the independent operator binding, source replay, and one-accumulator bill.
+The phase recipes and common-grid method are retained repository work.
+This work used substantial OpenAI Codex assistance and independent agent
+review. It is not independent human review.
diff --git a/research/joint-query/evidence/CLEAN-J-CHECKS.json b/research/joint-query/evidence/CLEAN-J-CHECKS.json
new file mode 100644
index 0000000000..c8ca09c4e9
--- /dev/null
+++ b/research/joint-query/evidence/CLEAN-J-CHECKS.json
@@ -0,0 +1,67 @@
+{
+  "J_row_support": {
+    "52": 112
+  },
+  "R_column_support": {
+    "4": 112
+  },
+  "R_row_support": {
+    "56": 8
+  },
+  "archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754",
+  "clean_program_payload_sha256": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877",
+  "geometry": {
+    "axes": 9,
+    "helpers": 480,
+    "ports": 112
+  },
+  "orientations": {
+    "backward": {
+      "canonical_scalar_frames": "PASS",
+      "child_profile": {
+        "1": 2412,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      },
+      "child_rank_mass": 5522,
+      "correction_adds": 580,
+      "correction_clears": 16,
+      "independent_input_columns": 712,
+      "missing_clear_control": "REJECT",
+      "missing_correction_control": "REJECT",
+      "persistent_helpers_restored": 480,
+      "persistent_native_events": 5056,
+      "primitive_bound_real_components": 202138,
+      "private_outputs_zero": 8,
+      "removed_centre_rank_mass": 64,
+      "scalar_macros": 20089
+    },
+    "forward": {
+      "canonical_scalar_frames": "PASS",
+      "child_profile": {
+        "1": 2412,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      },
+      "child_rank_mass": 5522,
+      "correction_adds": 580,
+      "correction_clears": 16,
+      "independent_input_columns": 712,
+      "missing_clear_control": "REJECT",
+      "missing_correction_control": "REJECT",
+      "persistent_helpers_restored": 480,
+      "persistent_native_events": 5056,
+      "primitive_bound_real_components": 202138,
+      "private_outputs_zero": 8,
+      "removed_centre_rank_mass": 64,
+      "scalar_macros": 20089
+    }
+  },
+  "scope": "Exact scalar maps, canonical frame access and retained native events. Native recipe phases, global hosting and supplier admission are separate.",
+  "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "status": "PASS_PINNED_CLEAN_J_RECONSTRUCTION"
+}
diff --git a/research/joint-query/evidence/CONSERVED-QQ16.json b/research/joint-query/evidence/CONSERVED-QQ16.json
new file mode 100644
index 0000000000..7a155a27dc
--- /dev/null
+++ b/research/joint-query/evidence/CONSERVED-QQ16.json
@@ -0,0 +1,428 @@
+{
+  "B_cases": 28,
+  "F_cases": 9,
+  "complete_common_chart_input_columns_per_orientation": 712,
+  "controls": [
+    "late A input read",
+    "early T query",
+    "early F source update",
+    "early F target copy",
+    "positive inverse replacement",
+    "omitted payload translation",
+    "payload-only owner route"
+  ],
+  "full_cover_map_inverse_orders": true,
+  "invoices": {
+    "B": {
+      "arbitrary_helpers": 480,
+      "arbitrary_private_inputs_discarded": 8,
+      "complete_scalar": {
+        "macros": 21401,
+        "operations": {
+          "add": 20654,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 214986
+      },
+      "existing_owned_C0_fields": 1,
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 73,
+        "formal_triangle_Horner_bound": "573411134169296526275133/64"
+      },
+      "native_mass": 5546,
+      "native_profile": {
+        "1": 2436,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      },
+      "new_fields": 0,
+      "private_outputs_zero": 8
+    },
+    "F": {
+      "arbitrary_helpers": 480,
+      "arbitrary_private_inputs_discarded": 8,
+      "complete_scalar": {
+        "macros": 21025,
+        "operations": {
+          "add": 20278,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 211210
+      },
+      "existing_owned_C0_fields": 1,
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 55,
+        "formal_triangle_Horner_bound": "5413950274051752469/256"
+      },
+      "native_mass": 5530,
+      "native_profile": {
+        "1": 2420,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      },
+      "new_fields": 0,
+      "private_outputs_zero": 8
+    }
+  },
+  "native_cases": {
+    "B_1_2": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 2,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 1
+    },
+    "B_1_3": {
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+      "explicit_cover_maps": 528,
+      "future": 3,
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+      "orientation": "B",
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+    },
+    "B_1_4": {
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+      "orientation": "B",
+      "stage": 1
+    },
+    "B_1_5": {
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+      "orientation": "B",
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+    },
+    "B_1_6": {
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+      "orientation": "B",
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+    },
+    "B_1_7": {
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+      "future": 7,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 1
+    },
+    "B_1_8": {
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+      "explicit_cover_maps": 528,
+      "future": 8,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 1
+    },
+    "B_2_3": {
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+      "explicit_cover_maps": 528,
+      "future": 3,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 2
+    },
+    "B_2_4": {
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+      "explicit_cover_maps": 528,
+      "future": 4,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 2
+    },
+    "B_2_5": {
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
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+    },
+    "B_2_6": {
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+      "future": 6,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 2
+    },
+    "B_2_7": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 7,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 2
+    },
+    "B_2_8": {
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 2
+    },
+    "B_3_4": {
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+      "explicit_cover_maps": 528,
+      "future": 4,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 3
+    },
+    "B_3_5": {
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+      "future": 5,
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+      "orientation": "B",
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+    },
+    "B_3_6": {
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+      "future": 6,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 3
+    },
+    "B_3_7": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 7,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 3
+    },
+    "B_3_8": {
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+      "orientation": "B",
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+    },
+    "B_4_5": {
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+      "future": 5,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
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+    },
+    "B_4_6": {
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
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+    },
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+      "future": 7,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 4
+    },
+    "B_4_8": {
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+      "future": 8,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 4
+    },
+    "B_5_6": {
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+      "future": 6,
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+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 5
+    },
+    "B_5_7": {
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+      "future": 7,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 5
+    },
+    "B_5_8": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 8,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 5
+    },
+    "B_6_7": {
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+      "explicit_cover_maps": 528,
+      "future": 7,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 6
+    },
+    "B_6_8": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 8,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 6
+    },
+    "B_7_8": {
+      "added_rank1_children": 24,
+      "explicit_cover_maps": 528,
+      "future": 8,
+      "matching_phase_ADD_reads": 1288,
+      "native_wrapper_maps": 48,
+      "orientation": "B",
+      "stage": 7
+    },
+    "F_0": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 0,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 0
+    },
+    "F_1": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 1
+    },
+    "F_2": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 2
+    },
+    "F_3": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 3
+    },
+    "F_4": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 4
+    },
+    "F_5": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 5
+    },
+    "F_6": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 6
+    },
+    "F_7": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 7
+    },
+    "F_8": {
+      "added_rank1_children": 8,
+      "explicit_cover_maps": 288,
+      "matching_phase_ADD_reads": 912,
+      "native_wrapper_maps": 16,
+      "orientation": "F",
+      "stage": 8
+    }
+  },
+  "native_kernel_columns": 16384,
+  "owner_route_negative_control": {
+    "correct_owner_view_output_at_I": 1,
+    "incorrect_payload_only_output_at_I": 0,
+    "owner_I_input": 0,
+    "owner_rho_input": 1,
+    "payload_address": 0
+  },
+  "payload_sha256": "2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef",
+  "retained_core_frame_and_byte_checks": true,
+  "scalar_phase_controls": 32,
+  "scope": "Exact local full-cover operator words with explicit sweep order, native maps and phases, the inherited local core, and complete local scalar/native invoices. Global helper owners, controller closure, child hosting, precision, stream/address costs and the complete supplier invoice are not admitted here.",
+  "source_pins": {
+    "B_native_component": "d7f75b34a56fc7acfb582d3a133c3eb817a29584a1f7136896420138cc155b35",
+    "F_native_component": "232035827945f2c13e32b7ced955f222eb1f349f0b409326c83fea5847088b1a",
+    "base": "40fdf1ce79720f810729e2bb8db7470c648e67c91fc365cd632c72eb2bcce44a",
+    "bridge_proof": "d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3",
+    "bridge_review": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc",
+    "charts": "498d85807dd3032de01b5da72a67717f02ee0ecf068e8c47f67d4f21034cd896",
+    "cover_action": "4bb4a68d8b4811b6d8364150612056bc124d38f1974d6f603dae68a99c4682fb",
+    "pair_proof": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75",
+    "pair_receipt": "1f32819591103ab323c69cf50cf6579b0e881e105ca4a93b48125d5b89214c31",
+    "phase_helper": "416d50a33dab69fea7c775ac6f747163073b077169754663d2e8db353e17c2d9",
+    "positive_lines": "500c09dfc1d27ffd107341adf4c3c6874ee2c84e1a8afad91d931ed9e88fd1d7",
+    "scalar": "6b8d647a8ce2ff86f39b1947d11cbcdfd0f366e90c2816ff6cca09d47c75869c",
+    "scalar_producer": "48b8d2cf81c4b8d50c3aa0dcfe75090862a53fbbf9d051fd6985604e6191ba20",
+    "scalar_receipt": "c9729d71890df17027c75b028c535ad3bd8dc11633812bae856f80c38c52a0a1"
+  },
+  "status": "PASS_CONSERVED_QQ16_COMPLETE_LOCAL_WORDS"
+}
diff --git a/research/joint-query/evidence/CONSERVED-QQ16.md b/research/joint-query/evidence/CONSERVED-QQ16.md
new file mode 100644
index 0000000000..4639583c1b
--- /dev/null
+++ b/research/joint-query/evidence/CONSERVED-QQ16.md
@@ -0,0 +1,338 @@
+# Complete local query words with conserved selected sums
+
+This construction uses sixteen existing data ports to carry centre
+queries through a forward or backward call. The forward word puts its
+full current source query in eight completed X ports. It moves the old
+selected X value to another eight X ports. The backward word puts a
+future source query in eight Y ports and a current query, with an
+explicit selected-input term, in eight completed X ports. Both words
+preserve the logical X-plus-Y sum at each of the sixteen selected ports.
+Both complete maps are invertible on arbitrary data inputs.
+
+The emitted backward word has scalar bound 214986 and native mass 5546.
+It adds twenty-four rank-one children. The forward word has scalar bound
+211210 and native mass 5530. It adds eight rank-one children. Each uses
+one existing owned private field C0 and no new field. All 480 arbitrary
+ordinary helper inputs are restored. The eight owned private input
+values may be arbitrary; the words discard them and return zero.
+
+These are complete local full-cover operator words. The payload gives
+the exact owner maps, payload translations, intrinsic line recipes,
+scalar gates, sweep barriers, and retained local core. It is not a
+complete supplier. Global owner placement for the new sweeps and
+children, controller closure, stream and address costs, precision, and
+recursive admission remain open. No complete kappa improvement is
+claimed. Independent review of this full-word payload is pending.
+
+## Sources and field contract
+
+The literal payload is `CONSERVED-QQ16-PROGRAMS.json.gz`. Its decompressed
+SHA256 is
+
+    2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef.
+
+`CONSERVED-QQ16.json` gives the complete producer receipt. The emitter
+pins each consumed source. The main inputs are:
+
+- `../CENTRE-FREE-PROGRAMS.json.gz`: the complete reviewed clean-J core;
+- `../../residual-syndrome/physical-algebra/CONSERVED-QQ16-SCALARS.json.gz`:
+  the two fixed scalar words;
+- `../../cover-algebra/JOINT-QUERY-TRANSFER.md`: the ordered pair maps,
+  inverses, and conserved-sum extension;
+- `../../coherent-port/QQ16-CONSERVED-COMPONENT.json` and
+  `../../coherent-port/QQ16-CONSERVED-FORWARD.json`: the intrinsic native
+  recipes and component frame checks;
+- `../../coherent-port/QQ16-COVER-ACTION-ADDENDUM.md` and
+  `../../interface-proof/BRIDGE-REVIEW.md`: the exact cover action and
+  its relation to the retained local core.
+
+The field namespace is L0 through L703 and C0 through C7. X is L0
+through L111. Y is L112 through L223. L224 through L703 are the 480
+ordinary helper fields. The formal replay has all 712 input columns.
+No assumption is made that an input data, helper, or private value is
+zero. Only owned private fields may be cleared. C0 is returned to
+zero in frame I after each target row, before it is used for the next
+cover owner. C1 through C7 are not used by the new wrappers. The
+retained core clears all eight private fields.
+
+The core has 25155 events in each orientation. This includes 20089
+scalar macros, 3486 recursive child events, 1090 adapters, 480 residual
+adapters, and ten phase markers. The payload retains all these bytes.
+Their scalar bound is 202138 and their native mass is 5522. The existing
+local frame checker is rerun on the complete core in both orientations.
+
+## Exact logical maps
+
+Use the actual matrix R, K=R^T/4, and J=I-KR. Then RK=14I. Set
+
+    A=[0,7,20,27,36,46,57,111],
+    T=[21,37,47,76,81,87,92,110].
+
+The two minors satisfy R_A R_A^T=R_T R_T^T=4I. Their inverses are
+R_A^T/4 and R_T^T/4. Let U be the remaining 96 ports. An injection
+with subscript A, T, or U is zero outside that set.
+
+For a current chart s, let D_s be the actual port-diagonal cover
+route. Use the normalized queries and injections
+
+    R_s=R D_s,             K_s=D_s^-1 K,
+    P_s=D_s^-1 iota_T R_T^-1,
+    ell_s=R_T pi_T D_s.
+
+Thus R_s P_s=ell_s P_s=I, K_(s,T)=P_s, and R_s K_(s,U)=12I.
+For a future chart t>s set
+
+    E_t=I+P_(t,A)(R_t-ell_(t,A)).
+
+This is a unit. Its added term has only A output rows and no A input
+columns, so its square is zero. Its inverse has the opposite sign.
+
+For the backward word define
+
+    u=E_t y,       a=ell_s x,       b=R_s u.
+
+The exact output is
+
+    y'_A=u_A,
+    y'_U=y_U+K_(s,U)a,
+    y'_T=u_T-P_s(b+11a),
+    x'_U=x_U-y_U,
+    x'_A=x_A+y_A-u_A,
+    x'_T=P_s(b+12a).                              (1)
+
+Consequently
+
+    R_s y'=a,
+    ell_(t,A)y'=R_t y,
+    ell_s x'=b+12a,
+    x'_p+y'_p=x_p+y_p for p in A union T.         (2)
+
+The T target contains b+12a, not b alone. The future selected query
+and the current full query are different operator-valued quantities.
+
+For an explicit inverse, put Z_s=K_(s,U)-12P_s and
+H_s=I+Z_sR_s. Since R_sZ_s=0, H_s^-1=I-Z_sR_s. From x',y' compute
+
+    a=R_s y',       b=ell_s x'-12a,
+    v=H_s^-1y',    u=v+P_s(b-a),    y=E_t^-1u.
+
+Then restore x_U=x'_U+y_U, x_T=P_sa, and
+x_A=x'_A+y'_A-y_A. These equations prove both inverse orders.
+They do not establish that all inverse reads are free at the output
+frames.
+
+For the forward word put f=R_s x. Its output is
+
+    x'_U=x_U-K_(s,U)f,
+    x'_A=P_(s,A)ell_s x,
+    x'_T=P_s f,
+    y'_U=y_U+x'_U,
+    y'_S=x_S+y_S-x'_S,       S=A union T.         (3)
+
+In normalized source coordinates (z,a,c), where a=ell_(s,A)x and
+c=ell_s x, this is
+
+    (z,a,c) -> (w,c,f),
+    f=R_(s,U)z+a+c,       w=z-K_(s,U)f.
+
+Its inverse is z=w+K_(s,U)f and
+a=-R_(s,U)w-11f-c. The Y inverse follows directly from (3).
+This proves invertibility and conservation of all sixteen selected
+pair sums. The two orientations are companions, not inverse circuits.
+
+The proof in the pinned pair note uses ordered multiplication. It
+does not require two chart routes to commute. The common-chart
+712-column replay checks the emitted coefficient word. The ordered
+proof extends that word to the actual full-cover routes. The two
+claims are recorded separately.
+
+## Cover action and native phases
+
+At cover owner d, the operator C_(d q) is the inherited complex line
+
+    C_q=(1+i)I/2+(1-i)T_q/2.
+
+It satisfies C_q^2=T_q and C_q^-1=T_q C_q. A negative line therefore
+uses the inherited positive rank-one recipe with translation q fused
+into its left wrapper. A canonical binary line subspace does not
+specify this phase and is not used as a replacement.
+
+At a positive backward stage s, the physical input frames are
+
+    X_p: F_(d U_(s-1)),
+    Y_p: F_(d U_(s-1)) C_(d q_p)^-1,
+
+where U_j=L+E_1+...+E_j. After either retained local core, the frames
+are F_(d U_s) on X and F_(d U_s) C_(d q_p)^-1 on Y.
+
+For each port and positive chart v, the pinned involution rho_v(p)
+fixes q_p and swaps the eight chart vectors in q_p-perp with E_v.
+Let beta_p[i]=(weight(B_p[i])-1)/2 modulo two. The Y alignment uses
+
+    delta_Y(v,p)=q_p XOR lift_v(beta_p).
+
+The completed-X alignment uses
+
+    delta_X(v,p)=B_p beta_p XOR lift_v(beta_p).
+
+The actual full-array map is
+
+    M(g,delta) f(d,z_1,...,z_lambda)
+      = f(d g,z_1 XOR d delta,...,z_lambda XOR d delta).    (4)
+
+Here g=rho_v(p). The owner changes by right multiplication. The
+payload has a separate translation on every tensor layer. Spectators
+are unchanged. There is no amplitude phase in (4). The phase of the
+native frame changes because its owner and its payload translation
+change. The registry gives the complete 73-column owner matrix and
+translation for every map used.
+
+For operator composition,
+
+    (g,a)(h,b)=(g h,a XOR g b),
+    (g,a)^-1=(g^-1,g^-1 a).
+
+The emitter checks both inverse orders, including the translation.
+It computes the full Z4 phase polynomial after every map and native
+line. Every new scalar ADD is checked against exact equal phase
+polynomials, not just equal binary ranks. For a selected source q
+read in target p's frame, the map is A_v(p)^-1 A_v(q).
+
+During emission, an incorrect interpretation of rho as a payload
+permutation in one fixed array was identified and rejected before
+the payload was frozen. The accepted bridge proof distinguishes
+the two actions. The receipt includes a direct witness: give owner I
+the constant value zero and owner rho the constant value one. The
+correct map reads one at owner I. A payload-only permutation still
+reads zero. Independent owner inputs cannot be identified.
+
+Stage-zero F has a separate base case. All X fields already have
+the same FULL9 frame, D_0=I, and the source scalar suffix needs no
+alignment. Its A output copies still need the eight inverse lines.
+No stage-zero Y alignment is inferred.
+
+## Literal sweeps and private lifetime
+
+Every `cover_map` event is the declared bijection (4). A `cover_sweep`
+must finish over the full cover before the next event. It is not a
+local operation that assumes the other owners have already changed.
+The `private_sweep` body is different: for each owner, execute the
+whole clear, form, native child, add, and clear sequence before the
+next owner. This uses one C0 array, not a full-cover C0 bank.
+
+The backward order is:
+
+1. Apply inverse C_p to the eight X_T fields.
+2. For each p in A, move its four selected X source cohorts by the
+   exact current paths. Run the private sweep that forms
+   original y_p-(K_(s,A)a)_p, applies positive C_p, and adds it to X_p.
+   Return C0 to zero/I, then undo all four source-cohort maps.
+3. Align all Y fields to chart t. Complete the E_t source sweep and
+   undo that alignment.
+4. Align Y and the normalized X_T fields to chart s. Complete the U
+   scatter sweep, the eight selected swaps, and the final T-query
+   sweep in that order. The final query reads the changed U fields.
+5. Undo the current alignment and restore X_T with positive C_p.
+6. Run the complete retained backward core in its existing embedding.
+
+The forward order is:
+
+1. Run the complete retained forward core.
+2. Align all X fields to the current completed chart, except at
+   stage zero. Run all five source scalar blocks in the frozen
+   order, with a completion barrier after each block. Undo alignment.
+3. For each p in A, move its four selected source cohorts into the
+   X_p frame. Form the correction from the changed source, apply
+   inverse C_p on C0, and add it to Y_p. Clear C0 to zero/I and undo
+   all source-cohort maps.
+
+Each aligned port is a bijective view of one complete data family.
+Thus, for a fixed common owner, distinct local blocks have disjoint
+physical field addresses. The local scalar dependencies are exact
+within this view. The barriers make later reads use the completed
+earlier update. A target copy reads only unchanged selected source
+cohorts and the same-port source until its private body is complete.
+The temporary source maps are undone before the next copy row.
+
+These facts define a valid full-cover operator sequence. They do not
+assign the new recursive children to unused helper owners, prove that
+all sweeps fit the retained controller's live intervals, or price the
+address implementation. Those are separate supplier obligations.
+
+## Complete local invoice
+
+All scalar bounds use the retained complex-to-real primitive ledger.
+The count includes all new CLEARs, ADDs, signs, and the complete core.
+It excludes the separate monomial maps and recursive child costs.
+
+| Word | Added scalar bound | Complete scalar bound | Added rank-one children | Native mass | Added map bound |
+|---|---:|---:|---:|---:|---:|
+| Backward, positive s<t |12848|214986|24|5546|576|
+| Forward, positive s |9072|211210|8|5530|304|
+| Forward, s=0 |9072|211210|8|5530|16|
+
+The map bound counts both directions of every full-cover map and two
+wrappers for each native line child. Identity maps in positive-stage
+formulas are retained in the conservative count.
+
+Backward has 21401 scalar macros: 20654 ADDs, 715 SCALEs, and 32
+CLEARs. Forward has 21025 scalar macros: 20278 ADDs, 715 SCALEs, and
+32 CLEARs. Each has the original 480 helper fields and eight owned
+private fields. Neither adds a productive family.
+
+The backward native profile is
+
+    {1:2436, 2:418, 3:432, 4:142, 5:82}.
+
+The forward native profile is
+
+    {1:2420, 2:418, 3:432, 4:142, 5:82}.
+
+The formal scalar triangle and Horner prefix ceilings are 73 bits
+for B and 55 bits for F. These are bounds for this finite scalar
+word. They are not a recursive precision theorem or a completed
+finite supplier invoice.
+
+## Verification and limits
+
+From the workspace root run:
+
+```sh
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/circuit-interface/qq16/emit_conserved_qq16.py
+```
+
+The expected first output is
+
+    PASS_CONSERVED_QQ16_COMPLETE_LOCAL_WORDS
+
+The producer checks both complete words on all 712 formal columns
+at the common-chart specialization. It verifies all 480 helper
+outputs, all eight private outputs, and all sixteen conserved sums.
+It emits and checks 28 native backward cases with 1<=s<t<=8 and nine
+forward cases with 0<=s<=8. The retained schedule uses a subset of
+these cases. The payload retains their exact full-cover maps and
+their scalar-phase order.
+
+All 32 distinct used positive and inverse line recipes are compared
+on every 9-axis basis column: 16384 exact Gaussian columns. All 32
+scalar-phase mutations are rejected. Other controls reject a late A
+input read, an early T query, an early F source update, an early F
+target copy, a positive line in place of an inverse line, a missing
+payload translation, and a payload-only owner route.
+
+The ordered pair proof and the accepted bridge operator theorem are
+material dependencies. The arbitrary-cover conclusion is derived
+from them and the literal native frame checks. It is not inferred
+from the finite common-chart replay alone. No full multiplication
+or supplier verification was run for this candidate.
+
+The parent and encoded-controller lanes supplied the conserved-sum
+interface. The cover-algebra lane supplied the ordered inverse and
+its extension. The residual-syndrome lane supplied the short scalar
+words and their coefficient invoices. The coherent-port lane supplied
+the native component bindings and the explicit cover-action correction.
+The interface-proof bridge review supplies the exact retained local
+embedding. This lane assembles and checks the complete local words.
+The construction and its validation used substantial OpenAI Codex
+assistance and separate agent work. They have not received independent
+human review.
diff --git a/research/joint-query/evidence/JOINT-QUERY-TRANSFER-REVIEW.json b/research/joint-query/evidence/JOINT-QUERY-TRANSFER-REVIEW.json
new file mode 100644
index 0000000000..1331831eed
--- /dev/null
+++ b/research/joint-query/evidence/JOINT-QUERY-TRANSFER-REVIEW.json
@@ -0,0 +1,23 @@
+{
+  "status": "PASS_INDEPENDENT_ORDERED_PAIR_PROOF_REVIEW",
+  "reviewed_proof": "../cover-algebra/JOINT-QUERY-TRANSFER.md",
+  "reviewed_proof_sha256": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75",
+  "method": "Direct ordered-ring proof review plus separate actual-R 448-column tests with noncommuting port routes. No cover-algebra producer or checker import.",
+  "checks": [
+    "The actual A and T minors are disjoint dyadic sections and the U centre product is12I.",
+    "RZ=0 gives both source inverse orders and JH=I-(K_A+13P)R.",
+    "The original QQ pair and its inverse preserve all arbitrary input data.",
+    "The short four-step scalar word uses the changed off-T source in the final read.",
+    "The conserved B variant uses original y_A before E_t and logs b+12a in selected X_T.",
+    "The conserved B and F pairs have both inverse orders and preserve all16 logical selected sums.",
+    "The forward source word has the required query outputs and the correction uses final changed X.",
+    "The ordered M extension needs no inverse of M and does not commute M through another factor.",
+    "The future query relation retains the old A baseline; a constant-cover unit does not decide its routed pivot."
+  ],
+  "separate_checkers": {
+    "original_QQ": "b1a35f1f6501f021bafdb02b8f61fdee28ebdb2d97d68dbc104b6e25b3cdaefa",
+    "conserved_B": "b367076f65ec282eb28349c795c78a41212468d38cfa38f43f24c905fd4861fc",
+    "conserved_F": "d8312bade0fff5d4fdac608375fcc6223fbc46120a8270946a0c6e61908d93d1"
+  },
+  "scope": "Ordered local pair algebra and displayed inverse/source words only. This receipt does not accept complete native lowering, address-map costs, helper-owner admission, recursive precision, selected-sum access, or a changing-chart controller. The native component checks in the named lane are separate producer evidence, not independent native review."
+}
diff --git a/research/joint-query/evidence/JOINT-QUERY-TRANSFER.json b/research/joint-query/evidence/JOINT-QUERY-TRANSFER.json
new file mode 100644
index 0000000000..e361c1e9ca
--- /dev/null
+++ b/research/joint-query/evidence/JOINT-QUERY-TRANSFER.json
@@ -0,0 +1,77 @@
+{
+  "actual_column_checks": {
+    "clean_current_query": {
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "conserved_pair_sums": {
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "forward_conserved_pair_sums": {
+      "A_only_target_correction": true,
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "in_place_source_word": true
+    }
+  },
+  "checker_sha256": "fb60403444aa0a7cea8c1a3774a4aa85fb238013dd94796f8ffd4020c68f4073",
+  "noncentral_M": [
+    [
+      "1",
+      "3"
+    ],
+    [
+      "0",
+      "1"
+    ]
+  ],
+  "noncentral_matrix_checks": {
+    "clean_current_query": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "conserved_pair_sums": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "forward_conserved_pair_sums": {
+      "A_only_target_correction": true,
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "in_place_source_word": true
+    }
+  },
+  "proof_sha256": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75",
+  "scope": "Actual scalar R and a noncentral-matrix regression. Both pair inverses and both short scalar words are checked. No actual two-chart route, native phase, emitted full word, scalar invoice, owner allocation or global controller is checked.",
+  "selected_A": [
+    0,
+    7,
+    20,
+    27,
+    36,
+    46,
+    57,
+    111
+  ],
+  "selected_T": [
+    21,
+    37,
+    47,
+    76,
+    81,
+    87,
+    92,
+    110
+  ],
+  "source_sha256": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+  "status": "PASS_EXACT_JOINT_QUERY_TRANSFER"
+}
diff --git a/research/joint-query/evidence/JOINT-QUERY-TRANSFER.md b/research/joint-query/evidence/JOINT-QUERY-TRANSFER.md
new file mode 100644
index 0000000000..a6805c58f2
--- /dev/null
+++ b/research/joint-query/evidence/JOINT-QUERY-TRANSFER.md
@@ -0,0 +1,303 @@
+# A joint current-query exchange with two selected minors
+
+This construction uses an existing selected X minor as an arbitrary
+query register. It does not clear that input or add a productive field.
+The joint map retains all original X and Y inputs. It gives two distinct
+query records: the future query in Y_A and the current query before
+exchange in X_T. The ordinary source response is driven by the old
+selected X_T value. This is an ordered local algebra result. The native
+word, its complete invoice, and the changing-chart controller remain
+separate checks.
+
+## Maps and selected coordinates
+
+Use the actual disjoint orthogonal minors
+
+    A=[0,7,20,27,36,46,57,111],
+    T=[21,37,47,76,81,87,92,110].
+
+Let S=A union T and let U be its 96-port complement. In the current
+chart s write R=R_s, K=K_s, J=I-KR. The injections K_A and K_U have
+zero rows outside their named sets. Set
+
+    P=P_(s,T),      L=ell_(s,T),      Pi=P L.
+
+Here P=D_s^-1 iota_T R_T^-1 and L=R_T pi_T D_s. Thus RP=LP=I,
+Pi is the ordinary coordinate projector onto T, and K_T=P. Also
+
+    R K_A=I,       R K_U=12I.
+
+All these formulas hold over the ordered cover coefficient ring. The
+normalization by R_T is part of the query basis; it must not be omitted.
+
+Define a source transvection
+
+    Z=K_U-12P,     H=I+ZR,     H^-1=I-ZR.         (1)
+
+Since RZ=0, both inverse orders in (1) are exact. The source query is
+unchanged by H. The target response has only selected error rows:
+
+    RH=R,         JH=I-(K_A+13P)R.               (2)
+
+Let t be the next chart, and use the systematic future logger
+
+    E=E_t=I+N_t,
+    N_t=P_(t,A)(R_t-ell_(t,A)).
+
+Then N_t has only A output rows and no A input columns, N_t^2=0,
+and ell_(t,A) E=R_t. Its inverse is I-N_t. The source matrix H in
+(1) changes the T rows. Therefore this construction is outside the
+selected-baseline interface in SELECTED-BLOCK-NECESSITY.md.
+
+## Complete pair map
+
+For arbitrary original inputs x and y define
+
+    u=E y,        a=Lx,        b=Ru,
+    v=u+P(a-b).                                      (3)
+
+The change (u,a) to (v,b) is the full-query exchange. Since RP=I,
+
+    Rv=a,         u=v+P(b-Rv).                       (4)
+
+Thus this change is an involution on the source and the eight selected
+register values. It does not require an initialized register.
+
+The complete desired backward map is
+
+    y'=H v,
+    x'=(I-Pi)(x-y)+P b.                             (5)
+
+All X rows outside T perform the exact subtraction x-y. The T rows
+contain the clean normalized current query P b. They do not perform
+the original target subtraction. The source output has the exact rows
+
+    y'_U=y_U+K_U a,
+    y'_A=u_A,
+    y'_T=u_T-P(b+11a).                              (6)
+
+In particular,
+
+    ell_(t,A)y'=R_t y,
+    Lx'=b=R_s E_t y,
+    R_s y'=a=ell_(s,T)x.                            (7)
+
+The three expressions in (7) are different values. The first is the
+future query of the original source. The second is the current query
+after the future source encoding and before the exchange. The third
+is the old normalized selected target input. No equality between these
+queries is assumed.
+
+The 96 ordinary source rows in (6) depend on the old selected target
+input a, rather than on an unrecorded new ordinary source query. The
+Y_A record is in its ordinary source endpoint frame. The X_T record
+is in its completed target endpoint frame. A clean scalar query does
+not by itself put those two records into one common native frame.
+
+## Exact inverse and restoration boundary
+
+Given all of x' and y', compute in this order
+
+    v=H^-1 y',
+    b=Lx',        a=Rv=R_s y',
+    u=v+P(b-a),
+    y=E^-1 u,
+    x=(I-Pi)(x'+y)+P a.                            (8)
+
+Equations (3)--(4) prove both inverse orders. This restores arbitrary
+selected target inputs and arbitrary source inputs, not just their
+centre projections. It is an algebraic inverse. It is not a free
+decoder at the final Y hole frames: the read a=R_s y' can be an old
+chart query there. A controller must retain a usable selected history,
+or give a native implementation of that read and its later writes.
+
+For the next chart put
+
+    L_ts=R_tP,
+    D_ts=R_tK_U-11L_ts.
+
+Then the exact future query relation is
+
+    R_t y'=R_tu-L_ts b+D_ts a.                     (9)
+
+The leading term R_tu is not the stored future query q=R_t y. Instead,
+
+    R_tu=2q-ell_(t,A)y.                           (10)
+
+A unit D_ts would recover a from the other terms only when those
+terms have actual access. Its value is I in the constant-chart centre
+sector. That value does not prove that the actual routed D_ts is a
+dyadic operator unit. Equation (9) does not remove the old A baseline
+in (10).
+
+## A core-compatible native sequence to check
+
+At the actual backward entrance, Y has its common local source type
+and X_p has the intrinsic input line C_p. The following sequence gives
+(5) algebraically and identifies the needed native operations.
+
+1. Apply E_t to Y, obtaining u. This uses the future source alignment.
+2. Apply the inverse intrinsic line to each of the eight X_T fields.
+   Align those fields with the current common Y frame. Their normalized
+   contents are the arbitrary selected register a.
+3. Before changing that register, prepare the eight A target rows with
+   N_t u-K_A a. Use one owned copy field and one positive intrinsic line
+   per A row. The target remains in its original X entrance type.
+4. In physical T coordinates set c=X_T, z=u_T and d=u_offT. Define
+   D=K_U R_T and B=R_T^-1 R_offT, so BD=12I. Apply these four
+   scalar steps in the displayed order:
+
+       Y_U += D X_T;
+       SWAP(X_T,Y_T);
+       X_T -= 12 Y_T;
+       Y_T -= B Y_offT.
+
+   The last read uses the updated off-T source. The result is
+
+       X_T=z-12c,
+       Y_U=u_U+D c,  Y_A=u_A,  Y_T=-B d-11c.
+
+   Thus Y=Hv and X_T=P b+(JHv)_T in the normalized coordinates.
+   These steps combine the full-query exchange, H, and the selected
+   target correction. Each step is invertible on arbitrary inputs.
+5. Undo the selected alignment and apply the eight positive intrinsic
+   input lines to X_T.
+6. Run the retained clean-J backward core.
+
+For the A rows, (2) gives (JHv)_A=u_A-K_Aa. Since y_A=u_A-(N_tu)_A,
+the preparation in step3 is exactly (JHv)_A-y_A. Outside S, (JHv)_U
+equals y_U, so no target copy is needed. The selected pre-core source
+has normalized current query c. Its J image on T is -Bd-12c. Hence
+the core leaves X_T=z+Bd=R_T^-1 b. This proves the scalar purpose
+of every preparation row.
+
+The component native count is therefore a candidate of eight inverse
+X_T lines, eight positive X_T lines, and eight positive A copies. This
+is 24 rank-one children if all stated current and future alignments
+and the retained core entry types are bound literally. The input and
+output maps, scalar bounds, C0 lifetimes, recursive child owners and
+whole-cover sweep order still need the independent native check.
+The owned private copy may be cleared. None of the eight X_T register
+inputs may be cleared.
+
+## Ordered extension with a matrix centre response
+
+The number 12 is not needed for invertibility. Suppose instead that
+K=K_A+P+K_U, RP=I, and each injection has the stated output support.
+Let M=R K_U be any matrix over the ordered coefficient ring. Put
+
+    Z=K_U-P M,     H=I+ZR.
+
+Then RZ=0 and
+
+    H^-1=I-ZR,    RH=R,
+    JH=I-[K_A+P(I+M)]R.
+
+Use the same future map E and exchange (3). Equations (5), (7) and
+(8) still hold. The selected source row in (6) becomes
+
+    y'_T=u_T-P b+P(I-M)a.
+
+In the four-step scalar word replace 12 by R_T^-1 M R_T. Indeed,
+BD=R_T^-1 M R_T, so the same cancellation proves the output map.
+There is no inverse of M and no commutation of its factors. This is
+an ordered local theorem. It does not supply native access to a new
+matrix M or remove a later controller restoration obligation.
+
+## A variant that preserves both selected pair sums
+
+Keep the same source output y'=Hv. Define the arbitrary original
+selected pair sums p_A=x_A+y_A and p_T=x_T+y_T. Replace only the
+selected target outputs in (5) by
+
+    x'_A=p_A-y'_A,       x'_T=p_T-y'_T.
+
+The U target output is still x_U-y_U. Both selected pair sums are
+unchanged. The exact selected query in the T target is now
+
+    Lx'=b+M a,                                             (11)
+
+with M=12I in the actual instance. It is not the clean query b alone.
+The source identities ell_(t,A)y'=R_t y and R_s y'=a are unchanged.
+
+The inverse first sets a=R_s y' and b=Lx'-M a. It then uses (8) to
+recover v,u and y. Restore x_U=x'_U+y_U, x_T=P a, and
+x_A=x'_A+y'_A-y_A. This proves invertibility on all original inputs.
+
+The short scalar source word remains valid after two changes. The A
+input target copy is original y_A-K_A a, so make that copy before E_t
+changes y_A. Omit the step X_T-=12Y_T. The selected pre-core target
+is then u_T, and the core gives x'_T=P(b+12a). Thus the candidate
+native count remains 24, subject to the same actual alignment checks.
+
+The conserved sums are logical equations. Their two terms have
+different physical endpoint types. A controller must supply legal
+access before it uses either sum. The variant does not prove that a
+final selected sum can be read by an ordinary scalar ADD.
+
+## A forward map with the same conserved inputs
+
+For this companion use R K_A=R K_T=I, as in the actual two minors.
+Write the current X coordinates as (z,a,c), where z=x_U,
+a=ell_(s,A)x and c=ell_(s,T)x. Set
+
+    f=R_U z+a+c,
+    w=z-K_U f,
+    x'_U=w,       x'_A=P_(s,A)c,       x'_T=P_(s,T)f.
+
+Set y'_U=y_U+w and y'_S=x_S+y_S-x'_S. This preserves the same
+two selected pair sums on arbitrary inputs. It moves the previous
+selected T value to A and puts the new current query f in T.
+
+The source inverse reads f=ell_(s,T)x' and c=ell_(s,A)x'. It then
+sets
+
+    z=w+K_U f,
+    a=(I-M)f-R_U w-c.
+
+Restore y_U=y'_U-w and y_S=x'_S+y'_S-x_S. These formulas prove
+both inverse orders without a centre inverse. In the actual instance
+M=12I, so the second source equation is a=-11f-R_U w-c.
+
+There is an in-place scalar source word at the common completed X
+frame. In normalized selected coordinates it is
+
+    c += R_U z+a;
+    z -= K_U c;
+    a = -a-R_U z+(I-M)c.
+
+The final values are (w,old c,f). The last assignment has diagonal
+coefficient -I on a, so it is an invertible scalar update. Raw forward
+J transfer already gives the required U and T target outputs. On A
+its target differs by P_(s,A)(f-old c), which can be formed from the
+two completed selected X outputs. Eight one-way target copies are
+the proposed native correction. Their inverse-line phases and the
+complete source scalar invoice need the literal native check.
+
+These two local maps give an invertible pair with conserved selected
+data. They do not yet give a nine-stage controller. Intervening bank
+bridges, chart changes, and the final source and target frames remain
+part of that proof.
+
+## Comparison with the earlier forty-row exchange
+
+The preceding five-minor normalizer was H_40=I-K_U R/8 and preserved
+all forty selected source fields. Replacing u_T by the old X_T value
+while logging b=Ru gave an H_40 query b+a-Lu. That was a new hidden
+baseline debt. A full-query exchange instead made that query a, but
+retained the forty-row target support. The transvection (1) keeps the
+full-query exchange and relaxes the selected T baseline requirement.
+It reduces the target support to A union T.
+
+This comparison is about the displayed local interfaces. It does not
+prove a global reduction in native work. The complete controller must
+route or recover the old selected input in (8), account for intervening
+bank writes, and match the final physical source and target frames.
+
+The parent supplied the 16-row transvection. The controller lane
+identified the full-query exchange variant. This lane derived the
+ordered pair map, inverse and target preparation. The residual-syndrome
+lane reduced the scalar source word to four steps. The coherent-port
+and residual-syndrome lanes are checking native access and costs.
+Research used substantial OpenAI Codex assistance under the user's
+direction. New material uses Apache-2.0.
diff --git a/research/joint-query/evidence/NATIVE-CHECKS.json b/research/joint-query/evidence/NATIVE-CHECKS.json
new file mode 100644
index 0000000000..67699da21b
--- /dev/null
+++ b/research/joint-query/evidence/NATIVE-CHECKS.json
@@ -0,0 +1,450 @@
+{
+  "actual_routes_reconstructed": 1008,
+  "affine_map_registry_entries": 3650,
+  "cases": {
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+    },
+    "F_4": {
+      "added_map_bound": 304,
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "native_wrapper_maps": 16,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_5": {
+      "added_map_bound": 304,
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "native_wrapper_maps": 16,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_6": {
+      "added_map_bound": 304,
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "native_wrapper_maps": 16,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_7": {
+      "added_map_bound": 304,
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "native_wrapper_maps": 16,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_8": {
+      "added_map_bound": 304,
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "native_wrapper_maps": 16,
+      "private_sweeps": 8,
+      "reads": 912
+    }
+  },
+  "exact_gaussian_kernel_columns": 16384,
+  "inherited_native_scope": "Exact core bytes and local frame ledger are checked. The pinned bridge proof supplies the global owner embedding and endpoint adapters. Old child kernels are not rerun.",
+  "invoices": {
+    "B": {
+      "complete_scalar": {
+        "macros": 21401,
+        "operations": {
+          "add": 20654,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 214986
+      },
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 73,
+        "formal_triangle_Horner_bound": "573411134169296526275133/64"
+      },
+      "native_mass": 5546,
+      "native_profile": {
+        "1": 2436,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      }
+    },
+    "F": {
+      "complete_scalar": {
+        "macros": 21025,
+        "operations": {
+          "add": 20278,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 211210
+      },
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 55,
+        "formal_triangle_Horner_bound": "5413950274051752469/256"
+      },
+      "native_mass": 5530,
+      "native_profile": {
+        "1": 2420,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      }
+    }
+  },
+  "native_controls": [
+    "wrong inverse sign",
+    "missing payload translation",
+    "payload-only owner permutation"
+  ],
+  "phase_registry_entries": 1054,
+  "retained_core_event_counts": {
+    "backward": {
+      "adapter": 1090,
+      "climb": 3486,
+      "phase": 10,
+      "residual_adapter": 480,
+      "scalar": 20089
+    },
+    "forward": {
+      "adapter": 1090,
+      "climb": 3486,
+      "phase": 10,
+      "residual_adapter": 480,
+      "scalar": 20089
+    }
+  },
+  "scalar_phase_mutations_rejected": 32,
+  "scope": "Local full-cover words under bijective views and sweep barriers. No new-child hosting, global controller closure, physical address costs, recursive precision, complete supplier or kappa claim.",
+  "status": "PASS_QQ16_NATIVE_OWNER_PATHS_AND_PHASES"
+}
diff --git a/research/joint-query/evidence/NATIVE-REVIEW.json b/research/joint-query/evidence/NATIVE-REVIEW.json
new file mode 100644
index 0000000000..87b2ce9bfa
--- /dev/null
+++ b/research/joint-query/evidence/NATIVE-REVIEW.json
@@ -0,0 +1,397 @@
+{
+  "actual_routes_reconstructed": 1008,
+  "affine_map_registry_entries": 3650,
+  "cases": {
+    "B_1_2": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_3": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_4": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_5": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_6": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_1_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_3": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_4": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_5": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_6": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_2_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_3_4": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_3_5": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_3_6": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_3_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_3_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_4_5": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_4_6": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_4_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_4_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_5_6": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_5_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_5_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_6_7": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_6_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "B_7_8": {
+      "cores": 1,
+      "cover_sweeps": 4,
+      "lines": 24,
+      "maps": 528,
+      "private_sweeps": 8,
+      "reads": 1288
+    },
+    "F_0": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_1": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_2": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_3": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_4": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_5": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_6": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_7": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    },
+    "F_8": {
+      "cores": 1,
+      "cover_sweeps": 5,
+      "lines": 8,
+      "maps": 288,
+      "private_sweeps": 8,
+      "reads": 912
+    }
+  },
+  "checker_sha256": "a4029bc65ac4149adc7043dc6da254e03630dc0037d32c903058162c46003c16",
+  "exact_gaussian_kernel_columns": 16384,
+  "inherited_native_scope": "Exact retained core bytes and local frame ledger were checked here. The pinned bridge review supplies the global owner embedding and endpoint adapters. Old child kernels were not rerun.",
+  "invoices": {
+    "B": {
+      "complete_scalar": {
+        "macros": 21401,
+        "operations": {
+          "add": 20654,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 214986
+      },
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 73,
+        "formal_triangle_Horner_bound": "573411134169296526275133/64"
+      },
+      "native_mass": 5546,
+      "native_profile": {
+        "1": 2436,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      }
+    },
+    "F": {
+      "complete_scalar": {
+        "macros": 21025,
+        "operations": {
+          "add": 20278,
+          "clear": 32,
+          "scale": 715
+        },
+        "real_primitives": 211210
+      },
+      "formal_prefix": {
+        "formal_prefix_ceiling_log2": 55,
+        "formal_triangle_Horner_bound": "5413950274051752469/256"
+      },
+      "native_mass": 5530,
+      "native_profile": {
+        "1": 2420,
+        "2": 418,
+        "3": 432,
+        "4": 142,
+        "5": 82
+      }
+    }
+  },
+  "maximum_resident_bytes": 216940544,
+  "phase_registry_entries": 1054,
+  "retained_core_event_counts": {
+    "backward": {
+      "adapter": 1090,
+      "climb": 3486,
+      "phase": 10,
+      "residual_adapter": 480,
+      "scalar": 20089
+    },
+    "forward": {
+      "adapter": 1090,
+      "climb": 3486,
+      "phase": 10,
+      "residual_adapter": 480,
+      "scalar": 20089
+    }
+  },
+  "scalar_maps_and_inverse_dependency": "The pinned independent scalar receipt proves both complete maps on all 712 inputs, both data inverse orders, all 480 helper outputs, eight owned zero outputs, and the 16 conserved sums.",
+  "scalar_phase_mutations_rejected": 32,
+  "scope": "Full-cover component words under the stated bijective views and sweep barriers. No global owner admission, new-child hosting, controller closure, stream or address invoice, recursive precision, complete supplier, or kappa result.",
+  "seconds": 5.005,
+  "source_pins": {
+    "B_native_component": "d7f75b34a56fc7acfb582d3a133c3eb817a29584a1f7136896420138cc155b35",
+    "F_native_component": "232035827945f2c13e32b7ced955f222eb1f349f0b409326c83fea5847088b1a",
+    "R": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+    "bridge_proof": "d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3",
+    "bridge_review": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc",
+    "charts": "498d85807dd3032de01b5da72a67717f02ee0ecf068e8c47f67d4f21034cd896",
+    "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877",
+    "cover_action": "4bb4a68d8b4811b6d8364150612056bc124d38f1974d6f603dae68a99c4682fb",
+    "pair_proof": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75",
+    "pair_receipt": "1f32819591103ab323c69cf50cf6579b0e881e105ca4a93b48125d5b89214c31",
+    "payload": "2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef",
+    "positive_lines": "500c09dfc1d27ffd107341adf4c3c6874ee2c84e1a8afad91d931ed9e88fd1d7",
+    "producer": "5b29a1c24ace64023e3bd6e1c7136f4ca4f2f45c4f2f157901dbafb4b7f74a64",
+    "proof": "60f0de3a7205ba5046b5ae7ffa8bf2b1ea42ea46b498face0a77966b59e7f3fb",
+    "receipt": "b91eb8599c403db55c889bb225a1cd93f46fdb83eb339f101d18843d52b1c920",
+    "scalar_checker": "4bbbefd65cc06a3120bc30072979e6597dd002460a952385bde7e98196ea9fb9",
+    "scalar_payload": "6b8d647a8ce2ff86f39b1947d11cbcdfd0f366e90c2816ff6cca09d47c75869c",
+    "scalar_proof": "aa7b9f74430b56c42e1099029a501a9b6be9ab56b81bfdc681e4c2e6ff5bc97d",
+    "scalar_review": "171bdbec200359c82aba79e4153d73bfcbf14ac3ae4e07b15476b79b7fcbf091",
+    "word": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219"
+  },
+  "status": "PASS_INDEPENDENT_CONSERVED_QQ16_FULL_COVER_NATIVE_COMPONENTS"
+}
diff --git a/research/joint-query/evidence/NATIVE-REVIEW.md b/research/joint-query/evidence/NATIVE-REVIEW.md
new file mode 100644
index 0000000000..525b38dbde
--- /dev/null
+++ b/research/joint-query/evidence/NATIVE-REVIEW.md
@@ -0,0 +1,203 @@
+# Independent review of the conserved QQ16 native words
+
+The frozen payload passes this component review. No material defect was
+found. The payload SHA256, after decompression, is
+
+    2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef.
+
+This review accepts the two complete local operators under the stated
+full-cover view and sweep contract. It does not admit their new children
+or sweeps to the global supplier. In particular, it does not prove a
+complete controller, helper-owner assignment, recursive hosting, address
+implementation, precision bound, or kappa improvement.
+
+## Independent finite checks
+
+Run from the workspace root, without `-O`:
+
+```sh
+python3 -I -B work/centre-encoding-campaign-20261014/lanes/residual-syndrome/physical-algebra/review-gauss/conserved-qq16/native/verify_native_review.py
+```
+
+The first output is
+
+    PASS_INDEPENDENT_CONSERVED_QQ16_FULL_COVER_NATIVE_COMPONENTS
+
+The checker imports no producer or phase helper. It reconstructs each
+73-axis chart from the pinned doubled data. It then derives every route
+as eight disjoint swaps of orthogonal basis vectors. This checks all
+1008 actual port and stage routes. It checks both inverse orders of all
+3650 affine cover maps, including each translation.
+
+The checker expands each parity polynomial directly modulo four. It
+checks all 1054 registered phase polynomials, and then follows the phase
+through every wrapper event in all 28 backward and nine forward cases.
+It checks the complete event sequence against the ordered construction.
+This includes the exact relative owner path of every selected source,
+not only equality of the source and target frames.
+
+All 32 positive and inverse line recipes are compared with the pinned
+component bytes. Their 16384 Gaussian integer columns are evaluated
+independently, including the constant scalar phase. A scalar phase
+mutation fails for each recipe. Separate controls reject the positive
+line in place of an inverse line and an omitted payload translation.
+
+Both retained core words equal the pinned complete words. Their local
+frame ledger, endpoint frames, scalar accesses, and child profiles are
+rechecked. The old child kernels and global core embedding are inherited
+from the pinned native and bridge reviews; they are not re-proved here.
+
+Every native case has exactly the scalar projection checked by the
+independent scalar review in the parent directory. That review checked
+the complete B and F words on all 712 formal inputs, all 480 helper
+outputs, the eight owned zero outputs, both data inverse orders, and
+all sixteen selected sums. It also rebuilt the coefficient matrices and
+each scalar block from the actual R. This review pins that receipt and
+checker. It does not treat the producer's common-chart output as an
+independent oracle.
+
+## Owner action, phases, and order
+
+For a cover map use the right action
+
+    M(g,a) f(d,z) = f(dg,z XOR d a).
+
+Direct substitution gives
+
+    M(g,a) M(h,b) = M(gh,a XOR g b),
+    M(g,a)^-1 = M(g^-1,g^-1 a).
+
+The owner action and the payload translation have distinct roles. To
+test the distinction, give owner I constant input zero and owner g
+constant input one, with g nonidentity. The correct map reads one at I.
+A payload-only permutation at owner I still reads zero. The actual
+chart routes in this packet include such a nonidentity g.
+
+If the frame phase at the identity owner is phi(w), the map changes it
+to phi(g^T w)+2 a dot w modulo four. A line with axis q therefore changes
+to a line with axis g q. This follows from the changed owner in the
+input frame. It does not follow from applying g to the payload address.
+The checker uses this exact identity and checks all constant phases
+through the line kernels.
+
+Write the native boundary operator at port p as T_p. The accepted bridge
+identity is A_p T_p=T_common D_p, where D_p is the right-owner route.
+Thus a scalar source block between aligned ports acts logically by
+D^-1 M D. For a source q read at target p without moving the target,
+
+    A_p^-1 A_q T_q = T_p D_p^-1 D_q.
+
+This proves the required order of the relative path. The checker
+compares each literal path with this group product, including its
+translation, and checks its undo. The paths may not be reversed merely
+because the before and after native phases are equal.
+
+In B, inverse C_q first gives each selected X_T field the current Y
+type. The A copies read the original Y before E_t changes it. Each
+positive line on C0 changes that copy to the X target type. The future
+logger precedes the current U update, selected swaps, and final T query.
+The final T query reads the changed U fields. All source paths are
+undone, and positive C_q restores the eight X_T types before the core.
+
+In F, the retained forward core reads the original source first. The
+five source blocks then run in their fixed order. The A target copies
+read the changed source. Their inverse C_q gives the Y target type.
+Stage zero has a separate completed-X base case with no owner maps.
+This review uses the pinned core lift for the incoming F frame; the
+wrapper phase replay starts from the completed frame after that core.
+
+These statements hold for every tensor length. Each physical address
+layer has the same owner route and translation, and its exact line
+identity is already fixed, including scalar phase. The phase equality
+is summed over the layers. The scalar coefficient acts once on the
+port index. It is not replaced by a tensor power of R. Spectator axes
+are unchanged.
+
+## Ordered maps and inverses
+
+The full-cover conclusion uses the ordered pair proof, not the
+common-chart coefficient replay alone. In chart s let
+
+    R_s=R D_s,    K_s=D_s^-1 K,    P_s=K_(s,T),
+    ell_s=R_T pi_T D_s,    Pi_T=P_s ell_s.
+
+Portwise routes preserve coordinate supports. Therefore
+R_s P_s=ell_s P_s=I, R_s K_(s,A)=I, and R_s K_(s,U)=12I.
+No relation between D_s and a future D_t is needed.
+
+For the future logger E_t, its added term has only A rows and no A
+columns. Hence E_t^-1=2I-E_t. Put
+
+    u=E_t y,    a=ell_s x,    b=R_s u.
+
+The backward word gives
+
+    Y'_A=u_A,
+    Y'_U=y_U+K_(s,U)a,
+    Y'_T=u_T-P_s(b+11a),
+    X'_U=x_U-y_U,
+    X'_A=x_A+y_A-u_A,
+    X'_T=P_s(b+12a).
+
+To invert it, first read a=R_s Y' and b=ell_s X'-12a. Recover
+u_U=Y'_U-K_(s,U)a, u_A=Y'_A, and u_T=Y'_T+P_s(b+11a).
+Then y=E_t^-1u, x_U=X'_U+y_U, x_T=P_s a, and
+x_A=X'_A+Y'_A-y_A. All products retain their order.
+
+For F, put f=R_s x. The source becomes
+
+    X'_U=x_U-K_(s,U)f,
+    X'_A=P_(s,A)ell_s x,
+    X'_T=P_s f.
+
+Its target has Y'_U=y_U+X'_U and Y'_S=y_S+x_S-X'_S for
+S=A union T. Read f=ell_s X' and c=ell_(s,A)X'. Recover
+x_U=X'_U+K_(s,U)f, x_T=P_s c, and
+x_A=P_(s,A)(f-c-R_(s,U)x_U). The target equations then recover y.
+These are two invertible data maps. B and F are not mutual inverses.
+Their inverse formulas do not provide free inverse native access at
+the output frames. Neither complete map is invertible on the discarded
+owned private input values.
+
+## Sweeps, scratch, and invoices
+
+Every common-frame scalar block is a full-cover sweep with a completion
+barrier. A subsequent block can therefore read its completed output.
+Each port route is a bijection on its data family. At a fixed common
+owner, the different port fields occupy distinct addresses. Within one
+sweep the frozen scalar order gives the exact dependency order.
+
+Each private body starts with CLEAR C0 and ends with CLEAR C0 in frame I.
+It forms one target correction, applies its native line, and adds the
+result before the next owner starts. The temporary source fields are
+unchanged during this body. This needs one serial owned C0 array, not
+one C0 for each cover owner. The checker verifies all eight row bodies,
+their source paths, their reversals, and their complete boundaries in
+each case. C1 through C7 are untouched by the wrappers; the retained
+core clears them. The 480 ordinary helpers are untouched by the new
+wrappers and restored by the inherited complete core.
+
+The complete invoices agree exactly with the producer:
+
+| Word | Added scalar | Complete scalar | Added rank-one children | Native mass | Added map bound |
+|---|---:|---:|---:|---:|---:|
+| B |12848|214986|24|5546|576|
+| F, positive stage |9072|211210|8|5530|304|
+| F, stage zero |9072|211210|8|5530|16|
+
+B has profile {1:2436,2:418,3:432,4:142,5:82}. F has profile
+{1:2420,2:418,3:432,4:142,5:82}. The map bound includes two wrappers
+per new line child. The independently recomputed formal scalar prefix
+bounds are 573411134169296526275133/64 for B and
+5413950274051752469/256 for F, with ceiling logarithms 73 and 55.
+These are finite scalar bounds, not recursive precision certificates.
+
+The sweep and scratch argument specifies the abstract component access
+contract. It does not allocate helpers for the new recursive children,
+show that their live intervals fit the selected supplier, or price a
+physical implementation of the cover views. Those remain material
+obligations for any supplier claim.
+
+This review used separate OpenAI Codex agent work. It is not independent
+human review. No frozen producer artifact was edited, and no PR or
+commit was made.
diff --git a/research/joint-query/evidence/ORDERED-CHECKS.json b/research/joint-query/evidence/ORDERED-CHECKS.json
new file mode 100644
index 0000000000..25b6d3abe0
--- /dev/null
+++ b/research/joint-query/evidence/ORDERED-CHECKS.json
@@ -0,0 +1,74 @@
+{
+  "actual_R_checks": {
+    "clean_current_query": {
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "conserved_pair_sums": {
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "forward_conserved_pair_sums": {
+      "A_only_target_correction": true,
+      "all_input_columns": 224,
+      "both_inverse_orders": true,
+      "in_place_source_word": true
+    }
+  },
+  "noncentral_M": [
+    [
+      "1",
+      "3"
+    ],
+    [
+      "0",
+      "1"
+    ]
+  ],
+  "noncentral_M_checks": {
+    "clean_current_query": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "conserved_pair_sums": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "forward_conserved_pair_sums": {
+      "A_only_target_correction": true,
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "in_place_source_word": true
+    }
+  },
+  "scope": "Exact finite checks of both data inverse orders, the short source words, selected sums, and a noncentral and singular M. The general associative-ring result is proved in the source note; it is not inferred from these tests.",
+  "singular_M_checks": {
+    "clean_current_query": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "conserved_pair_sums": {
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "omitted_exchange_control": "REJECTED",
+      "short_word": true
+    },
+    "forward_conserved_pair_sums": {
+      "A_only_target_correction": true,
+      "all_input_columns": 12,
+      "both_inverse_orders": true,
+      "in_place_source_word": true
+    }
+  },
+  "status": "PASS_ORDERED_JOINT_QUERY_REGRESSIONS"
+}
diff --git a/research/joint-query/evidence/PACKAGE-COLD-REVIEW.json b/research/joint-query/evidence/PACKAGE-COLD-REVIEW.json
new file mode 100644
index 0000000000..cd3374d038
--- /dev/null
+++ b/research/joint-query/evidence/PACKAGE-COLD-REVIEW.json
@@ -0,0 +1,128 @@
+{
+  "audit_checker_sha256": "71d0ec6095f103b324defeba0c7e08a7408a3a4d843612b4164ca39f720112dd",
+  "cold_directory": "/private/tmp/qq16-package-independent-kr4otw5g",
+  "command": [
+    "/opt/homebrew/opt/python@3.14/bin/python3.14",
+    "-I",
+    "-O",
+    "-B",
+    "/private/tmp/qq16-package-independent-kr4otw5g/package/replay.py",
+    "--repo",
+    "/Users/aliromman/Projects/IntegerMultiplicationBounds",
+    "--out",
+    "/private/tmp/qq16-package-independent-kr4otw5g/output"
+  ],
+  "file_count": 30,
+  "frozen_package_unchanged": true,
+  "git_provenance": {
+    "notices/LICENSE": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:LICENSE",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    "notices/research/gauge44-slots-t16/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/NOTICE.md",
+      "sha256": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf"
+    },
+    "notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/UPSTREAM-NOTICE.md",
+      "sha256": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610"
+    },
+    "notices/research/gauge44-slots-t16/construction/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/construction/NOTICE.md",
+      "sha256": "defe7e44af610e25a6c50c1c3b2efd0972d0690574995c0c872fc50eebf4c816"
+    },
+    "notices/research/gauge44-slots-t16/t16/NOTICE.md": {
+      "git_source": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f:research/gauge44-slots-t16/t16/NOTICE.md",
+      "sha256": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5"
+    },
+    "source_data.py": {
+      "sha256": "d23924511e3aed41e5e64511ca70126a636d91c8aa02e656cb61d6ceca1fe0a0",
+      "source_commit": "7649d9ceecec949541bec4bbde5929344166ba59",
+      "source_path": "research/native-source-codes/source_data.py"
+    }
+  },
+  "imports": {
+    "replay.py": [
+      "argparse",
+      "gzip",
+      "hashlib",
+      "importlib",
+      "json",
+      "pathlib"
+    ],
+    "source_data.py": [
+      "argparse",
+      "collections",
+      "fractions",
+      "gzip",
+      "hashlib",
+      "io",
+      "json",
+      "pathlib",
+      "subprocess",
+      "tarfile"
+    ],
+    "verify_native.py": [
+      "collections",
+      "copy",
+      "fractions",
+      "functools"
+    ],
+    "verify_ordered.py": [
+      "fractions"
+    ],
+    "verify_scalar.py": [
+      "fractions"
+    ]
+  },
+  "interpreter": "3.14.7 (main, Aug  5 2026, 10:29:49) [Clang 21.0.0 (clang-2100.1.1.101)]",
+  "manifest_sha256": "f1db775cc3ae6b1108449dabd15ebe1d3aea0130e7011791c8ad3ed7b8539018",
+  "maximum_child_resident_bytes": 280313856,
+  "output_sha256": {
+    "CLEAN-J-CHECKS.json": "2946d03237300839c08acb33b3df993ce61334a55589bf2f9eb17c3d5f463791",
+    "NATIVE-CHECKS.json": "fe959be0bf2490f99efcf6b8109b19cc8d79036d9df54b59598f32de92295054",
+    "ORDERED-CHECKS.json": "c0b3474406807199aae80bc48dc188f03035b5869f113572828615de0b41563a",
+    "REPLAY.json": "70fcedb5160b1347f500ce6db0e2e09c182a42839f8a81196f9aa88fb5892561",
+    "SCALAR-CHECKS.json": "7205aa5f24294f6d6422830719aae6d5b01efb08747fdf746fa9f2f5594a0387"
+  },
+  "package_files": {
+    "NOTICE.md": "0e6f26a1453a98dc73c2d50e9bdd76a78e57411cd1b3f84331dc1590b128b0ff",
+    "README.md": "fa6ee7ca95274267b2cb5a848f1c6a2b0e740240c242317ea10780687d1778fa",
+    "SOURCES.json": "fabc6686e5d3ac0e4bb4397c147037b9285abfa671614590dad6d4e16b4dc0fc",
+    "certificate.json.gz": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7",
+    "evidence/BRIDGE-OPERATOR-REVIEW.json": "c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc",
+    "evidence/BRIDGE-REVIEW.md": "d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3",
+    "evidence/CONSERVED-QQ16.json": "b91eb8599c403db55c889bb225a1cd93f46fdb83eb339f101d18843d52b1c920",
+    "evidence/CONSERVED-QQ16.md": "60f0de3a7205ba5046b5ae7ffa8bf2b1ea42ea46b498face0a77966b59e7f3fb",
+    "evidence/JOINT-QUERY-TRANSFER-REVIEW.json": "28d9d525c9eec07c91cb51edfdb5a0cf01ff75fddd39046b3d2fda03456e9153",
+    "evidence/JOINT-QUERY-TRANSFER.json": "1f32819591103ab323c69cf50cf6579b0e881e105ca4a93b48125d5b89214c31",
+    "evidence/JOINT-QUERY-TRANSFER.md": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75",
+    "evidence/NATIVE-REVIEW.json": "e9e9287a4a4d1be3c802899a42f70ff5dd5efd1e144a48bd585386fe234832e5",
+    "evidence/NATIVE-REVIEW.md": "2247e3cbe73f3f0da55c647ffae15f98dd9445b2366ba9e255b9bebc9f742b70",
+    "evidence/QQ16-COVER-ACTION-ADDENDUM.md": "4bb4a68d8b4811b6d8364150612056bc124d38f1974d6f603dae68a99c4682fb",
+    "evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json": "588a3ce4593576ae921e97c6ced6a050f88736f29708cfee117385b254cd358f",
+    "evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md": "9a06ff40830ef80d3566fce77c78639cb64d519d487a0a7f57d543c3146e2c49",
+    "evidence/QQ16-SELECTED-WITNESS.json": "e35e5868a1322e406191079c0675975b139692ba50b1e2e5fb8a40b6480519f4",
+    "evidence/QQ16-SELECTED-WITNESS.md": "52f2ee565320f05282c637aa79eee100606c24240b1b5866f0c8d62e7913c9fc",
+    "evidence/SCALAR-REVIEW.json": "171bdbec200359c82aba79e4153d73bfcbf14ac3ae4e07b15476b79b7fcbf091",
+    "evidence/SCALAR-REVIEW.md": "aa7b9f74430b56c42e1099029a501a9b6be9ab56b81bfdc681e4c2e6ff5bc97d",
+    "notices/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "notices/research/gauge44-slots-t16/NOTICE.md": "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+    "notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md": "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+    "notices/research/gauge44-slots-t16/construction/NOTICE.md": "defe7e44af610e25a6c50c1c3b2efd0972d0690574995c0c872fc50eebf4c816",
+    "notices/research/gauge44-slots-t16/t16/NOTICE.md": "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5",
+    "replay.py": "61a3c2ddc3e62f965bfc9ee47b6a1e8c03b0071c5021feb6612ebbdd9561038e",
+    "source_data.py": "d23924511e3aed41e5e64511ca70126a636d91c8aa02e656cb61d6ceca1fe0a0",
+    "verify_native.py": "1c58e7b6e8e1cde4df455c2129601c145ed763fc63a3ab427eb1058d1fc08bd2",
+    "verify_ordered.py": "0e23ed4bef58ed8375a9d43b0b9cbcab8e825ec7d5d702e74973ccc41d97ffa6",
+    "verify_scalar.py": "33bdbad17a0531fe527aff306eb235d9c38c1629db4fd167b989725930b0327a"
+  },
+  "return_code": 0,
+  "scope": "Cold execution, manifest/source provenance, and portable adaptation. The mathematical native review is the existing accepted dependency; this does not add a global supplier or controller claim.",
+  "seconds": 12.257,
+  "source_archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754",
+  "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "status": "PASS_INDEPENDENT_QQ16_PACKAGE_COLD_REPLAY",
+  "total_bytes": 938818,
+  "working_directory": "/private/tmp"
+}
diff --git a/research/joint-query/evidence/PACKAGE-MUTATION-REVIEW.json b/research/joint-query/evidence/PACKAGE-MUTATION-REVIEW.json
new file mode 100644
index 0000000000..c6fc58c8a3
--- /dev/null
+++ b/research/joint-query/evidence/PACKAGE-MUTATION-REVIEW.json
@@ -0,0 +1,20 @@
+{
+  "bytecode_disabled": true,
+  "checker_sha256": "ed0dc60b5e3179cb0a47f4ab2478c0b9cf385999209affcea3f7f16cc1aa5efc",
+  "controls": {
+    "missing_initial_private_clear": {
+      "reason": "Private lifetime bounds",
+      "status": "REJECTED"
+    },
+    "phase_preserving_wrong_owner": {
+      "reason": "Full owner paths, native signs, copy sources, and event order: F_2",
+      "status": "REJECTED"
+    }
+  },
+  "isolated": true,
+  "manifest_sha256": "f1db775cc3ae6b1108449dabd15ebe1d3aea0130e7011791c8ad3ed7b8539018",
+  "optimization_level": 1,
+  "scope": "Targeted portable checker validation on in-memory mutations. The unchanged full source reconstruction and positive replay are supplied by the separate cold run.",
+  "seconds": 3.192,
+  "status": "PASS_INDEPENDENT_QQ16_PORTABLE_MUTATION_CHALLENGE"
+}
diff --git a/research/joint-query/evidence/PACKAGE-REVIEW.json b/research/joint-query/evidence/PACKAGE-REVIEW.json
new file mode 100644
index 0000000000..67614ccd8a
--- /dev/null
+++ b/research/joint-query/evidence/PACKAGE-REVIEW.json
@@ -0,0 +1,29 @@
+{
+  "cold_output_sha256": {
+    "CLEAN-J-CHECKS.json": "2946d03237300839c08acb33b3df993ce61334a55589bf2f9eb17c3d5f463791",
+    "NATIVE-CHECKS.json": "fe959be0bf2490f99efcf6b8109b19cc8d79036d9df54b59598f32de92295054",
+    "ORDERED-CHECKS.json": "c0b3474406807199aae80bc48dc188f03035b5869f113572828615de0b41563a",
+    "REPLAY.json": "70fcedb5160b1347f500ce6db0e2e09c182a42839f8a81196f9aa88fb5892561",
+    "SCALAR-CHECKS.json": "7205aa5f24294f6d6422830719aae6d5b01efb08747fdf746fa9f2f5594a0387"
+  },
+  "cold_return_code": 0,
+  "documentation_links_checked": 15,
+  "file_count": 30,
+  "manifest_sha256": "f1db775cc3ae6b1108449dabd15ebe1d3aea0130e7011791c8ad3ed7b8539018",
+  "material_findings": [],
+  "portable_mutations_rejected": [
+    "missing_initial_private_clear",
+    "phase_preserving_wrong_owner"
+  ],
+  "review_files": {
+    "COLD-REVIEW.json": "4cb4065fecadc08cd438b7cd438e24665b562b564c3c8f8f8c172cf3e6857374",
+    "MUTATION-REVIEW.json": "ecc4eb8090b056c0932ced463cb420af20a98700b7733d320508327d32107a7f",
+    "REVIEW.md": "f716890c7dabb8b062267134a70d74ab36e4587380ccf46ac01c8a4b4c45e0e2",
+    "challenge_controls.py": "ed0dc60b5e3179cb0a47f4ab2478c0b9cf385999209affcea3f7f16cc1aa5efc",
+    "cold.stderr.txt": "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855",
+    "cold.stdout.txt": "70425007fbbe7a9185c237f78923486196653997031e2fbca105383e55f95c12",
+    "cold_audit.py": "71d0ec6095f103b324defeba0c7e08a7408a3a4d843612b4164ca39f720112dd"
+  },
+  "scope": "Independent package adaptation audit. Existing native mathematics is inherited from this reviewer's earlier accepted review. No global supplier, controller, hosting, precision, physical map cost, kappa, or publication claim.",
+  "status": "PASS_INDEPENDENT_QQ16_PORTABLE_PACKAGE_REVIEW"
+}
diff --git a/research/joint-query/evidence/PACKAGE-REVIEW.md b/research/joint-query/evidence/PACKAGE-REVIEW.md
new file mode 100644
index 0000000000..2cf6689934
--- /dev/null
+++ b/research/joint-query/evidence/PACKAGE-REVIEW.md
@@ -0,0 +1,133 @@
+# Independent cold audit of the joint-query package
+
+The thirty-file package passes this audit. No material package finding
+remains open. The reviewed PACKAGE-HASHES.json SHA256 is
+
+    f1db775cc3ae6b1108449dabd15ebe1d3aea0130e7011791c8ad3ed7b8539018.
+
+This review concerns portability, source attribution, manifest integrity,
+the new checker adaptation, and the stated claim. The reviewer also
+supplied the original native mathematical review. This is not presented
+as a second independent proof of that same native theorem.
+
+## Cold execution
+
+The audit copied exactly the thirty declared files, totaling 938818
+bytes, into a fresh directory:
+
+    /private/tmp/qq16-package-independent-kr4otw5g/package
+
+It copied no staging handoff, package hash record, cold-evidence output,
+scratch-lane module, or predecessor package. The command used the copied
+entrypoint with `-I -O -B`, working directory `/private/tmp`, and the
+workspace Git repository as the explicit `--repo` source. It returned
+zero in 12.257 seconds. Peak child resident memory was 280313856 bytes.
+The first output was
+
+    PASS_PORTABLE_QQ16_LOCAL_JOINT_QUERY
+
+All five JSON outputs match the manifest byte for byte. The REPLAY.json
+SHA256 is
+
+    70fcedb5160b1347f500ce6db0e2e09c182a42839f8a81196f9aa88fb5892561.
+
+The copied directory still contains exactly those thirty unchanged files.
+Every frozen package file also retains its original hash. No package
+file was edited. The audit stores the command, interpreter version,
+all input and output hashes, timings, and captured output separately.
+
+The source loader reads immutable Git blobs with `git show`; it does not
+read the corresponding worktree files. The archive and each named member
+are checked before parsing. The runtime source commit is
+bce54fb3f895cbe5cd4c0eb477c3afeed100190f. The source archive hash is
+22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754.
+No network operation or installed third-party package is used.
+
+All five Python files have only standard-library static imports. Their
+explicit local module loads stay inside the copied package. An AST scan
+finds no assertion statements. The checks use exceptions and remain
+active under `-O`. Source reconstruction and all mathematical checks ran
+in one process, apart from the loader's read-only Git subprocesses.
+
+## Source and attribution audit
+
+All thirty file hashes and the compressed and decompressed certificate
+hashes match their declared modes. Every packaged proof and receipt is
+byte-equal to its stated campaign source. All adapted-checker source pins
+and the original dependency audit pin also match.
+
+The unchanged source_data.py equals the Git blob at
+7649d9ceecec949541bec4bbde5929344166ba59 in
+research/native-source-codes/source_data.py. Each of the five license or
+notice files equals its exact declared blob at the source base. The
+notices preserve the gauge44, frame, X4, t16, and earlier supplier credit,
+including the original authors and AI disclosures. The new NOTICE.md
+credits the campaign roles and states that the independent reviews are
+agent reviews, not independent human review. The audit found no source
+claim transferred to the new package as uncredited original work.
+
+All nine README document links and all six NOTICE document links resolve
+to declared files in the cold package. Frozen evidence can still contain
+its original workspace commands and historical pending-review sentences.
+README gives the portable command and identifies the later native review
+that supersedes the older native status. This new receipt supersedes the
+portable adaptation's pending-review status in the frozen staging prose.
+No PR links, GitHub rendering, or publication action were audited here.
+
+## Checker adaptation and mutation challenges
+
+The portable code rebuilds the actual R and both clean-J words from the
+pinned archive. It checks the complete 712-column scalar words, borrowed
+helper restoration, owned zero outputs, both data inverse orders,
+selected sums, native source paths, exact phases, and finite local bills.
+The native code builds its charts from the original single-layer phase
+source and checks that source's entry and exit translations. It compares
+the resulting literal paths with the frozen accepted certificate.
+
+The ordered tests cover the actual R, a noncentral response M, and the
+singular case M=0. README correctly attributes the general ring theorem
+to its proof rather than to these finite tests. The old child kernels
+and the global embedding of the retained core remain stated inherited
+dependencies. This package does not claim to rerun those old kernels.
+
+Two additional in-memory mutations challenge the portable native checks
+under `-I -O -B`. They do not change a file or a frozen certificate.
+
+1. In F_2, replace both full-cover maps on one X_A source cohort with
+   identity maps. Both original maps preserve the exact native phase.
+   The scalar and line gates are unchanged. The checker reaches the
+   complete owner-path comparison and rejects the altered F_2 word.
+   This is a substantive path check, not a payload-hash rejection.
+2. Remove the initial C0 clear from the first F_0 private row. The checker
+   rejects it at the private-lifetime boundary check. The test therefore
+   does not accept an implicit zero value for an arbitrary owned input.
+
+Both controls fail for their specific expected reasons. They ran in
+3.192 seconds. The copied and frozen package files stayed unchanged.
+The cold run also executed the package's scalar timing, private-clear,
+odd-denominator, Gaussian phase, inverse-line, and translation controls.
+
+## Claim boundary
+
+README faithfully states a local full-cover construction. The exact
+base bills remain B scalar 214986/native 5546 and F scalar 211210/native 5530.
+The map columns distinguish explicit cover maps from native wrappers;
+their combined counts are 576, 304, and 16 for B, positive F, and F_0.
+They are not presented as priced stream or address implementations.
+The eight private inputs are owned and discarded, while the 480 ordinary
+helper inputs are arbitrary and restored. B and F are invertible data
+maps and companion circuits; they are not mutual inverse circuits.
+
+The selected-observation obstruction is clearly limited to the fixed
+first pair, retained ordinary schedule, and specified later observation
+class. README says that the global witness is preserved evidence and is
+not rerun by this entrypoint. It leaves changed first maps,
+ordinary-to-selected reads, affine helpers, and paid query access open.
+
+Controller closure, endpoint recovery, new child and helper hosting,
+physical map costs, recursive precision, and the complete supplier bill
+remain open. Optional fusion is excluded from this base certificate.
+The package makes no new kappa or selected-frontier claim. This review
+does not change those boundaries.
+
+The audit used separate OpenAI Codex agent work. No PR or commit was made.
diff --git a/research/joint-query/evidence/QQ16-COVER-ACTION-ADDENDUM.md b/research/joint-query/evidence/QQ16-COVER-ACTION-ADDENDUM.md
new file mode 100644
index 0000000000..3dd1a990d7
--- /dev/null
+++ b/research/joint-query/evidence/QQ16-COVER-ACTION-ADDENDUM.md
@@ -0,0 +1,76 @@
+# Exact cover action for the QQ16 native components
+
+This note fixes the representation of each alignment map used in
+QQ16-NATIVE-COMPONENT.md and QQ16-CONSERVED-COMPONENT.md. Their
+scalar formulas, native phases, line recipes and counts are unchanged.
+The symbol P_rho in their alignment notation means the cover route
+defined here. It must not be implemented as a payload permutation
+within one fixed cover array.
+
+Let d be a cover element, p a port, and z_1,...,z_lambda the physical
+payload addresses. Different cover positions contain independent
+arbitrary arrays. For a binary orthogonal g and binary vector delta,
+define the combined array view
+
+    (M_(g,delta)f)_p(d,z_1,...,z_lambda)
+      =f_p(dg,z_1+d delta,...,z_lambda+d delta).      (1)
+
+Each addition in (1) is binary XOR. All compact and other spectator
+coordinates stay unchanged. The map has no amplitude phase. It
+changes both the cover-owner index and the payload translation. It
+does not apply g to the payload addresses. The exact composition is
+
+    M_(g,a) M_(h,b)=M_(gh,a+gb),
+    M_(g,a)^-1=M_(g^-1,g^-1a).                    (2)
+
+Use the actual rho_v(p) and beta_p from the pinned native chart.
+At a Y boundary before v, the alignment in both component notes is
+
+    A_v(p)=M_(rho_v(p),p+lift_v(beta_p)).
+
+At a completed X boundary at or after v it is
+
+    A_v^X(p)=M_(rho_v(p),B_p beta_p+lift_v(beta_p)).
+
+These are precisely A=ZD from sections 1--4 of the independently
+checked interface-proof/BRIDGE-REVIEW.md. Here D changes the cover
+index by right multiplication and Z translates the payload at its
+new view position. The identity A T=T_common D proves that the
+logical scalar word is conjugated by D, without an extra payload
+operator. Its proof applies to arbitrary cover fields and tensor
+powers; it does not restrict data to cover-invariant fields.
+
+For a target p and source q in one chart, the relative path is
+
+    A_v(p)^-1 A_v(q)
+      =M_(rho_p rho_q, rho_p(delta_p+delta_q)).     (3)
+
+The g and delta in (3) are exactly those used by the component phase
+checker. That checker transports the source frame axes by g because
+the source owner is dg. It does not certify a payload-only substitute
+for (1). Such a substitute is false on arbitrary independent cover
+inputs, even if it has the same binary frame calculation.
+
+The map counts in the component invoices count one combined
+bijection (1) as one map, and count its inverse separately. They do
+not say that computing a cover product or a tensor translation is
+free. The complete supplier must price their physical realization.
+For each fixed port, d to dg is a bijection. A common-frame scalar
+word can therefore use these views without merging independent
+owners or copying a complete extra bank. A full emitted word must
+still record the cover action, phase correction, source reads,
+target writes, and all helper-owner conflicts.
+
+The binding source pins are:
+
+    interface-proof/BRIDGE-REVIEW.md
+    d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3
+
+    interface-proof/BRIDGE-OPERATOR-REVIEW.json
+    c905a19d70f34c435c5f5454c6190bbfb1ce4594b1513bf76156acf620d7c6fc
+
+The latter review checks all 1008 actual entry/exit recipes and
+32256 selected data owner routes. This note uses that result; it
+does not repeat the owner audit. An earlier informal schema message
+gave a payload-only interpretation. Equation (1) replaces that
+message before native word emission.
diff --git a/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json b/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json
new file mode 100644
index 0000000000..e649641e9b
--- /dev/null
+++ b/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.json
@@ -0,0 +1,410 @@
+{
+  "A": [
+    0,
+    7,
+    20,
+    27,
+    36,
+    46,
+    57,
+    111
+  ],
+  "B2_h_identity_coefficient": 2112,
+  "T": [
+    21,
+    37,
+    47,
+    76,
+    81,
+    87,
+    92,
+    110
+  ],
+  "U": [
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    8,
+    9,
+    10,
+    11,
+    12,
+    13,
+    14,
+    15,
+    16,
+    17,
+    18,
+    19,
+    22,
+    23,
+    24,
+    25,
+    26,
+    28,
+    29,
+    30,
+    31,
+    32,
+    33,
+    34,
+    35,
+    38,
+    39,
+    40,
+    41,
+    42,
+    43,
+    44,
+    45,
+    48,
+    49,
+    50,
+    51,
+    52,
+    53,
+    54,
+    55,
+    56,
+    58,
+    59,
+    60,
+    61,
+    62,
+    63,
+    64,
+    65,
+    66,
+    67,
+    68,
+    69,
+    70,
+    71,
+    72,
+    73,
+    74,
+    75,
+    77,
+    78,
+    79,
+    80,
+    82,
+    83,
+    84,
+    85,
+    86,
+    88,
+    89,
+    90,
+    91,
+    93,
+    94,
+    95,
+    96,
+    97,
+    98,
+    99,
+    100,
+    101,
+    102,
+    103,
+    104,
+    105,
+    106,
+    107,
+    108,
+    109
+  ],
+  "all_tensor_sizes": "Use payload-constant fields at every lambda. Exact payload translations act trivially; arbitrary cover values remain.",
+  "checker_sha256": "ea6e533db90c57a10c8c0055e2aee0ebe8eb05efb565fb236b60ea496b05a150",
+  "cross_gram_square_identity_coefficient": 192,
+  "distinct_relative_routes": 96,
+  "forward_query_values": [
+    0,
+    0,
+    0,
+    0,
+    0
+  ],
+  "geometry_payload_sha256": "498d85807dd3032de01b5da72a67717f02ee0ecf068e8c47f67d4f21034cd896",
+  "independent_missing_selected_directions": 8,
+  "not_claimed": [
+    "A lower bound for paid ordinary-Y reads",
+    "A general native decoder obstruction",
+    "A supplier or kappa result"
+  ],
+  "proof_scope": "The universal first-two-call proof is read and recorded in the companion note. This checker independently binds its nonzero witness to actual routes and replays the remaining ordered content events.",
+  "relative_route_count": 96,
+  "source_pins": {
+    "circuit-interface/INTERFACE.json": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+    "coherent-port/QQ16-COVER-ACTION-ADDENDUM.md": "4bb4a68d8b4811b6d8364150612056bc124d38f1974d6f603dae68a99c4682fb",
+    "cover-algebra/QQ16-COVER-ACTION-REVIEW.json": "2563bad8bb6b086c603cedc4ec9dcc883fd9a4665437bab6fb21ad45a2367a64",
+    "encoded-controller/NORMALIZATION-PROGRAMS.json": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9",
+    "encoded-controller/QQ16-CONSERVED-CONTROLLER.json": "33490295eeb02c3d4af7c9a199afd8dd72ec821fe377416547d7cb2136782dde",
+    "encoded-controller/QQ16-CONSERVED-CONTROLLER.md": "e18594af767a26b0202e857d45202f5f563db2a190b81a7ade8fd62fcef850b9",
+    "encoded-controller/QQ16-SELECTED-WITNESS.json": "e35e5868a1322e406191079c0675975b139692ba50b1e2e5fb8a40b6480519f4",
+    "encoded-controller/QQ16-SELECTED-WITNESS.md": "52f2ee565320f05282c637aa79eee100606c24240b1b5866f0c8d62e7913c9fc",
+    "encoded-controller/check_qq16_selected_witness.py": "b1a6315b7919a48dd20eeabf71487fe6cfd7ee59bfa0ee5ebd3ad3699b2c3a0a"
+  },
+  "status": "PASS_INDEPENDENT_QQ16_RATIONAL_OBSERVATION_WITNESS",
+  "tail_trace": [
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        -1,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        -1,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "local",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "bridge",
+      "x_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ]
+    },
+    {
+      "kind": "terminal",
+      "x_coefficients": [
+        1,
+        0,
+        0,
+        0
+      ],
+      "y_coefficients": [
+        0,
+        0,
+        0,
+        0
+      ]
+    }
+  ]
+}
diff --git a/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md b/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md
new file mode 100644
index 0000000000..c6ecf75654
--- /dev/null
+++ b/research/joint-query/evidence/QQ16-RATIONAL-OBSERVATION-REVIEW.md
@@ -0,0 +1,95 @@
+# Rational inversion does not close the fixed QQ16 observation set
+
+The selected-output witness passes independent review. It rules out the
+proposed selected solve from all selected endpoints, all completed-X
+descendants and all five F-query histories. The statement holds over the
+rational numbers. It does not rule out a paid old-Y query, a changed local
+map or a different controller.
+
+This review reads the frozen `QQ16-CONSERVED-CONTROLLER.md` and
+`QQ16-SELECTED-WITNESS.md` in the encoded-controller lane. The receipt
+records their exact hashes. The reviewer checker imports no producer code.
+It reads the actual query matrix and the serialized native route columns.
+
+## The actual nonzero input
+
+Keep the producer's A, T and U96 sets. Let B_s be the stage-s query on U.
+The exact column Grams give B_s B_s*=48I. On fields constant in every
+payload coordinate, each retained payload translation is the identity.
+The cover values are still arbitrary. This subspace is not the
+cover-invariant subspace. The actual action is the regular right cover
+action, as in the reviewed map M_(g,delta).
+
+The reviewer reads the doubled geometry only to recover the original
+73-dimensional route columns. It checks the diagonal doubling, each
+original route's orthogonality and inverse, and all 96 products
+rho_2(p) rho_1(p) for p in U. Those products are distinct. Therefore the
+identity coefficient of B2 B1* B1 B2* is
+
+    sum_p (r_p r_p^T)^2 = 4 sum_p r_p r_p^T = 192I.
+
+For each centre coordinate e_k at the identity cover element, put
+
+    h_k = (48I-B1* B1) B2* e_k.
+
+Then B1 h_k=0 and the identity coefficient of B2 h_k is 2112 e_k.
+These are eight independent missing query directions. The construction
+has integer coefficients. It is valid at every positive tensor size by
+using fields constant in all payload blocks. No approximation or omitted
+complex phase is used. The exact endpoint phases are handled by the
+inherited logical frame convention.
+
+## Ordered first two calls
+
+Write h for any one of these inputs. Set all other pairs to zero and set
+
+    X_U=h, Y_U=0,
+    X_A=-P_0,A B0 h-P_2,A B2 h, Y_A=-X_A,
+    X_T=P_0,T ell_0,A P_2,A B2 h, Y_T=-X_T.
+
+The selected sums are zero. In f0, the B0 h terms cancel. The remaining
+terms are -ell_0,A P_2,A B2 h and its positive copy from X_T. Thus f0=0.
+The two-sided selected inverse identities give, after F0,
+
+    X_U=Y_U=h,
+    X_A=P_2,A B2 h, Y_A=-P_2,A B2 h,
+    X_T=Y_T=0.
+
+At B1, q2=B2 h+ell_2,A Y_A=0. The future code E2 replaces the A field
+by P_2,A q2=0. Its other selected field is zero, so its query b1 is
+B1 h=0. The driver a1 is also zero. Substitution in each frozen B output
+formula leaves only Y_0,U=h. No operator factors were commuted in this
+calculation.
+
+The checker then replays every remaining ordinary event from that exact
+state. The first plus bridge places -h in Y1. F2 has zero X source and
+leaves it unchanged. The minus bridge cancels it before B3. All later
+active sources are zero. Every later selected state is zero. The final
+terminal leaves h only in named X0, which has the old-Y native type.
+Every completed-X descendant and every F query is zero. Removing the
+first minus bridge makes the same check fail at B3.
+
+The initial X_T is nonzero because P_0,T ell_0,A P_2,A is a unit between
+the two selected coordinate spaces. The zero input has the same allowed
+observations but a different required selected output. Thus rational
+coefficients, including division by 3 or 13, cannot reconstruct this
+input from those observations. Later homogeneous selected-only maps
+cannot change the witness: they keep their zero input at zero. An
+ordinary-to-selected read is a different interface and is outside this
+result.
+
+## Reproduction and scope
+
+Run from the workspace root:
+
+```text
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/interface-proof/rational-decoder/check_qq16_missing_observation.py
+PASS_INDEPENDENT_QQ16_RATIONAL_OBSERVATION_WITNESS
+96 distinct actual routes; B2*h identity coefficient 2112; all five F queries zero
+```
+
+The first-two-call proof is an ordered symbolic proof. The executable
+checks its actual nonzero source, the retained tail schedule and the
+mutation control. It does not emit a complete native QQ16 word. Its scope
+is this fixed observation set; it is not a general native lower bound or
+a kappa result.
diff --git a/research/joint-query/evidence/QQ16-SELECTED-WITNESS.json b/research/joint-query/evidence/QQ16-SELECTED-WITNESS.json
new file mode 100644
index 0000000000..5082d791d0
--- /dev/null
+++ b/research/joint-query/evidence/QQ16-SELECTED-WITNESS.json
@@ -0,0 +1,410 @@
+{
+  "A": [
+    0,
+    7,
+    20,
+    27,
+    36,
+    46,
+    57,
+    111
+  ],
+  "T": [
+    21,
+    37,
+    47,
+    76,
+    81,
+    87,
+    92,
+    110
+  ],
+  "U": [
+    1,
+    2,
+    3,
+    4,
+    5,
+    6,
+    8,
+    9,
+    10,
+    11,
+    12,
+    13,
+    14,
+    15,
+    16,
+    17,
+    18,
+    19,
+    22,
+    23,
+    24,
+    25,
+    26,
+    28,
+    29,
+    30,
+    31,
+    32,
+    33,
+    34,
+    35,
+    38,
+    39,
+    40,
+    41,
+    42,
+    43,
+    44,
+    45,
+    48,
+    49,
+    50,
+    51,
+    52,
+    53,
+    54,
+    55,
+    56,
+    58,
+    59,
+    60,
+    61,
+    62,
+    63,
+    64,
+    65,
+    66,
+    67,
+    68,
+    69,
+    70,
+    71,
+    72,
+    73,
+    74,
+    75,
+    77,
+    78,
+    79,
+    80,
+    82,
+    83,
+    84,
+    85,
+    86,
+    88,
+    89,
+    90,
+    91,
+    93,
+    94,
+    95,
+    96,
+    97,
+    98,
+    99,
+    100,
+    101,
+    102,
+    103,
+    104,
+    105,
+    106,
+    107,
+    108,
+    109
+  ],
+  "centre_coordinate": 0,
+  "checker_sha256": "b1a6315b7919a48dd20eeabf71487fe6cfd7ee59bfa0ee5ebd3ad3699b2c3a0a",
+  "identity_coefficients": [
+    "2112",
+    "2112",
+    "2112",
+    "2112",
+    "2112",
+    "2112",
+    "2112",
+    "2112"
+  ],
+  "nonzero_required_input": "X0_T=P0_T ell0_A P2_A B2h",
+  "ordinary_gram": 48,
+  "proof_sha256": "52f2ee565320f05282c637aa79eee100606c24240b1b5866f0c8d62e7913c9fc",
+  "relative_routes_checked": 96,
+  "scope": "Fixed F0/B1 and retained ordinary schedule, with any later homogeneous selected-only linear controller. Does not exclude a changed local pair, ordinary-to-selected reads, affine helper states, or paid source queries.",
+  "source_pins": {
+    "interface": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+    "route_evidence": "284a2cb12b00ddf066afb1c4b22692640e4421ac027e40d775c8aa112423abcd",
+    "schedule": "7ce02810ecaca13ba084c365ec9c781a211e3c94dbf0f64e8717ca6d1c0b0ca9"
+  },
+  "status": "PASS_QQ16_INTEGER_SELECTED_WITNESS",
+  "trajectory_after_B1": [
+    {
+      "coefficient": 1,
+      "dst": 0,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        -1,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 1
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        -1,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 2
+    },
+    {
+      "coefficient": -1,
+      "dst": 0,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 1
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 3
+    },
+    {
+      "coefficient": 1,
+      "dst": 1,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 2
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 4
+    },
+    {
+      "coefficient": -1,
+      "dst": 1,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 2
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 5
+    },
+    {
+      "coefficient": 1,
+      "dst": 2,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 3
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 6
+    },
+    {
+      "coefficient": -1,
+      "dst": 2,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 3
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 7
+    },
+    {
+      "kind": "local",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "stage": 8
+    },
+    {
+      "coefficient": 1,
+      "dst": 3,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 2
+    },
+    {
+      "coefficient": 1,
+      "dst": 2,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 1
+    },
+    {
+      "coefficient": 1,
+      "dst": 1,
+      "kind": "bridge",
+      "ordinary": [
+        0,
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ],
+      "src": 0
+    },
+    {
+      "kind": "terminal",
+      "ordinary": [
+        1,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0
+      ]
+    }
+  ],
+  "witness": "(48I-B1*B1)B2* e_0 delta_identity",
+  "zero_observations": [
+    "all selected endpoints",
+    "all completed-X descendants",
+    "f0",
+    "f2",
+    "f4",
+    "f6",
+    "f8"
+  ]
+}
diff --git a/research/joint-query/evidence/QQ16-SELECTED-WITNESS.md b/research/joint-query/evidence/QQ16-SELECTED-WITNESS.md
new file mode 100644
index 0000000000..307650f45e
--- /dev/null
+++ b/research/joint-query/evidence/QQ16-SELECTED-WITNESS.md
@@ -0,0 +1,124 @@
+# A selected-output witness for the conserved QQ16 pair
+
+The conserved QQ16 pair needs one more source observation before its
+selected inputs can be restored. This statement holds even if all five
+forward query values are supplied without cost. It concerns the fixed
+F0 and B1 maps and the retained ordinary bank program. It does not
+exclude a change to those maps, a later ordinary-to-selected read,
+an affine helper state, or a paid query operation.
+
+Use the A, T, and U96 sets from QQ16-CONSERVED-CONTROLLER.md. Write
+B_s=R_s iota_U. The actual columns give
+
+```text
+B_s B_s* = 48 I
+```
+
+where * reverses the cover route and transposes the real coefficient.
+Every port column has squared norm four. Let e be the first centre
+coordinate at the identity element of the regular cover, and set
+
+```text
+h = (48 I - B1* B1) B2* e.
+```
+
+This is an integer vector of finite support in the regular cover. The
+same-stage Gram identity gives B1 h=0. For distinct actual stage-1 and
+stage-2 routes, only equal port indices contribute to the identity
+coefficient in B2 B1* B1 B2*. Therefore the first coordinate of B2 h
+has identity coefficient
+
+```text
+48^2 - 4*48 = 2112.
+```
+
+In particular B2 h is not zero. No division by 3, 11, or 13 occurs in
+the witness. The checker verifies the exact 96 route labels and the
+coefficient count. It does not enumerate the full regular cover.
+
+## Arbitrary input and its exact trajectory
+
+Set all banks except pair 0 to zero. In pair 0 use
+
+```text
+X_U = h,                 Y_U = 0
+X_A = -P_0,A B0 h - P_2,A B2 h
+Y_A = -X_A
+X_T = P_0,T ell_0,A P_2,A B2 h
+Y_T = -X_T.
+```
+
+Both selected pair sums are zero. All factors P and ell are the actual
+selected route maps. Each is a dyadic unit between its eight selected
+coordinates and the query coordinates. Thus X_T is not zero.
+
+At F0, the full source query is zero. Its output is
+
+```text
+X_U = h,                 Y_U = h
+X_A = P_2,A B2 h,        Y_A = -P_2,A B2 h
+X_T = 0,                 Y_T = 0.
+```
+
+At B1, the future query is
+
+```text
+q2 = R2 Y = B2 h - B2 h = 0.
+```
+
+The future query code E2 removes the selected A value. Its source u is
+(h,0,0), so b1=B1 h=0. The old X_T driver a1 is zero. The output
+after B1 is therefore exactly
+
+```text
+Y_0,U = h,
+all other ordinary and selected fields = 0.
+```
+
+The positive ordinary bridge (0,1) places -h in Y_1,U. F2 has a zero
+X source and changes no field. The negative bridge removes that -h.
+Every later active ordinary pair is zero. The last three ordinary
+bridges leave Y_0,U=h and all other ordinary fields zero. The terminal
+moves h to final X_0,U. This is a former Y field with the phased native
+output type. Every completed-X descendant is zero.
+
+All selected registers are zero after B1. Consequently, any subsequent
+homogeneous linear operation that reads and writes selected registers
+only keeps them zero. This includes arbitrary cross-bank, port, and
+cover maps, and any selected terminal. The assertion does not permit a
+selected operation to read an ordinary bank. The later local calls also
+have zero active inputs in the retained ordinary schedule. Thus the
+trajectory holds for every such later selected controller, not only
+for the first-six-swap choice in the frozen recurrence.
+
+All five forward queries f0,f2,f4,f6,f8 are zero. The complete observation
+set consisting of all selected outputs, all completed-X descendants,
+and all five forward query histories is therefore zero. The initial
+X_0,T is nonzero. No linear decoder from only those observations can
+restore that input. This remains true over the rational numbers.
+
+The actual missing information includes B2 h. The initial A correction
+also contains B0 h. This result does not make either query expensive by
+itself. It identifies an actual required source read or an earlier
+change in the content controller.
+
+## Check
+
+Run from the workspace root:
+
+```text
+python3 -I -O -B work/centre-encoding-campaign-20261014/lanes/encoded-controller/check_qq16_selected_witness.py
+```
+
+Expected output:
+
+```text
+PASS_QQ16_INTEGER_SELECTED_WITNESS
+```
+
+The checker pins the actual R, route evidence, and schedule. It checks
+the actual Grams, all 96 route distinctions for stages 1 and 2, all
+eight identity coefficients, and the ordinary trajectory after B1.
+The ordered selected identities above use only the two-sided selected
+inverse relations. An independent review must keep the same observation
+scope. No general native lower bound or supplier claim is made.
diff --git a/research/joint-query/evidence/REPLAY.json b/research/joint-query/evidence/REPLAY.json
new file mode 100644
index 0000000000..dd3c9c22d1
--- /dev/null
+++ b/research/joint-query/evidence/REPLAY.json
@@ -0,0 +1,35 @@
+{
+  "certificate_payload_sha256": "2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef",
+  "code_sha256": {
+    "replay.py": "61a3c2ddc3e62f965bfc9ee47b6a1e8c03b0071c5021feb6612ebbdd9561038e",
+    "source_data.py": "d23924511e3aed41e5e64511ca70126a636d91c8aa02e656cb61d6ceca1fe0a0",
+    "verify_native.py": "1c58e7b6e8e1cde4df455c2129601c145ed763fc63a3ab427eb1058d1fc08bd2",
+    "verify_ordered.py": "0e23ed4bef58ed8375a9d43b0b9cbcab8e825ec7d5d702e74973ccc41d97ffa6",
+    "verify_scalar.py": "33bdbad17a0531fe527aff306eb235d9c38c1629db4fd167b989725930b0327a"
+  },
+  "common_chart_input_columns_per_orientation": 712,
+  "exact_new_native_gaussian_columns": 16384,
+  "inherited": [
+    "The bridge proof for the retained core at each owner",
+    "The original child kernels and recursive native contract"
+  ],
+  "native_cases": 37,
+  "not_checked": [
+    "An implementation of the algebraic inverse in output native frames",
+    "Global controller closure or an endpoint decoder",
+    "New child and helper hosting",
+    "Stream and address implementation costs",
+    "Recursive precision and the complete supplier invoice",
+    "A new kappa bound"
+  ],
+  "outputs": {
+    "CLEAN-J-CHECKS.json": "2946d03237300839c08acb33b3df993ce61334a55589bf2f9eb17c3d5f463791",
+    "NATIVE-CHECKS.json": "fe959be0bf2490f99efcf6b8109b19cc8d79036d9df54b59598f32de92295054",
+    "ORDERED-CHECKS.json": "c0b3474406807199aae80bc48dc188f03035b5869f113572828615de0b41563a",
+    "SCALAR-CHECKS.json": "7205aa5f24294f6d6422830719aae6d5b01efb08747fdf746fa9f2f5594a0387"
+  },
+  "source_archive_sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754",
+  "source_base": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "source_manifest_sha256": "fabc6686e5d3ac0e4bb4397c147037b9285abfa671614590dad6d4e16b4dc0fc",
+  "status": "PASS_PORTABLE_QQ16_LOCAL_JOINT_QUERY"
+}
diff --git a/research/joint-query/evidence/SCALAR-CHECKS.json b/research/joint-query/evidence/SCALAR-CHECKS.json
new file mode 100644
index 0000000000..3c9e2e4092
--- /dev/null
+++ b/research/joint-query/evidence/SCALAR-CHECKS.json
@@ -0,0 +1,46 @@
+{
+  "data_compositions_with_algebraic_inverses": 2,
+  "odd_denominator_control": "REJECTED",
+  "orientations": {
+    "B": {
+      "arbitrary_helpers_restored": 480,
+      "block_costs": {
+        "A_input_copies": 480,
+        "Y_T_query_subtract": 4160,
+        "Y_U_from_X_T": 3840,
+        "eight_unsigned_swaps": 208,
+        "future_E_t": 4160
+      },
+      "conserved_pair_sums": 16,
+      "formal_input_columns": 712,
+      "inverse_orders": 2,
+      "owned_private_outputs_zero": 8,
+      "scalar_real_primitives": 214986
+    },
+    "F": {
+      "arbitrary_helpers_restored": 480,
+      "block_costs": {
+        "A_output_copies": 480,
+        "X_A_fused_query": 4096,
+        "X_A_restore_selected": 320,
+        "X_T_query_subtract": 320,
+        "X_T_sign": 16,
+        "X_U_query_subtract": 3840
+      },
+      "conserved_pair_sums": 16,
+      "formal_input_columns": 712,
+      "inverse_orders": 2,
+      "owned_private_outputs_zero": 8,
+      "scalar_real_primitives": 211210
+    }
+  },
+  "scope": "Exact common-chart scalar words and algebraic data inverses. B and F are not inverse circuits. Native access to the algebraic inverses and global controller closure are not established.",
+  "status": "PASS_QQ16_SCALAR_MAPS",
+  "timing_and_private_controls_rejected": [
+    "late_original_Y_copy",
+    "early_T_query",
+    "early_F_source_update",
+    "early_F_target_copy",
+    "missing_owned_clear"
+  ]
+}
diff --git a/research/joint-query/evidence/SCALAR-REVIEW.json b/research/joint-query/evidence/SCALAR-REVIEW.json
new file mode 100644
index 0000000000..8616c02d1c
--- /dev/null
+++ b/research/joint-query/evidence/SCALAR-REVIEW.json
@@ -0,0 +1,92 @@
+{
+  "B_added_scalar": 12848,
+  "B_block_cost": {
+    "A_input_copies": 480,
+    "Y_T_query_subtract": 4160,
+    "Y_U_from_X_T": 3840,
+    "eight_unsigned_swaps": 208,
+    "future_E_t": 4160
+  },
+  "B_complete_bill": {
+    "operations": {
+      "add": 20654,
+      "clear": 32,
+      "scale": 715
+    },
+    "real_primitives": 214986
+  },
+  "F_added_scalar": 9072,
+  "F_block_cost": {
+    "A_output_copies": 480,
+    "X_A_fused_query": 4096,
+    "X_A_restore_selected": 320,
+    "X_T_query_subtract": 320,
+    "X_T_sign": 16,
+    "X_U_query_subtract": 3840
+  },
+  "F_complete_bill": {
+    "operations": {
+      "add": 20278,
+      "clear": 32,
+      "scale": 715
+    },
+    "real_primitives": 211210
+  },
+  "arbitrary_helpers_restored_per_word": 480,
+  "backward_query_records_checked": [
+    "R Yout=ell_T Xin",
+    "ell_T Xout-12 R Yout=R E Yin"
+  ],
+  "coefficients_rebuilt_from_R": [
+    "K",
+    "R_A_inverse",
+    "R_T_inverse",
+    "B",
+    "C",
+    "C_inverse",
+    "D",
+    "future_N"
+  ],
+  "complete_scalar_input_columns_per_word": 712,
+  "conserved_sums_per_word": 16,
+  "data_inverse_columns": 224,
+  "exact_checks": [
+    "R_U K_U=12I",
+    "BD=12I",
+    "N^2=0",
+    "C C_inverse=I",
+    "C_inverse C=I"
+  ],
+  "excluded": [
+    "A native frame or scalar-phase replay",
+    "Native child construction or its complete cost",
+    "The general changing-chart operator proof",
+    "A complete controller or supplier",
+    "Recursive hosting or a kappa result"
+  ],
+  "forward_query_records_checked": [
+    "ell_T Xout=R Xin",
+    "ell_A Xout=ell_T Xin"
+  ],
+  "inverse_composition_orders_per_word": 2,
+  "literal_blocks_rebuilt": {
+    "B": 5,
+    "F": 6
+  },
+  "owned_private_outputs_zero_per_word": 8,
+  "pins": {
+    "R": "5c6c51fbffc07a683e922f17532fd90262ae9e23cc3560a696002073dd234ef3",
+    "core": "fa60b4af013dd8b8db289845e3ed597720ff955751ad270c3d58236b64080877",
+    "independent_arithmetic": "69bf5c3c9044c6a14605ca52100825a0a2ecb397df1f12465ecc83e6ddb621ae",
+    "note": "ba2feff4e5b7f958283a97237113997bb8182077a163f916864526edf35f2500",
+    "old_scalar_source": "20b70c7c4f26161a562163f4087619e76d0a566abd57bd921793e65427dbb61d",
+    "payload": "6b8d647a8ce2ff86f39b1947d11cbcdfd0f366e90c2816ff6cca09d47c75869c",
+    "producer": "48b8d2cf81c4b8d50c3aa0dcfe75090862a53fbbf9d051fd6985604e6191ba20",
+    "receipt": "c9729d71890df17027c75b028c535ad3bd8dc11633812bae856f80c38c52a0a1"
+  },
+  "producer_imported": false,
+  "retained_core_input_columns_per_orientation": 712,
+  "scope": "Exact scalar maps and data inverses at the common-chart specialization. The old private inputs are owned and discarded. Each data map is invertible; no claim that the B and F words are mutual inverses is made.",
+  "status": "PASS_INDEPENDENT_CONSERVED_QQ16_SCALAR_PAIR",
+  "typed_copy_groups_rebuilt": 16
+}
diff --git a/research/joint-query/evidence/SCALAR-REVIEW.md b/research/joint-query/evidence/SCALAR-REVIEW.md
new file mode 100644
index 0000000000..e060789dfa
--- /dev/null
+++ b/research/joint-query/evidence/SCALAR-REVIEW.md
@@ -0,0 +1,142 @@
+# Independent review of the conserved QQ16 scalar pair
+
+The frozen scalar pair passes review. No material error was found.
+Both data maps are invertible and preserve all sixteen selected sums.
+The complete scalar replays restore every arbitrary helper and clear
+the eight owned private outputs. The two data maps were checked with
+their own inverses; this is not a claim that the forward and backward
+words are mutual inverses.
+
+The scope is the common-chart scalar specialization. Native phases,
+legal changing-chart accesses, native child implementations, and the
+general ordered operator proof have separate reviews.
+
+## Sources and method
+
+The frozen payload has decompressed SHA256
+`6b8d647a8ce2ff86f39b1947d11cbcdfd0f366e90c2816ff6cca09d47c75869c`.
+The producer receipt has SHA256
+`c9729d71890df17027c75b028c535ad3bd8dc11633812bae856f80c38c52a0a1`.
+The producer and note were read without changes. All source pins are
+recorded in [REVIEW.json](REVIEW.json).
+
+The [independent checker](verify_conserved_review.py) imports only an
+earlier independent rational arithmetic engine. It does not import the
+producer, its algebra module, or a native compiler. It rebuilds K and
+both selected inverse minors directly from the pinned R. From these it
+rebuilds B, C, C^-1, D, and the future logger N, then reconstructs every
+literal added scalar event and both typed copy descriptions.
+
+The rebuilt coefficients satisfy
+
+\[
+ R_AK_A=R_TK_T=I,\quad R_UK_U=12I,\quad
+ BD=12I,\quad N^2=0,\quad CC^{-1}=C^{-1}C=I.
+\]
+
+Every nonzero B, C, C^-1, D, or N coefficient is a signed half.
+B and N have 52 entries in each of their eight rows. C and C^-1
+have four entries in each row, and D has four in each of its 96
+nonzero rows. These checks use the actual selected sets and the
+actual 8 by 112 matrix, without an assumed root-label symmetry.
+
+The checker also replays each pinned core on all 712 formal inputs
+and verifies its clean-J map and scalar bound. It then replays the
+new full words on all 712 inputs, including all arbitrary helper and
+private values. This replay checks scalar coefficients and chronology;
+it does not interpret a chart placeholder as a proved native frame.
+
+## Backward map and inverse
+
+Let u=Ey with E=I+N, let a=R_Tx_T, and let b=Ru. Before the core,
+the swap and subtraction give
+
+\[
+ X_T=u_T,\quad Y_U=u_U+D x_T,\quad
+ Y_T=-B u_{\mathrm{off}T}-11x_T.
+\]
+
+The current query is exactly a because BD=12I. Applying the clean
+backward core gives the displayed map in the frozen note. The input
+A copies must read old y_A before E changes it. Their correction
+is exactly what gives X'_A=x_A+y_A-u_A.
+
+The independent replay checks both records directly:
+
+\[
+ RY'=a,\qquad \ell_T X'-12RY'=b.
+\]
+
+Given arbitrary output data, these records recover u. Subtract K_Ua
+on U, add K_Tb+11K_Ta on T, and keep A. Then y=(I-N)u. Recover x_T
+as K_Ta, x_U as X'_U+y_U, and x_A as X'_A-y_A+u_A.
+Both composition orders were checked on all 224 data columns.
+
+For A, X'_A+Y'_A=x_A+y_A. For T, the b terms cancel and the a
+coefficients leave K_Ta=x_T. The checker verifies every selected
+sum on all 712 input columns, including possible helper or private
+dependence.
+
+## Forward map and inverse
+
+Put f=Rx. The rebuilt forward scalar sequence gives
+
+\[
+ X'_U=x_U-K_Uf,\quad X'_A=K_A\ell_Tx,\quad X'_T=K_Tf.
+\]
+
+The final A copies read the completed source code. They give
+Y'_U=y_U+X'_U and Y'_S=y_S+x_S-X'_S for S=A union T.
+All sixteen selected sums therefore hold.
+
+The independent replay checks the two output records
+
+\[
+ \ell_T X'=f,\qquad \ell_A X'=\ell_Tx.
+\]
+
+These recover x_U and x_T. Subtract their R contributions from f
+and apply K_A to recover x_A. The displayed Y equations then recover
+y. Both composition orders were checked on all 224 data columns.
+
+For both orientations, all 480 arbitrary helpers have identity output
+rows and all eight private output rows are zero. Private values are
+owned and discarded. The complete 712-field map is not claimed to be
+invertible on those discarded inputs.
+
+## Scalar invoice
+
+The backward added blocks cost, in execution order,
+480, 4160, 3840, 208, and 4160 real primitives. Their total is
+12,848. The forward added blocks cost 4096, 320, 320, 16, 3840,
+and 480, for a total of 9,072. Each retained core costs 202,138.
+Thus the complete displayed scalar words cost 214,986 backward and
+211,210 forward.
+
+The first forward block has 32 unit coefficients and 384 signed-half
+coefficients. Combining each pair of consecutive equal half reads
+into one unit read saves 32 times (20 minus 8), which is 384.
+X_T is unchanged between those reads, so this combination is valid.
+
+The native-order descriptions call for 24 backward and eight forward
+line slots. This review checks the scalar blocks around those slots
+and the typed copy descriptions. It does not verify the native lines,
+their scalar phases, or their full implementation invoice. Address
+maps and any extra scalar phases in the native bundle must be added
+before these bounds are used as a full construction cost.
+
+The independent run returned:
+
+```text
+PASS_INDEPENDENT_CONSERVED_QQ16_SCALAR_PAIR
+words=2 input_columns_each=712 data_inverse_orders_each=2 selected_sums_each=16
+B_added=12848 B_complete=214986 F_added=9072 F_complete=211210
+```
+
+No complete changing-chart controller, recursive hosting result, or
+kappa improvement is claimed. The result is an exact scalar premise
+for the separate operator and native construction reviews.
+
+This work uses the selected R, the retained centre-free cores, and
+the producer's conserved-sum construction. OpenAI Codex supplied
+independent proof and verification work under the user's direction.
diff --git a/research/joint-query/notices/LICENSE b/research/joint-query/notices/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/joint-query/notices/LICENSE
@@ -0,0 +1,201 @@
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+
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+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
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diff --git a/research/joint-query/notices/research/gauge44-slots-t16/NOTICE.md b/research/joint-query/notices/research/gauge44-slots-t16/NOTICE.md
new file mode 100644
index 0000000000..30d0c8cd3c
--- /dev/null
+++ b/research/joint-query/notices/research/gauge44-slots-t16/NOTICE.md
@@ -0,0 +1,24 @@
+# Gauge44 attribution and scope
+
+New contributions by icekylinx, with OpenAI GPT-6 Astra assistance.
+Local review and packaging used OpenAI Codex. Apache-2.0 applies;
+the license is included. The full original PR635 notice is preserved as
+UPSTREAM-NOTICE.md and construction/UPSTREAM-NOTICE.md.
+
+The new contribution is the changed source-branch gauge and retired-row
+completion, source-carried coordinate totals, exact 44-cold-end realization,
+and explicit all72 whole-family assignment using concave capacity matching
+with integer majorization certificates. The center-carrier generalization
+retains the exact ordered common frames and complete native local contract.
+Independent local, price, interface and owner fixed-point checks are included.
+
+The construction retains the credited PR635 K-triangle and porting machinery,
+earlier joint-prefix/HPE/frame ancestry and icekylinx's prior factory work.
+#645 used the same cited PR543 bit supplier as PR635. This package (research/gauge44-leaver8) cites the merged PR589 bit supplier instead, with a derived rank-mass deficit (PROOF-NOTE-BIT.md); #645's retained PR543-based evidence is historical. It builds #645's word without K-triangles (PartialK) and stacks earlier community jp8 layers on it (G44Stack), adds the p6n ends (NoTriReopen), entrance promotions (BlockInvert) a read-set exchange (BRoute), chafreaky's #741 frames, JointXF's joint exchange, NewBArch's triangle-hybrid B rewrite and LeaverSAT's eight k8 leaver cells (with LeaverSAT2's frame re-optimisation); see README. All-size, realization,
+hosting, precision/tape, analytic-transfer and bit H1-H5 assumptions remain
+conditional. No upstream license, credit, source pin or AI disclosure is
+replaced by this notice.
+
+PR641 and PR642 were checked as concurrent reported frontier comparisons.
+Their endpoints and owner maps are not included here. See CONSTRUCTION.md,
+hosting/PROOF.md, independent/ and README.md for the exact contribution scope.
diff --git a/research/joint-query/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md b/research/joint-query/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..ebc24a0168
--- /dev/null
+++ b/research/joint-query/notices/research/gauge44-slots-t16/UPSTREAM-NOTICE.md
@@ -0,0 +1,34 @@
+# Attribution and scope
+
+Four verified provider types are offered to every call: PR571's prefix word with twelve multi-cut cold kernels (PR568's unchanged constructor), the same word with forty width-five entrance promotions (PR569's unchanged frame constructor) before those kernels, PR575's plain joint-prefix provider, and PR568's eight-cold provider. A window MILP with an exact per-pattern model chooses the dispatch and a literal owner map. PR583's six source-bound kernel frame coalescences (its unchanged constructor and negative controls) are applied to every PR571-prefix provider word (ck and atm3), followed by two further coalescences that each first move one addition past two commuting additions (package code/build_gate_moves.py, extending PR583's constructor); a final hyperplane_end step (package code/build_hpe.py) then runs 46 single-gate cleanups h -= p right after part B at the dim-8 join U of their registers, so 46 width-8 entering helpers per call end at U with width 7; each such gate commutes with every earlier cleanup gate on its registers (for 8 of them the partner's one earlier gate x -= p only reads p), and the reordered program is replayed exactly. A window MILP (exact windows, RINS around an LP vertex) gives the dispatch ck 45 / atm3 21 / jp8 6 and the literal owner map.
+
+Pinned external sources (unchanged; `verify.py` checks their manifests and every file it uses):
+- PR568 (`research/complex-multicold`, commit `71c99ac935a33bb7b59a1b4a7af8725a939b0b90`).
+- PR571 (`research/structural-gain`, commit `b7bdc5a8de18fcf418cfb9c7d83a2b1097a5e4a3`).
+- PR569 (`research/larger-gain`, commit `897213a855b7fb8a1b8b0e552a2f5c42e6c1b326`).
+- PR575 (`research/complex-joint-prefix`, commit `eac6f7e378ab622dac50a2fd4b7ef6eab014de44`).
+- PR583 (`research/kernel-frame-coalescing`, commit `89be768f0157f5a3d8e4db69cf1748768605eac9`).
+
+Provider construction is described as typed steps in `data/SPEC.json` (`build`); `verify.py` runs only allowlisted step types with their paired omission audits and checks every input and output content hash. `code/` holds the spec-driven global admission scripts adapted from PR571's `frontier-composition/global-code/` (OpenAI Codex assisted, Apache-2.0): every expected value is read from `data/SPEC.json` and compared only after independent recomputation. `code/generated_identity.py` and `code/generated_identity_controls.py`, and the decompressed-content artifact identities in the bind, audit, invoice, assembly and phase-timing scripts, are taken unchanged from PR586 by chafreaky (`research/promoted-kernel-coalescing`, commit `4846fee5b06af770e9b3a10c36200f673d656725`, OpenAI Codex assisted, Apache-2.0), including its proof-content and reference/metadata mutation controls; the normalization of descriptive width metadata after frame changes follows the same PR.
+
+In PR601, the owner map was nominated by a HiGHS window MILP (adapted from PR569's `global/nominate_width7.py`) with lazy cross-time Hall cuts; this package's re-solved map is described below. Neither is an admission dependency.
+
+DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. (The PR601 package this one starts from states: "Prepared by Claude Code (Anthropic) research agents.") Apache-2.0 applies; LICENSE is included. All notices, licenses, source pins and AI disclosures of the pinned sources and their ancestry are retained in those packages and are not replaced by this notice. All inherited conditional assumptions remain conditional.
+
+**This package (complex-571-cold14, DreamingOfClouds).** It starts from PR601 (jeremykothe2, `research/complex-571-hpem46`, commit `529ab7dcb59d5ea7a5798e9e06cf5b3aee8a1550`). Everything above is kept unchanged except the following:
+- every provider chain (ck, atm3, jp8) gains the typed step `cold_end` (`code/build_cold_end.py`, `code/cold_end_controls.py`; recipes `data/recipes/*-cold_end.json.gz`);
+- the generalised native chain and the global admission scripts accept cold helpers that end below FULL (with `0:U` wrappers), a refactored exact cleanup, and check the wrapper order;
+- `data/PLAN.json` / `data/OWNERS.json.gz` (dispatch and literal owner map) come from a relocate/swap/ejection-chain/provider-flip annealing search started from PR601's map, refined by an exact pattern-restricted owner model (CP-SAT) with a literal edge-colouring expansion (not an admission dependency);
+- `data/SPEC.json` holds the expected values, recorded by a discovery run and then checked by a strict run.
+
+The cold-end construction (a row-plus-column cone condition for low-frame ends, a rank-0 dirt-spread premix and multi-gate lower-frame cleanup) builds on PR591 / PR592 / PR593 / PR601 (jeremykothe2) and our PR599 (Lean: multi-gate and cold hyperplane-end tails). DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. Build on this at your own risk.
+
+**This package (complex-571-cold14-b3, jeremykothe2).** It is PR604's `complex-571-cold14` (DreamingOfClouds) with ColdBeyond's second cold end per block (two new `cold_end` A-gate primitives, `PROOF-NOTE.md`), ColdSupply's E1 entering pair and reviewed controls, a free dispatch (jp8 ×60, atm3 ×12) and a literal owner map from an exact per-time-Hall window MIP. All other construction, code, controls and proofs are PR604's and earlier contributors', unchanged.
+
+**This package (complex-571-cold14-k492).** It is complex-571-cold14-b3 with these changes:
+- **K-triangle base words.** The leaver-read K-triangle skeleton atom and its read schedule (`data/TRI-SCHEDULE.json`) are by AtomScout, a Claude Code research agent. `code/construct_k_triangle.py` is PR531's `code/construct_504.py` (icekylinx, OpenAI Codex / GPT assisted, Apache-2.0; pinned source `direct_delivery`) extended with that atom.
+- **Ported chains.** The PR604/B3 chains are ported stage by stage onto the K-triangle words by `code/build_port_stage.py` (Port480, a Claude Code research agent). `code/build_frame_regroup.py` extends PR583's `build_frames.py` (chafreaky).
+- **Helper count R.** The generalisation of the global scripts to the provider helper count R is by GlobalR (a Claude Code research agent), with AtomReviewer's fixes (PROOF-NOTE-R.md).
+- **Owner map.** The owner map, the cold_end recipes on the K-triangle words and the package assembly are by Stack492, Port480 and ColdBeyond (Claude Code research agents).
+
+Build on this at your own risk.
diff --git a/research/joint-query/notices/research/gauge44-slots-t16/construction/NOTICE.md b/research/joint-query/notices/research/gauge44-slots-t16/construction/NOTICE.md
new file mode 100644
index 0000000000..16b0507070
--- /dev/null
+++ b/research/joint-query/notices/research/gauge44-slots-t16/construction/NOTICE.md
@@ -0,0 +1,9 @@
+# Construction delta notice
+
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+
+`construct_gauge_xcentre.py` modifies PR635's credited `construct_k_triangle.py`, which in turn extends icekylinx's PR531/PR514/PR425 factory lineage. Its original source comments are retained. The K-triangle schedule and the upstream porting, JP8 frame, kernel and HPE procedures are reused from the pinned source checkouts and are not new contributions of this delta.
+
+The new source-copy exchanges, complementary factory basis, carrier assignment, exact cold44 constructor and compact reproduction driver are described in `../CONSTRUCTION.md`.
+
+`UPSTREAM-NOTICE.md` is the complete unmodified notice from the pinned PR635 package. `LICENSE` is that package's Apache-2.0 license. All further notices and source credits of the referenced upstream packages remain applicable and are retained in the source checkouts rather than vendored again here.
diff --git a/research/joint-query/notices/research/gauge44-slots-t16/t16/NOTICE.md b/research/joint-query/notices/research/gauge44-slots-t16/t16/NOTICE.md
new file mode 100644
index 0000000000..403f4afffb
--- /dev/null
+++ b/research/joint-query/notices/research/gauge44-slots-t16/t16/NOTICE.md
@@ -0,0 +1,39 @@
+# Attribution and license
+
+Apache-2.0. New construction and integration: Hao Yan (@FanPUYen), 2026.
+Prepared with substantial OpenAI Codex assistance, including separately tasked
+AI agents for owner construction, independent mathematical/code checking and
+native verification. These are not claims of independent human peer review.
+
+The exact local supplier is Jeremy Kothe's accepted PR799 X4 word, layered on
+Chafik Boukhalfa's PR741 frame changes and PR685 owner construction. Chafik's
+PR795 fixed-inventory optimality result motivated changing the replica count.
+The original owner bytes, scalar program, local frame and width inventory,
+native phase and wrapper implementations retain their existing authorship.
+
+Credit icekylinx for the source gauge and supplier/admission pipeline;
+DreamingOfClouds for the PR589 bit transport and inherited cold-end work;
+eumemic for the PR555 bit supplier and earlier supplier work; Rohan Arun for
+the native exact-complex recurrence correction; Jeremy Diviney, jaymosley07,
+and the other retained owner/allocation contributors; and the complete
+PR514/PR484/PR507/PR558 controller, physical hosting and verification lineage.
+This list is cumulative credit, not approval of every claim in those PRs.
+
+All original notices and licenses remain in the referenced source packages:
+
+- `research/gauge44-frames-x/{NOTICE,UPSTREAM-NOTICE}.md`
+- `research/complex-sw4-frame8/PROVENANCE.md`
+- `research/e8-bit-p111-tuned/tune/README.md`
+- the repository `CONTRIBUTORS.md` and source-package licenses.
+
+The verifier copies pinned global source files into an external replay
+directory and applies an explicit checked edit list. Original attribution
+comments are preserved in those generated derivatives. No original source
+file or historical certificate is rewritten.
+
+The optional ancestry-reuse coverage guard addresses the omission issue
+identified by Lucas (@ljste) in PR838 and the related PR847 integration by
+Chinmay (@chinmayarvind23). Its fixed inventories were read from the accepted
+PR741 source; no pending implementation is imported. Charles Bethin's
+concurrent PR850 strengthens the fixed-inventory owner-profile theorem and
+was checked for overlap before publication; that inventory is changed here.
diff --git a/research/joint-query/replay.py b/research/joint-query/replay.py
new file mode 100644
index 0000000000..3e85a06d18
--- /dev/null
+++ b/research/joint-query/replay.py
@@ -0,0 +1,89 @@
+"""Verify the frozen QQ16 local joint-query words from pinned sources."""
+
+from hashlib import sha256
+from pathlib import Path
+import argparse
+import gzip
+import importlib.util
+import json
+
+
+HERE = Path(__file__).resolve().parent
+PAYLOAD_SHA256 = '2efe83c59978aa9c0db2c3e4eccc14cbfdcd3c9ce499432601b5dd34083472ef'
+SOURCE_LOADER_SHA256 = 'd23924511e3aed41e5e64511ca70126a636d91c8aa02e656cb61d6ceca1fe0a0'
+CODE = ('source_data.py', 'verify_scalar.py', 'verify_native.py', 'verify_ordered.py', 'replay.py')
+
+
+def need(value, reason):
+    if not value:
+        raise ValueError(reason)
+
+
+def load_module(name):
+    spec = importlib.util.spec_from_file_location(name, HERE / (name + '.py'))
+    module = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(module)
+    return module
+
+
+def write_json(path, value):
+    raw = (json.dumps(value, indent=2, sort_keys=True) + '\n').encode('utf-8')
+    path.write_bytes(raw)
+    return sha256(raw).hexdigest()
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--repo', type=Path, required=True)
+    parser.add_argument('--out', type=Path, required=True)
+    args = parser.parse_args()
+    need(sha256((HERE / 'source_data.py').read_bytes()).hexdigest() == SOURCE_LOADER_SHA256,
+         'The unchanged reviewed source loader')
+    raw = gzip.decompress((HERE / 'certificate.json.gz').read_bytes())
+    need(sha256(raw).hexdigest() == PAYLOAD_SHA256, 'The frozen base QQ16 certificate')
+    packet = json.loads(raw)
+    need(packet['schema'] == 'conserved-qq16-full-cover-native-words-v1', 'The certificate schema')
+    manifest = json.loads((HERE / 'SOURCES.json').read_bytes())
+    for name, entry in manifest['evidence'].items():
+        need(sha256((HERE / name).read_bytes()).hexdigest() == entry['sha256'], 'Evidence pin: ' + name)
+    source = load_module('source_data')
+    scalar = load_module('verify_scalar')
+    native = load_module('verify_native')
+    ordered = load_module('verify_ordered')
+    data = source.reconstruct(args.repo)
+    blocks = scalar.rebuild(data['R'])
+    scalar_result = scalar.verify(data, packet, blocks)
+    native_result = native.verify(data, packet, blocks, scalar.scalar_cost)
+    ordered_result = ordered.verify(data['R'])
+    args.out.mkdir(parents=True, exist_ok=True)
+    outputs = {}
+    for name, value in (('CLEAN-J-CHECKS.json', data['checks']),
+                        ('SCALAR-CHECKS.json', scalar_result),
+                        ('NATIVE-CHECKS.json', native_result),
+                        ('ORDERED-CHECKS.json', ordered_result)):
+        outputs[name] = write_json(args.out / name, value)
+    report = {
+        'status': 'PASS_PORTABLE_QQ16_LOCAL_JOINT_QUERY',
+        'source_base': source.BASE, 'source_archive_sha256': source.ARCHIVE_SHA256,
+        'certificate_payload_sha256': PAYLOAD_SHA256,
+        'source_manifest_sha256': sha256((HERE / 'SOURCES.json').read_bytes()).hexdigest(),
+        'code_sha256': {name: sha256((HERE / name).read_bytes()).hexdigest() for name in CODE},
+        'outputs': outputs,
+        'native_cases': 37, 'common_chart_input_columns_per_orientation': 712,
+        'exact_new_native_gaussian_columns': native_result['exact_gaussian_kernel_columns'],
+        'inherited': ['The bridge proof for the retained core at each owner',
+                      'The original child kernels and recursive native contract'],
+        'not_checked': ['An implementation of the algebraic inverse in output native frames',
+                        'Global controller closure or an endpoint decoder',
+                        'New child and helper hosting', 'Stream and address implementation costs',
+                        'Recursive precision and the complete supplier invoice', 'A new kappa bound'],
+    }
+    write_json(args.out / 'REPLAY.json', report)
+    print(report['status'])
+    print('37 native cases; 712 scalar input columns per orientation; 16384 exact new native columns.')
+    print('B: scalar 214986, native mass 5546. F: scalar 211210, native mass 5530.')
+    print('Local construction only. The complete supplier and kappa calculation are not established.')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/joint-query/source_data.py b/research/joint-query/source_data.py
new file mode 100644
index 0000000000..c9d465ed47
--- /dev/null
+++ b/research/joint-query/source_data.py
@@ -0,0 +1,348 @@
+"""Load frozen source data and derive the two clean-J scalar words.
+
+The source notices retain the supplier credits. New code is Apache-2.0.
+The reconstruction follows the centre-encoding campaign's exact sparse
+replay. Research, code and verification used OpenAI Codex assistance.
+"""
+
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from io import BytesIO
+from pathlib import Path
+import argparse
+import gzip
+import json
+import subprocess
+import tarfile
+
+
+BASE = "bce54fb3f895cbe5cd4c0eb477c3afeed100190f"
+ARCHIVE = "research/community-frontier1042-audit/selected-replay.tar.gz"
+ARCHIVE_SHA256 = "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754"
+MEMBER_PINS = {
+    "slots/local/CANONICAL-WORD.json.gz":
+        "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "slots/local/LOCAL-PROGRAMS.json.gz":
+        "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+    "slots/local/CLIFFORD-RECIPES.json":
+        "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731",
+    "slots/local/RESIDUAL-ADAPTERS.json":
+        "383f40aadd00a4ac700dfd0d4c22d6c6c0be9a9863116e4d69c7acd23bafae0c",
+    "t16/global/base/work/complex-nine-native/DATA-PHASES.json":
+        "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa",
+}
+PAYLOAD_PINS = {
+    "CANONICAL-WORD.json.gz":
+        "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c",
+    "LOCAL-PROGRAMS.json.gz":
+        "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3",
+}
+CREDIT_PINS = {
+    "research/gauge44-slots-t16/NOTICE.md":
+        "7a8d17b04da1e6c9d0ec217fb5bda72faa09d9a21695128722dd1e2827870fcf",
+    "research/gauge44-slots-t16/construction/NOTICE.md":
+        "defe7e44af610e25a6c50c1c3b2efd0972d0690574995c0c872fc50eebf4c816",
+    "research/gauge44-slots-t16/UPSTREAM-NOTICE.md":
+        "a75967ebc34e3bf2ff2c25c08e6c7f1a61b0c0d171cfd1b62196ae2caaf2c610",
+    "research/gauge44-slots-t16/t16/NOTICE.md":
+        "902370e6bfcd39dbea2ece474f15fccbcce3b8e966b2b94066bd03e5174591b5",
+    "LICENSE":
+        "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+}
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def read_git(repo, path, expected_sha256):
+    """Read a blob at BASE. Do not read the worktree copy."""
+    raw = subprocess.check_output(
+        ["git", "show", BASE + ":" + path], cwd=Path(repo)
+    )
+    require(sha256(raw).hexdigest() == expected_sha256,
+            "Source pin differs: " + path)
+    return raw
+
+
+def archive_members(repo):
+    """Check the archive and each full member path before JSON parsing."""
+    raw = read_git(repo, ARCHIVE, ARCHIVE_SHA256)
+    result = {}
+    with tarfile.open(fileobj=BytesIO(raw), mode="r:gz") as archive:
+        for name, expected in MEMBER_PINS.items():
+            matches = [m for m in archive.getmembers() if m.name == name]
+            require(len(matches) == 1 and matches[0].isfile(),
+                    "Source member is not one regular file: " + name)
+            payload = archive.extractfile(matches[0]).read()
+            require(sha256(payload).hexdigest() == expected,
+                    "Member pin differs: " + name)
+            result[name] = payload
+    return result
+
+
+def load_local(repo):
+    """Return the five decoded objects, keyed by their file names."""
+    result = {}
+    for member, raw in archive_members(repo).items():
+        name = member.rsplit("/", 1)[1]
+        payload = gzip.decompress(raw) if name.endswith(".gz") else raw
+        require(sha256(payload).hexdigest() == PAYLOAD_PINS.get(
+            name, MEMBER_PINS[member]), "Payload pin differs: " + name)
+        result[name] = json.loads(payload)
+    return result
+
+
+def add(row, other, coefficient):
+    for column, value in other.items():
+        value = row.get(column, 0) + coefficient * value
+        if value:
+            row[column] = value
+        else:
+            row.pop(column, None)
+
+
+def product(left, right):
+    result = []
+    for row in left:
+        result.append({})
+        for k, coefficient in row.items():
+            add(result[-1], right[k], coefficient)
+    return result
+
+
+def difference(left, right):
+    result = [row.copy() for row in left]
+    require(len(left) == len(right), "Matrix row counts differ")
+    for row, other in zip(result, right):
+        add(row, other, Q(-1))
+    return result
+
+
+def scale(matrix, coefficient):
+    return [{j: coefficient * x for j, x in row.items() if coefficient * x}
+            for row in matrix]
+
+
+def replay(program, n=704, cut=None):
+    """Replay exact scalar contents on all n+8 independent input columns."""
+    rows = [{i: Q(1)} for i in range(n + 8)]
+    for index, event in enumerate(program):
+        if index == cut:
+            break
+        if event[0] != "scalar":
+            continue
+        op = event[1]
+        target = op[1][1] + (n if op[1][0] == "C" else 0)
+        if op[0] == "clear":
+            rows[target] = {}
+        elif op[0] == "scale":
+            rows[target] = {j: x * Q(op[2], op[3])
+                            for j, x in rows[target].items()}
+        else:
+            require(op[0] in ("copy", "add"), "Unknown scalar operation")
+            source = op[2][1] + (n if op[2][0] == "C" else 0)
+            if op[0] == "copy":
+                rows[target] = rows[source].copy()
+            else:
+                add(rows[target], rows[source], Q(op[3], op[4]))
+    return rows
+
+
+def primitive_bound(op):
+    """Return the retained one-real-component dyadic scalar allowance."""
+    if op[0] in ("clear", "copy"):
+        return 1
+    coefficient = Q(op[3], op[4]) if op[0] == "add" else Q(op[2], op[3])
+    a, b = abs(coefficient.numerator), coefficient.denominator
+    require(a > 0 and b & (b - 1) == 0, "Non-dyadic scalar allowance")
+    if op[0] == "scale":
+        require(a & (a - 1) == 0, "Scale is not a signed power of two")
+        return abs(a.bit_length() - b.bit_length()) + int(coefficient < 0)
+    require(op[0] == "add", "Unknown scalar allowance")
+    return 3 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1
+
+
+def corrected_program(program, H, D, backward):
+    prefix = []
+
+    def emit(target, source, coefficient):
+        prefix.append(["scalar", ["add", target, source,
+                       coefficient.numerator, coefficient.denominator], 0])
+
+    for k in range(8):
+        private = ["C", k]
+        prefix.append(["scalar", ["clear", private], 0])
+        if backward:
+            for j, row in enumerate(D):
+                if k in row:
+                    emit(private, ["L", 112 + j], row[k])
+            for j, coefficient in sorted(H[k].items()):
+                emit(["L", j], private, -coefficient)
+        else:
+            for j, coefficient in sorted(H[k].items()):
+                emit(private, ["L", j], coefficient)
+            for j, row in enumerate(D):
+                if k in row:
+                    emit(["L", 112 + j], private, row[k])
+        prefix.append(["scalar", ["clear", private], 0])
+    before = program.index(["phase", "A"])
+    begin = program.index(["phase", "centers"])
+    end = program.index(["phase", "B"])
+    return (program[:before] + [["phase", "centre_dirty_correction"]] +
+            prefix + program[before:begin] + program[end:]), prefix
+
+
+def check_frame_access(program, word):
+    """Check the canonical scalar ledger, between the retained adapters."""
+    current = word["start"].copy() + [None] * 8
+    n = len(word["start"])
+    for event in program:
+        if event[0] == "climb":
+            require(current[event[2]] == event[3], "Wrong climb input frame")
+            current[event[2]] = event[4]
+        elif event[0] == "scalar":
+            op, frame = event[1:]
+            target = op[1][1] + (n if op[1][0] == "C" else 0)
+            if op[0] == "clear":
+                current[target] = frame
+            else:
+                require(current[target] == frame, "Wrong scalar target frame")
+                if op[0] in ("add", "copy"):
+                    source = op[2][1] + (n if op[2][0] == "C" else 0)
+                    require(current[source] == frame, "Wrong scalar source frame")
+    require(current[:n] == word["final"], "Wrong persistent final frames")
+    require(current[n:] == [0] * 8, "Wrong private final frames")
+
+
+def reconstruct(repo):
+    """Derive R,H,D,J and both exact clean words from the frozen inputs."""
+    local = load_local(repo)
+    word = local["CANONICAL-WORD.json.gz"]
+    programs = local["LOCAL-PROGRAMS.json.gz"]
+    v, n = word["v"], 2 * word["v"] + word["R"]
+    require((v, n, word["h"]) == (112, 704, 9), "Wrong supplier geometry")
+    boundary = replay(programs["forward"], n,
+                      programs["forward"].index(["phase", "centers"]))
+    R = [{j: x for j, x in boundary[c].items() if j < v}
+         for c in word["centers"]]
+    H = [{j: x for j, x in boundary[c].items() if j >= 2 * v}
+         for c in word["centers"]]
+    require(len(R) == 8 and all(
+        boundary[c] == R[k] | H[k]
+        for k, c in enumerate(word["centers"])), "Unexpected centre dependence")
+    RT = [{k: row[j] for k, row in enumerate(R) if j in row}
+          for j in range(v)]
+    D = [{} for _ in range(v)]
+    for event in word["cut"]:
+        add(D[event[1] - v], {word["centers"].index(event[2]):
+                             Q(event[3], event[4])}, Q(1))
+    identity = [{i: Q(1)} for i in range(v)]
+    P = scale(product(RT, R), Q(1, 4))
+    J = difference(identity, P)
+    require(product(R, RT) == [{i: Q(56)} for i in range(8)],
+            "R R^T differs from 56 I")
+    require(product(P, P) == scale(P, Q(14)), "P^2 differs from 14 P")
+    require(product(J, J) == difference(scale(identity, Q(13)),
+                                       scale(J, Q(12))), "Wrong J polynomial")
+    checks, clean = {}, {}
+    for name, program in programs.items():
+        fixed, prefix = corrected_program(program, H, D, name == "backward")
+        rows = replay(fixed, n)
+        for i, row in enumerate(rows):
+            expected = {i: Q(1)} if i < n else {}
+            if name == "forward" and v <= i < 2 * v:
+                add(expected, J[i - v], Q(1))
+            if name == "backward" and i < v:
+                add(expected, {v + j: x for j, x in J[i].items()}, Q(-1))
+            require(row == expected, "Wrong clean-J map: " + name + ":" + str(i))
+        check_frame_access(fixed, word)
+        native = ("climb", "adapter", "residual_adapter")
+        require([e for e in fixed if e[0] in native] ==
+                [e for e in program if e[0] in native],
+                "Persistent native events changed")
+        require(not any(e[0] == "center" for e in fixed), "Centre child remains")
+        first_clear = next(i for i, e in enumerate(fixed)
+                           if e == ["scalar", ["clear", ["C", 0]], 0])
+        dirty = replay(fixed[:first_clear] + fixed[first_clear + 1:], n)
+        require(any(n in row for row in dirty[:n]),
+                "Missing-private-clear control did not fail")
+        start = fixed.index(["phase", "centre_dirty_correction"])
+        first_add = next(i for i in range(start, len(fixed))
+                         if fixed[i][0] == "scalar" and fixed[i][1][0] == "add")
+        require(replay(fixed[:first_add] + fixed[first_add + 1:], n) != rows,
+                "Missing-dirty-correction control did not fail")
+        profile = Counter(e[5] for e in fixed if e[0] == "climb")
+        mass = sum(r * count for r, count in profile.items())
+        require(mass == 5522, "Wrong clean-J child rank mass")
+        checks[name] = {
+            "independent_input_columns": n + 8,
+            "persistent_helpers_restored": word["R"],
+            "private_outputs_zero": 8,
+            "canonical_scalar_frames": "PASS",
+            "persistent_native_events": sum(e[0] in native for e in fixed),
+            "child_profile": dict(sorted(profile.items())),
+            "child_rank_mass": mass,
+            "removed_centre_rank_mass": sum(
+                e[4] for e in program if e[0] == "center"),
+            "scalar_macros": sum(e[0] == "scalar" for e in fixed),
+            "primitive_bound_real_components": 2 * sum(
+                primitive_bound(e[1]) for e in fixed if e[0] == "scalar"),
+            "correction_adds": sum(e[1][0] == "add" for e in prefix),
+            "correction_clears": sum(e[1][0] == "clear" for e in prefix),
+            "missing_clear_control": "REJECT",
+            "missing_correction_control": "REJECT",
+        }
+        clean[name] = fixed
+    clean_raw = json.dumps(clean, sort_keys=True, separators=(",", ":")).encode()
+    report = {
+        "status": "PASS_PINNED_CLEAN_J_RECONSTRUCTION",
+        "source_base": BASE,
+        "archive_sha256": ARCHIVE_SHA256,
+        "clean_program_payload_sha256": sha256(clean_raw).hexdigest(),
+        "geometry": {"ports": v, "helpers": word["R"], "axes": word["h"]},
+        "R_row_support": dict(Counter(map(len, R))),
+        "R_column_support": dict(Counter(map(len, RT))),
+        "J_row_support": dict(Counter(map(len, J))),
+        "orientations": checks,
+        "scope": "Exact scalar maps, canonical frame access and retained native events. Native recipe phases, global hosting and supplier admission are separate.",
+    }
+    return {"word": word, "programs": programs,
+            "recipes": local["CLIFFORD-RECIPES.json"],
+            "residuals": local["RESIDUAL-ADAPTERS.json"],
+            "phases": local["DATA-PHASES.json"],
+            "R": R, "H": H, "D": D, "J": J,
+            "clean_programs": clean, "checks": report}
+
+
+def source_manifest():
+    return {"base": BASE, "archive_path": ARCHIVE,
+            "archive_sha256": ARCHIVE_SHA256, "members": MEMBER_PINS,
+            "decompressed_payloads": PAYLOAD_PINS, "credit_sources": CREDIT_PINS}
+
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--repo", required=True, type=Path)
+    parser.add_argument("--out", required=True, type=Path)
+    args = parser.parse_args()
+    data = reconstruct(args.repo)
+    args.out.mkdir(parents=True, exist_ok=True)
+    raw = json.dumps(data["clean_programs"], sort_keys=True,
+                     separators=(",", ":")).encode()
+    (args.out / "CLEAN-J-PROGRAMS.json.gz").write_bytes(gzip.compress(raw, mtime=0))
+    for name, value in (("CLEAN-J-CHECKS.json", data["checks"]),
+                        ("SOURCE-MANIFEST.json", source_manifest())):
+        (args.out / name).write_text(json.dumps(value, indent=2, sort_keys=True) +
+                                    "\n", encoding="utf-8")
+    for path, expected in CREDIT_PINS.items():
+        target = args.out / "credit-evidence" / path
+        target.parent.mkdir(parents=True, exist_ok=True)
+        target.write_bytes(read_git(args.repo, path, expected))
+    print(data["checks"]["status"])
+
+
+if __name__ == "__main__":
+    main()
diff --git a/research/joint-query/verify_native.py b/research/joint-query/verify_native.py
new file mode 100644
index 0000000000..ede9e7e427
--- /dev/null
+++ b/research/joint-query/verify_native.py
@@ -0,0 +1,423 @@
+"""Check all QQ16 owner paths, native phases, and local invoices.
+
+Adapted from the independent full-cover QQ16 review. No emitter is
+imported. New code is Apache-2.0. Verification used Codex assistance.
+"""
+
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+from functools import lru_cache
+
+
+def need(value, reason):
+    if not value:
+        raise ValueError(reason)
+
+
+def bits(value):
+    while value:
+        bit = value & -value
+        yield bit.bit_length() - 1
+        value ^= bit
+
+
+AXES = tuple(1 << i for i in range(73))
+UNIT_MAP = (AXES, 0)
+
+
+def act(columns, vector):
+    result = 0
+    for i in bits(vector):
+        result ^= columns[i]
+    return result
+
+
+def product(left, right):
+    g, a = left
+    h, b = right
+    return tuple(act(g, v) for v in h), a ^ act(g, b)
+
+
+@lru_cache(None)
+def inverse(mapping):
+    g, a = mapping
+    gt = tuple(sum(((g[j] >> i) & 1) << j for j in range(73)) for i in range(73))
+    result = gt, act(gt, a)
+    need(product(mapping, result) == product(result, mapping) == UNIT_MAP, "Both affine inverse orders")
+    return result
+
+
+def terms(entries):
+    counts = Counter()
+    for axis, value in entries:
+        need(0 <= axis < 1 << 73, "A 73-bit line")
+        if axis:
+            counts[axis] = (counts[axis] + value) % 4
+    return tuple((axis, value) for axis, value in sorted(counts.items()) if value)
+
+
+@lru_cache(None)
+def polynomial(frame):
+    # XOR expansion modulo four has degree at most two.
+    linear, cross = [0] * 73, [0] * 73
+    for axis, value in frame:
+        support = tuple(bits(axis))
+        for i in support:
+            linear[i] = (linear[i] + value) % 4
+            if value % 2:
+                for j in support:
+                    if j > i:
+                        cross[i] ^= 1 << j
+    return tuple(linear), tuple(cross)
+
+
+@lru_cache(None)
+def move_frame(frame, mapping):
+    columns, shift = mapping
+    return terms([(act(columns, axis), value) for axis, value in frame]
+                 + [(AXES[j], 2) for j in bits(shift)])
+
+
+def completed(stage):
+    return terms((axis, 1) for axis in AXES[:9 + 8 * stage])
+
+
+def register(token):
+    name, index = token
+    need(name in ("L", "C") and 0 <= index < (704 if name == "L" else 8), "Declared register")
+    return index + (704 if name == "C" else 0)
+
+
+def verify(data, packet, scalar, scalar_cost):
+    core, word = data["clean_programs"], data["word"]
+    need(packet["core_words"] == core, "Both retained source words")
+    A, T, U = (packet[key] for key in ("A_ports", "T_ports", "U_ports"))
+    need((A, T) == ([0, 7, 20, 27, 36, 46, 57, 111], [21, 37, 47, 76, 81, 87, 92, 110]), "Exact selected minors")
+    need(U == [p for p in range(112) if p not in A + T], "Ordinary ports")
+    labels = word["ports"]
+    basis, route, beta = [], [], []
+    phases = data["phases"]
+    need(phases["m"] == 73 and len(phases["recipes"]) == 112, "Actual phase source dimensions")
+    for p, record in enumerate(phases["recipes"]):
+        b = tuple([record["q"]] + record["idle_children"][0]["orthogonal_axes"][:8]) + AXES[9:]
+        need(record["port"] == p and b[0] == labels[p], "Actual source port and normal")
+        need(all(((b[i] & b[j]).bit_count() % 2) == (i == j) for i in range(9) for j in range(9)),
+             "Actual source chart is orthonormal")
+        basis.append(b)
+        coefficient = sum(1 << i for i, v in enumerate(b[1:9]) if (v.bit_count() - 1) // 2 % 2)
+        beta.append(coefficient)
+        stages = []
+        for stage in range(9):
+            if stage == 0:
+                actual = AXES
+                entry = exit_value = 0
+            else:
+                swaps = [b[i+1] ^ AXES[9+8*(stage-1)+i] for i in range(8)]
+                actual = tuple(v ^ act(swaps, sum(((v & axis).bit_count() % 2) << i for i, axis in enumerate(swaps))) for v in AXES)
+                entry = labels[p] ^ act(b[1:9], coefficient)
+                exit_value = act(b[1:9], coefficient) ^ (coefficient << (9+8*(stage-1)))
+            need(product((actual, 0), (actual, 0)) == UNIT_MAP, "Actual route involution")
+            expected = {"entry_X": entry, "entry_Y": entry, "exit_X": exit_value, "exit_Y": exit_value}
+            need(record["stage_alignment"][stage] == expected, "Actual source entry and exit translations")
+            stages.append(actual)
+        route.append(stages)
+
+    @lru_cache(None)
+    def alignment(side, stage, port):
+        if stage == 0:
+            need(side == "X", "Only completed X has a stage-zero alignment")
+            return UNIT_MAP
+        shift = beta[port] << (9 + 8 * (stage - 1))
+        shift ^= labels[port] if side == "Y" else act(basis[port][1:9], beta[port])
+        return route[port][stage], shift
+
+    maps = {key: (tuple(value["owner_right_matrix_columns"]), value["payload_translation_at_identity_owner"])
+            for key, value in packet["map_registry"].items()}
+    for key, mapping in maps.items():
+        need(len(mapping[0]) == 73 and 0 <= mapping[1] < 1 << 73, "Map dimensions")
+        inverse(mapping)
+        need(packet["map_registry"][key]["action"] == "out(d,z_1,...,z_lambda)=in(d*g,z_1 XOR d*delta,...,z_lambda XOR d*delta)", "Owner action declaration")
+    frames = {}
+    for key, value in packet["native_frame_registry"].items():
+        phase = polynomial(terms(value["line_terms_Z4"]))
+        need(phase == (tuple(value["linear_Z4"]), tuple(value["quadratic_rows"])), "Exact frame polynomial")
+        frames[key] = phase
+
+    def mono(recipe, address):
+        indices = tuple(bits(address))
+        exponent = recipe["phase"] + sum(recipe["linear_Z4"][j] for j in indices)
+        exponent += 2 * sum(((recipe["quadratic_rows"][j] & address).bit_count()) for j in indices)
+        mapped = recipe["offset"]
+        for j, row in enumerate(recipe["matrix_rows"]):
+            mapped ^= ((row & address).bit_count() % 2) << j
+        return mapped, exponent % 4
+
+    def kernel(recipe, address):
+        middle, phase = mono(recipe["right"], address)
+        result = {}
+        for at, value in ((middle, (1, 1)), (middle ^ 1, (1, -1))):
+            dest, other = mono(recipe["left"], at)
+            a, b = value
+            for _ in range((phase + other) % 4):
+                a, b = -b, a
+            old = result.get(dest, (0, 0))
+            result[dest] = (old[0] + a, old[1] + b)
+        return {key: value for key, value in result.items() if value != (0, 0)}
+
+    lines = packet["native_line_recipes"]
+    kernel_columns = 0
+    for key, item in lines.items():
+        port, sign, q = item["port"], item["sign"], item["label"]
+        need(port in A + T and sign in (-1, 1) and q == labels[port], "Exact used native line")
+        need(item["rank"] == item["recipe"]["rank"] == 1, "Single rank-one child")
+        want = item["recipe"]
+        for side in ("left", "right"):
+            need(all(row >> (j+1) << (j+1) == row for j, row in enumerate(want[side]["quadratic_rows"])), "Strict upper quadratic rows")
+        for address in range(512):
+            need(kernel(item["recipe"], address) == {address: (1, sign), address ^ q: (1, -sign)}, "Exact Gaussian line column")
+            kernel_columns += 1
+        bad = deepcopy(item["recipe"])
+        bad["left"]["phase"] += 1
+        need(kernel(bad, 0) != kernel(item["recipe"], 0), "Scalar phase control")
+    need(len(lines) == 32, "All signed selected lines")
+    core_profiles = {}
+    for side, events in core.items():
+        state, profile = word["start"][:] + [None] * 8, Counter()
+        for event in events:
+            if event[0] == "climb":
+                _, _, at, old, new, rank = event
+                need(state[at] == old, "Retained child entry frame")
+                state[at] = new
+                profile[rank] += 1
+            elif event[0] == "scalar":
+                gate, frame = event[1:]
+                at = register(gate[1])
+                if gate[0] == "clear":
+                    need(at >= 704, "Retained clear is owned")
+                    state[at] = frame
+                else:
+                    need(state[at] == frame, "Retained scalar target")
+                    if gate[0] == "add":
+                        need(state[register(gate[2])] == frame and gate[1] != gate[2], "Retained scalar source")
+            else:
+                need(event[0] in ("phase", "adapter", "residual_adapter"), "Known inherited endpoint event")
+        need(state == word["final"] + [0] * 8, "Every retained endpoint")
+        need(profile == {1: 2412, 2: 418, 3: 432, 4: 142, 5: 82}, "Retained profile")
+        core_profiles[side] = profile
+
+    def boundary(stage):
+        full = completed(stage)
+        return [full] * 112 + [terms(full + ((q, -1),)) for q in labels]
+
+    def specification(side, stage, future=None):
+        out = []
+        move = lambda at, pair: out.append(("map", at, pair))
+        line = lambda at, port, sign: out.append(("line", at, port, sign))
+        sweep = lambda name: out.append(("sweep", name, [v[1] for v in scalar[side + "_blocks"][name]]))
+        core_event = ("core", "backward" if side == "B" else "forward", stage)
+
+        def copies():
+            for entry in scalar[side + "_typed_A_copies"]:
+                port = entry["target_port"]
+                source_key = "current_normalized_X_T_read" if side == "B" else "current_completed_X_T_read"
+                initial_key = "same_port_Y_read" if side == "B" else "same_port_X_read"
+                selected = entry[source_key]
+                paths = []
+                for read_event in selected:
+                    source_port = read_event[1][2][1]
+                    axis = "Y" if side == "B" else "X"
+                    path = product(inverse(alignment(axis, stage, port)), alignment(axis, stage, source_port))
+                    if stage:
+                        move(source_port, path)
+                        paths.append((source_port, path))
+                body = [("scalar", v[1]) for v in entry[initial_key] + selected]
+                body += [("line", 704, port, 1 if side == "B" else -1)]
+                body += [("scalar", v[1]) for v in entry["target_add_and_clear"]]
+                out.append(("private", side + "_A_copy_" + str(port), body))
+                for at, path in reversed(paths):
+                    move(at, inverse(path))
+
+        if side == "B":
+            for port in T:
+                line(port, port, -1)
+            copies()
+            for at in range(112, 224):
+                move(at, alignment("Y", future, at - 112))
+            sweep("future_E_t")
+            for at in range(112, 224):
+                move(at, inverse(alignment("Y", future, at - 112)))
+            active = list(range(112, 224)) + T
+            for at in active:
+                move(at, alignment("Y", stage, at % 112))
+            for name in ("Y_U_from_X_T", "eight_unsigned_swaps", "Y_T_query_subtract"):
+                sweep(name)
+            for at in active:
+                move(at, inverse(alignment("Y", stage, at % 112)))
+            for port in T:
+                line(port, port, 1)
+            out.append(core_event)
+        else:
+            out.append(core_event)
+            if stage:
+                for at in range(112):
+                    move(at, alignment("X", stage, at))
+            for name in ("X_A_fused_query", "X_T_query_subtract", "X_A_restore_selected", "X_T_sign", "X_U_query_subtract"):
+                sweep(name)
+            if stage:
+                for at in range(112):
+                    move(at, inverse(alignment("X", stage, at)))
+            copies()
+        return out
+
+    cases, scalar_projections = {}, {}
+    for name, events in packet["programs"].items():
+        parts = name.split("_")
+        side, stage = parts[0], int(parts[1])
+        future = int(parts[2]) if side == "B" else None
+        # The F entry itself is supplied by the pinned retained-core lift.
+        state = boundary(stage - 1 if side == "B" else stage) + [None] * 480 + [()] * 8
+        normalized, projection = [], []
+        counts = Counter()
+
+        def consume(event, in_private=False):
+            kind = event[0]
+            if kind == "cover_map":
+                _, token, label, old, new = event
+                at, pair = register(token), maps[label]
+                need(at < 224 and not in_private, "A full cover map acts only on data")
+                need(polynomial(state[at]) == frames[old], "Map input phase")
+                state[at] = move_frame(state[at], pair)
+                need(polynomial(state[at]) == frames[new], "Map output phase")
+                counts["maps"] += 1
+                return "map", at, pair
+            if kind == "native_line":
+                _, token, label, old, new = event
+                item, at = lines[label], register(token)
+                need(at < 224 or at == 704 and in_private, "Native line field and lifetime")
+                need(polynomial(state[at]) == frames[old], "Line input phase")
+                state[at] = terms(state[at] + ((item["label"], item["sign"]),))
+                need(polynomial(state[at]) == frames[new], "Line output phase")
+                counts["lines"] += 1
+                return "line", at, item["port"], item["sign"]
+            if kind == "scalar":
+                _, gate, label = event
+                at = register(gate[1])
+                need(at < 224 or at == 704 and in_private, "No new helper update")
+                if gate[0] == "clear":
+                    need(at == 704 and in_private, "Only owned C0 is newly cleared")
+                    state[at] = terms(packet["native_frame_registry"][label]["line_terms_Z4"])
+                else:
+                    need(polynomial(state[at]) == frames[label], "Scalar target phase")
+                    if gate[0] == "add":
+                        src = register(gate[2])
+                        need(src != at and (src < 224 or src == 704 and in_private), "Legal wrapper source")
+                        need(polynomial(state[src]) == frames[label], "Exact scalar source phase")
+                        counts["reads"] += 1
+                    else:
+                        need(gate[0] == "scale" and at < 224, "Data scalar sign")
+                projection.append(gate)
+                return "scalar", gate
+            if kind == "cover_sweep":
+                need(event[3] == "Complete this full-cover sweep before the next event.", "Full-cover barrier")
+                body = [consume(child) for child in event[2]]
+                need(all(child[0] == "scalar" for child in body), "Only scalar gates in a common sweep")
+                counts["cover_sweeps"] += 1
+                return "sweep", event[1], [child[1] for child in body]
+            if kind == "private_sweep":
+                need(event[3] == "For each cover owner, execute the whole body before the next owner. One ownedC0 is reused.", "Owner-serial private contract")
+                need(event[2][0][0:2] == ["scalar", ["clear", ["C", 0]]] and event[2][-1][0:2] == ["scalar", ["clear", ["C", 0]]], "Private lifetime bounds")
+                body = [consume(child, True) for child in event[2]]
+                need(polynomial(state[704]) == polynomial(()), "Private output is zero in I")
+                counts["private_sweeps"] += 1
+                return "private", event[1], body
+            need(kind == "retained_core", "No unrecognized event")
+            need(event[1:3] == ["backward" if side == "B" else "forward", stage], "Core orientation and stage")
+            if side == "B":
+                need([polynomial(v) for v in state[:224]] == [polynomial(v) for v in boundary(stage-1)], "All core entrance data phases restored")
+            state[:224] = boundary(stage)
+            state[704:] = [()] * 8
+            projection.extend(v[1] for v in core[event[1]] if v[0] == "scalar")
+            counts["cores"] += 1
+            return "core", event[1], stage
+
+        normalized = [consume(event) for event in events]
+        need(normalized == specification(side, stage, future), "Full owner paths, native signs, copy sources, and event order: " + name)
+        need([polynomial(v) for v in state[:224]] == [polynomial(v) for v in boundary(stage)], "Every data output native phase")
+        need(state[224:704] == [None]*480 and state[704:] == [()]*8, "Wrapper helper isolation and private endpoints")
+        need(counts["private_sweeps"] == 8 and counts["cores"] == 1, "Eight serial row copies and one core")
+        need(counts["lines"] == (24 if side == "B" else 8), "Exact added child count")
+        need(counts["maps"] == (528 if side == "B" else 288 if stage else 0), "Exact cover map count")
+        need(counts["reads"] == (1288 if side == "B" else 912), "All scalar reads checked")
+        recorded = packet["case_parameters"][name]
+        expected_record = {"orientation": side, "stage": stage,
+                           "added_rank1_children": counts["lines"],
+                           "explicit_cover_maps": counts["maps"],
+                           "native_wrapper_maps": 2 * counts["lines"],
+                           "matching_phase_ADD_reads": counts["reads"]}
+        if side == "B":
+            expected_record["future"] = future
+        need(recorded == expected_record, "Complete case invoice")
+        blocks = scalar[side + "_blocks"]
+        expected = [v[1] for block in scalar[side + "_order"] if block in blocks for v in blocks[block]]
+        core_scalar = [v[1] for v in core["backward" if side == "B" else "forward"] if v[0] == "scalar"]
+        expected = expected + core_scalar if side == "B" else core_scalar + expected
+        need(projection == expected, "Accepted full scalar word in every native instance")
+        if side in scalar_projections:
+            need(projection == scalar_projections[side], "Same scalar word for all stage instances")
+        scalar_projections[side] = projection
+        cases[name] = dict(counts)
+        cases[name]['native_wrapper_maps'] = 2 * counts['lines']
+        cases[name]['added_map_bound'] = counts['maps'] + 2 * counts['lines']
+    need(set(cases) == {"B_%d_%d" % (s, t) for s in range(1, 8) for t in range(s+1, 9)} | {"F_%d" % s for s in range(9)}, "Complete 37-case family")
+
+    invoices = {}
+    for side, gates in scalar_projections.items():
+        values, peak = [Fraction(1)]*712, Fraction(1)
+        for gate in gates:
+            at = register(gate[1])
+            if gate[0] == "clear":
+                values[at] = 0
+            elif gate[0] == "scale":
+                values[at] *= abs(Fraction(gate[2], gate[3]))
+            else:
+                src = register(gate[2])
+                coefficient = abs(Fraction(gate[3], gate[4]))
+                peak = max(peak, coefficient.numerator * values[src])
+                values[at] += coefficient * values[src]
+            peak = max(peak, values[at])
+        width = 0
+        while (1 << width) < peak:
+            width += 1
+        profile = core_profiles["backward" if side == "B" else "forward"].copy()
+        profile[1] += 24 if side == "B" else 8
+        invoice = {"complete_scalar": {"macros": len(gates), "operations": dict(Counter(g[0] for g in gates)), "real_primitives": sum(map(scalar_cost, gates))},
+                   "native_profile": {str(k): v for k, v in sorted(profile.items())}, "native_mass": sum(k*v for k, v in profile.items()),
+                   "formal_prefix": {"formal_triangle_Horner_bound": str(peak), "formal_prefix_ceiling_log2": width}}
+        expected_bill = (214986, 5546, 73, "573411134169296526275133/64") if side == "B" else (211210, 5530, 55, "5413950274051752469/256")
+        need((invoice["complete_scalar"]["real_primitives"], invoice["native_mass"], width, str(peak)) == expected_bill,
+             "Complete invoice and finite scalar guard")
+        invoices[side] = invoice
+
+    sample = alignment("Y", 2, A[0])
+    incoming = boundary(0)[112+A[0]]
+    need(sample[0] != AXES, "Nontrivial owner witness")
+    need(polynomial(move_frame(incoming, sample)) != polynomial(move_frame(incoming, (sample[0], 0))), "Translation is necessary")
+    need(kernel(lines["positive_" + str(T[0])]["recipe"], 0) != kernel(lines["inverse_" + str(T[0])]["recipe"], 0), "Inverse sign is necessary")
+    need(packet["owner_route_negative_control"] == {
+        "owner_I_input": 0, "owner_rho_input": 1, "payload_address": 0,
+        "correct_owner_view_output_at_I": 1, "incorrect_payload_only_output_at_I": 0},
+        "Independent owner inputs distinguish an owner view from a payload permutation")
+    return {
+        "status": "PASS_QQ16_NATIVE_OWNER_PATHS_AND_PHASES",
+        "actual_routes_reconstructed": 112 * 9,
+        "affine_map_registry_entries": len(maps),
+        "phase_registry_entries": len(frames),
+        "exact_gaussian_kernel_columns": kernel_columns,
+        "scalar_phase_mutations_rejected": len(lines),
+        "cases": cases, "invoices": invoices,
+        "retained_core_event_counts": {side: dict(Counter(event[0] for event in events)) for side, events in core.items()},
+        "native_controls": ["wrong inverse sign", "missing payload translation", "payload-only owner permutation"],
+        "inherited_native_scope": "Exact core bytes and local frame ledger are checked. The pinned bridge proof supplies the global owner embedding and endpoint adapters. Old child kernels are not rerun.",
+        "scope": "Local full-cover words under bijective views and sweep barriers. No new-child hosting, global controller closure, physical address costs, recursive precision, complete supplier or kappa claim."
+    }
diff --git a/research/joint-query/verify_ordered.py b/research/joint-query/verify_ordered.py
new file mode 100644
index 0000000000..e85527fed4
--- /dev/null
+++ b/research/joint-query/verify_ordered.py
@@ -0,0 +1,238 @@
+"""Check exact regressions for the ordered joint-query theorem.
+
+Adapted from the cover-algebra proof checker. Finite regressions support
+but do not replace the ring proof. New code is Apache-2.0. Research and
+verification used Codex assistance.
+"""
+
+from fractions import Fraction as F
+
+
+A = [0, 7, 20, 27, 36, 46, 57, 111]
+T = [21, 37, 47, 76, 81, 87, 92, 110]
+
+
+def need(condition, text):
+    if not condition:
+        raise ValueError(text)
+
+
+def eye(n):
+    return [[F(i == j) for j in range(n)] for i in range(n)]
+
+
+def tr(a):
+    return [list(row) for row in zip(*a)]
+
+
+def plus(a, b, scale=1):
+    return [[x + scale*y for x, y in zip(ar, br)] for ar, br in zip(a, b)]
+
+
+def apply(a, x):
+    result = []
+    width = len(x[0])
+    for row in a:
+        out = [F(0)] * width
+        for c, source in zip(row, x):
+            if c:
+                for j, value in enumerate(source):
+                    if value:
+                        out[j] += c*value
+        result.append(out)
+    return result
+
+
+def restrict_rows(a, ports):
+    ports = set(ports)
+    return [row[:] if i in ports else [F(0)]*len(row)
+            for i, row in enumerate(a)]
+
+
+def check(r, k, rt_inverse, aports, tports, future_n):
+    n, rdim = len(k), len(r)
+    uports = [p for p in range(n) if p not in aports+tports]
+    rt = [[row[p] for p in tports] for row in r]
+    p = restrict_rows(k, tports)
+    ka, ku = restrict_rows(k, aports), restrict_rows(k, uports)
+    l = [[v if i in tports else F(0) for i, v in enumerate(row)] for row in r]
+    m = apply(r, ku)
+    z = plus(ku, apply(p, m), -1)
+    j = plus(eye(n), apply(k, r), -1)
+    h, hinv = plus(eye(n), apply(z, r)), plus(eye(n), apply(z, r), -1)
+    e, einv = plus(eye(n), future_n), plus(eye(n), future_n, -1)
+    need(apply(r, p) == apply(l, p) == eye(rdim), "The current T section is a unit.")
+    need(apply(rt, rt_inverse) == apply(rt_inverse, rt) == eye(rdim), "Both selected inverse orders hold.")
+    need(apply(r, z) == [[F(0)]*rdim for _ in range(rdim)], "The source response has zero query.")
+    need(apply(h, hinv) == apply(hinv, h) == eye(n), "Both transvection inverse orders hold.")
+    need(apply(e, einv) == apply(einv, e) == eye(n), "Both future logger inverse orders hold.")
+    correction = plus(ka, apply(p, plus(eye(rdim), m)))
+    need(apply(j, h) == plus(eye(n), apply(correction, r), -1), "The target error has selected support.")
+
+    def pair(x, y, conserved):
+        u = apply(e, y)
+        a, b = apply(l, x), apply(r, u)
+        v = plus(u, apply(p, plus(a, b, -1)))
+        yy = apply(h, v)
+        xx = plus(x, y, -1)
+        if conserved:
+            for i in aports+tports:
+                xx[i] = [xi+yi-oi for xi, yi, oi in zip(x[i], y[i], yy[i])]
+        else:
+            pb = apply(p, b)
+            for i in tports:
+                xx[i] = pb[i]
+        need(apply(r, yy) == a, "The output source query is the old selected target.")
+        wanted = plus(b, apply(m, a)) if conserved else b
+        need(apply(l, xx) == wanted, "The selected target has its stated query.")
+        return xx, yy
+
+    def inverse(xx, yy, conserved):
+        a = apply(r, yy)
+        b = apply(l, xx)
+        if conserved:
+            b = plus(b, apply(m, a), -1)
+        v = apply(hinv, yy)
+        u = plus(v, apply(p, plus(b, a, -1)))
+        y = apply(einv, u)
+        x = plus(xx, y)
+        if conserved:
+            for i in aports:
+                x[i] = [oi+si-yi for oi, si, yi in zip(xx[i], yy[i], y[i])]
+        pa = apply(p, a)
+        for i in tports:
+            x[i] = pa[i]
+        return x, y
+
+    roff = [[v if i not in tports else F(0) for i, v in enumerate(row)] for row in r]
+    bmat, dmat = apply(rt_inverse, roff), apply(ku, rt)
+    mhat = apply(apply(rt_inverse, m), rt)
+    need(apply(bmat, dmat) == mhat, "The short source word has the correct ordered product.")
+
+    def short_word(x, y, conserved, omit_swap=False):
+        xx, yy = [row[:] for row in x], apply(e, y)
+        old_t = [x[i][:] for i in tports]
+        a = apply(rt, old_t)
+        ca = apply(ka, a)
+        na = apply(future_n, yy)
+        for i in aports:
+            source = y[i] if conserved else na[i]
+            xx[i] = [v+u-c for v, u, c in zip(xx[i], source, ca[i])]
+        yy = plus(yy, apply(dmat, old_t))
+        if not omit_swap:
+            for i in tports:
+                xx[i], yy[i] = yy[i], xx[i]
+        if not conserved:
+            delta = apply(mhat, [yy[i] for i in tports])
+            for i, row in zip(tports, delta):
+                xx[i] = [v-d for v, d in zip(xx[i], row)]
+        query = apply(bmat, yy)
+        for i, row in zip(tports, query):
+            yy[i] = [v-q for v, q in zip(yy[i], row)]
+        return plus(xx, apply(j, yy), -1), yy
+
+    basis = eye(2*n)
+    x, y = basis[:n], basis[n:]
+    records = {}
+    for conserved in (False, True):
+        output = pair(x, y, conserved)
+        need(inverse(*output, conserved) == (x, y), "The left full pair inverse restores all inputs.")
+        need(pair(*inverse(x, y, conserved), conserved) == (x, y), "The right full pair inverse restores all inputs.")
+        need(short_word(x, y, conserved) == output, "The short source and precompensation word matches every column.")
+        need(short_word(x, y, conserved, True) != output, "Omitting the selected exchange must fail.")
+        if conserved:
+            for i in aports+tports:
+                need(plus([output[0][i]], [output[1][i]]) == plus([x[i]], [y[i]]), "Each selected pair sum is unchanged.")
+        records["conserved_pair_sums" if conserved else "clean_current_query"] = {
+            "all_input_columns": 2*n,
+            "both_inverse_orders": True,
+            "short_word": True,
+            "omitted_exchange_control": "REJECTED"
+        }
+    la = [[v if i in aports else F(0) for i, v in enumerate(row)] for row in r]
+    ru = [[v if i in uports else F(0) for i, v in enumerate(row)] for row in r]
+    need(apply(r, ka) == eye(rdim), "The forward companion has a unit A section.")
+
+    def forward(x, y):
+        f, c = apply(r, x), apply(l, x)
+        xx = plus(x, apply(ku, f), -1)
+        ac, tf = apply(ka, c), apply(p, f)
+        for i in aports:
+            xx[i] = ac[i]
+        for i in tports:
+            xx[i] = tf[i]
+        yy = plus(y, xx)
+        for i in aports+tports:
+            yy[i] = [v+u-w for v, u, w in zip(x[i], y[i], xx[i])]
+        return xx, yy
+
+    def forward_inverse(xx, yy):
+        f, c = apply(l, xx), apply(la, xx)
+        x = plus(xx, apply(ku, f))
+        a = plus(plus(f, apply(m, f), -1), apply(ru, xx), -1)
+        a = plus(a, c, -1)
+        aa, tc = apply(ka, a), apply(p, c)
+        for i in aports:
+            x[i] = aa[i]
+        for i in tports:
+            x[i] = tc[i]
+        y = plus(yy, xx, -1)
+        for i in aports+tports:
+            y[i] = [v+u-w for v, u, w in zip(xx[i], yy[i], x[i])]
+        return x, y
+
+    output = forward(x, y)
+    need(forward_inverse(*output) == (x,y), "The forward left inverse restores every input.")
+    need(forward(*forward_inverse(x,y)) == (x,y), "The forward right inverse restores every input.")
+    for i in aports+tports:
+        need(plus([output[0][i]], [output[1][i]]) == plus([x[i]], [y[i]]), "The forward selected sums are unchanged.")
+    source = plus(x, apply(p, plus(apply(ru, x), apply(la, x))))
+    source = plus(source, apply(ku, apply(l, source)), -1)
+    anew = plus(plus(apply(plus(eye(rdim), m, -1), apply(l, source)), apply(ru, source), -1), apply(la, source), -1)
+    row_a = apply(ka, anew)
+    for i in aports:
+        source[i] = row_a[i]
+    need(source == output[0], "The full-frame forward scalar word is exact.")
+    raw_target = plus(y, apply(j, x))
+    fixed_target = plus(raw_target, apply(ka, plus(apply(l, source), apply(la, source), -1)))
+    need(fixed_target == output[1], "Exactly the A forward targets need correction.")
+    records["forward_conserved_pair_sums"] = {
+        "all_input_columns": 2*n,
+        "both_inverse_orders": True,
+        "in_place_source_word": True,
+        "A_only_target_correction": True
+    }
+    return records, m
+
+
+def verify(source_r):
+    r = [[row.get(p, F(0)) for p in range(112)] for row in source_r]
+    k = [[v/4 for v in row] for row in tr(r)]
+    rt = [[row[p] for p in T] for row in r]
+    rti = [[v/4 for v in row] for row in tr(rt)]
+    pa = restrict_rows(k, A)
+    la = [[v if i in A else F(0) for i, v in enumerate(row)] for row in r]
+    future_n = apply(pa, plus(r, la, -1))
+    actual, m = check(r, k, rti, A, T, future_n)
+    need(m == [[12*v for v in row] for row in eye(8)], "The actual ordinary Gram is 12I.")
+
+    # The second example tests the ordered extension with a noncentral M.
+    r2 = [[F(v) for v in row] for row in [[1,0,1,0,1,1],[0,1,0,1,0,1]]]
+    k2 = [[F(v) for v in row] for row in [[1,0],[0,1],[1,0],[0,1],[1,2],[0,1]]]
+    n2 = [[F(0)]*6 for _ in range(6)]
+    n2[0][3], n2[1][2], n2[1][5] = F(1), F(-1), F(2)
+    general, m2 = check(r2, k2, eye(2), [0,1], [2,3], n2)
+    swap = [[F(0),F(1)],[F(1),F(0)]]
+    need(apply(m2, swap) != apply(swap, m2), "The regression uses a noncentral M.")
+    singular_k = [row[:] for row in k2]
+    singular_k[4:] = [[F(0), F(0)], [F(0), F(0)]]
+    singular, zero_m = check(r2, singular_k, eye(2), [0,1], [2,3], n2)
+    need(zero_m == [[F(0), F(0)], [F(0), F(0)]], "A singular M is allowed")
+    return {
+        "status": "PASS_ORDERED_JOINT_QUERY_REGRESSIONS",
+        "actual_R_checks": actual,
+        "noncentral_M_checks": general,
+        "noncentral_M": [[str(v) for v in row] for row in m2],
+        "singular_M_checks": singular,
+        "scope": "Exact finite checks of both data inverse orders, the short source words, selected sums, and a noncentral and singular M. The general associative-ring result is proved in the source note; it is not inferred from these tests."
+    }
diff --git a/research/joint-query/verify_scalar.py b/research/joint-query/verify_scalar.py
new file mode 100644
index 0000000000..7a7051fa8a
--- /dev/null
+++ b/research/joint-query/verify_scalar.py
@@ -0,0 +1,267 @@
+"""Rebuild the QQ16 scalar blocks and check the complete local maps.
+
+This code follows the independent QQ16 scalar review. It does not import
+an emitter. The retained source loader has a separate sparse replay.
+New code is Apache-2.0. Research and verification used Codex assistance.
+"""
+
+from fractions import Fraction as F
+
+
+A = [0, 7, 20, 27, 36, 46, 57, 111]
+T = [21, 37, 47, 76, 81, 87, 92, 110]
+U = [p for p in range(112) if p not in A + T]
+
+
+def need(condition, reason):
+    if not condition:
+        raise ValueError(reason)
+
+
+def add(left, right, value=F(1)):
+    result = left.copy()
+    for j, x in right.items():
+        x = result.get(j, 0) + value * x
+        if x:
+            result[j] = x
+        else:
+            result.pop(j, None)
+    return result
+
+
+def multiply(left, right):
+    result = []
+    for row in left:
+        out = {}
+        for j, value in row.items():
+            out = add(out, right[j], value)
+        result.append(out)
+    return result
+
+
+def rational(matrix):
+    return [{int(j): F(x) for j, x in row.items()} for row in matrix]
+
+
+def register(token):
+    kind, i = token
+    need(kind in ('L', 'C') and 0 <= i < (704 if kind == 'L' else 8),
+         'Declared scalar register')
+    return i + (704 if kind == 'C' else 0)
+
+
+def scalar_cost(gate):
+    if gate[0] == 'clear':
+        return 2
+    value = F(gate[3], gate[4]) if gate[0] == 'add' else F(gate[2], gate[3])
+    a, b = abs(value.numerator), value.denominator
+    need(a and b & (b - 1) == 0, 'Nonzero dyadic coefficient')
+    if gate[0] == 'add':
+        return 2 * (2 + a.bit_length() + a.bit_count() + b.bit_length() - 1)
+    need(gate[0] == 'scale' and a & (a - 1) == 0, 'Signed power-of-two SCALE')
+    return 2 * (abs(a.bit_length() - b.bit_length()) + (value < 0))
+
+
+def replay(events, initial):
+    rows = [row.copy() for row in initial]
+    for event in events:
+        if event[0] != 'scalar':
+            need(event[0] in ('climb', 'phase', 'adapter', 'residual_adapter'),
+                 'Known retained event')
+            continue
+        gate = event[1]
+        at = register(gate[1])
+        if gate[0] == 'clear':
+            need(at >= 704, 'Only owned private contents are cleared')
+            rows[at] = {}
+        elif gate[0] == 'add':
+            source = register(gate[2])
+            need(source != at, 'Distinct scalar source and target')
+            rows[at] = add(rows[at], rows[source], F(gate[3], gate[4]))
+        else:
+            need(gate[0] == 'scale', 'Known scalar gate')
+            rows[at] = {j: x * F(gate[2], gate[3]) for j, x in rows[at].items()}
+    return rows
+
+
+def event(kind, at, source=None, value=F(1)):
+    value = F(value)
+    reg = lambda p: ['C', p - 704] if p >= 704 else ['L', p]
+    gate = [kind, reg(at)]
+    if kind == 'add':
+        gate += [reg(source), value.numerator, value.denominator]
+    elif kind == 'scale':
+        gate += [value.numerator, value.denominator]
+    else:
+        need(kind == 'clear', 'Known emitted scalar gate')
+    return ['scalar', gate, 'chart-bound-by-native-recipe']
+
+
+def rebuild(r):
+    """Derive each coefficient from the actual centre matrix R."""
+    k = [{i: row[p] / 4 for i, row in enumerate(r) if p in row} for p in range(112)]
+    minor = lambda ports: [{j: row[p] for j, p in enumerate(ports) if p in row} for row in r]
+    restrict = lambda ports: [{p: v for p, v in row.items() if p in ports} for row in r]
+    ra, rt, ru = minor(A), minor(T), restrict(U)
+    ka, kt = [k[p] for p in A], [k[p] for p in T]
+    identity = [{i: F(1)} for i in range(8)]
+    need(multiply(ra, ka) == multiply(ka, ra) == identity, 'Both A minor inverse orders')
+    need(multiply(rt, kt) == multiply(kt, rt) == identity, 'Both T minor inverse orders')
+    need(multiply(ru, k) == [{i: F(12)} for i in range(8)], 'R_U K_U = 12I')
+    need(multiply(r, k) == [{i: F(14)} for i in range(8)], 'RK = 14I')
+    b = multiply(kt, restrict([p for p in range(112) if p not in T]))
+    c, ci, d = multiply(ka, rt), multiply(kt, ra), multiply(k, rt)
+    nrows = multiply(ka, restrict([p for p in range(112) if p not in A]))
+    n = [nrows[A.index(p)] if p in A else {} for p in range(112)]
+    need(multiply(n, n) == [{} for _ in range(112)], 'Future query shear squares to zero')
+    need(multiply(c, ci) == multiply(ci, c) == identity, 'Selected change of basis')
+    need(multiply(b, [d[p] if p in U else {} for p in range(112)]) ==
+         [{i: F(12)} for i in range(8)], 'BD = 12I')
+    copies = {'B': [], 'F': []}
+    typed = {'B': [], 'F': []}
+    for j, p in enumerate(A):
+        for side in ('B', 'F'):
+            begin = [event('clear', 704), event('add', 704, 112 + p if side == 'B' else p,
+                                               1 if side == 'B' else -1)]
+            middle = [event('add', 704, T[i], -v if side == 'B' else v)
+                      for i, v in sorted(c[j].items())]
+            end = [event('add', p if side == 'B' else 112 + p, 704), event('clear', 704)]
+            copies[side] += begin + middle + end
+            typed[side].append({'target_port': p,
+                               'same_port_Y_read' if side == 'B' else 'same_port_X_read': begin,
+                               'current_normalized_X_T_read' if side == 'B' else 'current_completed_X_T_read': middle,
+                               'target_add_and_clear': end})
+    swaps = []
+    for p in T:
+        swaps += [event('add', p, 112 + p), event('add', 112 + p, p, -1),
+                  event('add', p, 112 + p), event('scale', 112 + p, value=-1)]
+    bblocks = {
+        'A_input_copies': copies['B'],
+        'future_E_t': [event('add', 112 + p, 112 + q, v) for p, row in zip(A, nrows) for q, v in sorted(row.items())],
+        'Y_U_from_X_T': [event('add', 112 + p, T[j], v) for p in U for j, v in sorted(d[p].items())],
+        'eight_unsigned_swaps': swaps,
+        'Y_T_query_subtract': [event('add', 112 + p, 112 + q, -v) for p, row in zip(T, b) for q, v in sorted(row.items())],
+    }
+    au = multiply(ka, ru)
+    fblocks = {
+        'X_A_fused_query': [event('add', p, T[j], 2*v) for p, row in zip(A, c) for j, v in sorted(row.items())]
+            + [event('add', p, q, v) for p, row in zip(A, au) for q, v in sorted(row.items())],
+        'X_T_query_subtract': [event('add', p, A[j], -v) for p, row in zip(T, ci) for j, v in sorted(row.items())],
+        'X_A_restore_selected': [event('add', p, T[j], v) for p, row in zip(A, c) for j, v in sorted(row.items())],
+        'X_T_sign': [event('scale', p, value=-1) for p in T],
+        'X_U_query_subtract': [event('add', p, T[j], -v) for p in U for j, v in sorted(d[p].items())],
+        'A_output_copies': copies['F'],
+    }
+    return {'R': r, 'K': k, 'N': n, 'R_U': ru, 'B_blocks': bblocks, 'F_blocks': fblocks,
+            'B_typed_A_copies': typed['B'], 'F_typed_A_copies': typed['F'],
+            'B_order': list(bblocks), 'F_order': list(fblocks)}
+
+
+def formulas(scalar):
+    r, k, n, ru = (scalar[key] for key in ('R', 'K', 'N', 'R_U'))
+    query = lambda ports, x: multiply([{p: v for p, v in row.items() if p in ports} for row in r], x)
+
+    def backward(data, inverse=False):
+        x, y = data[:112], data[112:224]
+        if inverse:
+            a = multiply(r, y)
+            b = [add(row, ar, -12) for row, ar in zip(query(T, x), a)]
+            ka, kb = multiply(k, a), multiply(k, b)
+            ey = [add(y[p], ka[p], -1) if p in U else
+                  add(add(y[p], kb[p]), ka[p], 11) if p in T else y[p].copy() for p in range(112)]
+            yy = [add(row, extra, -1) for row, extra in zip(ey, multiply(n, ey))]
+            xx = [add(x[p], yy[p]) if p in U else
+                  add(add(x[p], yy[p], -1), ey[p]) if p in A else ka[p] for p in range(112)]
+        else:
+            ey = [add(row, extra) for row, extra in zip(y, multiply(n, y))]
+            ka, kb = multiply(k, query(T, x)), multiply(k, multiply(r, ey))
+            xx = [add(x[p], y[p], -1) if p in U else
+                  add(add(x[p], y[p]), ey[p], -1) if p in A else add(kb[p], ka[p], 12)
+                  for p in range(112)]
+            yy = [add(y[p], ka[p]) if p in U else ey[p] if p in A else
+                  add(add(ey[p], kb[p], -1), ka[p], -11) for p in range(112)]
+        return xx + yy
+
+    def forward(data, inverse=False):
+        x, y = data[:112], data[112:224]
+        if inverse:
+            f, c = query(T, x), query(A, x)
+            kf, kc = multiply(k, f), multiply(k, c)
+            xx = [add(x[p], kf[p]) if p in U else kc[p] if p in T else x[p].copy()
+                  for p in range(112)]
+            a = [add(add(fr, cr, -1), ur, -1) for fr, cr, ur in zip(f, c, multiply(ru, xx))]
+            ka = multiply(k, a)
+            for p in A:
+                xx[p] = ka[p]
+            yy = [add(y[p], x[p], -1) if p in U else add(add(y[p], xx[p], -1), x[p])
+                  for p in range(112)]
+        else:
+            kf, kc = multiply(k, multiply(r, x)), multiply(k, query(T, x))
+            xx = [add(x[p], kf[p], -1) if p in U else kc[p] if p in A else kf[p]
+                  for p in range(112)]
+            yy = [add(y[p], xx[p]) if p in U else add(add(y[p], x[p]), xx[p], -1)
+                  for p in range(112)]
+        return xx + yy
+
+    return {'B': backward, 'F': forward}
+
+
+def verify(data, packet, scalar):
+    need(packet['R_rows'] and rational(packet['R_rows']) == scalar['R'] == data['R'], 'Actual R source')
+    need(rational(packet['K_rows']) == scalar['K'], 'K = R transpose / 4')
+    need((packet['A_ports'], packet['T_ports'], packet['U_ports']) == (A, T, U), 'Exact selected sets')
+    need(packet['core_words'] == data['clean_programs'], 'Both retained core words')
+    basis = [{i: F(1)} for i in range(712)]
+    contract = formulas(scalar)
+    cores = data['clean_programs']
+    blocks = {side: scalar[side + '_blocks'] for side in ('B', 'F')}
+    wrappers = {side: sum(blocks[side].values(), []) for side in ('B', 'F')}
+    programs = {'B': wrappers['B'] + cores['backward'], 'F': cores['forward'] + wrappers['F']}
+    results = {}
+    for side, events in programs.items():
+        result = replay(events, basis)
+        need(result[:224] == contract[side](basis[:224]), 'Complete data map: ' + side)
+        need(result[224:704] == basis[224:704] and result[704:] == [{} for _ in range(8)],
+             'All borrowed helpers restore and all private outputs are zero')
+        need(contract[side](result[:224], True) == basis[:224], 'Left data inverse: ' + side)
+        need(contract[side](contract[side](basis[:224], True)) == basis[:224], 'Right data inverse: ' + side)
+        for p in A + T:
+            need(add(result[p], result[112+p]) == {p: F(1), 112+p: F(1)}, 'Selected pair sum')
+        total = sum(scalar_cost(e[1]) for e in events if e[0] == 'scalar')
+        need(total == (214986 if side == 'B' else 211210), 'Complete scalar invoice')
+        results[side] = {'formal_input_columns': 712, 'inverse_orders': 2, 'conserved_pair_sums': 16,
+                         'arbitrary_helpers_restored': 480, 'owned_private_outputs_zero': 8,
+                         'scalar_real_primitives': total,
+                         'block_costs': {name: sum(scalar_cost(e[1]) for e in block)
+                                         for name, block in blocks[side].items()}}
+    # Composition is on data. The owned private contents are discarded.
+    composite = replay(programs['B'] + programs['F'], basis)
+    restored = contract['B'](contract['F'](composite[:224], True), True)
+    need(restored == basis[:224], 'The algebraic inverse of F after B')
+    opposite = replay(programs['F'] + programs['B'], basis)
+    need(contract['F'](contract['B'](opposite[:224], True), True) == basis[:224],
+         'The algebraic inverse of B after F')
+    b, f = blocks['B'], blocks['F']
+    tail = sum([b[key] for key in ('Y_U_from_X_T', 'eight_unsigned_swaps', 'Y_T_query_subtract')], [])
+    fbody = wrappers['F'][:-len(f['A_output_copies'])]
+    mutations = {
+        'late_original_Y_copy': b['future_E_t'] + b['A_input_copies'] + tail + cores['backward'],
+        'early_T_query': b['A_input_copies'] + b['future_E_t'] + b['Y_T_query_subtract']
+            + b['Y_U_from_X_T'] + b['eight_unsigned_swaps'] + cores['backward'],
+        'early_F_source_update': fbody + cores['forward'] + f['A_output_copies'],
+        'early_F_target_copy': cores['forward'] + f['A_output_copies'] + fbody,
+        'missing_owned_clear': programs['B'][1:],
+    }
+    for name, events in mutations.items():
+        side = 'F' if '_F_' in name else 'B'
+        need(replay(events, basis)[:224] != contract[side](basis[:224]), 'Mutation must fail: ' + name)
+    try:
+        scalar_cost(['add', ['L', 0], ['L', 1], 1, 13])
+    except ValueError:
+        pass
+    else:
+        raise ValueError('Odd denominator accepted by the dyadic cost ledger')
+    return {'status': 'PASS_QQ16_SCALAR_MAPS', 'orientations': results,
+            'data_compositions_with_algebraic_inverses': 2,
+            'timing_and_private_controls_rejected': list(mutations), 'odd_denominator_control': 'REJECTED',
+            'scope': 'Exact common-chart scalar words and algebraic data inverses. B and F are not inverse circuits. Native access to the algebraic inverses and global controller closure are not established.'}