diff --git a/research/r437-carrier-quotient-cut/.gitattributes b/research/r437-carrier-quotient-cut/.gitattributes
new file mode 100644
index 0000000000..a154a13b7c
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/.gitattributes
@@ -0,0 +1 @@
+inputs/** -text -diff
diff --git a/research/r437-carrier-quotient-cut/README.md b/research/r437-carrier-quotient-cut/README.md
new file mode 100644
index 0000000000..12b9c3825b
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/README.md
@@ -0,0 +1,165 @@
+# R437 node509: a source-quotient obstruction to a third carrier deletion
+
+**Scoped negative result; no new κ or physical supplier.** At current R437
+source `a24f9ff95c12fd0b6792e3f710569237efd72db2`, a promising next deletion is
+helper469, the SOURCE92 carrier. Even granting a free SOURCE77 read, its
+replacement by an early SOURCE92 injection into receiver444 cannot meet the
+fixed node509 output contract with an invertible linear register network.
+The source quotient has rank two at entry and rank one at the required exit.
+The obstruction persists with any number of borrowed registers returned modulo
+the allowed external source span. It excludes arbitrarily long networks in this
+specified alphabet, rather than only the six two-register matrices tried.
+
+This informs the next κ search: another GL rewrite at this unchanged boundary
+cannot supply the carrier saving. A candidate must change its accessible source
+space, retain an additional output dimension, move the receiver/source boundary,
+or supply and pay for a different operation. Such changes remain open.
+
+## Exact scope and evidence
+
+The verifier reads a byte-exact retained current R437 word. It independently
+checks its full 659-column arbitrary-DIRTY XOR identity and the rational closure
+of all 636 frames. Five helpers have exactly one single-SOURCE write in A/B,
+are not captured, and are otherwise only read: 462, 463, 466, 468 and469.
+At the first read of each, the destination's current frame is not contained in
+the SOURCE's current frame. Thus the immediate replacement by a read at that
+unchanged SOURCE frame fails. This census does not exclude earlier retiming or
+a coordinated rewrite.
+
+The focused cut concerns helper469, SOURCE92, node509 and writable receivers444
+and413. At entry before A1998, their SOURCE rows are respectively zero and
+`e87`; SOURCE92 is clean, at frame184. We optimistically replace the deleted
+carrier by an injection `444 += SOURCE92` at frame184. Frame184 is contained in
+509. The resulting source rows are `(e92,e87)`.
+
+Scanning all659 registers gives ten other roles whose frames can enter509 and
+then rejoin the next unchanged observation:
+
+`17, 67, 177, 185, 271, 293, 352, 371, 467, 468`.
+
+Targets177 and185 have zero SOURCE rows here. The inherited H1-H5 alphabet
+forbids target readout; allowing them as borrowed banks is an additional
+favorable relaxation and adds no quotient dimension. The other eight are
+SOURCE/helper roles.
+
+Their SOURCE rows span coordinates `17,22,33,38,50,60,67`. Add `e77` as an
+explicitly **free relaxed channel**, to avoid charging or assuming a solution to
+the incompatible early184/186 injection order. This larger span is called E.
+The two actual node outputs, modulo E, both equal `e87 + e92`. Hence the input
+quotient rank is two and the required output quotient rank is one.
+
+A second source census covers all 34 insertion cuts A2001 through A2034,
+before413 takes its next frame390 gate. The union of all newly eligible
+frame509 read channels adds no dimension to E. This is a finite eligibility
+fact. The theorem below still fixes the entry and exit SOURCE rows; it does not
+claim to rule out arbitrary delayed observations or a two-window program.
+
+The separately implemented checker propagates SOURCE87/92 one column at a time
+and checks all GL(2,2), GL(3,2), GL(4,2) matrices: 6, 168 and20,160 respectively.
+The added registers begin and end at zero **in the source quotient**, not with
+physically clean payloads. These finite checks support the implementation; the
+rank argument proves the arbitrary-register statement.
+
+## Theorem and proof
+
+Fix the retained entry/output rows and external space E described above.
+The allowed replacement uses any finite sequence of invertible linear updates
+among the writable registers, plus reads whose SOURCE row lies in E. Additional
+borrowed writable registers may be used if their entry and exit SOURCE rows lie
+in E. The replacement does not introduce an erasure, discard, new source
+channel, changed observation contract or separate physical primitive.
+
+Project every register's SOURCE row into `V/E`, where `V=F2^111`. Reads from E
+vanish. Every invertible linear register update left-multiplies the row matrix
+by an invertible matrix and therefore preserves its rank. Borrowed rows add
+zero rows at both boundaries. The initial matrix contains the independent rows
+`[e92]` and `[e87]`, so has rank two. The required final rows are both
+`[e92+e87]`, with all borrowed rows zero, so have rank one. Contradiction.
+
+Arbitrary dirty inputs cannot repair this source-column contradiction. Fresh
+D compensation only modifies target DIRTY responses; literal C restores the
+reversible word after its observations. Neither supplies a missing SOURCE
+identity at this fixed node boundary. This is a necessary-condition argument,
+not a proof that every source-correct candidate satisfies the full caller.
+
+The external-role test uses the exact rational closed-frame inclusions
+`current_frame <= 509 <= next_unchanged_observation_frame`. Captures are included
+before B when finding that next observation. Final frames cover roles with no
+later observation. This permits additional frame advances for free and is
+therefore favorable to a candidate. Exact closure reconstruction validates the
+set-inclusion representation of these retained frames.
+
+Three escape controls deliberately break the strict-loss certificate: grant
+an independent SOURCE87 channel; grant a SOURCE92 channel at the cut; or let a
+borrowed register retain the missing SOURCE87 quotient row. They are potential
+changes of contract, not free operations admitted by this package.
+
+## Budget gate, overlap and limits
+
+Pairing: reversible bit-circuit synthesis with quotient-space rank and frame
+partial orders. The initial objective was a fully paid κ improvement. Rohan
+Arun's pending PR3959 already realizes the unchanged width-eight pooled slot
+optimum supplied by mightyOil's PR1281 theorem, so another unchanged owner
+reshuffle was not pursued. The attempted changed local mechanism is an actual
+third-carrier deletion at this source. It fails before pricing. All hypothetical
+adapter and auxiliary costs were set to zero in the cut relaxation; no saving
+is booked when the necessary source contract fails.
+
+| Component | Status here |
+|---|---|
+| Current word's complete arbitrary-DIRTY linear identity | Checked, all659 columns |
+| Rational frames and this source boundary | Checked, all636 frames; exact ten-role frame cut (two target rows are zero) |
+| Immediate persistent-source replacements | Five candidates; all first-read gates fail |
+| Fixed node509 deletion with returned borrowed banks | Excluded by rank2-to-rank1 theorem |
+| Later eligible frame509 channel growth | 34 cuts checked; no new source dimension |
+| Native all-size realization, stock, preparation, tape/precision, full physical cost | Inherited and unresolved; not audited here |
+| New κ, a new local word, or a global carrier lower bound | Not established |
+
+Canonical main is `20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priorities revision6.
+The selected κ remains0.001672660197076918. The team claim is
+[PR3967 comment](https://github.com/CrocSwap/integer-mult-bounds/pull/3967#issuecomment-6263066320).
+Live overlap included PR3647/3700/3950/3958/3959/3967/3982/3995 and the parent
+team's Discussion review; coverage is partial. PR1281 already supplies generic
+width-seven packing and conditional price tables; this package claims neither.
+
+## Reproduce
+
+From the repository root (Python3.12 standard library):
+
+```sh
+python3 -B scripts/research_package.py --package research/r437-carrier-quotient-cut
+```
+
+The two direct commands are `python3 -I -B research/r437-carrier-quotient-cut/verify.py`
+and `python3 -I -B research/r437-carrier-quotient-cut/test_package.py`.
+The latter performs an actual optimized Git-free subprocess replay and rejects
+changed source bytes, changed certificate bytes and a missing retained notice.
+`RESULT.json` is immutable during ordinary verification. `--write NEW_FILE`
+regenerates a certificate explicitly. The source export includes its original
+license and notice; `RETAINED.json` records exact origin Git blobs and SHA256s.
+Those foreign-head origins are documentary pins, not runtime Git dependencies.
+The verifier hashes the self-contained retained bytes before using them.
+
+## Open next questions
+
+1. Can a paid source87 or source92 channel reach this cut without disturbing
+   the inherited SOURCE writes and future frames? Start with the exact
+   `current <= cut <= next` failure and price a changed source/consumer pair.
+   Its physical preparation, restoration and recursive bill are missing.
+2. Can a two-window rewrite retain the missing quotient dimension in an
+   existing bank and consume it later? Start with a proposed changed future
+   observation map for413/444 and the borrowed bank. The fixed-output theorem
+   does not apply, but all subsequent reads, COPY windows and full dirty
+   cleanup must be checked and charged.
+3. Can a different third-carrier construction change the boundary rather than
+   merely resynthesize this GL network? Use the five-source census as an
+   entry map, then derive a whole paid profile before an owner search.
+
+Credit ai-nanachi/PR3647 for R437 and the helper464 GL deletion; Ali Romman/PR1043
+for the retained helper470/SOURCE77 deletion; Sagar Thakrar/PR3700 and PR2423 for
+independent checks and OQ4; mightyOil/PR1281 for the slot optimum; Rohan Arun/
+PR3959 for pooled R437; eumemic, DreamingOfClouds, DaysSky, Crow, chafreaky and
+the full notices for the original word, geometry, native, hosting and compiler.
+New proof, implementation and checks by Chris R / Clear1nsight with substantial
+OpenAI Codex assistance. Apache-2.0. No independent human or formal-kernel review
+is claimed.
diff --git a/research/r437-carrier-quotient-cut/RESULT.json b/research/r437-carrier-quotient-cut/RESULT.json
new file mode 100644
index 0000000000..fe1d82e673
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/RESULT.json
@@ -0,0 +1,567 @@
+{
+  "census": [
+    {
+      "direct_current_source_frame_eligible": false,
+      "first_read": 1992,
+      "helper": 462,
+      "receiver": 340,
+      "receiver_frame": 506,
+      "source": 47,
+      "source_frame": 121,
+      "source_read_count": 2
+    },
+    {
+      "direct_current_source_frame_eligible": false,
+      "first_read": 1991,
+      "helper": 463,
+      "receiver": 241,
+      "receiver_frame": 506,
+      "source": 52,
+      "source_frame": 120,
+      "source_read_count": 3
+    },
+    {
+      "direct_current_source_frame_eligible": false,
+      "first_read": 1996,
+      "helper": 466,
+      "receiver": 385,
+      "receiver_frame": 76,
+      "source": 27,
+      "source_frame": 156,
+      "source_read_count": 1
+    },
+    {
+      "direct_current_source_frame_eligible": false,
+      "first_read": 2035,
+      "helper": 468,
+      "receiver": 413,
+      "receiver_frame": 390,
+      "source": 50,
+      "source_frame": 52,
+      "source_read_count": 1
+    },
+    {
+      "direct_current_source_frame_eligible": false,
+      "first_read": 1999,
+      "helper": 469,
+      "receiver": 444,
+      "receiver_frame": 186,
+      "source": 92,
+      "source_frame": 184,
+      "source_read_count": 2
+    }
+  ],
+  "controls": [
+    "source87_channel_breaks_cut",
+    "source92_channel_breaks_cut",
+    "borrowed_bank_keeps_missing_dimension"
+  ],
+  "eligible_external_roles": [
+    17,
+    67,
+    177,
+    185,
+    271,
+    293,
+    352,
+    371,
+    467,
+    468
+  ],
+  "frame509_dimension": 4,
+  "frames": 636,
+  "free_relaxation_source": 77,
+  "later_cut_count": 34,
+  "later_cuts": [
+    [
+      2001,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2002,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2003,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2004,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2005,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2006,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2007,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2008,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2009,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2010,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2011,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2012,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2013,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2014,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2015,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2016,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        293,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2017,
+      [
+        17,
+        67,
+        177,
+        185,
+        271,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2018,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2019,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2020,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2021,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2022,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2023,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2024,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2025,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2026,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2027,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2028,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2029,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2030,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2031,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2032,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2033,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ],
+    [
+      2034,
+      [
+        17,
+        67,
+        177,
+        185,
+        352,
+        371,
+        467,
+        468
+      ]
+    ]
+  ],
+  "quotient": {
+    "final": [
+      "0x108000000000000000000000",
+      "0x108000000000000000000000"
+    ],
+    "final_rank": 1,
+    "initial": [
+      "0x100000000000000000000000",
+      "0x8000000000000000000000"
+    ],
+    "initial_rank": 2
+  },
+  "scope": "fixed node509 boundaries, invertible linear register gates, existing external channels plus free SOURCE77, borrowed writable banks returned modulo E; no uniform supplier or new kappa",
+  "status": "PASS_R437_CARRIER_QUOTIENT_CUT",
+  "whole_dirty_columns": 659
+}
diff --git a/research/r437-carrier-quotient-cut/RETAINED.json b/research/r437-carrier-quotient-cut/RETAINED.json
new file mode 100644
index 0000000000..09d16921e7
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/RETAINED.json
@@ -0,0 +1,28 @@
+{
+  "files": [
+    {
+      "path": "inputs/R437-COMPOSED-WORD.json.gz",
+      "origin_repository": "CrocSwap/integer-mult-bounds",
+      "origin_commit": "a24f9ff95c12fd0b6792e3f710569237efd72db2",
+      "origin_path": "research/bit-p111-r437-gl464-470-20261018/data/r0042/R437-COMPOSED-WORD.json.gz",
+      "git_blob": "c558a221dd44cbdaa732a401f9876de4c096d4a7",
+      "sha256": "e432182d5b62c8bbefeb871fce30317234d707e5e18d4295e65ac21f7fd8365e"
+    },
+    {
+      "path": "inputs/LICENSE",
+      "origin_repository": "CrocSwap/integer-mult-bounds",
+      "origin_commit": "a24f9ff95c12fd0b6792e3f710569237efd72db2",
+      "origin_path": "research/bit-p111-r437-gl464-470-20261018/LICENSE",
+      "git_blob": "261eeb9e9f8b2b4b0d119366dda99c6fd7d35c64",
+      "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4"
+    },
+    {
+      "path": "inputs/UPSTREAM-NOTICE.md",
+      "origin_repository": "CrocSwap/integer-mult-bounds",
+      "origin_commit": "a24f9ff95c12fd0b6792e3f710569237efd72db2",
+      "origin_path": "research/bit-p111-r437-gl464-470-20261018/UPSTREAM-NOTICE.md",
+      "git_blob": "9b519b904d456b0b5861f7469a66c365e77799a6",
+      "sha256": "8ed83f2f0bde43a41e44279f44d29efaeae3df44850b86f0e3578edf3ee104e4"
+    }
+  ]
+}
diff --git a/research/r437-carrier-quotient-cut/SOURCES.json b/research/r437-carrier-quotient-cut/SOURCES.json
new file mode 100644
index 0000000000..0839f4876a
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    }
+  ]
+}
diff --git a/research/r437-carrier-quotient-cut/TASK.json b/research/r437-carrier-quotient-cut/TASK.json
new file mode 100644
index 0000000000..6784c9e4d5
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/TASK.json
@@ -0,0 +1,72 @@
+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md",
+      "research/complex-local-word-ceiling/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ],
+    "existing_checks": [
+      {
+        "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.",
+        "evidence": "docs/research/community-efficient1000-review.md",
+        "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.",
+        "status": "reviewed",
+        "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Exact source-bound quotient-rank obstruction to deleting the current R437 SOURCE92 carrier at fixed node509 boundaries, with returned borrowed registers and free SOURCE77 relaxation.",
+  "scope_change_reason": "The unchanged pooled slot optimum is already achieved by PR3959 using PR1281. This tests an actual changed local word mechanism before spending on hosting or repricing.",
+  "bottleneck_link": "A third carrier deletion could improve the bit budget, but this fixed-boundary rewrite fails a necessary source-column condition even with free adapters.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after actual boundary and complete carrier census, source-bound rank proof, independent finite/CLI controls; do not repeat generic packing or invent a new kappa.",
+  "outcome": "partial",
+  "evidence": "RESULT.json; fixed-boundary quotient-rank theorem in README; complete GL2/3/4 and actual optimized Git-free failure controls.",
+  "author": "Chris R / Clear1nsight",
+  "ai_assistance": "Substantial OpenAI Codex assistance.",
+  "open_questions": [
+    {
+      "question": "Can a paid source87/92 channel or changed two-window output contract evade the cut?",
+      "why_it_matters": "This supplies a precise structural change needed before another carrier-deletion search.",
+      "first_step": "Bind one changed channel to exact source frames and next observations, then derive its whole paid profile.",
+      "blocked_by": "Physical source delivery, complete future observations, dirty restoration, stock and full cost."
+    }
+  ]
+}
diff --git a/research/r437-carrier-quotient-cut/VALIDATION.json b/research/r437-carrier-quotient-cut/VALIDATION.json
new file mode 100644
index 0000000000..fcb73ff514
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/VALIDATION.json
@@ -0,0 +1,35 @@
+{
+  "status": "local_registered_replay_pass",
+  "utc": "2026-10-19T08:48:30.550838+00:00",
+  "python": "3.12.3",
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "command": [
+    "python3",
+    "-B",
+    "scripts/research_package.py",
+    "--package",
+    "research/r437-carrier-quotient-cut"
+  ],
+  "source_review": "Independent reviewer found two omitted zero-SOURCE target rows; all659 census corrected before publication and replay rerun. No earlier receipt claimed for corrected bytes.",
+  "claims": [
+    "659 arbitrary-DIRTY columns",
+    "636 rational closed frames",
+    "5 immediate current-SOURCE-frame candidates",
+    "10 frame-compatible external roles, including 2 zero-SOURCE target rows",
+    "quotient rank2 to rank1",
+    "34 later eligibility cuts",
+    "complete GL2/3/4 counts6,168,20160",
+    "actual optimized Git-free CLI with3 corruption controls"
+  ],
+  "file_sha256": {
+    "TASK.json": "96a4c3e7632fa168c094d8c9a6822cc3f2c6a25b9abf579690aec72f3aaca437",
+    "RETAINED.json": "46d27f2225ac6262198bbbd10e7b684452627b37f4551776eed661802fe8a4b4",
+    ".gitattributes": "a3c414970082c100e8f9cec6d96b7d5eec4c31660d670b50d46f2d8ac53a3b76",
+    "SOURCES.json": "e5822ba1b619af70e55e88a0b4bf81eddd8497bc98b5aac7b00c9d6b63b64bf9",
+    "RESULT.json": "57ce9eeb7247525956db5512cc115f457ded1ae7cae55e84f27810b4fbd4474b",
+    "README.md": "0d9ccaf42d26ca6f52858bce056d790dee03bafd3b2cf18d6f61880816c631e0",
+    "verify.py": "127c72733f48029bdbd1da77355c5cdbe3c101a1dcc7f3b64bb20a2456134877",
+    "test_package.py": "456f6304026742e45673f3f8606a63ba89f121a8b594fbd6742fa66a019bff76",
+    "VERIFY.json": "b081bcf44cef7b84cf0ccad3ba3d1e2b209d4a66bbdcdbdc421b13ee3b6b44f1"
+  }
+}
diff --git a/research/r437-carrier-quotient-cut/VERIFY.json b/research/r437-carrier-quotient-cut/VERIFY.json
new file mode 100644
index 0000000000..a07b1be0c6
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/VERIFY.json
@@ -0,0 +1,29 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Source hashes, 659-column dirty identity, 636 rational frames, complete five-carrier census, exact fixed-boundary quotient cut and 34 later eligibility cuts; three escape controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/test_package.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Independent SOURCE87/92 columns; complete GL2/3/4 checks; actual Git-free optimized CLI plus source/certificate/missing-notice controls."
+    }
+  ]
+}
diff --git a/research/r437-carrier-quotient-cut/inputs/LICENSE b/research/r437-carrier-quotient-cut/inputs/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/inputs/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
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+      "License" shall mean the terms and conditions for use, reproduction,
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+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
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+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   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
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
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+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
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+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+       http://www.apache.org/licenses/LICENSE-2.0
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+   Unless required by applicable law or agreed to in writing, software
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diff --git a/research/r437-carrier-quotient-cut/inputs/R437-COMPOSED-WORD.json.gz b/research/r437-carrier-quotient-cut/inputs/R437-COMPOSED-WORD.json.gz
new file mode 100644
index 0000000000..c558a221dd
Binary files /dev/null and b/research/r437-carrier-quotient-cut/inputs/R437-COMPOSED-WORD.json.gz differ
diff --git a/research/r437-carrier-quotient-cut/inputs/UPSTREAM-NOTICE.md b/research/r437-carrier-quotient-cut/inputs/UPSTREAM-NOTICE.md
new file mode 100644
index 0000000000..9b519b904d
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/inputs/UPSTREAM-NOTICE.md
@@ -0,0 +1,71 @@
+# Notice
+
+Apache-2.0 (`LICENSE`, copied from #493's package). Prepared by eumemic with substantial Anthropic Claude
+assistance.
+
+## New in this package
+
+- `code/gen_p3.py` (the generator of the punctured word: the L3 skeleton of #543 restricted to the live lines, the
+  pseudo-target totals, the phase-A mini-nodes and extra carriers), `code/pwordl.py` (word builder for a live subset
+  of the 120 lines; output in the bitE8/1 layout with the `ports_geom` and `punctured` fields introduced by #545),
+  `data/bitE8mut-p111.json.gz` (the word), `data/punct.json` (its frozen parameters), `discovery/choose.py` and
+  `discovery/search.py` (the nomination of P and of the parameters; not run by `verify.sh`).
+- `code/gen_p3.py` carries `derive`, `ex_part` and `plan_thirds` from #543's `code/gen_l3.py` (eumemic), and
+  `data/plan-l3.json` is #543's CP-SAT plan, unchanged. `code/nodeopt.py`, `code/planio.py`, `code/mutants.py`,
+  `code/mutrec_b.py` and `code/provenance.py` are #543's files, unchanged.
+- `code/xcheck_p.py`: #543's independent checker `code/xcheck.py` with nine listed edits for v <= 120 live labels
+  (root-line enumeration of the lattice, frame closure and target frames over the live labels) and a new part T (the
+  frame and COPY rank of every retained total at the scatter, and whether it is the hyperplane of a punctured line).
+- `code/mutants_p.py` (punctured-design controls), `code/adapt9p.py` (#510's nine-stage files parameterised for
+  v <= 120 and any copy ranks, the way #545's `adapt.py` parameterises #493's eleven-stage files), `code/cited.py`,
+  `code/receipt_kappa.py`, `code/summary.py`, `verify.sh`, `EXPECTED.json`, `DEPENDS.json`, `requirements.txt`,
+  `data/complex-b.json`, `data/selection9-p111.json` and `data/hosting11-p111.json` (frozen nominations of #442's
+  hosting programme, rediscovered by `verify.sh`), `.github/workflows/e8-bit-p111.yml`.
+
+## Vendored, byte-identical (git blob ids in `SOURCE-pr*.json`, checked by `code/provenance.py`)
+
+- **PR #510 (DreamingOfClouds, with Claude Opus 5.5 via Claude Code), commit 64edee1** (`vendor/pr510/`): the same 19
+  files as #543's package (#510's nine-stage chain with the files it vendors from #463, #443, #442 and #315, and #503's
+  R480 word). Their notices are listed in #543's NOTICE and in the files.
+- **PR #545 (DreamingOfClouds, with Claude Opus 5.5 via Claude Code; draft), commit 376426f** (`vendor/pr545/`):
+  `code/adapt.py` and `code/punct_cfg.py`, run unchanged on this package's word; `data/bitE8mut-v111-r489.json.gz`,
+  `data/hosting-v111-r489.json` and `EXPECTED.json` (a control).
+- **PR #548 (Dugongue), commit 66dbc2b** (`data/complex/pr548/`): `EXPECTED.json` and `evidence/EXACT-ASSEMBLY.json`.
+- **PR #544 (chafreaky, with OpenAI Codex assistance), commit 4858bb3** (`data/complex/pr544/`): `EXPECTED.json` and
+  the Linux exact-assembly receipt.
+- **PR #535 (icekylinx, with GPT-6 Astra assistance), commit 8b758a1** (`data/complex/pr535/`): `EXPECTED.json` and
+  `evidence/audit/EXACT-ASSEMBLY-PR493.json`.
+
+## Used from main, unchanged (pinned in `DEPENDS.json`)
+
+- `research/e8-bit-carrier-skeleton` (PR #493, eumemic): the skeleton modules and D4 partition the generator imports,
+  #370's checker (run here in #545's v <= 120 form), the official cohort checkers, `gram_frames.py`, the record
+  exporter, the geometries and the eleven-stage chain that #545's `adapt.py` parameterises, #442's hosting programme,
+  the R489 word, the control receipts and #315's engines.
+- `research/direct-delivery504-global/EXPECTED.json` (PR #531, icekylinx): its complex b and kappa.
+
+## Cited, not rebuilt
+
+Complex coarse savings in `data/complex-b.json`, each bound to its PR's receipt by `code/cited.py`: PR #548 (primary;
+open), PR #544 and PR #535 (open), PR #531 (merged), and PR #484, #471 and #458 (controls).
+
+## Ideas used
+
+- PR #545 (DreamingOfClouds): the punctured-star unit. Nine lines are neither sources nor targets; each retained total
+  is a pseudo-target that reads what the removed target would read, at frame rank 7, so the decoder constant is 63;
+  the rank-mass identity with v and the decoder constant as parameters; the parameterisation of the hub chain.
+- PR #543 (eumemic): the R420 L3 skeleton with keepers read by targets and rewritten in phase B.
+- PR #493 (eumemic), PR #503 and #510 (DreamingOfClouds), PR #425 (Zhihao Chen / jacklightChen), PR #370 (Dylan Crow),
+  PR #472, #445, #443 (chafreaky), PR #442 (DaysSky), PR #463 and #315 (DreamingOfClouds), PR #386 (Zhihao Chen): the
+  skeleton, the scalar-interface lemma, the format, and the pricing pipelines.
+- PR #523 (icekylinx): the puncture pattern on the complex side, cited by #545.
+- Jacob Sussman introduced the E8 unit.
+
+R437 composition: Ali Romman (@aliromman), with substantial OpenAI Codex assistance, authored the public1043 helper470 source-boundary deletion. Its exact canonical-main package and NOTICE are retained in public1043/. The new contribution here composes that credited deletion with the independently validated helper464 GL, then reconstructs actual owners, full invoice, independent checks and portable replay.
+
+Sagar Thakrar (thakrarsagar), PR3700 Open question4, proposed the exact
+window6 two-leftover coalescing used by this follow-up. No code from that
+PR is imported by the author pipeline; root independently replayed its
+hosting and price engines. Full owner/template/invoice regeneration and
+packaging used substantial OpenAI Codex assistance. All prior credits and
+Apache-2.0 notices remain in place.
diff --git a/research/r437-carrier-quotient-cut/test_package.py b/research/r437-carrier-quotient-cut/test_package.py
new file mode 100644
index 0000000000..ea4a758d53
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/test_package.py
@@ -0,0 +1,60 @@
+#!/usr/bin/env python3
+"""Independent finite linear check and actual optimized Git-free CLI controls."""
+import gzip,json,os,shutil,subprocess,sys,tempfile
+from pathlib import Path
+P=Path(__file__).resolve().parent
+
+def require(ok,why):
+    if not ok:raise SystemExit('FAIL: '+why)
+def check_matrices():
+    counts={}
+    for n in (2,3,4):
+        count=0
+        for packed in range(1<<(n*n)):
+            rows=[(packed>>(n*j))&((1<<n)-1) for j in range(n)]
+            span={0}
+            for row in rows:span|={x^row for x in tuple(span)}
+            if len(span)!=(1<<n):continue
+            count+=1
+            # Quotient input coordinates are e_92,e_87, then zero borrowed rows.
+            out=[r&3 for r in rows];s={0}
+            for r in out:s|={x^r for x in tuple(s)}
+            require(len(s)==4,'invertible borrowed-bank network lost source rank')
+            require(out!=[3,3]+[0]*(n-2),'forbidden output reached')
+        counts[n]=count
+    require(counts=={2:6,3:168,4:20160},'complete GL census')
+    return counts
+
+def main():
+    counts=check_matrices()
+    word=json.loads(gzip.decompress((P/'inputs/R437-COMPOSED-WORD.json.gz').read_bytes()))
+    # Structurally separate one-column propagation for the two witnesses.
+    for col in (87,92):
+        active={col};before=None;after=None
+        for i,(_,d,ss) in enumerate(word['A']):
+            if i==1998:before=set(active)
+            if sum(s in active for s in ss)%2:
+                if d in active:active.remove(d)
+                else:active.add(d)
+            if i==2000:after=set(active);break
+        require((413 in before)==(col==87) and 444 not in before,'independent input columns')
+        require(413 in after and 444 in after,'independent target columns')
+    controls=[]
+    with tempfile.TemporaryDirectory(prefix='r437-cut-export-') as td:
+        out=Path(td)/'package';shutil.copytree(P,out,ignore=shutil.ignore_patterns('__pycache__'))
+        env=os.environ.copy();env.pop('PYTHONPATH',None)
+        def run():
+            return subprocess.run([sys.executable,'-I','-O','-B',str(out/'verify.py')],cwd=td,env=env,text=True,capture_output=True,timeout=30)
+        r=run();require(r.returncode==0 and 'PASS_R437_CARRIER' in r.stdout,'actual Git-free optimized replay: '+r.stdout+r.stderr)
+        for name,path,change in [
+            ('changed_source','inputs/R437-COMPOSED-WORD.json.gz',lambda b:b[:-1]+bytes([b[-1]^1])),
+            ('changed_certificate','RESULT.json',lambda b:b.replace(b'"initial_rank": 2',b'"initial_rank": 1')),
+            ('missing_notice','inputs/UPSTREAM-NOTICE.md',None)]:
+            f=out/path;b=f.read_bytes()
+            if change is None:f.unlink()
+            else:
+                new=change(b);require(new!=b,'control changes bytes');f.write_bytes(new)
+            r=run();require(r.returncode!=0 and 'FAIL:' in r.stderr,'CLI mutation accepted: '+name)
+            f.write_bytes(b);controls.append(name)
+    print('PASS_INDEPENDENT_CUT_CHECK',json.dumps({'GL_counts':counts,'single_columns':[87,92],'Git_free_optimized':True,'CLI_controls':controls},sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/r437-carrier-quotient-cut/verify.py b/research/r437-carrier-quotient-cut/verify.py
new file mode 100644
index 0000000000..04d5d7b643
--- /dev/null
+++ b/research/r437-carrier-quotient-cut/verify.py
@@ -0,0 +1,150 @@
+#!/usr/bin/env python3
+"""Source-bound fixed-boundary carrier cut. Apache-2.0; Chris R with Codex."""
+import argparse, gzip, hashlib, json, math
+from pathlib import Path
+
+P = Path(__file__).resolve().parent
+WORD_SHA = 'e432182d5b62c8bbefeb871fce30317234d707e5e18d4295e65ac21f7fd8365e'
+RAW_SHA = 'da77deaf11368d016622348227657b98404b6afbc7e4f3d6fe9a246baae0dcce'
+class Reject(Exception): pass
+def need(ok, why):
+    if not ok: raise Reject(why)
+def xor_rows(xs):
+    out=0
+    for x in xs: out ^= x
+    return out
+def basis(xs):
+    piv={}
+    for v in xs:
+        while v:
+            j=v.bit_length()-1
+            if j in piv: v ^= piv[j]
+            else: piv[j]=v; break
+    return piv
+def rem(x, piv):
+    for j in sorted(piv,reverse=True):
+        if x>>j&1: x ^= piv[j]
+    return x
+def rank(xs): return len(basis(xs))
+def obstruction(initial, final, external):
+    piv=basis(external)
+    a=[rem(x,piv) for x in initial]; b=[rem(x,piv) for x in final]
+    need(rank(a)>rank(b), 'strict quotient rank loss required')
+    return dict(initial=[hex(x) for x in a],final=[hex(x) for x in b],initial_rank=rank(a),final_rank=rank(b))
+def norm(v):
+    g=math.gcd(*v)
+    if not g:return tuple(v)
+    sign=1 if next(x for x in v if x)>0 else -1
+    return tuple(sign*x//g for x in v)
+def reduce_q(v,bs):
+    v=tuple(v)
+    for j,row in bs:
+        if v[j]:v=norm([row[j]*x-v[j]*y for x,y in zip(v,row)])
+    return v
+def basis_q(rows):
+    bs=[]
+    for row in rows:
+        v=reduce_q(row,bs)
+        if any(v):bs.append((next(i for i,x in enumerate(v) if x),norm(v)));bs.sort()
+    return bs
+
+def audit(w):
+    need(w['R']==437 and w['v']==111,'actual R437 dimensions')
+    fr=list(map(set,w['frames'])); n=659
+    dimensions=[]
+    for f in fr:
+        bs=basis_q([w['lines'][j] for j in sorted(f)])
+        need({j for j,v in enumerate(w['lines']) if not any(reduce_q(v,bs))}==f,'closed rational frame')
+        dimensions.append(len(bs))
+    # Whole arbitrary-DIRTY linear identity; this does not assert physical realization.
+    full=[1<<r for r in range(n)]
+    for sec in ['D','A']:
+        for _,d,ss in w[sec]:full[d]^=xor_rows(full[s] for s in ss)
+    captured=[full[r] for r in w['ret']]
+    for t,js in enumerate(w['scatter']):full[111+t]^=xor_rows(captured[j] for j in js)
+    for sec in ['B','C']:
+        for _,d,ss in w[sec]:full[d]^=xor_rows(full[s] for s in ss)
+    need(full==[(1<<r)^((1<<(r-111)) if 111<=r<222 else 0) for r in range(n)],'659-column complete dirty identity')
+    rows=[1<<r if r<111 else 0 for r in range(n)]; cur=w['start'][:]; states=[]
+    for f,d,ss in w['A']:
+        states.append((rows[:],cur[:]))
+        for r in [d]+ss:
+            need(fr[cur[r]]<=fr[f],'baseline monotone frame')
+            cur[r]=f
+        rows[d]^=xor_rows(rows[s] for s in ss)
+    states.append((rows[:],cur[:])); endframes=cur[:]
+    uses={h:[] for h in range(222,n)}
+    for sec in ['A','B']:
+        for i,(f,d,ss) in enumerate(w[sec]):
+            for h in set([d]+ss)&uses.keys():uses[h].append((sec,i,f,d,ss))
+    census=[]
+    for h,u in uses.items():
+        writes=[z for z in u if z[3]==h]
+        if len(writes)!=1 or len(writes[0][4])!=1 or writes[0][4][0]>=111 or h in w['ret']:continue
+        s=writes[0][4][0]; reads=[z for z in u if z[3]!=h]
+        first=reads[0]; sec,i,f,d,ss=first
+        need(sec=='A','census first observation in A')
+        raw,frames=states[i]
+        need(raw[s]==1<<s,'first observation SOURCE remains clean')
+        census.append(dict(helper=h,source=s,first_read=i,receiver=d,receiver_frame=frames[d],source_frame=frames[s],direct_current_source_frame_eligible=fr[frames[d]]<=fr[frames[s]],source_read_count=len(reads)))
+    need([c['helper'] for c in census]==[462,463,466,468,469],'complete single-load carrier census')
+    need(not any(c['direct_current_source_frame_eligible'] for c in census),'all five immediate direct replacements blocked')
+    # Actual current node: SOURCE77 read, then the two frame509 grouped gates.
+    need(w['A'][1998:2001]==[[186,444,[77]],[509,444,[17,271,293,352,413,467,469]],[509,413,[17,271,293,352,371,469]]],'node binding')
+    raw,cur=states[1998]; after=states[2001][0]
+    need(raw[444]==0 and raw[413]==1<<87 and raw[469]==1<<92 and raw[92]==1<<92,'actual source rows')
+    need(cur[444]==0 and cur[92]==184 and fr[184]<=fr[509],'favorable early92 injection')
+    future={}
+    for f,d,ss in w['A'][2001:]:
+        for r in [d]+ss:future.setdefault(r,f)
+    for r in w['ret']:future.setdefault(r,endframes[r])
+    for f,d,ss in w['B']:
+        for r in [d]+ss:future.setdefault(r,f)
+    eligible=[r for r in range(n) if r not in [444,413,469] and fr[cur[r]]<=fr[509]<=fr[future.get(r,w['final'][r])]]
+    need(eligible==[17,67,177,185,271,293,352,371,467,468],'all boundary-compatible external roles')
+    need(raw[177]==raw[185]==0, 'two frame-compatible targets have zero SOURCE rows')
+    # SOURCE77 is deliberately free even though its early original186 read is
+    # incompatible with the hypothetical184 injection. Enlarging E only helps.
+    external=[raw[r] for r in eligible]+[1<<77]
+    cert=obstruction([1<<92,raw[413]],[after[444],after[413]],external)
+    need(cert['initial_rank']==2 and cert['final_rank']==1,'rank2-to-rank1 cut')
+    need(cert['final'][0]==cert['final'][1]==hex((1<<87)|(1<<92)),'actual common quotient')
+    # Union of newly legal frame509 channels over every cut before413 leaves509.
+    # This is an eligibility census; no all-window circuit theorem is inferred.
+    cutrows=[];union=[]
+    for cut in range(2001,2035):
+        rws,cr=states[cut];fu={}
+        for f,d,ss in w['A'][cut:]:
+            for r in [d]+ss:fu.setdefault(r,f)
+        for r in w['ret']:fu.setdefault(r,endframes[r])
+        for f,d,ss in w['B']:
+            for r in [d]+ss:fu.setdefault(r,f)
+        av=[r for r in range(n) if r not in [444,413,469] and fr[cr[r]]<=fr[509]<=fr[fu.get(r,w['final'][r])]]
+        union.extend(rws[r] for r in av);cutrows.append([cut,av])
+    need(rank(external+union)==rank(external),'34 later eligibility cuts add no external source dimension')
+    controls=[]
+    for name,a,b,e in [
+        ('source87_channel_breaks_cut',[1<<92,1<<87],[after[444],after[413]],external+[1<<87]),
+        ('source92_channel_breaks_cut',[1<<92,1<<87],[after[444],after[413]],external+[1<<92]),
+        ('borrowed_bank_keeps_missing_dimension',[1<<92,1<<87,0],[after[444],after[413],1<<87],external)]:
+        try:obstruction(a,b,e)
+        except Reject:controls.append(name)
+        else:raise Reject('false obstruction accepted: '+name)
+    return dict(status='PASS_R437_CARRIER_QUOTIENT_CUT',whole_dirty_columns=n,frames=len(fr),frame509_dimension=dimensions[509],census=census,eligible_external_roles=eligible,free_relaxation_source=77,quotient=cert,later_cut_count=len(cutrows),later_cuts=cutrows,controls=controls,scope='fixed node509 boundaries, invertible linear register gates, existing external channels plus free SOURCE77, borrowed writable banks returned modulo E; no uniform supplier or new kappa')
+
+def main():
+    ap=argparse.ArgumentParser();ap.add_argument('--write');args=ap.parse_args()
+    retained=json.loads((P/'RETAINED.json').read_text())
+    for row in retained['files']:
+        raw=(P/row['path']).read_bytes()
+        need(hashlib.sha256(raw).hexdigest()==row['sha256'],'retained source SHA256')
+        need(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()==row['git_blob'],'retained Git blob')
+    raw=(P/'inputs/R437-COMPOSED-WORD.json.gz').read_bytes();need(hashlib.sha256(raw).hexdigest()==WORD_SHA,'frozen word bytes')
+    payload=gzip.decompress(raw);need(hashlib.sha256(payload).hexdigest()==RAW_SHA,'canonical word bytes')
+    result=audit(json.loads(payload))
+    if args.write:Path(args.write).write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+    else:need(result==json.loads((P/'RESULT.json').read_text()),'frozen certificate equality')
+    print(result['status'], 'columns=659 frames=636 direct_candidates=5 quotient=2->1 later_cuts=34 controls=3')
+if __name__=='__main__':
+    try:main()
+    except (Reject,OSError,ValueError,KeyError) as e:raise SystemExit('FAIL: '+str(e))