From 224bd5e56041c40078ff6b5fa7393733a215de5c Mon Sep 17 00:00:00 2001
From: Mason Hale <10054724+mason-hale@users.noreply.github.com>
Date: Fri, 16 Oct 2026 06:51:42 -0400
Subject: [PATCH] Improve conditional kappa with nine paired helper extractions

---
 .../paired-helper-extension/.gitattributes    |     5 +
 .../ALLOCATION-PINS.json                      |    14 +
 research/paired-helper-extension/CLAIM.json   |    35 +
 .../paired-helper-extension/CONSTRUCTION.md   |   228 +
 research/paired-helper-extension/CREDITS.md   |    40 +
 .../paired-helper-extension/MANIFEST.json     |    64 +
 research/paired-helper-extension/PINS.json    |    17 +
 research/paired-helper-extension/README.md    |   104 +
 research/paired-helper-extension/SOURCES.json |    46 +
 research/paired-helper-extension/TASK.json    |    72 +
 research/paired-helper-extension/VERIFY.json  |    12 +
 .../allocation/DISPATCH.json                  |     1 +
 .../allocation/FILL.json.gz                   |   Bin 0 -> 1482544 bytes
 .../allocation/ORDER.json                     |     1 +
 .../allocation/PROFILE.json                   |    13 +
 .../allocation/PROVIDERS.json                 |   842 ++
 .../allocation/SEARCH.json                    |    39 +
 .../allocation/baseline/CLAIM.json            |    35 +
 .../allocation/baseline/ORDER.json            |     1 +
 .../allocation/baseline/PROFILE.json          |     1 +
 .../allocation/vendor/PLAN.json.gz            |   Bin 0 -> 29933 bytes
 .../allocation/vendor/TEMPLATE.json.gz        |   Bin 0 -> 1124331 bytes
 .../allocation/vendor/independent_owners.py   |   111 +
 .../check_allocation.py                       |   108 +
 .../data/PARENT-base.json.gz                  |   Bin 0 -> 69992 bytes
 .../data/PARENT-extra.json.gz                 |   Bin 0 -> 69989 bytes
 .../data/TRANSFORM-299.json                   |   274 +
 .../data/TRANSFORM-304.json                   |   296 +
 .../data/TRANSFORM-320.json                   |   249 +
 .../data/TRANSFORM-331.json                   |   266 +
 .../data/TRANSFORM-412.json                   |   258 +
 .../data/TRANSFORM-424.json                   |   250 +
 .../data/TRANSFORM-428.json                   |   258 +
 .../data/TRANSFORM-499.json                   |   322 +
 .../data/TRANSFORM-511.json                   |   298 +
 .../data/WORD-base.json.gz                    |   Bin 0 -> 69818 bytes
 .../data/WORD-extra.json.gz                   |   Bin 0 -> 69814 bytes
 .../evidence/ADAPTER-DERIVATION.json          |   111 +
 .../evidence/ADMISSION-RESULT.json            |   386 +
 .../evidence/COMPLETE-VERIFY-STAGES.json      |    98 +
 .../evidence/ENVIRONMENT.json                 |    13 +
 .../evidence/EXACT-OWNER-MOMENT.json          |   135 +
 .../evidence/FRESHNESS.json                   |   214 +
 .../evidence/FULL-NATIVE-RECEIPT.json         |   113 +
 .../evidence/FULL-NATIVE-RESULT.json          |    41 +
 .../evidence/FULL-REPLAY-RESULT.json          |    66 +
 .../evidence/FULL-REPLAY-STAGES.json          |    56 +
 .../evidence/LOCAL-RESULT.json                |   988 ++
 .../evidence/PHYSICAL-INVOICE.json            | 11156 ++++++++++++++++
 .../evidence/RELEASE-RECEIPT.json             |     7 +
 .../evidence/RETAINED-ORIGIN.json             |    47 +
 .../evidence/SEARCH.json                      |   194 +
 .../evidence/SOURCE-DERIVATION.json           |   127 +
 research/paired-helper-extension/producer.py  |    91 +
 research/paired-helper-extension/reproduce.py |   145 +
 .../paired-helper-extension/run_registered.py |    85 +
 research/paired-helper-extension/structure.py |    41 +
 .../tools/audit_allocation_moment.py          |    81 +
 .../tools/build_extension.py                  |   106 +
 .../tools/derive_adapters.py                  |    85 +
 .../vendor/audit_local.py                     |   501 +
 .../vendor/preload_move.py                    |   133 +
 research/paired-helper-extension/verify.py    |   105 +
 63 files changed, 19385 insertions(+)
 create mode 100644 research/paired-helper-extension/.gitattributes
 create mode 100644 research/paired-helper-extension/ALLOCATION-PINS.json
 create mode 100644 research/paired-helper-extension/CLAIM.json
 create mode 100644 research/paired-helper-extension/CONSTRUCTION.md
 create mode 100644 research/paired-helper-extension/CREDITS.md
 create mode 100644 research/paired-helper-extension/MANIFEST.json
 create mode 100644 research/paired-helper-extension/PINS.json
 create mode 100644 research/paired-helper-extension/README.md
 create mode 100644 research/paired-helper-extension/SOURCES.json
 create mode 100644 research/paired-helper-extension/TASK.json
 create mode 100644 research/paired-helper-extension/VERIFY.json
 create mode 100644 research/paired-helper-extension/allocation/DISPATCH.json
 create mode 100644 research/paired-helper-extension/allocation/FILL.json.gz
 create mode 100644 research/paired-helper-extension/allocation/ORDER.json
 create mode 100644 research/paired-helper-extension/allocation/PROFILE.json
 create mode 100644 research/paired-helper-extension/allocation/PROVIDERS.json
 create mode 100644 research/paired-helper-extension/allocation/SEARCH.json
 create mode 100644 research/paired-helper-extension/allocation/baseline/CLAIM.json
 create mode 100644 research/paired-helper-extension/allocation/baseline/ORDER.json
 create mode 100644 research/paired-helper-extension/allocation/baseline/PROFILE.json
 create mode 100644 research/paired-helper-extension/allocation/vendor/PLAN.json.gz
 create mode 100644 research/paired-helper-extension/allocation/vendor/TEMPLATE.json.gz
 create mode 100644 research/paired-helper-extension/allocation/vendor/independent_owners.py
 create mode 100644 research/paired-helper-extension/check_allocation.py
 create mode 100644 research/paired-helper-extension/data/PARENT-base.json.gz
 create mode 100644 research/paired-helper-extension/data/PARENT-extra.json.gz
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-299.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-304.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-320.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-331.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-412.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-424.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-428.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-499.json
 create mode 100644 research/paired-helper-extension/data/TRANSFORM-511.json
 create mode 100644 research/paired-helper-extension/data/WORD-base.json.gz
 create mode 100644 research/paired-helper-extension/data/WORD-extra.json.gz
 create mode 100644 research/paired-helper-extension/evidence/ADAPTER-DERIVATION.json
 create mode 100644 research/paired-helper-extension/evidence/ADMISSION-RESULT.json
 create mode 100644 research/paired-helper-extension/evidence/COMPLETE-VERIFY-STAGES.json
 create mode 100644 research/paired-helper-extension/evidence/ENVIRONMENT.json
 create mode 100644 research/paired-helper-extension/evidence/EXACT-OWNER-MOMENT.json
 create mode 100644 research/paired-helper-extension/evidence/FRESHNESS.json
 create mode 100644 research/paired-helper-extension/evidence/FULL-NATIVE-RECEIPT.json
 create mode 100644 research/paired-helper-extension/evidence/FULL-NATIVE-RESULT.json
 create mode 100644 research/paired-helper-extension/evidence/FULL-REPLAY-RESULT.json
 create mode 100644 research/paired-helper-extension/evidence/FULL-REPLAY-STAGES.json
 create mode 100644 research/paired-helper-extension/evidence/LOCAL-RESULT.json
 create mode 100644 research/paired-helper-extension/evidence/PHYSICAL-INVOICE.json
 create mode 100644 research/paired-helper-extension/evidence/RELEASE-RECEIPT.json
 create mode 100644 research/paired-helper-extension/evidence/RETAINED-ORIGIN.json
 create mode 100644 research/paired-helper-extension/evidence/SEARCH.json
 create mode 100644 research/paired-helper-extension/evidence/SOURCE-DERIVATION.json
 create mode 100644 research/paired-helper-extension/producer.py
 create mode 100644 research/paired-helper-extension/reproduce.py
 create mode 100644 research/paired-helper-extension/run_registered.py
 create mode 100644 research/paired-helper-extension/structure.py
 create mode 100644 research/paired-helper-extension/tools/audit_allocation_moment.py
 create mode 100644 research/paired-helper-extension/tools/build_extension.py
 create mode 100644 research/paired-helper-extension/tools/derive_adapters.py
 create mode 100644 research/paired-helper-extension/vendor/audit_local.py
 create mode 100644 research/paired-helper-extension/vendor/preload_move.py
 create mode 100644 research/paired-helper-extension/verify.py

diff --git a/research/paired-helper-extension/.gitattributes b/research/paired-helper-extension/.gitattributes
new file mode 100644
index 0000000000..f7f56c2d0a
--- /dev/null
+++ b/research/paired-helper-extension/.gitattributes
@@ -0,0 +1,5 @@
+# Preserve the exact pinned predecessor bytes, including CRLF source files.
+vendor/** -text -whitespace
+data/** -text
+allocation/** -text
+evidence/** -text
diff --git a/research/paired-helper-extension/ALLOCATION-PINS.json b/research/paired-helper-extension/ALLOCATION-PINS.json
new file mode 100644
index 0000000000..325f196087
--- /dev/null
+++ b/research/paired-helper-extension/ALLOCATION-PINS.json
@@ -0,0 +1,14 @@
+{
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/FILL.json.gz": "19b551af07274931b443ac42588e15df20ec0140fa69b54f3b62a4df9a54ff8e",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/PROFILE.json": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+  "allocation/PROVIDERS.json": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+  "allocation/SEARCH.json": "6e461e5746313dfefada9a7a07cddd363883adf39c84662cbb72edb3697f92ef",
+  "allocation/baseline/CLAIM.json": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+  "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/baseline/PROFILE.json": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+}
diff --git a/research/paired-helper-extension/CLAIM.json b/research/paired-helper-extension/CLAIM.json
new file mode 100644
index 0000000000..50cc0eeeba
--- /dev/null
+++ b/research/paired-helper-extension/CLAIM.json
@@ -0,0 +1,35 @@
+{
+  "baseline_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "baseline_kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2908,
+  "calls": 666,
+  "complete_package_manifest_sha256": "bf852fb4ecfa28dddfb8cc6fe7bf53019b3932114e01cba3e026b63ef2b1babd",
+  "complex_lower": "344317729439560376121/200000000000000000000000",
+  "gain": "595154921781997337/500000000000000000000000",
+  "helpers": 408,
+  "independent_inputs": 632,
+  "kappa": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017215886471978018806049999999999999999999998999999999999999999999999",
+  "live_families": 66304,
+  "native_receipt_sha256": "5c1ea6f03e48673d9b56563494fff2258ee18bc8dacdeb72ba5c07e2044008ca",
+  "physical_families": 66804,
+  "profile": {
+    "1": 1625724,
+    "2": 426240,
+    "24": 1,
+    "3": 191980,
+    "32": 207,
+    "4": 73260,
+    "48": 26958,
+    "5": 24951,
+    "6": 167,
+    "7": 45,
+    "8": 5328
+  },
+  "release_receipt_sha256": "f7639e51fd620070767b8e2a855a0a613ae9bfd19f86a1ba023d88316193ae06",
+  "replicas": 74,
+  "scope": "Conditional finite supplier/outer certificate. Inherited all-size/compiler/theorem hypotheses remain. No selected frontier change, optimality or independent-human-review claim. Both changed native chains are fresh; unchanged retained parent/native evidence is explicitly authenticated and reused.",
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+  "zero_buffers": 82
+}
diff --git a/research/paired-helper-extension/CONSTRUCTION.md b/research/paired-helper-extension/CONSTRUCTION.md
new file mode 100644
index 0000000000..2704ab1525
--- /dev/null
+++ b/research/paired-helper-extension/CONSTRUCTION.md
@@ -0,0 +1,228 @@
+# Nine further paired helper extractions
+
+This construction starts from Jeremy Diviney's PR2908 at
+`51309592971e3b5be935599eed2a95404dc7781e`, including its restored helper408.
+It restores nine further arbitrary dirty helper inputs at rank8 instead of
+rank9. Three directions fit the predecessor's terminal frames. Six more become
+available after explicit changes to thirteen inherited gate frames. Every new
+restored endpoint gets its own charged private zero buffer.
+
+The paired input/output method, its structural checker and its compensation
+rule are inherited from PR2908. The new contribution is the ordered nine-step
+composition, the six directions enabled by the declared frame changes, and
+their complete allocation and admission. Jeremy Kothe's PR2894 supplies the
+frame-accounting and inverse-cleanup routines. Further attribution is recorded
+in `CREDITS.md` and retained source notices.
+
+## Exact two-sided certificate
+
+Fix the current word immediately before one extraction. Let `M` be its
+complete non-target forward operator: the A gates after the entry prelude,
+the B gates with their formal invertible warps, and the restore gates. Omit
+target writes from this definition. Coefficients belong to the exact rational
+free algebra of the warp operators and their inverses. Distinct operator words
+are not identified by numerical evaluation.
+
+Let `H` contain the live, zero-entry helpers except for previously restored
+helpers and the sources of the initial operator corrections. Let
+
+```
+E_n = {x in F_2^9 : x dot n = 0}.
+```
+
+For a nonzero nine-bit normal `n`, this is a rank8 hyperplane. The admissible
+output registers `R` have terminal frames contained in `E_n`, after any
+declared frame changes for this step.
+
+Choose a scalar row `alpha` and scalar column `y` supported on `R`, and scalar
+vectors `u,v` supported on `H`, with
+
+```
+alpha M = u,       M v = y,       alpha y = 1.
+```
+
+These identities imply `u v = 1`. We also require `C v = 0`, where `C` is the
+current scalar target-compensation map. The input and output changes `S,T`
+are literal invertible dyadic gate sequences satisfying
+
+```
+S e_h = v,        u S = e_h^T,
+T y = e_h,        e_h^T T = alpha.
+```
+
+Consequently,
+
+```
+(T M S) e_h = T M v = T y = e_h,
+e_h^T (T M S) = alpha M S = u S = e_h^T.
+```
+
+Both the entire column and the entire row of helper `h` are therefore the
+corresponding identity column and row. Its original arbitrary dirty input is
+restored, and no other non-target output depends on that input. Restoring the
+row alone, or preserving only the target map, would not establish this
+isolation property.
+
+The unchanged PR2908 `structure.py` derives `S,T,M,alpha,y,u,v` from the
+literal gates. It checks all seven displayed identities defining the paired
+certificate over exact rational free-operator coefficients. It does not
+accept search vectors or a numerical nullspace as evidence. `producer.py`
+separately requires that the new compensation has no column for `h`;
+because `S e_h = v`, this is the condition `C v = 0`. The full local auditor
+checks the target map and its dual orientation separately.
+
+## Legal insertion and composition
+
+The input gates are inserted immediately after the unchanged entry prelude.
+They use only unprotected live zero-entry helpers and have frame zero. Their
+coefficients are dyadic. Thus they neither modify a prior restored endpoint
+nor alter an initial operator-correction source. All output gates for a step
+use its single rank8 frame `E_n` and are appended to the current restore
+sequence.
+
+The target compensation is replaced by `C S`. The producer computes this
+right multiplication by visiting the literal input gates in reverse order.
+The initial operator corrections are unchanged. The cut, warp interfaces,
+ports, target levels, removed helpers and entry prelude are also unchanged.
+Exactly these six word sections change: `A`, `restore`, `helper_final`,
+`compensation`, `report` and `cleanup`.
+
+Inverse-reverse cleanup is regenerated from the full new word at every step.
+The new isolated cold coordinate is included in its protected cold set and
+receives one additional private zero buffer. The local auditor checks the
+resulting restore/isolation and zero-buffer identities; native admission
+checks the realized operator program and its complete physical contract.
+
+Composition is sequential. Each certificate is derived against the result
+of the preceding step, and its protected set includes every endpoint already
+extracted. The producer enforces this exact helper order:
+
+| Step | Helper | Hyperplane normal | Inherited frame edits | Per-call profile change | Private buffers |
+| --- | ---: | ---: | ---: | --- | ---: |
+| Parent PR2908 | 408 already present | 52 | — | — | 73 |
+| 1 | 424 | 52 | 0 | `3H1 - 2H2` | 74 |
+| 2 | 428 | 76 | 0 | `3H1 - 2H2` | 75 |
+| 3 | 412 | 127 | 0 | `3H1 - 2H2` | 76 |
+| 4 | 331 | 30 | 2 | `H2 + 3H3 - 3H4` | 77 |
+| 5 | 299 | 51 | 2 | `H2 + 3H3 - 3H4` | 78 |
+| 6 | 320 | 75 | 2 | `H2 + 3H3 - 3H4` | 79 |
+| 7 | 511 | 85 | 2 | `H2 + 3H3 - 3H4` | 80 |
+| 8 | 304 | 102 | 2 | `H2 + 3H3 - 3H4` | 81 |
+| 9 | 499 | 120 | 3 | `H2 + 3H3 - 3H4` | 82 |
+
+Here `Hr` denotes one rank-r term in the paid profile. The changes in the
+table include the complete local frame bill for each step, not just its
+new output gates.
+
+## Why the six frame changes expose new directions
+
+An extraction search restricted to the current literal terminal frames can
+miss a direction whose supporting registers were lifted unnecessarily early.
+For each of the last six steps, two inherited A additions can instead use a
+particular rank7 frame. Their scalar coefficients and order stay unchanged.
+The complete frame replay checks the resulting inclusions at every use and
+the unchanged later cut and warp requirements. These substitutions allow the
+small output support of the paired certificate to meet in its rank8
+hyperplane without the previous terminal-frame obstruction.
+
+The sparse output rows and columns for the six steps are:
+
+| Helper | `alpha` | `y` |
+| ---: | --- | --- |
+| 331 | `e331^T + e22^T - e34^T` | `e22` |
+| 299 | `e299^T + e40^T - e54^T` | `e40` |
+| 320 | `e320^T - e324^T + e326^T` | `e320` |
+| 511 | `e511^T + e23^T - e322^T` | `e23` |
+| 304 | `e304^T - e308^T + e310^T` | `e304` |
+| 499 | `e499^T + e35^T - e306^T` | `e35` |
+
+The full input vectors generally have larger support; the literal dyadic
+input gates in `data/TRANSFORM-<helper>.json` define them exactly. They are
+checked against the current composed word, not reused from an earlier
+nullspace computation.
+
+There are twelve rank8-to-rank7 edits in A. The thirteenth edit lowers the
+existing `scale 499 by -1` restore gate from the full rank9 frame to the
+normal120 rank8 frame. That scale is retained, and its coefficient is
+unchanged. Omitting this edit would retain an unnecessary full-frame touch
+and would not implement the stated endpoint and bill.
+
+Each transform records the section, index in that step's immediate parent,
+complete scalar gate, old frame and new frame. `producer.refit` checks the
+exact old gate and frame before applying the substitution. It applies the
+edits before inserting that step's input and output gates. Verification uses
+these fixed records and does not run a frame optimizer. Frame-only edits
+leave the formal scalar/warp operator `M` unchanged; their geometric legality
+and paid cost are separate obligations checked from the complete word.
+
+## Complete local accounting
+
+The predecessor and final local profiles are respectively
+
+```
+PR2908: 2407 H1 + 640 H2 + 262 H3 + 128 H4 + 26 H5 + 8 H8
+final:  2416 H1 + 640 H2 + 280 H3 + 110 H4 + 26 H5 + 8 H8.
+```
+
+Thus the exact local difference is
+
+```
+3(3H1 - 2H2) + 6(H2 + 3H3 - 3H4)
+    = 9H1 + 18H3 - 18H4.
+```
+
+The helper-width inventory changes from
+
+```
+{4:26, 5:2, 7:62, 8:87, 9:231}
+```
+
+to
+
+```
+{4:26, 5:2, 7:62, 8:96, 9:222}.
+```
+
+There remain 408 live helper roles per call and 632 independent inputs.
+Exactly nine width9 roles become width8; no role disappears. The local
+rank-mass decrease is nine, consistent with those nine endpoint changes.
+The buffer count increases from 73 to 82.
+
+In the unchanged T74 architecture there are 666 calls and 271,728 helper
+roles. Its complete physical stock is
+
+```
+66304 live families + 408 helper slots + 8 centres
+    + 82 private zero buffers + 2 scratch = 66804.
+```
+
+The saved local rank mass must reappear in the owner residual accounting.
+Accordingly, the local difference alone is not a claim of a higher kappa.
+The literal allocation must fit all whole-width roles in legal owner windows,
+respect same-call family exclusions, and charge every unused remainder. Its
+actual profile, physical stock and complete outer inequalities determine the
+conditional exponent.
+
+## Evidence and scope
+
+`verify.py` authenticates every shipped vendor/data byte, derives each
+transformation in order, checks its exact paired identities, reproduces both
+published words, and runs the inherited full local auditor on both provider
+variants. The auditor covers all 632 independent columns and the dual
+orientation. The verifier also regenerates cleanup for 36 semantic mutants
+and requires rejection: in each provider and at each step, it either removes
+the final output gate or reverses that gate's sign. These checks establish
+finite symbolic identities and local invoices, rather than tests of a sample
+of integer inputs.
+
+`tools/build_extension.py` binds the local parent words to the exact PR2908
+export and appends this stage to its complete rebuild chain. The remaining
+native, literal-owner, block-norm, physical-stock, prefix and outer-admission
+checks are separate from the local certificate. Their final receipts, not
+the local proof alone, authorize a published conditional kappa. No allocation
+optimality or impossibility of further paired extractions is claimed.
+
+Even after complete finite admission, the multiplication bound remains
+conditional on the repository's inherited all-size, compiler and outer-theorem
+assumptions. This construction does not close those assumptions or establish
+a measured practical multiplication speedup.
diff --git a/research/paired-helper-extension/CREDITS.md b/research/paired-helper-extension/CREDITS.md
new file mode 100644
index 0000000000..153868a3eb
--- /dev/null
+++ b/research/paired-helper-extension/CREDITS.md
@@ -0,0 +1,40 @@
+# Credit and scope
+
+Mason Hale, with substantial OpenAI Codex assistance, contributed the ordered
+nine-step paired extraction, the explicit frame refits enabling six of those
+steps, the actual allocation repair, and the source-bound 82-buffer integration.
+Parallel Codex agents searched, implemented and cross-checked the construction;
+this is not independent human review.
+
+The immediate predecessor is Jeremy Diviney's PR2908 at
+`51309592971e3b5be935599eed2a95404dc7781e`. His paired input/output extraction
+of helper408, structural certificate, compensation rule, owner repair and
+73-buffer integration are the foundation of this contribution.
+`structure.py` is unchanged from that package. This work uses ordinary exact
+linear algebra and does not claim to invent basis changes or nullspaces.
+
+Jeremy Kothe / `jeremykothe2`'s PR2894 at
+`18d03c447886895ef9abf888398178e0428533ca` supplies the preload-resynthesized
+quartets, T74 chronology, packing and inverse cleanup conventions.
+`vendor/preload_move.py` is unchanged from the pinned parent package.
+
+The inherited chain includes Yiyang Lu / `Lyy-iiis`'s PR2857 staged shared
+kernels and native/overlay/release tools; Dugongue's PR2863 packing;
+Marius-Paul Dumitrean's PR2843/2802 pattern-flow and retired-helper lineage;
+Jeremy Kothe's PR2833 dirt-entry supplier; Philippe Van Velzen's PR2853 cost
+and block-energy work; and Tekalign's PR2751/2839 owner and admission tools.
+The exact free-operator auditor retains icekylinx's attribution. The full
+native replay retains the PR2768 sparse engine and PR2226 Clifford/operator
+notices, without modifying their frozen sources.
+
+The public replay exports exact predecessor Git objects and checks their
+complete manifests before executing their code. Admission adapters are derived
+with explicit, counted source substitutions, preserving all inherited checks.
+Changes include the declared source identity, the nine additional buffers and
+the comparison against PR2908. The dimension73 and Sp(72,2) stock factor remain
+the inherited quantities; neither is a buffer count.
+
+All new material is Apache-2.0. Source-specific notices remain in the pinned
+predecessor exports and copied files. The selected result is unchanged. A
+passing finite certificate remains conditional on the inherited all-size,
+compiler and outer-theorem hypotheses.
diff --git a/research/paired-helper-extension/MANIFEST.json b/research/paired-helper-extension/MANIFEST.json
new file mode 100644
index 0000000000..80da18ce56
--- /dev/null
+++ b/research/paired-helper-extension/MANIFEST.json
@@ -0,0 +1,64 @@
+{
+  ".gitattributes": "31d8f1090e5584ce239fe348aacfc6db5f02dedc01bc9c61b35c00a5671ea480",
+  "ALLOCATION-PINS.json": "7ab6a3add8b3eb285789cf36d8463335b391ec77f5d91b9a692453767b2d7f03",
+  "CLAIM.json": "e6c836c0178661a53a69cd91f29d83585e876f2511ff40c6b6204cd270fbdeac",
+  "CONSTRUCTION.md": "2efe3e56f914993aa34bcac29f6127828b9f50de1142b36a60fb991f2a2b778d",
+  "CREDITS.md": "a4e845cbd7cd430d7b53899b3148fb908c3af1924137412e44f19a9031fdc86a",
+  "PINS.json": "3d49ca62f3242444db52a21b9de10f18293757842f64a2b3189ad8f4e61fad36",
+  "README.md": "22469e9c1dae5103a5dcd804881235fe094c52197eff550065ba0b0e78b2535e",
+  "SOURCES.json": "23aa763c74ef9ec2378e59c7bb68d1692df77308c70157ed82aadcc2fb0b9209",
+  "TASK.json": "2b59f3a868876d184833b9329298a2a12de1c72cb6d4da43475f8bfde3191b55",
+  "VERIFY.json": "14da2d0b8056949eac7684ba86a07be3dfa450e7e68bbd35909b072e88000005",
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/FILL.json.gz": "19b551af07274931b443ac42588e15df20ec0140fa69b54f3b62a4df9a54ff8e",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/PROFILE.json": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+  "allocation/PROVIDERS.json": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+  "allocation/SEARCH.json": "6e461e5746313dfefada9a7a07cddd363883adf39c84662cbb72edb3697f92ef",
+  "allocation/baseline/CLAIM.json": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+  "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/baseline/PROFILE.json": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461",
+  "check_allocation.py": "7c94239afa5d6cac3ce11926077f7bb02e2239c45f6ad37f8bedd5662bd4cc7d",
+  "data/PARENT-base.json.gz": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+  "data/PARENT-extra.json.gz": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+  "data/TRANSFORM-299.json": "781585f68449c30f63e40ee4bf58d1fa194e4faf8cf4394505437fc15137ba34",
+  "data/TRANSFORM-304.json": "024515c6e47d952dfaf307fcefda9f2106049ccc28875ae620d95241fdec72ed",
+  "data/TRANSFORM-320.json": "0e4c0216221ab21c4bf48a11eab34ff6cc245014d664dc1523cfae9d437dc00d",
+  "data/TRANSFORM-331.json": "355bcfd60ffcb672f66882e66bae1b046d1bfb979f725b411b034f811dfb68bb",
+  "data/TRANSFORM-412.json": "54328a8436d7abed6433da5e4384a36ad95b266070479b496e0e96416a5f5a79",
+  "data/TRANSFORM-424.json": "42747fa1332af1ca0827edebfff7490ee761f84f662527f593e975a502400dbc",
+  "data/TRANSFORM-428.json": "89e8fbd5a5d1d64d386cdc38f257cae18d8e7428e868f618ed1f0be5a22aba3e",
+  "data/TRANSFORM-499.json": "f86eef40cd96b45c67755903eae6a86432e2aeb6d53812621222db7c062d88f6",
+  "data/TRANSFORM-511.json": "48e0749f1c82594841c88923a38b0308ed777639631a4c3f2414500617f2e34b",
+  "data/WORD-base.json.gz": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+  "data/WORD-extra.json.gz": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+  "evidence/ADAPTER-DERIVATION.json": "2e8d4ba717294738780e179d4ffc734c64d6d05a4ad3c50f60b6c64c737a1d5d",
+  "evidence/ADMISSION-RESULT.json": "1d580dc9edcc70d01a51a18c831aa3b0fc5885b49e9c815fc7d423d3da7701ad",
+  "evidence/COMPLETE-VERIFY-STAGES.json": "8ee4ed4639c3b8361d19d089044a929d93632496a4a1bca53c1c971b86c75930",
+  "evidence/ENVIRONMENT.json": "c6d3ce212bd2cd82d580158a39f6d7048c109daa1a695aa0d1eee280eb620213",
+  "evidence/EXACT-OWNER-MOMENT.json": "5be25d5479f63b7dab276f50973abc9334ec1a0dd1aec26369f4e7ea467768dd",
+  "evidence/FRESHNESS.json": "8ee0019c01005eec3eac244bacc0cf1377ff3a4242c7de438f3e6210a180d3c4",
+  "evidence/FULL-NATIVE-RECEIPT.json": "5c1ea6f03e48673d9b56563494fff2258ee18bc8dacdeb72ba5c07e2044008ca",
+  "evidence/FULL-NATIVE-RESULT.json": "94d76ba883bdb38d44dc960d615e42da9b06074a802305e596064600392ac5ec",
+  "evidence/FULL-REPLAY-RESULT.json": "737f4e56a3b736f0fe3d1dc5868042f716591b0f0fc6fb3b0c54bc838f23e604",
+  "evidence/FULL-REPLAY-STAGES.json": "a6e085252f39cb1a7b23ae49d73af36055327b19fd35e9c0ae67e33515ad311f",
+  "evidence/LOCAL-RESULT.json": "987cfcf4b8b76b2b8dfbc29bd40c9a93a4abac664c1bcbe6d692155845cc806c",
+  "evidence/PHYSICAL-INVOICE.json": "f9d865732c9e6cb918be3b8924350f852610bc0d7fa6b6c2a7c3d2cdb437c1ba",
+  "evidence/RELEASE-RECEIPT.json": "f7639e51fd620070767b8e2a855a0a613ae9bfd19f86a1ba023d88316193ae06",
+  "evidence/RETAINED-ORIGIN.json": "bc24de8d3d49a30cb37895b8780acbbe5255f76ccba446605ce29b721399bdf8",
+  "evidence/SEARCH.json": "5cf7d543c99dbefb8ac93e5c7f4c4f1254fa110ed8279fec22f92bf545623906",
+  "evidence/SOURCE-DERIVATION.json": "3e95bdf16abfe58d56642b7a2888bda3f770bc50aa05d1e576fb6b2920902278",
+  "producer.py": "c60546ca68a905d237401b2a255ccb60e17285b004211d523b5d8fd57b758f5a",
+  "reproduce.py": "64cd79b8460b0795097099b0c4615f17bde37ee3351157f74260ab89fbee8ece",
+  "run_registered.py": "a9b0e0bb04e8047509b1f5b8ba2b1d329a4d7f01e13f1384742752079e9182d6",
+  "structure.py": "83f63b6d9a1a543ecfa2c98d479dbe4e7a1c3caf6fd1c3566123308efbc32e96",
+  "tools/audit_allocation_moment.py": "d0b925495b0d28c107f72ec76a85e6e975db6f46396d70ae70a5719908fed28d",
+  "tools/build_extension.py": "24de3c08bf6fa8844ed17a426b24ae108d8d55d76ea5d1509bdef042731ea8b5",
+  "tools/derive_adapters.py": "5e4c47f8e91b5a29927e3a69a51512f92003fa8483707184431f84eea06c308b",
+  "vendor/audit_local.py": "a38940094f7d19cd6376aafdd4734fa68eabc9aff4c98c3c4a3e9540328b1c90",
+  "vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044",
+  "verify.py": "5fb7984329ce7213294c8f76a3151f06759005456940968b4cc84712933321ee"
+}
diff --git a/research/paired-helper-extension/PINS.json b/research/paired-helper-extension/PINS.json
new file mode 100644
index 0000000000..f5ce309523
--- /dev/null
+++ b/research/paired-helper-extension/PINS.json
@@ -0,0 +1,17 @@
+{
+  "data/PARENT-base.json.gz": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+  "data/PARENT-extra.json.gz": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+  "data/TRANSFORM-299.json": "781585f68449c30f63e40ee4bf58d1fa194e4faf8cf4394505437fc15137ba34",
+  "data/TRANSFORM-304.json": "024515c6e47d952dfaf307fcefda9f2106049ccc28875ae620d95241fdec72ed",
+  "data/TRANSFORM-320.json": "0e4c0216221ab21c4bf48a11eab34ff6cc245014d664dc1523cfae9d437dc00d",
+  "data/TRANSFORM-331.json": "355bcfd60ffcb672f66882e66bae1b046d1bfb979f725b411b034f811dfb68bb",
+  "data/TRANSFORM-412.json": "54328a8436d7abed6433da5e4384a36ad95b266070479b496e0e96416a5f5a79",
+  "data/TRANSFORM-424.json": "42747fa1332af1ca0827edebfff7490ee761f84f662527f593e975a502400dbc",
+  "data/TRANSFORM-428.json": "89e8fbd5a5d1d64d386cdc38f257cae18d8e7428e868f618ed1f0be5a22aba3e",
+  "data/TRANSFORM-499.json": "f86eef40cd96b45c67755903eae6a86432e2aeb6d53812621222db7c062d88f6",
+  "data/TRANSFORM-511.json": "48e0749f1c82594841c88923a38b0308ed777639631a4c3f2414500617f2e34b",
+  "data/WORD-base.json.gz": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+  "data/WORD-extra.json.gz": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+  "vendor/audit_local.py": "a38940094f7d19cd6376aafdd4734fa68eabc9aff4c98c3c4a3e9540328b1c90",
+  "vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044"
+}
diff --git a/research/paired-helper-extension/README.md b/research/paired-helper-extension/README.md
new file mode 100644
index 0000000000..54637f9551
--- /dev/null
+++ b/research/paired-helper-extension/README.md
@@ -0,0 +1,104 @@
+# Nine additional paired helper extractions
+
+Starting from [Jeremy Diviney's PR2908](https://github.com/CrocSwap/integer-mult-bounds/pull/2908)
+at `51309592971e3b5be935599eed2a95404dc7781e`, this package restores nine more
+helpers while preserving all previously restored endpoints. Three extractions
+use the existing frames; six more become possible after explicit frame refits.
+The complete local profile changes by **9H1 + 18H3 − 18H4**. A literal owner
+allocation realizes the resulting improvement after charging all nine extra
+private buffers. The resulting bound is
+
+**κ = 0.001721588647197801880605 − 10⁻⁴⁶ − 10⁻⁷⁰**,
+
+an increase of **0.000001190309843563994674** (about **0.06919%**) over
+pinned PR2908. The exact claim and release bindings are in [CLAIM.json](CLAIM.json).
+
+This is a finite conditional supplier/outer certificate, with the inherited
+all-size, compiler and theorem hypotheses still outstanding. It does not change
+the maintainer-selected result or claim an unconditional multiplication theorem,
+practical timing improvement, packing optimum, or independent human review.
+
+| Quantity | Pinned PR2908 | This construction |
+|---|---:|---:|
+| Independent input columns | 632 | 632 |
+| Live helpers | 408 | 408 |
+| Private zero buffers | 73 | 82 |
+| Width8 helpers | 87 | 96 |
+| Width9 helpers | 231 | 222 |
+| Local H1 / H2 / H3 / H4 / H5 / H8 counts | 2407 / 640 / 262 / 128 / 26 / 8 | 2416 / 640 / 280 / 110 / 26 / 8 |
+| Live / physical families | 66304 / 66795 | 66304 / 66804 |
+
+The 74 replicas, 666 calls, 271728 helper roles and inherited chronology are
+retained. The paid global histogram includes every actual unused owner
+remainder. [CONSTRUCTION.md](CONSTRUCTION.md) proves the paired identities and
+explains the frame changes; `data/TRANSFORM-*.json` supplies every literal gate
+and frame edit. The source-bound builder preserves the predecessor chain.
+
+## Reproduce
+
+The bounded registered replay uses Python 3.12 and the standard library:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/paired-helper-extension --check-only
+python3.12 -B scripts/research_package.py --package research/paired-helper-extension
+```
+
+It reruns the exact nine-stage construction, both all-input forward/dual
+audits, 36 semantic rejection controls, the actual owner allocation and
+directed rational moment. It authenticates the recorded native and complete
+outer-release receipts. It does **not** rerun native or integrated outer
+admission; the complete command below does that.
+
+For separate local and allocation checks, use fresh output directories:
+
+```sh
+python3.12 -B research/paired-helper-extension/verify.py --work /tmp/paired-local
+python3.12 -B research/paired-helper-extension/check_allocation.py --work /tmp/paired-owners
+```
+
+For complete source/native/physical/outer admission, obtain the exact ancestor
+Git objects, then run the public driver. It exports and authenticates the
+predecessors without changing the checkout and does not fetch from the network.
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git \
+  51309592971e3b5be935599eed2a95404dc7781e \
+  18d03c447886895ef9abf888398178e0428533ca \
+  e9307b48d7d1b690939935ecef0f8e524e6d92f4
+env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+  python3.12 -B research/paired-helper-extension/reproduce.py \
+  --repo . --work /tmp/paired-complete
+```
+
+Use the numerical dependencies recorded in `evidence/ENVIRONMENT.json` for
+the complete inherited replay. The default rebuilds the retained parent/native
+evidence. `--retained /path/to/prior-run` explicitly reuses its `native-cache`
+and `NATIVE-RECEIPT.json`, after complete source/claim/cache and all 16 retained
+parent stages are authenticated. Both changed native providers are always
+fresh in the public driver. The recorded public run used explicit retained-cache reuse; both changed
+native chains and the full current admission were fresh. The reused parent
+cache came from an earlier fresh PR2894 replay in the same session. See
+`evidence/RETAINED-ORIGIN.json` and `evidence/FULL-REPLAY-RESULT.json`.
+`--dry-run` only authenticates the PR2908 export and writes a recipe.
+
+Exact hashes bind immutable source archives. Regenerated words are compared
+by complete decoded content, so gzip container differences do not change the
+mathematical comparison. The source identity is closed: all 632 files in the
+derived source are accounted for, including the declared producer and checks.
+
+## Open next questions
+
+1. Can another profitable paired direction be extracted while preserving all 82
+   restored endpoints? Recompute exact paired nullspaces on the final word and
+   price the input/output gates, frame changes and new buffer before synthesis.
+   A nominated direction alone does not establish another improvement.
+2. Can a better literal allocation close more of the packing relaxation gap?
+   Start from the shipped fill and explore bounded relay moves or changes to
+   chronology, with exact owner-window and family checks. A fractional optimum
+   is not an admitted bound.
+
+Credit: Jeremy Diviney's paired extraction and structural checker; Jeremy
+Kothe's PR2894/2833 supplier, frame accounting and cleanup; Yiyang Lu's staged
+native/overlay tooling; and the retained owner, packing and exact-audit authors.
+See [CREDITS.md](CREDITS.md) for the complete immediate lineage. Mason Hale,
+with substantial OpenAI Codex assistance, including parallel cross-checks.
diff --git a/research/paired-helper-extension/SOURCES.json b/research/paired-helper-extension/SOURCES.json
new file mode 100644
index 0000000000..1096d9b016
--- /dev/null
+++ b/research/paired-helper-extension/SOURCES.json
@@ -0,0 +1,46 @@
+{
+  "base_commit": "0706e744cbda1e4d0da5a6c569ad9b47876c6960",
+  "refreshed_main_commit": "5a0dc2c0f4685b02bef7776bc196c7c1231cbac1",
+  "upstream_repository": "https://github.com/CrocSwap/integer-mult-bounds",
+  "immediate_parent": {
+    "pr": 2908,
+    "head": "51309592971e3b5be935599eed2a95404dc7781e",
+    "package": "research/two-sided-helper-extraction",
+    "manifest_sha256": "9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f",
+    "derived_source_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83"
+  },
+  "upstream_exports": [
+    {
+      "pr": 2894,
+      "head": "18d03c447886895ef9abf888398178e0428533ca",
+      "package": "research/shared-kernel-packing",
+      "manifest_sha256": "3cb842b93dd3b0707ceea825bef2afeaa68f8df0d554867761b4752b69077293"
+    },
+    {
+      "pr": 2833,
+      "head": "e9307b48d7d1b690939935ecef0f8e524e6d92f4",
+      "role": "Source materialized and authenticated by exact PR2894 tool; nested retained manifests stay unchanged."
+    }
+  ],
+  "derived_source": {
+    "manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+    "files": 632,
+    "builder": "tools/build_extension.py"
+  },
+  "source_boundary": "Only the scoped new package is submitted. Exact frozen ancestor exports remain unchanged. Full replay performs no network fetch.",
+  "schema_version": 1,
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "889b95d936746df124872133ae1e7cc339adcb92",
+      "sha256": "7d185cd8c2af35988d638d969748ad7b670f902606444dbfc748e4402c340df6"
+    }
+  ]
+}
diff --git a/research/paired-helper-extension/TASK.json b/research/paired-helper-extension/TASK.json
new file mode 100644
index 0000000000..61624d0f6d
--- /dev/null
+++ b/research/paired-helper-extension/TASK.json
@@ -0,0 +1,72 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 5,
+  "base_commit": "0706e744cbda1e4d0da5a6c569ad9b47876c6960",
+  "original_card": {
+    "id": "complex-new-helper-inventory",
+    "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/complex-local-word-ceiling/README.md",
+      "research/heterogeneous-owner-assembly/README.md",
+      "certificates/selected-result.json",
+      "research/selected-k8-unrestricted-ends/README.md"
+    ],
+    "methods": [
+      "Propose a changed helper inventory and derive an optimistic exact moment.",
+      "Design a small completed instance and independently verify its endpoint and rank bill."
+    ],
+    "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-local-word-ceiling/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+      "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+      "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+    "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+    "allowed_variations": [
+      "Narrow to one changed boundary or helper type with explicit counts.",
+      "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": [
+      "Mixing only providers already inside the pinned catalogue.",
+      "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+      "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+    ],
+    "overlap_terms": [
+      "helper inventory",
+      "heterogeneous-owner",
+      "mutable leaver"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Compose nine additional paired input/output extractions on exact PR2908, including six enabled by declared frame refits; realize their budget with a literal T74 owner allocation and complete 82-buffer admission.",
+  "scope_change_reason": "Explicit donor request to beat the latest conditional bound. The paired basis change alters the scalar word and endpoint contract; this is outside the fixed-word entry/refit screens. Finite exact identities and a fully charged literal allocation are required.",
+  "bottleneck_link": "Nine helpers change width9 to8; the paired changes plus refits change the local profile by9H1+18H3\u221218H4. All nine additional private buffers and the actual owner residuals are charged.",
+  "budget_minutes": 240,
+  "stop_rule": "Freeze the nine-step composition after exact local checks; publish a higher conditional kappa only if both native providers, literal owner geometry, physical stock, prefix and complete outer admission pass. Do not expand the search after the frozen candidate.",
+  "outcome": "completed",
+  "evidence": "CLAIM.json and evidence/; reproduce.py reruns complete source/native/owner/outer admission.",
+  "author": "Mason Hale",
+  "ai_assistance": "Substantial OpenAI Codex assistance, including parallel search, implementation and cross-checks. No independent human review claimed.",
+  "open_questions": [
+    {
+      "question": "Can remaining paired directions be extracted profitably after this nine-step composition?",
+      "why_it_matters": "Changed terminal frames can reveal directions missed by a search on the old literal frames.",
+      "first_step": "Recompute paired exact nullspaces on the final word, preserving all82 restored endpoints, and price all input/output and frame changes before synthesis.",
+      "blocked_by": "No further directions are claimed; each candidate needs complete local/native/owner/outer admission."
+    },
+    {
+      "question": "Can a better literal owner allocation close more of the fractional packing gap?",
+      "why_it_matters": "The exhibited allocation is feasible, not an optimum.",
+      "first_step": "Start from the shipped fill and explore bounded relay moves or changed chronology, with exact window/family checks.",
+      "blocked_by": "A relaxation or numerical root alone is not a new admitted bound."
+    }
+  ]
+}
diff --git a/research/paired-helper-extension/VERIFY.json b/research/paired-helper-extension/VERIFY.json
new file mode 100644
index 0000000000..e05c18c758
--- /dev/null
+++ b/research/paired-helper-extension/VERIFY.json
@@ -0,0 +1,12 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [{
+    "argv": ["{python}", "-B", "{package}/run_registered.py"],
+    "timeout_seconds": 300,
+    "checks": "Complete package pins; exact nine-stage construction and free-operator structural identities; both 632-input forward/dual audits and36 semantic rejection controls; literal T74 owner geometry, allocation controls and directed rational moment; binding of stored complete native and outer-release receipts to the exact words/source/fill. Native and full integrated admission are rerun separately by reproduce.py from exact Git sources."
+  }]
+}
diff --git a/research/paired-helper-extension/allocation/DISPATCH.json b/research/paired-helper-extension/allocation/DISPATCH.json
new file mode 100644
index 0000000000..9544fee4e6
--- /dev/null
+++ b/research/paired-helper-extension/allocation/DISPATCH.json
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diff --git a/research/paired-helper-extension/allocation/SEARCH.json b/research/paired-helper-extension/allocation/SEARCH.json
new file mode 100644
index 0000000000..e03a04b425
--- /dev/null
+++ b/research/paired-helper-extension/allocation/SEARCH.json
@@ -0,0 +1,39 @@
+{
+  "changed_offsets": 103323,
+  "changed_owner_rows": 103059,
+  "methods": [
+    "Exhaustive unequal-width exchanges within an actual call preserve its physical family set.",
+    "Whole-role relocations preserve source windows and per-call physical-family distinctness.",
+    "Equal-width two-role relays preserve the intermediate bin total.",
+    "Subset dynamic programming moves all3..6 roles of a48-bin into eligible spare bins, retaining only strictly improved complete residual moments.",
+    "Cost-neutral equal-width cross-call swaps change only temporal incidence and are followed by the preceding improving passes."
+  ],
+  "neutral_rewiring_rounds": [
+    {
+      "accepted": 12000,
+      "seed": 1
+    },
+    {
+      "accepted": 12000,
+      "seed": 2
+    },
+    {
+      "accepted": 50000,
+      "seed": 3
+    }
+  ],
+  "numeric_root_for_discovery": "0.0017215886471978018806051293282625451738999963743107355795274760820981327521127712",
+  "order_and_dispatch_unchanged": true,
+  "parent_fill_sha256": "d6585a3b05fb86efd08b1925c5ae0a03265c30f895f5e2c4e1cdfe91978cd3ef",
+  "parent_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "parent_pr": 2908,
+  "roles": 271728,
+  "scope": "Discovery history only. Final independently checked literal owners and directed moment provide the certificate; neither global optimality nor fractional-LP attainment is claimed.",
+  "source_words_unchanged_by_allocation": true,
+  "status": "BOUNDED_ALLOCATION_DISCOVERY_NOT_OPTIMALITY",
+  "stopping_rule": "Two initial fills and three deterministic neutral-rewiring rounds; final fill frozen after the third round, with no remaining improving move in the implemented fixed-point pass.",
+  "word_sha256": {
+    "base": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+    "extra": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f"
+  }
+}
diff --git a/research/paired-helper-extension/allocation/baseline/CLAIM.json b/research/paired-helper-extension/allocation/baseline/CLAIM.json
new file mode 100644
index 0000000000..4edc2cb723
--- /dev/null
+++ b/research/paired-helper-extension/allocation/baseline/CLAIM.json
@@ -0,0 +1,35 @@
+{
+  "baseline_head": "18d03c447886895ef9abf888398178e0428533ca",
+  "baseline_kappa": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2894,
+  "calls": 666,
+  "complete_package_manifest_sha256": "a6d0e45723ea87f43ed8026758306adbf44b5cfc8473464c77acb57f32530783",
+  "complex_lower": "1720398337354237885931/1000000000000000000000000",
+  "gain": "213808976768352857/1000000000000000000000000",
+  "helpers": 408,
+  "independent_inputs": 632,
+  "kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017203983373542378859309999999999999999999998999999999999999999999999",
+  "live_families": 66304,
+  "native_receipt_sha256": "3280682ab975f412ab25e8ec433b2e52d8d3b6226db712ccabbbd2babcc2b84d",
+  "physical_families": 66795,
+  "profile": {
+    "1": 1620344,
+    "2": 426241,
+    "23": 1,
+    "3": 180732,
+    "32": 14,
+    "4": 85248,
+    "48": 26837,
+    "5": 25700,
+    "6": 120,
+    "7": 1,
+    "8": 5328
+  },
+  "release_receipt_sha256": "c3fd39e0645b10681a26b74afd08b429e04a139222e156f533654486c4f70214",
+  "replicas": 74,
+  "scope": "Conditional finite supplier/outer certificate. Inherited all-size/compiler/theorem hypotheses remain; no selected frontier change, no optimality or independent-human-review claim. Both changed native chains are fresh; retained parent/native evidence explicitly reused by complete receipts.",
+  "source_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "status": "CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE",
+  "zero_buffers": 73
+}
diff --git a/research/paired-helper-extension/allocation/baseline/ORDER.json b/research/paired-helper-extension/allocation/baseline/ORDER.json
new file mode 100644
index 0000000000..7409c4df10
--- /dev/null
+++ b/research/paired-helper-extension/allocation/baseline/ORDER.json
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new file mode 100644
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diff --git a/research/paired-helper-extension/allocation/vendor/independent_owners.py b/research/paired-helper-extension/allocation/vendor/independent_owners.py
new file mode 100644
index 0000000000..16013201b1
--- /dev/null
+++ b/research/paired-helper-extension/allocation/vendor/independent_owners.py
@@ -0,0 +1,111 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent integer-time and mask check of the actual parameterized-replica owner allocation with PR2802 retired7 providers.
+
+Chronology/mask method derives from Tekalign's PR2751 independent_owners.py;
+Marius-Paul Dumitrean's PR2802 retired7 native construction and the retained
+provider frame checker keep their
+upstream attribution. No solver, producer, emitter or floating arithmetic is
+imported. This checks finite geometry, not global native/outer admission.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+import argparse,hashlib,gzip,json,sys,types
+sys.dont_write_bytecode=True
+def need(v,msg):
+ if not v:raise ValueError(msg)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def read(p):
+ b=Path(p).read_bytes();return json.loads(gzip.decompress(b)if str(p).endswith('.gz')else b)
+def inputs(PROVIDER):
+ provider_pins={'inputs/PLAN.json.gz':'afb3c5c8134fc2cfce0b50a21758490c225574994b2c3c5161e53e2355acc6fa','inputs/GLOBAL-TEMPLATE.json.gz':'21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e','independent_local.py':'ee1faab70095fa312fc61d375ddf015b76104cb1a542ae7876a149e7999faa20','inputs/PROVIDERS.json':'391075b1411a3976850c633f92f58c35ed3f046f09d55bd435d7545124543fd4','inputs/WORD-base.json.gz':'dca8becca633ffc5e998985631bcbcab1123b27ca7f10ac6a96b1ec21ce69a66','inputs/WORD-extra.json.gz':'6bcb3c2c73eaf7558ddc6ef6b484334f8d96b9d2b227e265483b657de00f4bb7'}
+ hashes={}
+ for n,pin in provider_pins.items():
+  p=PROVIDER/n;need(sha(p)==pin,'pinned PR2802 provider source '+n);hashes[str(p)]=pin
+ L=types.ModuleType('retained_independent_frames');exec(compile((PROVIDER/'independent_local.py').read_bytes(),'pinned_PR2802_independent_local.py','exec'),L.__dict__);providers=read(PROVIDER/'inputs/PROVIDERS.json')
+ for tag,pid in [('base','gauge44'),('extra','extra')]:
+  word=read(PROVIDER/f'inputs/WORD-{tag}.json.gz');report,start,ends=L.check_frames(word);L.check_cleanup(word);L.algebra(word)
+  widths=[L.dm(ends[k])-L.dm(start[k])for k in sorted(start)if k>=224]
+  need(widths==providers[pid]['widths']and len(widths)==408,'actual ordered provider frame widths');need(len(word['centers'])==8,'eight centres');providers[pid]['actual_paid_profile']={int(k):v for k,v in report['profile'].items()}
+ return read(PROVIDER/'inputs/PLAN.json.gz'),read(PROVIDER/'inputs/GLOBAL-TEMPLATE.json.gz'),providers,hashes
+
+def windows(template,order,T):
+ ranks={c['child']:c['rank']for c in template['idle_children']};pairs={e['stage']:e['pair']for e in template['recipe']if e['kind']=='local'}
+ blocks={};stage=None
+ for event in template['execution_schedule']:
+  if event['kind']in('bank_padding_cover_sweep','translate_every_live_family'):continue
+  if event['kind']=='local_cover_sweep':stage=event['stage'];blocks[stage]=[]
+  need(stage is not None,'source event before local call');blocks[stage].append(event)
+ need(set(blocks)==set(range(9)),'nine source stages')
+ progress=[0]*T;last={};result={}
+ for t,(stage,replica)in enumerate(order):
+  need(0<=replica<T and stage==progress[replica],'order chronology');progress[replica]+=1
+  for j,event in enumerate(blocks[stage]):
+   kind=event['kind']
+   if kind=='local_cover_sweep':need(j==0,'local first position');last[replica,pairs[stage]]=t
+   elif kind=='bridge':last[replica,event['src']]=last[replica,event['dst']]=t
+   elif kind=='idle_cover_sweep':
+    need(j>0,'idle source position');start=last.get((replica,event['pair']),-1)
+    for child in event['child_indices']:
+     if child in ranks:result[replica,child]=(ranks[child],start,t)
+   elif kind in ('terminal_Y_translations','terminal'):pass  # inherited terminal phase; no pending-window endpoints
+   else:raise ValueError('unknown source event kind')
+ need(progress==[9]*T,'complete replica source progression');return result
+
+def check(T,order,fill,dispatch,claimed,plan,template,providers):
+ need(type(T)is int and T>0,'positive T');N=9*T
+ need(len(order)==N and set(map(tuple,order))=={(s,r)for s in range(9)for r in range(T)},'complete T call coverage')
+ win=windows(template,order,T)
+ need(set(dispatch)==set(map(tuple,order))and all(p in providers for p in dispatch.values()),'provider dispatch coverage')
+ for s,r,pid in fill.get('dispatch_overrides',[]):need(dispatch.get((s,r))==pid,'final dispatch override binding')
+ need(fill['columns']==['time','helper','owner_replica','child','port','offset'],'literal role columns')
+ need(len(fill['rows'])==N*408,'complete role count');helpers=[0]*N;families=[0]*N;occupied={};lastrow={}
+ for idx,row in enumerate(fill['rows']):
+  need(len(row)==6 and all(type(x)is int for x in row),'integer role shape');t,h,o,c,p,z=row
+  need(0<=t<N and 0<=h<408 and 0<=p<112 and(o,c)in win,'role bounds')
+  cap,lo,hi=win[o,c];need(lo<t<=hi,'literal source window');hb=1<<h;need(not helpers[t]&hb,'duplicate helper');helpers[t]|=hb
+  family=o*896+(2*plan['pairs'][str(c)]+plan['sides'][str(c)])*112+p;fb=1<<family
+  need(not families[t]&fb,'same-call family collision');families[t]|=fb
+  w=providers[dispatch[tuple(order[t])]]['widths'][h];need(0<=z and z+w<=cap,'bin capacity')
+  key=(o,c,p);mask=((1<<w)-1)<<z;need(not occupied.get(key,0)&mask,'bin overlap');occupied[key]=occupied.get(key,0)|mask
+  if key not in lastrow or z>lastrow[key][0]:lastrow[key]=(z,idx,w)
+ need(helpers==[(1<<408)-1]*N,'all helper identities');idle=Counter()
+ for(o,c),(cap,_,_)in win.items():
+  for p in range(112):
+   key=(o,c,p);mask=occupied.get(key,0);used=mask.bit_count();need(mask==(1<<used)-1,'compact bin prefix')
+   if used<cap:idle[cap-used]+=1
+ profile=Counter(idle)
+ for call in order:profile.update(providers[dispatch[tuple(call)]]['actual_paid_profile'])
+ if claimed is not None:need(profile==Counter({int(k):v for k,v in claimed.items()}),'complete claimed profile')
+ mass=sum(r*n for r,n in profile.items());need(mass==65088*T,'complete rank-mass identity')
+ return dict(replicas=T,calls=N,roles=N*408,live=896*T,physical=896*T+490,rank_mass=mass,idle=dict(sorted(idle.items())),profile=dict(sorted(profile.items()))),win,lastrow
+
+def write_receipt(out,result):
+ out.parent.mkdir(parents=True,exist_ok=True);lock=out.with_name(out.name+'.lock');handle=lock.open('x')
+ try:
+  with out.open('x',encoding='utf8',newline='\n')as target:target.write(json.dumps(result,sort_keys=True,indent=2)+chr(10))
+ finally:handle.close();lock.unlink()
+
+def main():
+ need(__debug__,'assertions required for retained provider frame checker')
+ ap=argparse.ArgumentParser();ap.add_argument('--provider-root',type=Path,default=Path(__file__).resolve().parent/'vendor/frontier');ap.add_argument('--replicas',type=int,required=True);ap.add_argument('--order',type=Path,required=True);ap.add_argument('--fill',type=Path,required=True);ap.add_argument('--dispatch',type=Path,required=True);ap.add_argument('--profile',type=Path);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();need(not a.out.exists(),'fresh verification output')
+ plan,template,providers,pins=inputs(a.provider_root);files=[a.order,a.fill,a.dispatch]+([a.profile]if a.profile else[]);before={str(p.resolve()):sha(p)for p in files};order=read(a.order);fill=read(a.fill);rawdispatch=read(a.dispatch);need(len(rawdispatch)==9*a.replicas and all(len(row)==3 and type(row[0])is int and type(row[1])is int and type(row[2])is str for row in rawdispatch),'literal dispatch shape and count');dispatch={(s,r):p for s,r,p in rawdispatch};need(len(dispatch)==len(rawdispatch),'unique literal dispatch calls');claimed=read(a.profile)if a.profile else None
+ result,win,lastrow=check(a.replicas,order,fill,dispatch,claimed,plan,template,providers);rejected=[]
+ def reject(name,fn,reason):
+  try:fn()
+  except ValueError as e:need(str(e)==reason,'wrong rejection reason '+name+': '+str(e));rejected.append(dict(name=name,reason=reason))
+  else:raise ValueError('accepted corruption '+name)
+ def rerun(T=a.replicas,f=fill,d=dispatch,p=providers,c=claimed):return check(T,order,f,d,c,plan,template,p)
+ reject('false_replica_count',lambda:rerun(T=a.replicas+1),'complete T call coverage')
+ reject('missing_literal_helper_role',lambda:rerun(f={**fill,'rows':fill['rows'][:-1]}),'complete role count')
+ bad=dict(dispatch);bad[tuple(order[0])]='unknown-provider';reject('unbound_provider_at_actual_call',lambda:rerun(d=bad),'provider dispatch coverage')
+ def mutate(i,new):rows=list(fill['rows']);rows[i]=new;return{**fill,'rows':rows}
+ row=fill['rows'][0];t,h,o,c,p,z=row;owner,child=next(k for k,(cap,lo,hi)in win.items()if not lo<t<=hi)
+ reject('unavailable_source_window',lambda:rerun(f=mutate(0,[t,h,owner,child,p,z])),'literal source window')
+ j=next(i for i,r in enumerate(fill['rows'][1:],1)if r[0]==t);r=fill['rows'][j];reject('same_call_physical_family_collision',lambda:rerun(f=mutate(j,[r[0],r[1],o,c,p,r[5]])),'same-call family collision')
+ key,(z,i,w)=next((k,v)for k,v in lastrow.items()if v[0]+v[2]<win[k[:2]][0]);r=list(fill['rows'][i]);r[5]+=1
+ reject('unpaid_hole_in_compact_pending_prefix',lambda:rerun(f=mutate(i,r)),'compact bin prefix')
+ wrong=dict(result['profile']);wrong[1]=wrong.get(1,0)+1;reject('changed_total_paid_profile',lambda:rerun(c=wrong),'complete claimed profile')
+ need({str(p.resolve()):sha(p)for p in files}==before,'candidate input drift');need(all(sha(Path(p))==h for p,h in pins.items()),'baseline input drift')
+ result.update(status='PASS_INDEPENDENT_T_OWNER_CHRONOLOGY_MASKS',controls=rejected,candidate_sha256={label:sha(path)for label,path in [('ORDER',a.order),('FILL',a.fill),('DISPATCH',a.dispatch)]+([('PROFILE',a.profile)]if a.profile else[])},provider_source_sha256={Path(path).relative_to(a.provider_root).as_posix():digest for path,digest in pins.items()},scope='PR2802 head17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd; finite literal whole-owner geometry, scalar endpoints and paid profile only; full native/global/outer admission remains separate.')
+ write_receipt(a.out,result);print(json.dumps({k:result[k]for k in['status','replicas','roles','live','physical','profile']}),flush=True)
+if __name__=='__main__':main()
diff --git a/research/paired-helper-extension/check_allocation.py b/research/paired-helper-extension/check_allocation.py
new file mode 100644
index 0000000000..8f8be54df1
--- /dev/null
+++ b/research/paired-helper-extension/check_allocation.py
@@ -0,0 +1,108 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Derive actual widths/costs, verify literal owners, private stock, and moment.
+
+Retains Tekalign's independent integer chronology/mask checker as credited in
+allocation/vendor/independent_owners.py and Jeremy Diviney's PR2908 integration.
+Mason Hale, with substantial OpenAI Codex assistance: changed source binding,
+actual 82-buffer namespace, complete local frame recount, and new literal fill.
+Full native/global/outer admission remains separate.
+"""
+import argparse, gzip, hashlib, json, sys, types
+from pathlib import Path
+P = Path(__file__).resolve().parent
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if raw[:2] == b'\x1f\x8b' else raw)
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+def load(name, path):
+    module = types.ModuleType(name)
+    module.__file__ = str(path)
+    sys.modules[name] = module
+    exec(compile(path.read_bytes(), str(path), 'exec'), module.__dict__)
+    return module
+
+def main():
+    parser = argparse.ArgumentParser()
+    parser.add_argument('--work', type=Path, required=True)
+    args = parser.parse_args()
+    out = args.work.resolve()
+    assert __debug__ and not out.exists() and not out.is_relative_to(P)
+    allocation_pins = read(P / 'ALLOCATION-PINS.json')
+    actual_pins = {p.relative_to(P).as_posix(): sha(p) for p in (P / 'allocation').rglob('*') if p.is_file()}
+    assert actual_pins == allocation_pins, 'complete allocation inventory binding'
+    word_pins = read(P / 'PINS.json')
+    assert all(sha(P / name) == digest for name, digest in word_pins.items()), 'source word/code pins'
+    out.mkdir(parents=True)
+    owners = load('paired_extension_owners', P / 'allocation/vendor/independent_owners.py')
+    moment = load('paired_extension_moment', P / 'tools/audit_allocation_moment.py')
+    frames = load('paired_extension_frames', P / 'vendor/preload_move.py')
+    providers, word_records, private_counts = {}, {}, set()
+    for tag, provider in [('base', 'gauge44'), ('extra', 'extra')]:
+        path = P / f'data/WORD-{tag}.json.gz'
+        word = read(path)
+        profile, inventory = frames.frame_report(word)
+        assert profile == word['report']['local_profile'] and inventory == word['report']['width_inventory']
+        helpers = sorted(set(range(224, 704)) - set(word['removed']))
+        widths = [len(word['helper_final'].get(str(h), [0] * 9)) - len(word['start_extra'].get(str(h), [])) for h in helpers]
+        assert len(helpers) == 408 and len(word['centers']) == 8
+        buffers = {r for gate in word['cleanup'] for r in (gate[1:3] if gate[0] == 'add' else gate[1:2]) if r >= 704}
+        assert buffers == {704 + int(h) for h in word['helper_final']}, 'actual cleanup buffer/end-point bijection'
+        assert len(buffers) == 82, 'all nine extra private buffers charged'
+        private_counts.add(len(buffers))
+        providers[provider] = {'widths': widths, 'actual_paid_profile': {int(k): v for k, v in profile.items()}}
+        word_records[tag] = {'sha256': sha(path), 'local_profile': profile, 'width_inventory': inventory, 'private_buffers': len(buffers)}
+    assert len(private_counts) == 1
+    registry = read(P / 'allocation/PROVIDERS.json')
+    assert {k: {'widths': v['widths'], 'actual_paid_profile': {int(r): n for r, n in v['actual_paid_profile'].items()}} for k, v in registry.items()} == providers
+    base = P / 'allocation'
+    order, fill = read(base / 'ORDER.json'), read(base / 'FILL.json.gz')
+    raw_dispatch = read(base / 'DISPATCH.json')
+    dispatch = {(s, r): provider for s, r, provider in raw_dispatch}
+    assert len(dispatch) == len(raw_dispatch), 'unique actual call/provider binding'
+    profile = read(base / 'PROFILE.json')
+    plan, template = read(base / 'vendor/PLAN.json.gz'), read(base / 'vendor/TEMPLATE.json.gz')
+    T = len(order) // 9
+    def check(candidate=fill, claimed=profile):
+        return owners.check(T, order, candidate, dispatch, claimed, plan, template, providers)
+    result, _, _ = check()
+    assert T == 74 and result['roles'] == 271728
+    result['physical'] = result['live'] + len(helpers) + len(word['centers']) + next(iter(private_counts)) + 2
+    assert result['physical'] == 66804
+    result['physical_source'] = 'Actual 82-register private cleanup namespace, 408 live helpers, eight centres and two guards; global stock checked separately.'
+    controls = {}
+    def reject(name, candidate=fill, claimed=profile):
+        try:
+            check(candidate, claimed)
+        except ValueError as error:
+            controls[name] = str(error)
+        else:
+            raise AssertionError('owner corruption accepted: ' + name)
+    reject('missing_role', {**fill, 'rows': fill['rows'][:-1]})
+    first = fill['rows'][0]
+    j = next(i for i, r in enumerate(fill['rows'][1:], 1) if r[0] == first[0])
+    def mutate(index, row):
+        rows = list(fill['rows']); rows[index] = row
+        return {**fill, 'rows': rows}
+    duplicate = list(fill['rows'][j]); duplicate[1] = first[1]
+    reject('duplicate_helper', mutate(j, duplicate))
+    collision = list(fill['rows'][j]); collision[2:5] = first[2:5]
+    reject('same_call_family_collision', mutate(j, collision))
+    overflow = list(first); overflow[5] = 49
+    reject('capacity_overflow', mutate(0, overflow))
+    wrong = dict(profile); wrong['1'] = wrong.get('1', 0) + 1
+    reject('changed_paid_profile', claimed=wrong)
+    exact = moment.run(base, base / 'baseline')
+    assert all(sha(P / name) == digest for name, digest in {**word_pins, **allocation_pins}.items()), 'input drift'
+    result.update(status='PASS_PAIRED_EXTENSION_LITERAL_OWNERS_AND_EXACT_MOMENT', providers=word_records,
+                  controls=controls, moment=exact, allocation_sha256=allocation_pins,
+                  scope='Recounted local frames, exact whole-owner geometry and directed moment; algebra/native/global/outer admission remains separately required.')
+    (out / 'RESULT.json').write_text(json.dumps(result, sort_keys=True, indent=2) + '\n')
+    print(result['status'], exact['target_decimal'], exact['gain_decimal'])
+
+if __name__ == '__main__':
+    main()
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new file mode 100644
index 0000000000..7d35aab299
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new file mode 100644
index 0000000000..e62dd449d7
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new file mode 100644
index 0000000000..4fae6d1bb3
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new file mode 100644
index 0000000000..1593c52045
--- /dev/null
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new file mode 100644
index 0000000000..7c22cd7a66
--- /dev/null
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diff --git a/research/paired-helper-extension/evidence/ADAPTER-DERIVATION.json b/research/paired-helper-extension/evidence/ADAPTER-DERIVATION.json
new file mode 100644
index 0000000000..de4ab3f54e
--- /dev/null
+++ b/research/paired-helper-extension/evidence/ADAPTER-DERIVATION.json
@@ -0,0 +1,111 @@
+{
+  "status": "PASS_CHECKED_82_BUFFER_ADAPTER_DERIVATION",
+  "parent_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "parent_manifest_sha256": "9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f",
+  "source_commit": "paired-helper-extension-pr2908",
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "source_files": 632,
+  "comparison_sha256": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+  "retained_receipt_sha256": "02a4d46fe4e1e368d2d22794a2c769ee28470d6797651848d261ca42b90f23d9",
+  "buffer_count": 82,
+  "physical_overhead": 500,
+  "changes": {
+    "prepare_extension_native.py": {
+      "source": "/private/tmp/kappa-round6/public-complete/pr2908/tools/prepare_channel_native.py",
+      "before_sha256": "4d207b9bbe3e0b8a86d10ad5d5f329a81da0cf56dce6c03e6fdd5b78e581ce91",
+      "after_sha256": "c5ad3e3d086aae7c9000b7d8c769cbc22a943c738d5808cee52fe71e571a595d",
+      "replacements": [
+        {
+          "old": "SOURCE_SHA='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'",
+          "new": "SOURCE_SHA='98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1'"
+        },
+        {
+          "old": "SOURCE_FILES=610",
+          "new": "SOURCE_FILES=632"
+        },
+        {
+          "old": "SOURCE_COMMIT='two-sided-helper408-pr2894'",
+          "new": "SOURCE_COMMIT='paired-helper-extension-pr2908'"
+        },
+        {
+          "old": "OLD_RECEIPT_SHA='dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'",
+          "new": "OLD_RECEIPT_SHA='02a4d46fe4e1e368d2d22794a2c769ee28470d6797651848d261ca42b90f23d9'"
+        },
+        {
+          "old": "len(can['zero_buffers'])==73",
+          "new": "len(can['zero_buffers'])==82"
+        }
+      ]
+    },
+    "admit_extension.py": {
+      "source": "/private/tmp/kappa-round6/public-complete/pr2908/tools/admit_channel408.py",
+      "before_sha256": "a62c21eac4e0df502cbfb78c88b19a763fd351cde3c11c0588874f84db6992bf",
+      "after_sha256": "04abab54626f0c512fdf57232f8ce64835fe47d24984838f85cc5bae4934466a",
+      "replacements": [
+        {
+          "old": "    'channel408': dict(commit='two-sided-helper408-pr2894',manifest='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83',helpers=408,source_file_count=610,upstream_head='18d03c447886895ef9abf888398178e0428533ca'),",
+          "new": "    'paired-extension': dict(commit='paired-helper-extension-pr2908',manifest='98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1',helpers=408,source_file_count=632,upstream_head='51309592971e3b5be935599eed2a95404dc7781e'),"
+        },
+        {
+          "old": "COMPARISONS = {",
+          "new": "COMPARISONS = {\n    'pr2908': dict(pr=2908,head='51309592971e3b5be935599eed2a95404dc7781e',sha256='2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf',field='kappa'),"
+        },
+        {
+          "old": "ap.add_argument('--source-profile', choices=['channel408'], default='channel408')",
+          "new": "ap.add_argument('--source-profile', choices=['paired-extension'], default='paired-extension')"
+        },
+        {
+          "old": "ap.add_argument('--comparison-profile', choices=['pr2894'], default='pr2894')",
+          "new": "ap.add_argument('--comparison-profile', choices=['pr2908'], default='pr2908')"
+        },
+        {
+          "old": "zero_buffers_allocated_and_cleared=73",
+          "new": "zero_buffers_allocated_and_cleared=82"
+        },
+        {
+          "old": "len(c.get('zero_buffers',[]))==73, 'helper408 physical ABI including all 73 private buffers'",
+          "new": "len(c.get('zero_buffers',[]))==82, 'paired extension physical ABI including all 82 private buffers'"
+        },
+        {
+          "old": "896*T+expected_helpers+8+73+2, 'complete physical cost including all actual helpers and 73 buffers'",
+          "new": "896*T+expected_helpers+8+82+2, 'complete physical cost including all actual helpers and 82 buffers'"
+        }
+      ]
+    },
+    "extension_blocknorm.py": {
+      "source": "/private/tmp/kappa-round6/public-complete/pr2908/tools/channel_blocknorm.py",
+      "before_sha256": "b53ebd53e3948f658c6da4f487a9ea10c9cb0a6acf2435750a32d6efeb9869c0",
+      "after_sha256": "d3893ef2265b1027f90b33832a3631b7a664bfdcac47962b83149d904bb7578f",
+      "replacements": [
+        {
+          "old": "len(allocated)==73, 'all73 private zero buffers released'",
+          "new": "len(allocated)==82, 'all82 private zero buffers released'"
+        },
+        {
+          "old": "'zero_buffers_allocated_and_cleared':73",
+          "new": "'zero_buffers_allocated_and_cleared':82"
+        },
+        {
+          "old": "r['zero_buffers_returned_to_zero']==73",
+          "new": "r['zero_buffers_returned_to_zero']==82"
+        },
+        {
+          "old": "physical==live+8+408+73+2",
+          "new": "physical==live+8+408+82+2"
+        },
+        {
+          "old": "'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]",
+          "new": "'zero_buffers':[live+416,live+498], 'coefficient':[live+498,live+500]"
+        },
+        {
+          "old": "len(mp)==73 and set(mp.values())==set(range(*ns['zero_buffers'])), '73distinct private Z slots'",
+          "new": "len(mp)==82 and set(mp.values())==set(range(*ns['zero_buffers'])), '82distinct private Z slots'"
+        },
+        {
+          "old": "T=len(order)//9; live=896*T; physical=live+490",
+          "new": "T=len(order)//9; live=896*T; physical=live+500"
+        }
+      ]
+    }
+  }
+}
diff --git a/research/paired-helper-extension/evidence/ADMISSION-RESULT.json b/research/paired-helper-extension/evidence/ADMISSION-RESULT.json
new file mode 100644
index 0000000000..4de28b893a
--- /dev/null
+++ b/research/paired-helper-extension/evidence/ADMISSION-RESULT.json
@@ -0,0 +1,386 @@
+{
+  "actual_expected_helpers": 408,
+  "comparison_claim_sha256": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+  "comparison_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "comparison_kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "comparison_pr": 2908,
+  "complex_lower": "344317729439560376121/200000000000000000000000",
+  "dispatch_sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "external_input_sha256": {
+    "/Users/masonhale/Documents/Codex/2026-10-13/files-pasted-by-the-user-contribute/work/integer-mult-round6/research/paired-helper-extension/allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+    "/Users/masonhale/Documents/Codex/2026-10-13/files-pasted-by-the-user-contribute/work/integer-mult-round6/research/paired-helper-extension/allocation/FILL.json.gz": "19b551af07274931b443ac42588e15df20ec0140fa69b54f3b62a4df9a54ff8e",
+    "/Users/masonhale/Documents/Codex/2026-10-13/files-pasted-by-the-user-contribute/work/integer-mult-round6/research/paired-helper-extension/allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+    "/private/tmp/kappa-round6/public-complete/adapters/extension_blocknorm.py": "d3893ef2265b1027f90b33832a3631b7a664bfdcac47962b83149d904bb7578f",
+    "/private/tmp/kappa-round6/public-complete/parent-export/pr2894/vendor/pr2857/vendor/pr2839/lift_parent.py": "9a1edd7d4ab4a2f2ac8d15b42b7e40f93653d65026bac59e4c1ce80b486bd60e",
+    "/private/tmp/kappa-round6/public-complete/parent-export/pr2894/vendor/pr2857/vendor/pr2839/reconstruct_replica.py": "5472811c24aef3852dc7e189dff5060076a6c0b25bfde928da50dcfe9b5bdc15",
+    "/private/tmp/kappa-round6/public-complete/parent-export/pr2894/vendor/pr2857/vendor/pr2839/replica_parent.py": "48bdbf28f59d80edb266803ec61bf5e22e8fb5e5a0e2b88004b6039147589bd4",
+    "/private/tmp/kappa-round6/public-complete/pr2908/CLAIM.json": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf"
+  },
+  "fill_sha256": "19b551af07274931b443ac42588e15df20ec0140fa69b54f3b62a4df9a54ff8e",
+  "gain": "595154921781997337/500000000000000000000000",
+  "kappa": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017215886471978018806049999999999999999999998999999999999999999999999",
+  "native_receipt_sha256": "5c1ea6f03e48673d9b56563494fff2258ee18bc8dacdeb72ba5c07e2044008ca",
+  "order_sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "package_manifest_sha256": "bf852fb4ecfa28dddfb8cc6fe7bf53019b3932114e01cba3e026b63ef2b1babd",
+  "patches": [
+    {
+      "after_sha256": "52f8b4cec2dab69cbe590e1fd0f7a68e1b35de5a540bd22fd2adfce07a92b46b",
+      "before_sha256": "faf283eb4edd2e6a1ccb40b3cb3ba30ae54338eaf5ea0a10d84d11d7939502af",
+      "path": "new/rebind.py",
+      "replacements": [
+        [
+          "physical=spec['expected']['live'] + 8 + R + 2)",
+          "physical=spec['expected']['live'] + 8 + R + 2 + max(len(rd(d / 'CANONICAL-WORD.json.gz').get('zero_buffers', [])) for d in locs.values()))"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "99bef04f24a99088e5c0c9b8f6bbc8386669d8315b8f572d6bbfb932c5d51145",
+      "before_sha256": "7edb4732b34e5814b27650a55c938626cb50d68f06397744dd4fe451437e90e0",
+      "path": "geometry_controls.py",
+      "replacements": [
+        [
+          " i['complete_invocation_sweeps']=i['bridge_sweeps']=333",
+          " i['complete_invocation_sweeps']-=1;i['bridge_sweeps']-=1"
+        ],
+        [
+          " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);oh=digest(o);i['owner_audit_sha256']=oh",
+          " o,i=copy.deepcopy(owner),copy.deepcopy(invoice);fn(o,i);assert (o,i)!=(owner,invoice), 'geometry mutant must change actual receipts';oh=digest(o);i['owner_audit_sha256']=oh"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+      "before_sha256": "c43680a2da390f79925547a5ee1919d8a76637cccf98e2c8164b6f667fbc3183",
+      "path": "verify_release.py",
+      "replacements": [
+        [
+          "Fraction(1, 10 ** 3046) - Fraction(1, 10 ** 3022)",
+          "Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 46)) - Fraction(1, 10 ** (spec['outer_refinement']['endpoint_digits'] + 22))"
+        ],
+        [
+          "epsilon=1-(1025/1024)e-3080",
+          "epsilon=1-(1025/1024)e-{spec['outer_refinement']['endpoint_digits']+80}"
+        ],
+        [
+          "at the one 3000-digit rejection call",
+          "at the one {spec['outer_refinement']['endpoint_digits']}-digit rejection call"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98",
+      "before_sha256": "9e12909c73d3b3a31a45d801ae76c034510d6306400412e474df79bc4f1dc67e",
+      "path": "outer/check_ledger.py",
+      "replacements": [
+        [
+          "assert (m,W)==(73,66304)",
+          "T=spec['geometry']['replicas']\nassert type(T) is int and T>0\nassert m==73 and W==896*T and W==BJ['live']"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+      "before_sha256": "08ca58abff11bdfba721dc56ab8acf06ec1b7c48a8699a0955cf35324680aca7",
+      "path": "code/witness.py",
+      "replacements": [
+        [
+          "   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))",
+          "   import time as _wr_time\n   _wr_path=Path(os.environ['WITNESS_RECORD'])\n   _wr_lock=_wr_path.with_name(_wr_path.name+'.append.lock')\n   _wr_deadline=_wr_time.monotonic()+60\n   _wr_fd=None\n   while _wr_fd is None:\n    try:_wr_fd=os.open(_wr_lock,os.O_CREAT|os.O_EXCL|os.O_WRONLY)\n    except FileExistsError:\n     if _wr_time.monotonic()>=_wr_deadline:raise TimeoutError('discovery record lock timeout; existing lock preserved')\n     _wr_time.sleep(.005)\n   try:\n    with _wr_path.open('a',encoding='utf-8',newline='\\n')as _wr_out:\n     _wr_out.write(json.dumps([key,got],default=str)+chr(10))\n     _wr_out.flush()\n   finally:\n    os.close(_wr_fd)\n    _wr_lock.unlink()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "680b6de474a8226777c5a17191470b21cd5cc524cc22921d12dff6cef25c43ee",
+      "before_sha256": "b0d5f4217b4699c37609dc7c3633d570acbccd205840777d38f891846b4b918c",
+      "path": "verify.py",
+      "replacements": [
+        [
+          "run('lift-parent',P/'lift_parent.py','--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')",
+          "run('lift-parent',P/'lift_parent.py','--package',P,'--owners',work/'rebuilt-owners','--out',work/'rebuilt-parent')"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "0d8cc021d2401d047aaec79060ec2ea28ba06f12eca8dbf4c60c78bb31975c4e",
+      "before_sha256": "ebaf637f1f818dac9c0fce0ee3f18df300873105818cea29a8ae9e8b737b5c7d",
+      "path": "code/witness.py",
+      "replacements": [
+        [
+          "PAYLOAD==1<<(192+(GEO['dimension']+1)//2+2*CALLS+4).bit_length()",
+          "PAYLOAD==1<<(128+(GEO['dimension']+1)//2+18+1330+1+4).bit_length()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+      "before_sha256": "bb213d0af12218ff7c9c572717e522d8bbeeb2856b87a253f4a7f44e0fd71f15",
+      "path": "code/invoice_allcold.py",
+      "replacements": [
+        [
+          "    required_prefix=localbits+input_l2_bits+call_count+bridge_sweeps+4",
+          "    from blocknorm_certificate import certify\n    blocknorm=certify(template, {pid:base/'providers'/pid for pid in template['local_providers']})\n    assert blocknorm['status'] == 'PASS_TENSOR_BLOCK_NORM_CERTIFICATE'\n    assert localbits <= 128, 'actual native scalar/Horner prefix exceeds charged local reserve'\n    required_prefix=localbits+input_l2_bits+blocknorm['max_active_depth']+blocknorm['stock_l2_bits']+1+4"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+      "before_sha256": "02502a217fe8c9e10229075b50745518beac512c48db20e64c3e06514a4da5b5",
+      "path": "independent_core.py",
+      "replacements": [
+        [
+          "    payload = 1 << (192 + (M+1)//2 + 2*len(c['order']) + 4).bit_length()",
+          "    require(localbits <= 128, 'measured native prefix exceeds local reserve')\n    payload = 1 << (128 + (M+1)//2 + 18 + 1330 + 1 + 4).bit_length()"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "d598a2ac1e2e8eaee14a8c285e0277a7ae44ca6a15bd2b5cfc67fb40844fb387",
+      "before_sha256": "c5106e0d7a97382677fa228fbade989262347968a0e54acfcf6712aa37e02f47",
+      "path": "code/invoice_allcold.py",
+      "replacements": [
+        [
+          "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,",
+          "        complete_invocation_sweeps=call_count,bridge_sweeps=bridge_sweeps,row_prefix_extra=2*payload,blocknorm=blocknorm,"
+        ],
+        [
+          "        primitive_arithmetic_margin_bits=4,controller_audit_sha256=",
+          "        tensor_block_norm=blocknorm,partial_cover_margin_bits=1,physical_stock_l2_bits=blocknorm['stock_l2_bits'],primitive_arithmetic_margin_bits=4,controller_audit_sha256="
+        ],
+        [
+          "Sum every actual invocation and bridge sweep and take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
+          "All invocations and bridge sweeps remain charged. Bound completed-boundary energy by at most eighteen active steps per owner replica, using exact tensor-isomorphic whole-family helper unitaries. Add the full group-indexed physical-stock sup-to-l2 factor and one partial-cover margin, then the maximum local scalar/Horner prefix."
+        ]
+      ]
+    },
+    {
+      "after_sha256": "e051aaa166e01263780d5ae03699690670b597fed6593af4c37a7e978825eb85",
+      "before_sha256": "0d522b09c7fe6a5e62fe80c28f3eefe733557a82d77c6212e5d4b91ffb7e3421",
+      "path": "independent_core.py",
+      "replacements": [
+        [
+          "    prefix = localbits + (M + 1) // 2 + len(c['order']) + c['bridges'] + 4",
+          "    bn=c['blocknorm']\n    require(bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['max_active_depth']==18 and bn['stock_l2_bits']<=1330, 'independent tensor block certificate')\n    prefix = localbits + (M + 1) // 2 + bn['max_active_depth'] + bn['stock_l2_bits'] + 1 + 4"
+        ],
+        [
+          "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], margin=4)",
+          "prefix_formula=dict(local_scalar=localbits, input_l2=(M + 1) // 2, invocations=len(c['order']), bridges=c['bridges'], active_block_depth=18,stock_l2=bn['stock_l2_bits'],partial_cover=1,margin=4),blocknorm=bn"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "393323f150d0bb686419804d51cf43d0f58450d2a1e7929725acdd26fdbb3640",
+      "before_sha256": "2286f00e462ff28abbb3f396095463482a1e063213b9526a7225275980c77eaf",
+      "path": "audit_mixed.py",
+      "replacements": [
+        [
+          "pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)",
+          "import blocknorm_certificate as BN;ctx['blocknorm']=BN.certify_context(ctx,roles,dirs,source_parent=parent);pending=A.check_pending_axes(ctx);receipt=A.check_roles(ctx,roles)"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "3ef9b2a2fa0dcf2d53884e205b7ac20ae6ef47d173b0d8a5bc97fb2a445fc143",
+      "before_sha256": "f25e1e870df5d5a16a1e367b3df8843cb01644ab4b75895d7939af81e4fcb833",
+      "path": "code/assemble.py",
+      "replacements": [
+        [
+          " assert invoice['global_prefix_bits']==max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())+37+CALLS+CALLS+4",
+          " bn=invoice['blocknorm']\n assert bn['status']=='PASS_TENSOR_BLOCK_NORM_CERTIFICATE' and bn['replicas']==REPLICAS\n assert bn['max_active_depth']==bn['boundary_depth_bits']==18 and bn['active_calls_per_block']==bn['bridges_per_block']==9\n assert bn['block_width_families']==896 and bn['physical_families']==invoice['physical'] and bn['live_families']==invoice['live']\n assert bn['partial_cover_bits']==1 and bn['input_l2_bits']==37 and bn['local_reserve_bits']==128 and bn['retained_payload_bits']==PAYLOAD\n localbits=max(z['prefix_bits']for p in invoice['providers'].values()for z in p['local'].values())\n assert bn['local_actual_prefix_bits']==localbits and localbits<=128\n assert invoice['global_prefix_bits']==bn['actual_prefix_bits']==localbits+37+18+bn['stock_l2_bits']+1+4\n assert bn['required_reserve_bits']==128+37+18+bn['stock_l2_bits']+1+4<PAYLOAD\n expected_endpoint=dict(all_arbitrary_columns=632,helper_to_data_response_zero=True,centres_first_clear_and_terminal_zero=8,zero_buffers_allocated_and_cleared=82,coefficient_work_contract='unchanged audited clear-before-and-after Horner macro')\n assert bn['endpoint_replay']=={pid:{o:expected_endpoint for o in ('forward','backward')} for pid in invoice['providers']}"
+        ],
+        [
+          " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']",
+          " stock=group*invoice['physical'];streamed_mass=group*owner['rank_mass']\n assert bn['physical_stock_bits']==stock.bit_length() and bn['stock_l2_bits']==(stock.bit_length()+1)//2<=1330"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "b7a6a7dbca02aec52d7807ed3104362b0fab1014d2f624b5fe638a3f30f65133",
+      "before_sha256": "d7675ff0b0994b29541d37eaa3010c5f39bb1447700c9f8e750522bf8c951f56",
+      "path": "code/assembly_controls.py",
+      "replacements": [
+        [
+          "        i['global_prefix_bits'] = 1 + 37 + CALLS + CALLS + 4",
+          "        i['global_prefix_bits'] = 1 + 37 + 18 + i['blocknorm']['stock_l2_bits'] + 1 + 4"
+        ],
+        [
+          "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),",
+          "        ('wrong_global_prefix_sum', lambda o, i: i.__setitem__('global_prefix_bits', 224)),\n        ('missing_blocknorm', lambda o,i:i.pop('blocknorm')),\n        ('understated_active_depth',lambda o,i:i['blocknorm'].__setitem__('max_active_depth',17)),\n        ('understated_full_stock_norm',lambda o,i:i['blocknorm'].__setitem__('stock_l2_bits',10)),\n        ('missing_partial_cover_margin',lambda o,i:i['blocknorm'].__setitem__('partial_cover_bits',0)),\n        ('forged_helper_response',lambda o,i:i['blocknorm']['endpoint_replay'][next(iter(i['providers']))]['forward'].__setitem__('helper_to_data_response_zero',False)),"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "9612cc95bfa2a36a9d9cbdcedc557f28f52e83f20f113ab21d0d54cf9c190be2",
+      "before_sha256": "1d965b7a329b98008fcc67e73d03dcf6e75f0f33c2858a39f1182bb3d0ed0ea1",
+      "path": "freeze_spec.py",
+      "replacements": [
+        [
+          "spec['expected']['assembly_controls_rejected'] = 32 + sum(",
+          "spec['expected']['assembly_controls_rejected'] = 37 + sum("
+        ]
+      ]
+    },
+    {
+      "after_sha256": "cda0f3a63c5c92c0ff45f7f3a200567d7931fd421836e72ea3b8534f6ee24dcc",
+      "before_sha256": "3ec4330ede0db3c6daa453b0366817be9435c85c8c3213a0c35c442c96c1a955",
+      "path": "replay.py",
+      "replacements": [
+        [
+          "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==114",
+          "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==119"
+        ]
+      ]
+    },
+    {
+      "after_sha256": "d281f230c1b4defef003e3994ead92ac628d3b7eb715f1367efd900a6ececb79",
+      "before_sha256": "680b6de474a8226777c5a17191470b21cd5cc524cc22921d12dff6cef25c43ee",
+      "path": "verify.py",
+      "replacements": [
+        [
+          "['replay.py','freeze_spec.py','audit_mixed.py','independent_core.py','geometry_controls.py','audit_fast.py']",
+          "['replay.py','freeze_spec.py','audit_mixed.py','independent_core.py','geometry_controls.py','audit_fast.py','blocknorm_certificate.py']"
+        ],
+        [
+          "controls=dict(admission=114,bit=12,controller=15,independent_owner=8,geometry=6)",
+          "controls=dict(admission=119,bit=12,controller=15,independent_owner=8,geometry=6)"
+        ]
+      ]
+    }
+  ],
+  "profile": {
+    "1": 1625724,
+    "2": 426240,
+    "24": 1,
+    "3": 191980,
+    "32": 207,
+    "4": 73260,
+    "48": 26958,
+    "5": 24951,
+    "6": 167,
+    "7": 45,
+    "8": 5328
+  },
+  "release_receipt_sha256": "f7639e51fd620070767b8e2a855a0a613ae9bfd19f86a1ba023d88316193ae06",
+  "replicas": 74,
+  "scope": "Conditional finite construction and modern outer arithmetic. Exact inherited theorem obligations remain. Both native providers explicitly reused from authenticated fresh five-stage runs.",
+  "source_commit": "paired-helper-extension-pr2908",
+  "source_file_count": 632,
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "source_profile": "paired-extension",
+  "source_upstream_head": "51309592971e3b5be935599eed2a95404dc7781e",
+  "stages": [
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/reconstruct.py",
+        "--out",
+        "/private/tmp/kappa-round6/public-complete/candidate/owners"
+      ],
+      "exit_code": 0,
+      "log_sha256": "df2168b51340a5406c925c2083c3e5307c0c593e7bf514cecca82ed360408541",
+      "name": "owners",
+      "script_sha256": "5472811c24aef3852dc7e189dff5060076a6c0b25bfde928da50dcfe9b5bdc15",
+      "seconds": 2.7750773748848587
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/lift_parent.py",
+        "--package",
+        "/private/tmp/kappa-round6/public-complete/candidate/package",
+        "--owners",
+        "/private/tmp/kappa-round6/public-complete/candidate/owners",
+        "--out",
+        "/private/tmp/kappa-round6/public-complete/candidate/parent-data"
+      ],
+      "exit_code": 0,
+      "log_sha256": "7b6249a123ca39fae7b7a6339dd9e8ae8777b081f4336418f2cc101704b70644",
+      "name": "parent-lift",
+      "script_sha256": "9a1edd7d4ab4a2f2ac8d15b42b7e40f93653d65026bac59e4c1ce80b486bd60e",
+      "seconds": 7.089626208180562
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/new/rebind.py",
+        "/private/tmp/kappa-round6/public-complete/candidate/package",
+        "/private/tmp/kappa-round6/public-complete/native/native-cache/fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8/local",
+        "/private/tmp/kappa-round6/public-complete/native/native-cache/e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f/local",
+        "/private/tmp/kappa-round6/public-complete/candidate/rebound"
+      ],
+      "exit_code": 0,
+      "log_sha256": "a77c588eae97fa3934f1877169deebf4afe11f0b2b16b4c06a8f5300045eab0f",
+      "name": "rebind",
+      "script_sha256": "52f8b4cec2dab69cbe590e1fd0f7a68e1b35de5a540bd22fd2adfce07a92b46b",
+      "seconds": 0.50111841596663
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/layout/packing74/replay.py",
+        "--data",
+        "/private/tmp/kappa-round6/public-complete/candidate/layout/packing74/candidate",
+        "--work",
+        "/private/tmp/kappa-round6/public-complete/candidate/discovery",
+        "--local",
+        "/private/tmp/kappa-round6/public-complete/native/native-cache/fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8/local",
+        "--discover"
+      ],
+      "exit_code": 0,
+      "log_sha256": "f8177f09ed230eadab75a896b1c672869b90ee4e5e6c59933ca0b9e9f2b7f51c",
+      "name": "discovery",
+      "script_sha256": "cda0f3a63c5c92c0ff45f7f3a200567d7931fd421836e72ea3b8534f6ee24dcc",
+      "seconds": 78.86982566700317
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/outer/check_ledger.py"
+      ],
+      "exit_code": 0,
+      "log_sha256": "b410cb4ac139452619f90a2d84e4db63ad11001c1035f0a97470be866c372151",
+      "name": "outer-check_ledger.py",
+      "script_sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98",
+      "seconds": 0.08752237493172288
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/outer/independent_check.py"
+      ],
+      "exit_code": 0,
+      "log_sha256": "7cd050699dcf11a21e4c3e279b08ad6ea5c28ac487119b83d05ff7c7d9bca53b",
+      "name": "outer-independent_check.py",
+      "script_sha256": "a5a0361539ec7cae9eb6c0371f857919335a1720040f22af291aa3e34fc864c7",
+      "seconds": 0.07646658294834197
+    },
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/candidate/package/verify_release.py",
+        "--main",
+        "/private/tmp/kappa-round6",
+        "--work",
+        "/private/tmp/kappa-round6/public-complete/candidate/release",
+        "--native-cache",
+        "/private/tmp/kappa-round6/public-complete/native/native-cache",
+        "--jobs",
+        "1"
+      ],
+      "exit_code": 0,
+      "log_sha256": "0902c1944f678a4a2412c0fee24604298eaa848a3b9baa4fffae66e13043610a",
+      "name": "release",
+      "script_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+      "seconds": 260.6920444581192
+    }
+  ],
+  "status": "PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE"
+}
diff --git a/research/paired-helper-extension/evidence/COMPLETE-VERIFY-STAGES.json b/research/paired-helper-extension/evidence/COMPLETE-VERIFY-STAGES.json
new file mode 100644
index 0000000000..a16d9add62
--- /dev/null
+++ b/research/paired-helper-extension/evidence/COMPLETE-VERIFY-STAGES.json
@@ -0,0 +1,98 @@
+[
+  {
+    "name": "fine-engine-oracle",
+    "exit_code": 0,
+    "seconds": 2.336777999997139,
+    "log_sha256": "ea6df7be568d6461ac54e0d56754797de0f70f2f1ecc335114791445b75795d3"
+  },
+  {
+    "name": "retained-provider-and-parent-admission",
+    "reused_receipt": "e0eefc96567fbb45e19e6de0ca295381dbe0e686c08ddc783639b065c7c791d4",
+    "exit_code": 0,
+    "seconds": 0.29532562498934567
+  },
+  {
+    "name": "rebuild-words-566",
+    "exit_code": 0,
+    "seconds": 2.4734135000035167,
+    "log_sha256": "dcbcbeda80423df29ef008bfac58409378f1fd0a3b9b23fc31ab9f03659dd86f"
+  },
+  {
+    "name": "reconstruct-owners",
+    "exit_code": 0,
+    "seconds": 4.480227916967124,
+    "log_sha256": "df2168b51340a5406c925c2083c3e5307c0c593e7bf514cecca82ed360408541"
+  },
+  {
+    "name": "lift-parent",
+    "exit_code": 0,
+    "seconds": 11.287675583036616,
+    "log_sha256": "7b6249a123ca39fae7b7a6339dd9e8ae8777b081f4336418f2cc101704b70644"
+  },
+  {
+    "name": "rebuild-borrow-words",
+    "exit_code": 0,
+    "seconds": 127.72072108299471,
+    "log_sha256": "13ad91c9af5823ad3ff38c35a70a84a7e020b9700903cdf0213a7bad2cb7e55d"
+  },
+  {
+    "name": "shared-kernel-independent-review",
+    "exit_code": 0,
+    "seconds": 7.396305416943505,
+    "log_sha256": "3dc6eb8940cf8a4b993f80129c98b6c4846ad346ccf773a78af225cff3339cc3"
+  },
+  {
+    "name": "preload-move-independent-review",
+    "exit_code": 0,
+    "seconds": 9.151817250065506,
+    "log_sha256": "c456d3e39c09e960ceebf80251d5e808fa9299991471fd86f4093d9bc4dd3eda"
+  },
+  {
+    "name": "two-sided-helper408-review",
+    "exit_code": 0,
+    "seconds": 3.055341790895909,
+    "log_sha256": "4f4b56af805227534dc690df09e4f751a14903d23d15755b485690cf4773c286"
+  },
+  {
+    "name": "paired-extension-review",
+    "exit_code": 0,
+    "seconds": 19.35407220898196,
+    "log_sha256": "9758347091a8c2b3f5229187dc17cdeb0b1a9add22ca7cfdd0394baecf3702e9"
+  },
+  {
+    "name": "audit-local-566-base",
+    "exit_code": 0,
+    "seconds": 0.5692847080063075,
+    "log_sha256": "e4918a06f51b6962d1114d618096b0c3ee790491168963809927244819d74391"
+  },
+  {
+    "name": "audit-local-566-extra",
+    "exit_code": 0,
+    "seconds": 0.5512716248631477,
+    "log_sha256": "c9440bdf3f3e0eb875714edd0de46c7166468f24cbaba4089c4fe55bee9ab066"
+  },
+  {
+    "name": "rebind-566",
+    "exit_code": 0,
+    "seconds": 0.5521749169565737,
+    "log_sha256": "a77c588eae97fa3934f1877169deebf4afe11f0b2b16b4c06a8f5300045eab0f"
+  },
+  {
+    "name": "lemmag-labels",
+    "exit_code": 0,
+    "seconds": 16.11887999996543,
+    "log_sha256": "91fafdc76824e278546bb51465cf84d60a3513df3f2e8ab9854919c416cd3469"
+  },
+  {
+    "name": "strict-t74",
+    "exit_code": 0,
+    "seconds": 69.6006551249884,
+    "log_sha256": "9653af6384cd5e24da5bde01de79788e8a9d7a0314ab764b0119fc86c4196cf0"
+  },
+  {
+    "name": "geometry-controls",
+    "exit_code": 0,
+    "seconds": 0.35114508401602507,
+    "log_sha256": "0a3ecf05cfa2bebb61fffd2fbb4b244c03d742069e2705d02512699bbf4b01f9"
+  }
+]
\ No newline at end of file
diff --git a/research/paired-helper-extension/evidence/ENVIRONMENT.json b/research/paired-helper-extension/evidence/ENVIRONMENT.json
new file mode 100644
index 0000000000..362242f58e
--- /dev/null
+++ b/research/paired-helper-extension/evidence/ENVIRONMENT.json
@@ -0,0 +1,13 @@
+{
+  "assertions_enabled": true,
+  "dependency_versions": {
+    "gmpy2": null,
+    "mpmath": "1.3.0",
+    "numpy": "2.3.5",
+    "psutil": null,
+    "scipy": "1.18.1",
+    "sympy": "1.14.0"
+  },
+  "executable": "/tmp/kappa-venv/bin/python",
+  "python": "3.12.14"
+}
diff --git a/research/paired-helper-extension/evidence/EXACT-OWNER-MOMENT.json b/research/paired-helper-extension/evidence/EXACT-OWNER-MOMENT.json
new file mode 100644
index 0000000000..5b12471b63
--- /dev/null
+++ b/research/paired-helper-extension/evidence/EXACT-OWNER-MOMENT.json
@@ -0,0 +1,135 @@
+{
+  "allocation_sha256": {
+    "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+    "allocation/FILL.json.gz": "19b551af07274931b443ac42588e15df20ec0140fa69b54f3b62a4df9a54ff8e",
+    "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+    "allocation/PROFILE.json": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+    "allocation/PROVIDERS.json": "1fbbe45a0b70b909bf764fab7d89ec05b10c6c3dec5340a59a69b871d309c6ab",
+    "allocation/SEARCH.json": "6e461e5746313dfefada9a7a07cddd363883adf39c84662cbb72edb3697f92ef",
+    "allocation/baseline/CLAIM.json": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+    "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+    "allocation/baseline/PROFILE.json": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+    "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+    "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+    "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+  },
+  "calls": 666,
+  "controls": {
+    "capacity_overflow": "bin capacity",
+    "changed_paid_profile": "complete claimed profile",
+    "duplicate_helper": "duplicate helper",
+    "missing_role": "complete role count",
+    "same_call_family_collision": "same-call family collision"
+  },
+  "idle": {
+    "1": 16668,
+    "3": 5500,
+    "5": 7635,
+    "6": 167,
+    "7": 45,
+    "24": 1,
+    "32": 207,
+    "48": 26958
+  },
+  "live": 66304,
+  "moment": {
+    "W": 66304,
+    "baseline_claim_sha256": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
+    "baseline_profile_sha256": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+    "controls": [
+      "zero log/exp identities",
+      "overstated endpoint",
+      "added rank32 charge"
+    ],
+    "gain": "595154921781997337/500000000000000000000000",
+    "gain_decimal": "0.000001190309843563994674",
+    "lower": "5379964522493130876891/3125000000000000000000000",
+    "method": "Independent 128-term atanh / degree24 exponential with explicit positive tails and outward 192-bit dyadic rounding",
+    "new_moment_at_full_prior": [
+      "6277080434959167101328354775534002008514998558972773728915/6277101735386680763835789423207666416102355444464034512896",
+      "6277080434959167101328354775534002008514998558972773728917/6277101735386680763835789423207666416102355444464034512896"
+    ],
+    "normalized_profile_delta": {
+      "1": 356715520,
+      "2": -66304,
+      "3": 745787392,
+      "4": -794852352,
+      "5": -49661696,
+      "6": 3116288,
+      "7": 2917376,
+      "23": -66304,
+      "24": 66304,
+      "32": 12796672,
+      "48": 8022784
+    },
+    "oldW": 66304,
+    "outer_endpoint": "344317729439560376121/200000000000000000000000",
+    "previous": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "profile_sha256": "07ee0cfe8d88073de9b75cd3262a98f4ac428b1bdd3922b5a077dbf3436be00c",
+    "scope": "Complete paid histogram and exact moment only; full native/physical/outer release is separate.",
+    "status": "PASS_SEPARATE_EXACT_RATIONAL_FRONTIER_MOMENT",
+    "target": "17215886471978018806049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "target_decimal": "0.0017215886471978018806049999999999999999999998999999999999999999999999",
+    "upper": "172158864719780188060513/100000000000000000000000000"
+  },
+  "physical": 66804,
+  "physical_source": "Actual 82-register private cleanup namespace, 408 live helpers, eight centres and two guards; global stock checked separately.",
+  "profile": {
+    "1": 1625724,
+    "2": 426240,
+    "3": 191980,
+    "4": 73260,
+    "5": 24951,
+    "6": 167,
+    "7": 45,
+    "8": 5328,
+    "24": 1,
+    "32": 207,
+    "48": 26958
+  },
+  "providers": {
+    "base": {
+      "local_profile": {
+        "1": 2416,
+        "2": 640,
+        "3": 280,
+        "4": 110,
+        "5": 26,
+        "8": 8
+      },
+      "private_buffers": 82,
+      "sha256": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+      "width_inventory": {
+        "4": 26,
+        "5": 2,
+        "7": 62,
+        "8": 96,
+        "9": 222
+      }
+    },
+    "extra": {
+      "local_profile": {
+        "1": 2416,
+        "2": 640,
+        "3": 280,
+        "4": 110,
+        "5": 26,
+        "8": 8
+      },
+      "private_buffers": 82,
+      "sha256": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+      "width_inventory": {
+        "4": 26,
+        "5": 2,
+        "7": 62,
+        "8": 96,
+        "9": 222
+      }
+    }
+  },
+  "rank_mass": 4816512,
+  "replicas": 74,
+  "roles": 271728,
+  "scope": "Recounted local frames, exact whole-owner geometry and directed moment; algebra/native/global/outer admission remains separately required.",
+  "status": "PASS_PAIRED_EXTENSION_LITERAL_OWNERS_AND_EXACT_MOMENT"
+}
diff --git a/research/paired-helper-extension/evidence/FRESHNESS.json b/research/paired-helper-extension/evidence/FRESHNESS.json
new file mode 100644
index 0000000000..c4dd0053bc
--- /dev/null
+++ b/research/paired-helper-extension/evidence/FRESHNESS.json
@@ -0,0 +1,214 @@
+{
+  "adjacent_active_claim": {
+    "author": "Ross Richardson with OpenAI Codex assistance",
+    "expiry": "2026-10-16T12:36:00Z",
+    "explicit_distinction": "No helper424 or owner-search claim; expressly complementary to our second/subsequent extractions.",
+    "result_status": "Claim only; no new kappa or positive nominee stated.",
+    "scope": "Helper408 rank-seven endpoint on exact PR2894 parent with fixed middle/72 prior cold helpers; arbitrary dyadic boundary mixing and exact pairing screen.",
+    "updated_at": "2026-10-16T10:37:24Z",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2612#discussioncomment-18970763"
+  },
+  "caveat": "This is a timestamped scoped search, not a novelty guarantee: latest100 PRs include every newly created PR through2914, but older changed PR bodies outside this list, arbitrary source diffs, unpublished work and updates after snapshot time are not covered. Four selected discussions have complete comments/replies; unchanged historical records were not all reread.",
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+        "updated_at": "2026-10-16T10:27:51Z",
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diff --git a/research/paired-helper-extension/evidence/FULL-NATIVE-RECEIPT.json b/research/paired-helper-extension/evidence/FULL-NATIVE-RECEIPT.json
new file mode 100644
index 0000000000..234436cc59
--- /dev/null
+++ b/research/paired-helper-extension/evidence/FULL-NATIVE-RECEIPT.json
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+  "reused_retained_parent": true,
+  "source_commit": "paired-helper-extension-pr2908",
+  "status": "PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE"
+}
diff --git a/research/paired-helper-extension/evidence/FULL-NATIVE-RESULT.json b/research/paired-helper-extension/evidence/FULL-NATIVE-RESULT.json
new file mode 100644
index 0000000000..fdd8582463
--- /dev/null
+++ b/research/paired-helper-extension/evidence/FULL-NATIVE-RESULT.json
@@ -0,0 +1,41 @@
+{
+  "environment_sha256": "c6d3ce212bd2cd82d580158a39f6d7048c109daa1a695aa0d1eee280eb620213",
+  "native_receipt_sha256": "5c1ea6f03e48673d9b56563494fff2258ee18bc8dacdeb72ba5c07e2044008ca",
+  "preparer_sha256": "c5ad3e3d086aae7c9000b7d8c769cbc22a943c738d5808cee52fe71e571a595d",
+  "scope": "Fresh changed base/extra native chains; two unchanged retained native chains and16-stage parent admission explicitly reused by exact full-tree receipts. No owner/controller/outer admission yet.",
+  "seconds": 74.23986270884052,
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "stages": [
+    {
+      "command": [
+        "/tmp/kappa-venv/bin/python",
+        "-B",
+        "/private/tmp/kappa-round6/public-complete/source/new/fastnative/run_native.py",
+        "/private/tmp/kappa-round6/public-complete/source/new/borrow/words/BORROW-WORD-43base.json.gz",
+        "/private/tmp/kappa-round6/public-complete/native/fresh-base"
+      ],
+      "exit_code": 0,
+      "log_sha256": "adfd551ad781bf2dd128a9f4b6bad56bad153c6a591b74e041a0f5558256462c",
+      "name": "fresh-current-base",
+      "result_sha256": "4b311068779994a5a2d6b558b6c953e9a35aa420252ba004a29f439061267e2f",
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+      "seconds": 42.079378166934475
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+        "/private/tmp/kappa-round6/public-complete/source/new/fastnative/run_native.py",
+        "/private/tmp/kappa-round6/public-complete/source/new/borrow/words/BORROW-WORD-43extra.json.gz",
+        "/private/tmp/kappa-round6/public-complete/native/fresh-extra"
+      ],
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+      "log_sha256": "04fae1af9438af02b8b8445321f0101f9b2d0004f9dd9504f85616ac65360128",
+      "name": "fresh-current-extra",
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+      "seconds": 31.98877645796165
+    }
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+  "status": "PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE"
+}
diff --git a/research/paired-helper-extension/evidence/FULL-REPLAY-RESULT.json b/research/paired-helper-extension/evidence/FULL-REPLAY-RESULT.json
new file mode 100644
index 0000000000..e65431524c
--- /dev/null
+++ b/research/paired-helper-extension/evidence/FULL-REPLAY-RESULT.json
@@ -0,0 +1,66 @@
+{
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+  "scope": "Conditional finite supplier/outer result; inherited all-size theorem obligations remain.",
+  "source_manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "stages": [
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+}
diff --git a/research/paired-helper-extension/evidence/FULL-REPLAY-STAGES.json b/research/paired-helper-extension/evidence/FULL-REPLAY-STAGES.json
new file mode 100644
index 0000000000..8d91cb9723
--- /dev/null
+++ b/research/paired-helper-extension/evidence/FULL-REPLAY-STAGES.json
@@ -0,0 +1,56 @@
+[
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+    "stage": "parent-paired-stage"
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diff --git a/research/paired-helper-extension/evidence/LOCAL-RESULT.json b/research/paired-helper-extension/evidence/LOCAL-RESULT.json
new file mode 100644
index 0000000000..123da3c6a7
--- /dev/null
+++ b/research/paired-helper-extension/evidence/LOCAL-RESULT.json
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+          "identities": [
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+            "u S = e_h^T",
+            "M v = y",
+            "alpha M = u",
+            "alpha y = 1",
+            "T y = e_h",
+            "e_h^T T = alpha"
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+          "scope": "Exact free-operator identities before target writes; full target correctness checked separately.",
+          "status": "PASS_EXACT_TWO_SIDED_SUBSPACE_CERTIFICATE",
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+            "M v = y",
+            "alpha M = u",
+            "alpha y = 1",
+            "T y = e_h",
+            "e_h^T T = alpha"
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+          "scope": "Exact free-operator identities before target writes; full target correctness checked separately.",
+          "status": "PASS_EXACT_TWO_SIDED_SUBSPACE_CERTIFICATE",
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+            "M v = y",
+            "alpha M = u",
+            "alpha y = 1",
+            "T y = e_h",
+            "e_h^T T = alpha"
+          ],
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+        {
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+            "M v = y",
+            "alpha M = u",
+            "alpha y = 1",
+            "T y = e_h",
+            "e_h^T T = alpha"
+          ],
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+            "alpha M = u",
+            "alpha y = 1",
+            "T y = e_h",
+            "e_h^T T = alpha"
+          ],
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+    }
+  },
+  "scope": "Exact finite local identity and invoice; full native/owner/outer checks separate.",
+  "semantic_controls": {
+    "base-299-omit-final-output": "restored cold input still read by 299",
+    "base-299-wrong-final-sign": "restored cold input still read by 299",
+    "base-304-omit-final-output": "restored cold row is not its own input 304",
+    "base-304-wrong-final-sign": "restored cold row is not its own input 304",
+    "base-320-omit-final-output": "restored cold row is not its own input 320",
+    "base-320-wrong-final-sign": "restored cold row is not its own input 320",
+    "base-331-omit-final-output": "restored cold input still read by 331",
+    "base-331-wrong-final-sign": "restored cold input still read by 331",
+    "base-412-omit-final-output": "restored cold input still read by 412",
+    "base-412-wrong-final-sign": "restored cold input still read by 412",
+    "base-424-omit-final-output": "restored cold input still read by 424",
+    "base-424-wrong-final-sign": "restored cold input still read by 424",
+    "base-428-omit-final-output": "restored cold input still read by 428",
+    "base-428-wrong-final-sign": "restored cold input still read by 428",
+    "base-499-omit-final-output": "restored cold input still read by 499",
+    "base-499-wrong-final-sign": "restored cold input still read by 499",
+    "base-511-omit-final-output": "restored cold input still read by 511",
+    "base-511-wrong-final-sign": "restored cold input still read by 511",
+    "extra-299-omit-final-output": "restored cold input still read by 299",
+    "extra-299-wrong-final-sign": "restored cold input still read by 299",
+    "extra-304-omit-final-output": "restored cold row is not its own input 304",
+    "extra-304-wrong-final-sign": "restored cold row is not its own input 304",
+    "extra-320-omit-final-output": "restored cold row is not its own input 320",
+    "extra-320-wrong-final-sign": "restored cold row is not its own input 320",
+    "extra-331-omit-final-output": "restored cold input still read by 331",
+    "extra-331-wrong-final-sign": "restored cold input still read by 331",
+    "extra-412-omit-final-output": "restored cold input still read by 412",
+    "extra-412-wrong-final-sign": "restored cold input still read by 412",
+    "extra-424-omit-final-output": "restored cold input still read by 424",
+    "extra-424-wrong-final-sign": "restored cold input still read by 424",
+    "extra-428-omit-final-output": "restored cold input still read by 428",
+    "extra-428-wrong-final-sign": "restored cold input still read by 428",
+    "extra-499-omit-final-output": "restored cold input still read by 499",
+    "extra-499-wrong-final-sign": "restored cold input still read by 499",
+    "extra-511-omit-final-output": "restored cold input still read by 511",
+    "extra-511-wrong-final-sign": "restored cold input still read by 511"
+  },
+  "status": "PASS_NINE_ADDITIONAL_PAIRED_EXTRACTIONS"
+}
diff --git a/research/paired-helper-extension/evidence/PHYSICAL-INVOICE.json b/research/paired-helper-extension/evidence/PHYSICAL-INVOICE.json
new file mode 100644
index 0000000000..d982745448
--- /dev/null
+++ b/research/paired-helper-extension/evidence/PHYSICAL-INVOICE.json
@@ -0,0 +1,11156 @@
+{
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+  "selected_real_component_primitives": 103963488,
+  "selected_coefficient_work_primitive_count": 50870560,
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+  "complete_invocation_sweeps": 666,
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+  "row_prefix_extra": 4096,
+  "blocknorm": {
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+    "physical_families": 66804,
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+    "boundary_depth_bits": 18,
+    "max_active_depth": 18,
+    "stocknorm_bits": 1322,
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+    "physical_stock_bits": 2644,
+    "partial_cover_bits": 1,
+    "stocknorm_condition": "sqrt(|Sp(72,2)| * physical_families) <= 2^stock_l2_bits",
+    "input_l2_bits": 37,
+    "local_actual_prefix_bits": 74,
+    "local_reserve_bits": 128,
+    "actual_prefix_bits": 1456,
+    "required_reserve_bits": 1510,
+    "retained_payload_bits": 2048,
+    "foreign_helper_roles_checked": 259770,
+    "endpoint_replay": {
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+          "helper_to_data_response_zero": true,
+          "centres_first_clear_and_terminal_zero": 8,
+          "zero_buffers_allocated_and_cleared": 82,
+          "coefficient_work_contract": "unchanged audited clear-before-and-after Horner macro"
+        },
+        "backward": {
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+          "helper_to_data_response_zero": true,
+          "centres_first_clear_and_terminal_zero": 8,
+          "zero_buffers_allocated_and_cleared": 82,
+          "coefficient_work_contract": "unchanged audited clear-before-and-after Horner macro"
+        }
+      },
+      "gauge44": {
+        "forward": {
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+          "helper_to_data_response_zero": true,
+          "centres_first_clear_and_terminal_zero": 8,
+          "zero_buffers_allocated_and_cleared": 82,
+          "coefficient_work_contract": "unchanged audited clear-before-and-after Horner macro"
+        },
+        "backward": {
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+          "helper_to_data_response_zero": true,
+          "centres_first_clear_and_terminal_zero": 8,
+          "zero_buffers_allocated_and_cleared": 82,
+          "coefficient_work_contract": "unchanged audited clear-before-and-after Horner macro"
+        }
+      }
+    },
+    "scope": "Completed native frame/phase/physical-primitive audits remain mandatory. Finite charts plus exact free-warp rows instantiate the separate universal block-energy bound; no child deletion is asserted."
+  },
+  "helpers": 408,
+  "centres": 8,
+  "private_zero_buffers": 82,
+  "live": 66304,
+  "physical": 66804,
+  "physical_stock_identity": {
+    "data_and_owner_families": 66304,
+    "local_helpers": 408,
+    "private_centres": 8,
+    "private_zero_buffers": 82,
+    "coefficient_work": 2
+  },
+  "local_adapters": 351920,
+  "local_primitive_bound": 9126811681248,
+  "wrapper_elementary_factors_charged": 35676288,
+  "factors_per_wrapper": 144,
+  "compiler": 25934336,
+  "unhosted_pervertex": 13824504561092432,
+  "hosted_rebased_pervertex": 13824504558097762,
+  "conservative_pervertex_used": 16702451550817000,
+  "retained_prior_overcharge": {
+    "sha256": "ce1bfa49be88ae67a404f606a11db2232b7e1f2610d4418058e39749d86d8478",
+    "previous_pervertex_allowance": 2877946989724568,
+    "added_complete_new_pervertex": 13824504561092432,
+    "policy": "Retain old allowance and add entire fresh mixed recount."
+  },
+  "finite": {
+    "physical_stock_bits": 2644,
+    "router_bits": 7993,
+    "literal_bits": 35288,
+    "physical_row_coefficient": 19545,
+    "retained_row_coefficient": 20161,
+    "required_C0_bits": 200012,
+    "halving_integer_inequality": [
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+      4608
+    ],
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000
+  },
+  "strict_checks": {
+    "local_primitive_bound": true,
+    "logical": true,
+    "router": true,
+    "literal": true,
+    "mass": true,
+    "precision": true,
+    "tape": true,
+    "row": true,
+    "halving": true
+  },
+  "scope": "Actual call-specific mixed scalar, Horner, wrappers and paid children recounted. The fixed provider uses fresh hash-bound independent all-column/frame/phase/normalization admission. Shared compiler uses conservative maxima; parent is geometry/overcharge only. All-size compiler, hosting, precision/tape and analytic transfer remain conditional."
+}
diff --git a/research/paired-helper-extension/evidence/RELEASE-RECEIPT.json b/research/paired-helper-extension/evidence/RELEASE-RECEIPT.json
new file mode 100644
index 0000000000..ca705bdc3b
--- /dev/null
+++ b/research/paired-helper-extension/evidence/RELEASE-RECEIPT.json
@@ -0,0 +1,7 @@
+{
+  "status": "PASS_RELEASE",
+  "kappa_decimal": "0.0017215886471978018806049999999999999999999998999999999999999999999999",
+  "manifest_sha256": "bf852fb4ecfa28dddfb8cc6fe7bf53019b3932114e01cba3e026b63ef2b1babd",
+  "proof": "Supplier: the package's own unchanged `verify.py` (retained PR1297 provider and parent admission, owner reconstruction, parent lift, strict T74 admission, geometry controls): `PASS_T74_EXACT_FILL_COMPLETE_FINITE_ADMISSION`, native reuse {'base': 'e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e', 'extra': '7b0e9fbda32749aabc7e156d9fe09bceb0624a178628fe69e5dfea783462f905'}; its complex endpoint 344317729439560376121/20000000... brackets the ledger's b = 172158864719780188060499999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000. Outer (PR1673 capped phase-cell fusion): regenerated exact ledger (63 strict inequalities: the 62 retained rows plus the explicit main-binding row gaussian_above_main, the fixed-grid maximum kappa = C - 1/F - B asserted, 17 rejecting controls incl. the old g-factor union row, the old linear and old-theta chirp guards, the old 2*beta tag test, epsilon at 1 or at the r0 slack and beta outside its window, larger endpoint rejected by the native moment), independent balance derivation, the exact union-schedule simulation, the (retained, not used for kappa) structured-boundary displacement-rank check, the gauge-free identity/symbol/circuit checks, PR1786's finite prime/underflow controls and 19 exact evidence replays all pass. Conditional kappa 0.0017215886471978018806049999999999999999999998999999999999999999999999 (union schedule outer/UNION-SCHEDULE.md; explicit Strassen boundary tau=45/16 (the structured boundary of outer/STRUCTURED-BOUNDARY.md is not used); gauge-free interiors outer/GAUGEFREE-INTERIORS.md; fine source-prime padding PR1786 at the free point epsilon=1-(1025/1024)e-104, outer/FINE-PADDING-COMPOSITION.md; fixed-grid maximum of PR2180/PR2161 (dataisfire), outer/PROOF-GRID-MAX.md; exact-integer coarse exponential PR2168/PR2184 (dataisfire) at the one 24-digit rejection call).",
+  "seconds": 260.58
+}
diff --git a/research/paired-helper-extension/evidence/RETAINED-ORIGIN.json b/research/paired-helper-extension/evidence/RETAINED-ORIGIN.json
new file mode 100644
index 0000000000..dc780aa8af
--- /dev/null
+++ b/research/paired-helper-extension/evidence/RETAINED-ORIGIN.json
@@ -0,0 +1,47 @@
+{
+  "origin_result": {
+    "candidate_result_sha256": "dcf2c2b0d6f9ec45869c3b9d4cc26e66142c39a77bd1c6679588f71e95a4762d",
+    "explicit_retained_reuse": false,
+    "fresh_changed_native_chains": 2,
+    "fresh_retained_bootstrap": true,
+    "kappa": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "native_receipt_sha256": "4c5b407e453a73440653432a471519193070fdaf377f59f8bd6e9e7a360f702c",
+    "scope": "Conditional finite and outer release; inherited all-size hypotheses remain.",
+    "stages": [
+      {
+        "exit_code": 0,
+        "log_sha256": "532054d2dd663878c341ce127001241b69d2eb733c2aaac2a948e0bd85adbc6d",
+        "seconds": 287.18860804196447,
+        "stage": "fresh-retained-bootstrap"
+      },
+      {
+        "exit_code": 0,
+        "log_sha256": "f2bbb6462b3f5bb8a6415bb33c0c35355353b13343ddb90961660f7473caa5a2",
+        "seconds": 0.6785032500047237,
+        "stage": "derive-source"
+      },
+      {
+        "exit_code": 0,
+        "log_sha256": "2eb7601c48840a39c58eb838886aed00a531349b259f0bbc3ea6421376b8ea3c",
+        "seconds": 0.6450308749917895,
+        "stage": "derive-preload-move"
+      },
+      {
+        "exit_code": 0,
+        "log_sha256": "d7581123b0f3330f2598e7758ccbca466018d2599124fc6ceb1b678a9ee27dec",
+        "seconds": 51.75157804181799,
+        "stage": "fresh-shared-native"
+      },
+      {
+        "exit_code": 0,
+        "log_sha256": "cd9ba235f73033cf079c9cfb832a3b4a534a6c775f966f5becd1e3f1b4911d98",
+        "seconds": 391.53515666583553,
+        "stage": "complete-admission"
+      }
+    ],
+    "status": "PASS_T74_PRELOAD_MOVE_PORTABLE_COMPLETE_REPLAY"
+  },
+  "retained_receipt_sha256": "02a4d46fe4e1e368d2d22794a2c769ee28470d6797651848d261ca42b90f23d9",
+  "scope": "Earlier fresh PR2894 replay prepared the unchanged retained source/cache. The current public replay authenticates all complete cache files and16 retained parent stages; both changed82-buffer native chains are fresh.",
+  "status": "EXPLICIT_REUSE_OF_PREVIOUS_FRESH_RETAINED_BOOTSTRAP"
+}
diff --git a/research/paired-helper-extension/evidence/SEARCH.json b/research/paired-helper-extension/evidence/SEARCH.json
new file mode 100644
index 0000000000..39651b3f4d
--- /dev/null
+++ b/research/paired-helper-extension/evidence/SEARCH.json
@@ -0,0 +1,194 @@
+{
+  "after_first_three_literal_frame_screen": {
+    "binary_hyperplanes_considered": 511,
+    "discovery_receipt_sha256": "425e2fbd9ae65c109604253366f86397e04e4cd9150292090a625b767e973a97",
+    "distinct_eligible_register_sets": 120,
+    "input_recipe": {
+      "parent": "data/PARENT-base.json.gz",
+      "prior_helpers": [
+        424,
+        428,
+        412
+      ]
+    },
+    "input_sha256": "773fbdaef29e13159a6b6ae5874598706c961b116c144a2ea9b404037c88c1f9",
+    "normals_with_nonzero_pairing": [
+      486,
+      504
+    ],
+    "paired_basis_nominees": 5,
+    "scope": "Fixed current terminal frames only; not an obstruction after changing legal gate frames."
+  },
+  "composition": {
+    "explicit_inherited_frame_edits": 13,
+    "final_profile": {
+      "1": 2416,
+      "2": 640,
+      "3": 280,
+      "4": 110,
+      "5": 26,
+      "8": 8
+    },
+    "final_width_inventory": {
+      "4": 26,
+      "5": 2,
+      "7": 62,
+      "8": 96,
+      "9": 222
+    },
+    "freshly_recomputed_each_step": true,
+    "local_profile_delta_from_pr2908": {
+      "1": 9,
+      "3": 18,
+      "4": -18
+    },
+    "ordered_helpers": [
+      424,
+      428,
+      412,
+      331,
+      299,
+      320,
+      511,
+      304,
+      499
+    ],
+    "private_buffers": 82,
+    "search_stopped": "No new directions searched after the nine-step word was frozen.",
+    "verification": "Public producer applies exact-preimage frame edits and literal input/output gates. verify.py rederives seven paired identities, both full632-input forward/dual maps and36 semantic rejection controls. check_allocation.py independently recounts actual frames, literal owners and directed moment. Full native/physical/outer admission is separate."
+  },
+  "existing_frame_extraction_phases": [
+    {
+      "binary_hyperplanes_considered": 511,
+      "discovery_receipt_sha256": "02b46b9ca1df7b104ac93daf222f31cd818224b1087a3b1f5dbdbfcdfaed332f",
+      "distinct_eligible_register_sets": 120,
+      "input_recipe": {
+        "parent": "data/PARENT-base.json.gz",
+        "prior_helpers": []
+      },
+      "input_sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+      "paired_basis_nominees": 10,
+      "selected_delta": {
+        "1": 3,
+        "2": -2
+      },
+      "selected_helper": 424,
+      "selected_transform": "data/TRANSFORM-424.json"
+    },
+    {
+      "binary_hyperplanes_considered": 511,
+      "discovery_receipt_sha256": "251cf3c1fd9b3e9ddc44396b0ed1006d3c2f970b99a91bacb7d6538742d474ef",
+      "distinct_eligible_register_sets": 120,
+      "input_recipe": {
+        "parent": "data/PARENT-base.json.gz",
+        "prior_helpers": [
+          424
+        ]
+      },
+      "input_sha256": "6c8ed5e984e3c552e8e034f2e984cef51a9e57eb198d427bf9e207bd198da61c",
+      "paired_basis_nominees": 7,
+      "selected_delta": {
+        "1": 3,
+        "2": -2
+      },
+      "selected_helper": 428,
+      "selected_transform": "data/TRANSFORM-428.json"
+    },
+    {
+      "binary_hyperplanes_considered": 511,
+      "discovery_receipt_sha256": "1407b559072fb5aa93c94e1204695cacd069117c850083f8d05ed2f3bcc3dcf9",
+      "distinct_eligible_register_sets": 120,
+      "input_recipe": {
+        "parent": "data/PARENT-base.json.gz",
+        "prior_helpers": [
+          424,
+          428
+        ]
+      },
+      "input_sha256": "d756d99e9c14e686a4d3084fa9bf504ff1fd7e5eb9c22b5f4fcf50d1c6112774",
+      "paired_basis_nominees": 6,
+      "selected_delta": {
+        "1": 3,
+        "2": -2
+      },
+      "selected_helper": 412,
+      "selected_transform": "data/TRANSFORM-412.json"
+    }
+  ],
+  "lower_frame_census": {
+    "binary_hyperplanes_considered": 511,
+    "candidate_constructions": 2147,
+    "completed_frame_refits": 2147,
+    "distinct_lower_frame_eligible_register_sets": 144,
+    "input_recipe": {
+      "parent": "data/PARENT-base.json.gz",
+      "prior_helpers": [
+        424,
+        428,
+        412
+      ]
+    },
+    "input_sha256": "773fbdaef29e13159a6b6ae5874598706c961b116c144a2ea9b404037c88c1f9",
+    "negative_shadow_price_constructions": 38,
+    "negative_shadow_price_constructions_by_normal": {
+      "102": 4,
+      "120": 2,
+      "30": 12,
+      "51": 14,
+      "75": 4,
+      "85": 2
+    },
+    "paired_basis_nominees": 170,
+    "pricing_receipt_sha256": "91ab7a9576c471c675e27f99ecc2d51eacbc9b6b0b0b62484e62b5c27e34221b",
+    "scope": "Each enumerated basis nominee was synthesized at the tested eligible helper pivots and globally refitted. Shadow prices only ranked exact local profiles; they did not establish actual packing, a rigorous global improvement or completeness over all linear combinations.",
+    "selected_normals": [
+      30,
+      51,
+      75,
+      85,
+      102,
+      120
+    ],
+    "selected_order": [
+      331,
+      299,
+      320,
+      511,
+      304,
+      499
+    ],
+    "selected_per_step_delta": {
+      "2": 1,
+      "3": 3,
+      "4": -3
+    },
+    "subspace_receipt_sha256": "c9600908e612bbde2e86bd2665671d1e2b4e81e078a3dcf0bf096aed8d6b586d"
+  },
+  "predecessor": {
+    "head": "51309592971e3b5be935599eed2a95404dc7781e",
+    "pr": 2908
+  },
+  "public_input_sha256": {
+    "data/PARENT-base.json.gz": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+    "data/PARENT-extra.json.gz": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+    "data/TRANSFORM-299.json": "781585f68449c30f63e40ee4bf58d1fa194e4faf8cf4394505437fc15137ba34",
+    "data/TRANSFORM-304.json": "024515c6e47d952dfaf307fcefda9f2106049ccc28875ae620d95241fdec72ed",
+    "data/TRANSFORM-320.json": "0e4c0216221ab21c4bf48a11eab34ff6cc245014d664dc1523cfae9d437dc00d",
+    "data/TRANSFORM-331.json": "355bcfd60ffcb672f66882e66bae1b046d1bfb979f725b411b034f811dfb68bb",
+    "data/TRANSFORM-412.json": "54328a8436d7abed6433da5e4384a36ad95b266070479b496e0e96416a5f5a79",
+    "data/TRANSFORM-424.json": "42747fa1332af1ca0827edebfff7490ee761f84f662527f593e975a502400dbc",
+    "data/TRANSFORM-428.json": "89e8fbd5a5d1d64d386cdc38f257cae18d8e7428e868f618ed1f0be5a22aba3e",
+    "data/TRANSFORM-499.json": "f86eef40cd96b45c67755903eae6a86432e2aeb6d53812621222db7c062d88f6",
+    "data/TRANSFORM-511.json": "48e0749f1c82594841c88923a38b0308ed777639631a4c3f2414500617f2e34b",
+    "data/WORD-base.json.gz": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8",
+    "data/WORD-extra.json.gz": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f",
+    "producer.py": "c60546ca68a905d237401b2a255ccb60e17285b004211d523b5d8fd57b758f5a",
+    "structure.py": "83f63b6d9a1a543ecfa2c98d479dbe4e7a1c3caf6fd1c3566123308efbc32e96",
+    "vendor/audit_local.py": "a38940094f7d19cd6376aafdd4734fa68eabc9aff4c98c3c4a3e9540328b1c90",
+    "vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044"
+  },
+  "reproducibility": "The accepted construction is fully reproduced from the shipped parent words and nine TRANSFORM files. The discovery receipt hashes identify the recorded exploration; those scratch receipts and search programs are not execution dependencies of any public verifier.",
+  "schema_version": 1,
+  "scope": "Discovery record only. The finite census is not an optimality theorem over all paired vectors, gates, frame choices, circuits or owner allocations. Public verification replays the explicit witness and does not run the discovery solver.",
+  "status": "COMPLETED_BOUNDED_DISCOVERY_FROZEN_NINE_STEP_WITNESS"
+}
diff --git a/research/paired-helper-extension/evidence/SOURCE-DERIVATION.json b/research/paired-helper-extension/evidence/SOURCE-DERIVATION.json
new file mode 100644
index 0000000000..174ba00ca0
--- /dev/null
+++ b/research/paired-helper-extension/evidence/SOURCE-DERIVATION.json
@@ -0,0 +1,127 @@
+{
+  "builder_sha256": "24de3c08bf6fa8844ed17a426b24ae108d8d55d76ea5d1509bdef042731ea8b5",
+  "changes": {
+    "new/BORROW-PROVIDERS.json": {
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+      "before": "578535f15325d82aa95bbb2b1770a22734c92c9c160cbe2967451df878c47cab"
+    },
+    "new/borrow/inputs/CHANNEL408-WORD-base.json.gz": {
+      "after": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+      "before": null
+    },
+    "new/borrow/inputs/CHANNEL408-WORD-extra.json.gz": {
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+      "before": null
+    },
+    "new/borrow/paired-extension/PINS.json": {
+      "after": "3d49ca62f3242444db52a21b9de10f18293757842f64a2b3189ad8f4e61fad36",
+      "before": null
+    },
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+      "after": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
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+    },
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+    },
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+    },
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+    },
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+    },
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+    },
+    "new/borrow/paired-extension/data/TRANSFORM-511.json": {
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+    },
+    "new/borrow/paired-extension/data/WORD-base.json.gz": {
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+    },
+    "new/borrow/paired-extension/data/WORD-extra.json.gz": {
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+      "before": null
+    },
+    "new/borrow/paired-extension/producer.py": {
+      "after": "c60546ca68a905d237401b2a255ccb60e17285b004211d523b5d8fd57b758f5a",
+      "before": null
+    },
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+    },
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+      "before": null
+    },
+    "new/borrow/paired-extension/vendor/preload_move.py": {
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+      "before": null
+    },
+    "new/borrow/paired-extension/verify.py": {
+      "after": "5fb7984329ce7213294c8f76a3151f06759005456940968b4cc84712933321ee",
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+    },
+    "new/borrow/paired_extension.py": {
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+      "before": null
+    },
+    "new/borrow/words/BORROW-WORD-43base.json.gz": {
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+    },
+    "new/borrow/words/BORROW-WORD-43extra.json.gz": {
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+      "before": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487"
+    },
+    "new/rebuild_borrow.py": {
+      "after": "c20933a7e507a3cef57310363c59d64e84a16e34cb6a30cb434e4cb6a67c1cd0",
+      "before": "9325dbe919c7035d728273de937445022485956ca6593ad6f617611d63b130d6"
+    },
+    "verify.py": {
+      "after": "b0d5f4217b4699c37609dc7c3633d570acbccd205840777d38f891846b4b918c",
+      "before": "63140c78372e088b3f34bc22549b169fd56bed8c66af9871281297bb8455b395"
+    }
+  },
+  "manifest_sha256": "98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1",
+  "parent_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "source_file_count": 632,
+  "status": "PASS_SOURCE_BOUND_PAIRED_EXTENSION_OVERLAY",
+  "words": {
+    "base": {
+      "parent_sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+      "word_sha256": "fec3c120db1a35022944628d34b56a36f2456248c274c2eaba1a325cdc690ce8"
+    },
+    "extra": {
+      "parent_sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+      "word_sha256": "e4d0c617df85bf8a824ff68310ca3373dc017c1ebf9ea733056a3ee4a784b36f"
+    }
+  }
+}
diff --git a/research/paired-helper-extension/producer.py b/research/paired-helper-extension/producer.py
new file mode 100644
index 0000000000..d01b1a93c3
--- /dev/null
+++ b/research/paired-helper-extension/producer.py
@@ -0,0 +1,91 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Compose nine declared paired extractions on Jeremy Diviney's PR2908 word.
+
+Mason Hale, with substantial OpenAI Codex assistance. The paired construction
+and compensation rule are credited to Diviney/2908; frame accounting and
+inverse cleanup are Jeremy Kothe's credited PR2894 code. This module is pure.
+"""
+import collections
+import copy
+from fractions import Fraction as Q
+import preload_move as pm
+
+HELPERS = (424, 428, 412, 331, 299, 320, 511, 304, 499)
+PROFILE = {'1': 2416, '2': 640, '3': 280, '4': 110, '5': 26, '8': 8}
+INVENTORY = {'4': 26, '5': 2, '7': 62, '8': 96, '9': 222}
+BUFFERS = 82
+ALLOWED = {'A', 'restore', 'helper_final', 'compensation', 'report', 'cleanup'}
+
+
+def refit(word, transform):
+    """Apply only the declared literal old-frame to new-frame substitutions."""
+    x = copy.deepcopy(word)
+    seen = set()
+    for edit in transform.get('frame_changes', []):
+        section, index = edit['section'], edit['parent_index']
+        pm.require(section in ('A', 'restore') and index >= 0 and
+                   (section != 'A' or index >= x['prelude_events']) and
+                   (section, index) not in seen, 'unique declared non-prelude frame edit')
+        seen.add((section, index))
+        gate = x[section][index]
+        pm.require(gate[:-1] == edit['gate'] and gate[-1] == edit['old_frame'],
+                   'exact frame edit preimage')
+        pm.require(gate[0] in ('add', 'scale') and not 112 <= gate[1] < 224 and
+                   list(pm.basis(edit['new_frame'])) == edit['new_frame'], 'canonical nontarget frame')
+        gate[-1] = list(edit['new_frame'])
+    return x
+
+
+def apply_stage(word, transform):
+    h = transform['helper']
+    before, after = transform['before'], transform['after']
+    pm.require(h in HELPERS and str(h) not in word['helper_final'], 'fresh declared helper')
+    pm.require(str(h) not in word['start_extra'], 'zero entrance')
+    protected = set(map(int, word['helper_final'])) | set(map(int, word['start_extra']))
+    protected |= {c['source'] for c in word['initial_corrections']}
+    for g in before:
+        pm.require(g[0] in ('add', 'scale') and g[-1] == [], 'scalar zero-frame input change')
+        roles = g[1:3] if g[0] == 'add' else g[1:2]
+        pm.require(all(224 <= r < 704 and r not in protected and r not in word['removed']
+                       for r in roles), 'unprotected live helpers only')
+    frame = list(pm.basis(after[0][-1]))
+    pm.require(len(frame) == 8 and all(g[0] in ('add', 'scale') and g[-1] == frame
+                                     for g in after), 'common terminal hyperplane')
+    x = refit(word, transform)
+    n = x['prelude_events']
+    x['A'] = x['A'][:n] + copy.deepcopy(before) + x['A'][n:]
+    x['restore'] += copy.deepcopy(after)
+    x['helper_final'][str(h)] = frame
+    C = collections.defaultdict(dict)
+    for g in x['compensation']:
+        C[g[2]][g[1]] = C[g[2]].get(g[1], Q(0)) + Q(g[3], g[4])
+    # Right multiplication C*S uses the reverse order of the literal input gates.
+    for g in reversed(before):
+        if g[0] == 'scale':
+            C[g[1]] = {t: a * Q(g[2], g[3]) for t, a in C[g[1]].items()}
+        else:
+            t, s = g[1:3]
+            for target, a in C[t].items():
+                C[s][target] = C[s].get(target, Q(0)) + Q(g[3], g[4]) * a
+    x['compensation'] = [['add', t, r, a.numerator, a.denominator, []]
+                         for r, col in sorted(C.items()) for t, a in sorted(col.items()) if a]
+    pm.require(not any(g[2] == h for g in x['compensation']), 'new cold column has no compensation')
+    profile, inventory = pm.frame_report(x)
+    x['report']['local_profile'], x['report']['width_inventory'] = profile, inventory
+    z = copy.deepcopy(x)
+    z['A'] = z['A'][n:]
+    x['cleanup'] = pm.derive_cleanup(z, set(map(int, x['helper_final'])))
+    pm.require({k for k in word if word[k] != x[k]} == ALLOWED, 'exact changed sections')
+    return x
+
+
+def apply(word, transforms):
+    pm.require(tuple(t['helper'] for t in transforms) == HELPERS, 'declared composition order')
+    pm.require(len(word['helper_final']) == 73, 'PR2908 cold endpoint count')
+    x = word
+    for transform in transforms:
+        x = apply_stage(x, transform)
+    pm.require(len(x['helper_final']) == BUFFERS, 'all nine added buffers charged')
+    pm.require(x['report']['local_profile'] == PROFILE and
+               x['report']['width_inventory'] == INVENTORY, 'complete local profile and inventory')
+    return x
diff --git a/research/paired-helper-extension/reproduce.py b/research/paired-helper-extension/reproduce.py
new file mode 100644
index 0000000000..dc1eb2d829
--- /dev/null
+++ b/research/paired-helper-extension/reproduce.py
@@ -0,0 +1,145 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Exact Git exports, declared source stages, fresh native chains, full admission.
+
+Mason Hale, with substantial OpenAI Codex assistance. The stage/native/release
+mechanisms retain Jeremy Diviney's PR2908 and its credited upstream lineage.
+No network fetch is performed. Fresh retained bootstrap is the default;
+--retained explicitly reuses a completely authenticated parent/native cache.
+"""
+import argparse
+import hashlib
+import io
+import json
+import os
+import subprocess
+import sys
+import tarfile
+import time
+from fractions import Fraction as Q
+from pathlib import Path, PurePosixPath
+
+P = Path(__file__).resolve().parent
+HEAD = '51309592971e3b5be935599eed2a95404dc7781e'
+PARENT_MANIFEST = '9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f'
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+
+def save(p, value):
+    p.write_text(json.dumps(value, indent=2, sort_keys=True) + '\n')
+
+
+def tree(p):
+    assert not any(f.is_symlink() for f in p.rglob('*'))
+    return {f.relative_to(p).as_posix(): sha(f) for f in p.rglob('*')
+            if f.is_file() and f != p / 'MANIFEST.json'}
+
+
+def export(repo, out):
+    prefix = PurePosixPath('research/two-sided-helper-extraction')
+    raw = subprocess.run(['git', '-C', str(repo), 'archive', '--format=tar',
+                          HEAD, str(prefix)], check=True, capture_output=True).stdout
+    out.mkdir()
+    with tarfile.open(fileobj=io.BytesIO(raw), mode='r:') as archive:
+        for member in archive.getmembers():
+            path = PurePosixPath(member.name)
+            assert not path.is_absolute() and '..' not in path.parts and '\\' not in member.name
+            if member.isdir() and (path == prefix or path in prefix.parents):
+                continue
+            assert path.is_relative_to(prefix) and (member.isfile() or member.isdir())
+            dest = out / path.relative_to(prefix)
+            if member.isdir():
+                dest.mkdir(parents=True, exist_ok=True)
+            else:
+                dest.parent.mkdir(parents=True, exist_ok=True)
+                dest.write_bytes(archive.extractfile(member).read())
+    assert sha(out / 'MANIFEST.json') == PARENT_MANIFEST
+    assert tree(out) == read(out / 'MANIFEST.json')
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    for name in ('repo', 'work'):
+        ap.add_argument('--' + name, type=Path, required=True)
+    ap.add_argument('--retained', type=Path)
+    ap.add_argument('--dry-run', action='store_true')
+    args = ap.parse_args()
+    assert __debug__
+    work, repo = args.work.resolve(), args.repo.resolve()
+    assert not work.exists() and not work.is_relative_to(P) and not P.is_relative_to(work)
+    pins = read(P / 'MANIFEST.json')
+    assert tree(P) == pins, 'complete public package inventory'
+    work.mkdir(parents=True)
+    parent = work / 'pr2908'
+    export(repo, parent)
+    upstream = work / 'parent-export/pr2894'
+    core = upstream / 'vendor/pr2857'
+    source = work / 'pr2833'
+    four, preload, channel, final = [work / n for n in ('source4', 'source-pm', 'source2908', 'source')]
+    native, candidate, adapters = [work / n for n in ('native', 'candidate', 'adapters')]
+    retained = args.retained.resolve() if args.retained else work / 'retained'
+    if args.retained:
+        assert not retained.is_relative_to(work) and not work.is_relative_to(retained)
+    py = [sys.executable, '-B']
+    recipe = [
+        ('export-pr2894', py + [parent / 'reproduce.py', '--repo', repo, '--work', work / 'parent-export', '--dry-run']),
+        ('export-pr2833', py + [upstream / 'tools/materialize_source.py', '--repo', repo, '--out', source]),
+    ]
+    if not args.retained:
+        recipe.append(('fresh-retained-bootstrap', py + [upstream / 'tools/prepare_retained.py', '--source', source, '--out', retained, '--jobs', '1']))
+    recipe += [
+        ('four-kernel-stage', py + [core / 'build_overlay.py', '--source', source, '--generator', core / 'shared_kernel.py', '--review', core / 'review_four_groups.py', '--candidate-dir', core / 'words', '--out', four]),
+        ('preload-stage', py + [upstream / 'vendor/pm/build_pm_overlay.py', '--overlay', four, '--pm-dir', upstream / 'vendor/pm', '--out', preload]),
+        ('parent-paired-stage', py + [parent / 'tools/build_channel_overlay.py', '--source', preload, '--local-package', parent, '--out', channel]),
+        ('paired-extension-stage', py + [P / 'tools/build_extension.py', '--source', channel, '--local-package', P, '--out', final]),
+        ('derive-closed-adapters', py + [P / 'tools/derive_adapters.py', '--parent-package', parent, '--source', final, '--source-manifest', read(P / 'CLAIM.json')['source_manifest_sha256'], '--retained-receipt', retained / 'NATIVE-RECEIPT.json', '--out', adapters]),
+        ('fresh-current-native', py + [adapters / 'prepare_extension_native.py', '--source', final, '--retained-cache', retained / 'native-cache', '--retained-receipt', retained / 'NATIVE-RECEIPT.json', '--out', native, '--jobs', '1']),
+        ('complete-admission', py + [adapters / 'admit_extension.py', '--source', final, '--fill', P / 'allocation/FILL.json.gz', '--order', P / 'allocation/ORDER.json', '--dispatch', P / 'allocation/DISPATCH.json', '--native-cache', native / 'native-cache', '--native-receipt', native / 'NATIVE-RECEIPT.json', '--work', candidate, '--replica-helper-dir', core / 'vendor/pr2839', '--reconstructor', core / 'vendor/pr2839/reconstruct_replica.py', '--blocknorm-checker', adapters / 'extension_blocknorm.py', '--comparison-claim', parent / 'CLAIM.json', '--source-profile', 'paired-extension', '--comparison-profile', 'pr2908', '--jobs', '1']),
+    ]
+    if args.dry_run:
+        save(work / 'PREFLIGHT.json', {'status': 'EXACT_PARENT_EXPORT_AND_RECIPE_ONLY_NOT_A_REPLAY', 'commands': [[n, list(map(str, c))] for n, c in recipe]})
+        print('PASS_PINNED_PR2908_EXPORT_RECIPE_ONLY')
+        return
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONPYCACHEPREFIX=str(work / 'bytecode'),
+               OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1', PYTHONINTMAXSTRDIGITS='0')
+    for name in ('PYTHONOPTIMIZE', 'PYTHONPATH', 'WITNESS_SPEC', 'WITNESS_RECORD', 'WITNESS_DISCOVER'):
+        env.pop(name, None)
+    stages = []
+    for name, command in recipe:
+        log, start = work / (name + '.log'), time.monotonic()
+        with log.open('w') as stream:
+            result = subprocess.run(list(map(str, command)), env=env, cwd=work,
+                                    stdin=subprocess.DEVNULL, stdout=stream, stderr=subprocess.STDOUT)
+        stages.append({'stage': name, 'exit_code': result.returncode,
+                       'seconds': time.monotonic() - start, 'log_sha256': sha(log)})
+        save(work / 'STAGES.json', stages)
+        assert result.returncode == 0, 'failed ' + name + '; see ' + str(log)
+        print('PASS', name, flush=True)
+    admission = read(candidate / 'RESULT.json')
+    receipt = read(candidate / 'release/RELEASE-RECEIPT.json')
+    claim = read(P / 'CLAIM.json')
+    assert admission['status'] == 'PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE'
+    assert receipt['status'] == 'PASS_RELEASE'
+    assert Q(admission['kappa']) == Q(receipt['kappa_decimal']) == Q(claim['kappa'])
+    assert admission['release_receipt_sha256'] == sha(candidate / 'release/RELEASE-RECEIPT.json')
+    assert admission['package_manifest_sha256'] == receipt['manifest_sha256']
+    assert tree(P) == pins and tree(parent) == read(parent / 'MANIFEST.json')
+    save(work / 'RESULT.json', {'status': 'PASS_PAIRED_EXTENSION_COMPLETE_REPLAY', 'kappa': admission['kappa'],
+                              'source_manifest_sha256': sha(final / 'MANIFEST.json'),
+                              'native_receipt_sha256': sha(native / 'NATIVE-RECEIPT.json'),
+                              'admission_result_sha256': sha(candidate / 'RESULT.json'),
+                              'explicit_retained_reuse': bool(args.retained),
+                              'fresh_retained_bootstrap': not bool(args.retained), 'stages': stages,
+                              'scope': 'Conditional finite supplier/outer result; inherited all-size theorem obligations remain.'})
+    print('PASS_PAIRED_EXTENSION_COMPLETE_REPLAY', admission['kappa'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-helper-extension/run_registered.py b/research/paired-helper-extension/run_registered.py
new file mode 100644
index 0000000000..d6e5dccdf4
--- /dev/null
+++ b/research/paired-helper-extension/run_registered.py
@@ -0,0 +1,85 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Exact local/owner/moment replay and binding of recorded complete release.
+
+This bounded command does not rerun the native or integrated outer replay;
+reproduce.py executes that separately from exact Git sources.
+"""
+import hashlib
+import json
+import os
+import subprocess
+import sys
+import tempfile
+from fractions import Fraction as Q
+from pathlib import Path
+
+P = Path(__file__).resolve().parent
+
+
+def read(p):
+    return json.loads(p.read_bytes())
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def tree():
+    assert not any(f.is_symlink() for f in P.rglob('*'))
+    return {f.relative_to(P).as_posix(): sha(f) for f in P.rglob('*')
+            if f.is_file() and f != P / 'MANIFEST.json'}
+
+
+def main():
+    assert __debug__
+    pins = read(P / 'MANIFEST.json')
+    assert tree() == pins
+    with tempfile.TemporaryDirectory(prefix='paired-extension-replay-') as tmp:
+        out = Path(tmp)
+        env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1')
+        for key in ('PYTHONOPTIMIZE', 'PYTHONPATH', 'WITNESS_SPEC', 'WITNESS_RECORD', 'WITNESS_DISCOVER'):
+            env.pop(key, None)
+        for script, name in [('verify.py', 'local'), ('check_allocation.py', 'owners')]:
+            log = out / (name + '.log')
+            with log.open('w') as stream:
+                result = subprocess.run([sys.executable, '-B', str(P / script), '--work', str(out / name)],
+                                        env=env, stdin=subprocess.DEVNULL, stdout=stream, stderr=subprocess.STDOUT)
+            if result.returncode:
+                print(log.read_text()[-8000:])
+                raise SystemExit(result.returncode)
+        local = read(out / 'local/RESULT.json')
+        owner = read(out / 'owners/RESULT.json')
+        claim = read(P / 'CLAIM.json')
+        admit = read(P / 'evidence/ADMISSION-RESULT.json')
+        release = read(P / 'evidence/RELEASE-RECEIPT.json')
+        native = read(P / 'evidence/FULL-NATIVE-RECEIPT.json')
+        assert local['status'] == 'PASS_NINE_ADDITIONAL_PAIRED_EXTRACTIONS'
+        assert len(local['semantic_controls']) == 36
+        assert claim['status'] == 'CONDITIONAL_CANDIDATE_COMPLETE_FINITE_RELEASE'
+        assert owner['status'] == 'PASS_PAIRED_EXTENSION_LITERAL_OWNERS_AND_EXACT_MOMENT'
+        assert admit['status'] == 'PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE'
+        assert release['status'] == 'PASS_RELEASE'
+        assert Q(owner['moment']['target']) == Q(claim['kappa']) == Q(admit['kappa']) == Q(release['kappa_decimal'])
+        assert owner['profile'] == claim['profile'] == admit['profile']
+        assert owner['physical'] == claim['physical_families'] == 66804
+        assert release['manifest_sha256'] == admit['package_manifest_sha256']
+        assert native['status'] == 'PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE'
+        assert native['fresh_current_provider_count'] == 2 and set(native['providers']) == {'base', 'extra'}
+        assert native['reused_retained_native_count'] == 2 and native['reused_retained_parent']
+        assert claim['release_receipt_sha256'] == admit['release_receipt_sha256'] == sha(P / 'evidence/RELEASE-RECEIPT.json')
+        assert claim['native_receipt_sha256'] == admit['native_receipt_sha256'] == sha(P / 'evidence/FULL-NATIVE-RECEIPT.json')
+        assert claim['source_manifest_sha256'] == native['manifest_sha256'] == admit['source_manifest_sha256']
+        assert Q(claim['baseline_kappa']) == Q(admit['comparison_kappa']) == Q(owner['moment']['previous'])
+        for tag in ('base', 'extra'):
+            assert native['providers'][tag]['word_sha256'] == sha(P / f'data/WORD-{tag}.json.gz')
+        assert admit['fill_sha256'] == sha(P / 'allocation/FILL.json.gz')
+        assert admit['order_sha256'] == sha(P / 'allocation/ORDER.json')
+        assert admit['dispatch_sha256'] == sha(P / 'allocation/DISPATCH.json')
+        assert tree() == pins
+        print('PASS_PAIRED_EXTENSION_LOCAL_OWNER_MOMENT_AND_STORED_RELEASE', claim['kappa'])
+        print('Native and full integrated admission are authenticated stored evidence here; reproduce.py reruns them.')
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-helper-extension/structure.py b/research/paired-helper-extension/structure.py
new file mode 100644
index 0000000000..8d5bd544ee
--- /dev/null
+++ b/research/paired-helper-extension/structure.py
@@ -0,0 +1,41 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Exact two-sided subspace certificate, independent of the word producer."""
+from collections import defaultdict
+from fractions import Fraction as Q
+
+def check(parent,transform,aud):
+    h=transform['helper'];live=sorted(set(range(704))-set(parent['removed'])-set(range(112,224)))
+    S={r:{r:Q(1)} for r in live};T={r:{r:Q(1)} for r in live}
+    for g in transform['before']:aud.apply(g,S)
+    for g in transform['after']:aud.apply(g,T)
+    v={r:row[h] for r,row in S.items() if h in row};alpha=T[h]
+    J={r:{r:Q(1)} for r in live}
+    for g in reversed(transform['after']):aud.apply(aud.invert(g),J)
+    y={r:row[h] for r,row in J.items() if h in row}
+    M={r:{(r,()):Q(1)} for r in live};program=list(parent['A'][parent['prelude_events']:]);bypos=defaultdict(list)
+    for op,rec in enumerate(parent['warps'],1):bypos[rec[0]].append(['warp',rec[1],op])
+    for p in range(len(parent['B'])+1):
+        program+=bypos[p]
+        if p<len(parent['B']):program.append(parent['B'][p])
+    program+=parent['restore']
+    for g in program:
+        if g[0]=='warp' or not 112<=g[1]<224:aud.walg_apply(g,M,False,10**6)
+    u=defaultdict(Q)
+    for r,a in alpha.items():
+        for key,c in M[r].items():u[key]+=a*c
+    u={key:c for key,c in u.items() if c}
+    protected=set(map(int,parent['helper_final']))|set(map(int,parent['start_extra']))|{c['source'] for c in parent['initial_corrections']}
+    H={r for r in live if r>=224 and r not in protected}
+    assert set(v)<=H and all(r in H and not ops for r,ops in u)
+    u={r:c for (r,ops),c in u.items()}
+    for r,row in M.items():
+        mv=defaultdict(Q)
+        for (c,ops),a in row.items():mv[ops]+=a*v.get(c,Q(0))
+        assert {ops:a for ops,a in mv.items() if a}==({():y[r]} if r in y else {})
+    assert sum(alpha.get(r,Q(0))*c for r,c in y.items())==1
+    us=defaultdict(Q)
+    for r,a in u.items():
+        for c,b in S[r].items():us[c]+=a*b
+    assert {r:c for r,c in us.items() if c}=={h:Q(1)}
+    assert all(sum(row.get(c,Q(0))*a for c,a in y.items())==(1 if r==h else 0) for r,row in T.items())
+    return {'status':'PASS_EXACT_TWO_SIDED_SUBSPACE_CERTIFICATE','helper':h,'v':{str(r):str(c) for r,c in v.items()},'u':{str(r):str(c) for r,c in u.items()},'alpha':{str(r):str(c) for r,c in alpha.items()},'y':{str(r):str(c) for r,c in y.items()},'identities':['S e_h = v','u S = e_h^T','M v = y','alpha M = u','alpha y = 1','T y = e_h','e_h^T T = alpha'],'scope':'Exact free-operator identities before target writes; full target correctness checked separately.'}
diff --git a/research/paired-helper-extension/tools/audit_allocation_moment.py b/research/paired-helper-extension/tools/audit_allocation_moment.py
new file mode 100644
index 0000000000..dfe0ec29e1
--- /dev/null
+++ b/research/paired-helper-extension/tools/audit_allocation_moment.py
@@ -0,0 +1,81 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent dyadic interval moment auditor, atlas D020.
+Retained PR2908 arithmetic by Jeremy Diviney and its credited upstream authors;
+Mason Hale with OpenAI Codex assistance changes only the authenticated baseline.
+Uses only Python integers/Fraction; imports no inherited numerical implementation.
+This authenticates a paid histogram and its root, not a physical realization.
+"""
+from fractions import Fraction as F
+from pathlib import Path
+from functools import lru_cache
+from collections import Counter
+import argparse,json,hashlib
+
+BITS=192
+SCALE=1<<BITS
+
+def need(c,m):
+    if not c:raise ValueError(m)
+def down(x):return F(x.numerator*SCALE//x.denominator,SCALE)
+def up(x):return F(-((-x.numerator*SCALE)//x.denominator),SCALE)
+@lru_cache(None)
+def log_bounds(q):
+    need(q>=1,'log domain');k=0
+    while q>2:q/=2;k+=1
+    def unit(y):
+        z=(y-1)/(y+1);z2=z*z;term=z;value=F(0)
+        for j in range(128):
+            value+=term/(2*j+1);term*=z2
+        remainder=2*term/(257*(1-z2))
+        return 2*value,2*value+remainder
+    l,u=unit(q);l2,u2=unit(F(2));return down(l+k*l2),up(u+k*u2)
+def exp_bounds(y):
+    need(0<=y<F(1,10),'small exponential domain');term=F(1);value=term
+    for j in range(1,25):term=term*y/j;value+=term
+    first=term*y/25;tail=first/(1-y/26)
+    return down(value),up(value+tail)
+def moment(profile,b,W):
+    need(0<=b<F(1,100),'saving domain');lo=hi=F(0)
+    for rank,count in profile.items():
+        need(0<rank<73 and count>0,'profile domain');l,u=log_bounds(F(73,rank));a=exp_bounds(b*l)[0];z=exp_bounds(b*u)[1];weight=F(rank*count,73*W);lo+=weight*a;hi+=weight*z
+    return down(lo),up(hi)
+def run(candidate,source):
+    import sys
+    if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0)
+    need(hashlib.sha256((source/'CLAIM.json').read_bytes()).hexdigest()=='2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf','exact pinned PR2908 full headline')
+    prof={int(k):v for k,v in json.loads((candidate/'PROFILE.json').read_bytes()).items()}
+    old={int(k):v for k,v in json.loads((source/'PROFILE.json').read_bytes()).items()}
+    W=896*(1+max(r for s,r in json.loads((candidate/'ORDER.json').read_bytes())))
+    oldW=896*(1+max(r for s,r in json.loads((source/'ORDER.json').read_bytes())))
+    need(sum(r*n for r,n in prof.items())==W*73-W*320//896,'new rank mass')
+    need(sum(r*n for r,n in old.items())==oldW*73-oldW*320//896,'old rank mass')
+    # No floating endpoint or inherited numerical implementation is used.
+    q=10**26;lo=0;hi=q//200
+    need(moment(prof,F(lo,q),W)[1]<1 and moment(prof,F(hi,q),W)[0]>1,'global root bracket')
+    while hi-lo>1:
+        mid=(lo+hi)//2;l,u=moment(prof,F(mid,q),W)
+        if u<1:lo=mid
+        elif l>1:hi=mid
+        else:raise ValueError('interval precision insufficient')
+    endpoint=F((lo//100),10**24)
+    target=endpoint-F(1,10**46)-F(1,10**70)
+    prior=F(json.loads((source/'CLAIM.json').read_bytes())['kappa'])
+    need(target>prior and target<F(lo,q),'strict frontier improvement and lower endpoint')
+    normalized_delta=Counter({r:n*oldW for r,n in prof.items()});normalized_delta.subtract({r:n*W for r,n in old.items()})
+    normalized_delta={r:n for r,n in normalized_delta.items()if n}
+    at_old=moment(prof,prior,W);need(at_old[1]<1,'new moment strictly below one at full previous headline')
+    # Positive root uniqueness: all charged ranks are strictly below m = 73,
+    # hence every nonzero summand increases strictly with the saving parameter.
+    need(log_bounds(F(1))==(0,0) and exp_bounds(F(0))==(1,1),'zero controls')
+    need(moment(prof,F(hi,q)+F(1,10**18),W)[0]>1,'overstated endpoint rejected')
+    wrong=dict(prof);wrong[32]=wrong.get(32,0)+1
+    need(moment(wrong,F(lo,q),W)[0]>1,'omitted rank charge rejected')
+    import decimal
+    with decimal.localcontext() as c:
+        c.prec=80
+        todec=lambda x:str(decimal.Decimal(x.numerator)/decimal.Decimal(x.denominator))
+        texttarget=todec(target);textgain=todec(target-prior)
+    return dict(status='PASS_SEPARATE_EXACT_RATIONAL_FRONTIER_MOMENT',lower=str(F(lo,q)),upper=str(F(hi,q)),outer_endpoint=str(endpoint),target=str(target),target_decimal=texttarget,previous=str(prior),gain=str(target-prior),gain_decimal=textgain,W=W,oldW=oldW,normalized_profile_delta=normalized_delta,new_moment_at_full_prior=[str(x)for x in at_old],profile_sha256=hashlib.sha256((candidate/'PROFILE.json').read_bytes()).hexdigest(),baseline_profile_sha256=hashlib.sha256((source/'PROFILE.json').read_bytes()).hexdigest(),baseline_claim_sha256=hashlib.sha256((source/'CLAIM.json').read_bytes()).hexdigest(),method='Independent 128-term atanh / degree24 exponential with explicit positive tails and outward 192-bit dyadic rounding',controls=['zero log/exp identities','overstated endpoint','added rank32 charge'],scope='Complete paid histogram and exact moment only; full native/physical/outer release is separate.')
+if __name__=='__main__':
+    p=argparse.ArgumentParser();p.add_argument('--candidate',type=Path,required=True);p.add_argument('--source',type=Path,required=True);p.add_argument('--out',type=Path,required=True);a=p.parse_args()
+    need(not a.out.exists(),'fresh output required');d=run(a.candidate,a.source);a.out.write_text(json.dumps(d,sort_keys=True,indent=2)+'\n',encoding='utf-8',newline='\n');print(json.dumps({k:d[k]for k in ['status','target_decimal','gain_decimal','lower','upper']}))
diff --git a/research/paired-helper-extension/tools/build_extension.py b/research/paired-helper-extension/tools/build_extension.py
new file mode 100644
index 0000000000..5d4afe8bc1
--- /dev/null
+++ b/research/paired-helper-extension/tools/build_extension.py
@@ -0,0 +1,106 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Append the declared nine-extraction stage to immutable PR2908 source.
+
+Overlay/rebuild conventions are credited to Jeremy Diviney's PR2908 builder.
+"""
+import argparse
+import gzip
+import hashlib
+import json
+import shutil
+from pathlib import Path
+
+PARENT = '56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def read(p):
+    b = p.read_bytes()
+    return json.loads(gzip.decompress(b) if p.suffix == '.gz' else b)
+
+
+def save(p, x):
+    p.write_text(json.dumps(x, indent=2, sort_keys=True) + '\n')
+
+
+def tree(p):
+    assert not any(f.is_symlink() for f in p.rglob('*'))
+    return {f.relative_to(p).as_posix(): sha(f) for f in sorted(p.rglob('*'))
+            if f.is_file() and f != p / 'MANIFEST.json'}
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--source', type=Path, required=True)
+    ap.add_argument('--local-package', type=Path, required=True)
+    ap.add_argument('--out', type=Path, required=True)
+    a = ap.parse_args()
+    src, out, p = a.source.resolve(), a.out.resolve(), a.local_package.resolve()
+    assert __debug__ and not out.exists() and not out.is_relative_to(src)
+    assert sha(src / 'MANIFEST.json') == PARENT and tree(src) == read(src / 'MANIFEST.json')
+    pins = read(p / 'PINS.json')
+    assert all(sha(p / n) == h for n, h in pins.items())
+    shutil.copytree(src, out)
+    local = out / 'new/borrow/paired-extension'
+    local.mkdir()
+    copied = ['PINS.json', 'verify.py', 'producer.py', 'structure.py', *pins]
+    for n in copied:
+        dest = local / n
+        dest.parent.mkdir(parents=True, exist_ok=True)
+        shutil.copy2(p / n, dest)
+    shutil.copy2(p / 'producer.py', out / 'new/borrow/paired_extension.py')
+    providers = read(src / 'new/BORROW-PROVIDERS.json')
+    records = {}
+    for tag, pid in [('base', 'gauge44'), ('extra', 'extra')]:
+        q = out / f'new/borrow/words/BORROW-WORD-43{tag}.json.gz'
+        assert q.read_bytes() == (p / f'data/PARENT-{tag}.json.gz').read_bytes()
+        shutil.copy2(q, out / f'new/borrow/inputs/CHANNEL408-WORD-{tag}.json.gz')
+        shutil.copy2(p / f'data/WORD-{tag}.json.gz', q)
+        word = read(q)
+        helpers = sorted(set(range(224, 704)) - set(word['removed']))
+        providers[pid] = {'widths': [len(word['helper_final'].get(str(h), [0] * 9)) -
+                                    len(word['start_extra'].get(str(h), [])) for h in helpers],
+                          'actual_paid_profile': word['report']['local_profile']}
+        records[tag] = {'parent_sha256': sha(p / f'data/PARENT-{tag}.json.gz'), 'word_sha256': sha(q)}
+    save(out / 'new/BORROW-PROVIDERS.json', providers)
+    path = out / 'new/rebuild_borrow.py'
+    text = path.read_text()
+    anchor = '    final=json.loads(gzip.decompress(shipped.read_bytes()))'
+    assert text.count(anchor) == 1
+    block = """    # Nine additional paired directions; all82 cold buffers are charged.
+    import paired_extension
+    extension_parent=json.loads(gzip.decompress((D/'inputs'/f'CHANNEL408-WORD-{wt}.json.gz').read_bytes()))
+    assert chain[-1]==extension_parent
+    extension_transforms=[json.loads((D/'paired-extension/data'/f'TRANSFORM-{h}.json').read_text()) for h in paired_extension.HELPERS]
+    extension_word=paired_extension.apply(chain[-1],extension_transforms)
+    assert set(k_ for k_ in chain[-1] if chain[-1][k_]!=extension_word[k_])==paired_extension.ALLOWED
+    chain.append(extension_word);steps.append('nine-additional-paired-extractions')
+"""
+    path.write_text(text.replace(anchor, block + anchor))
+    path = out / 'verify.py'
+    text = path.read_text()
+    line = next(s for s in text.splitlines() if s.startswith("run('two-sided-helper408-review'"))
+    assert text.count(line) == 1
+    path.write_text(text.replace(line, line + "\nrun('paired-extension-review',P/'new/borrow/paired-extension/verify.py','--work',work/'paired-extension-review')"))
+    before, after = tree(src), tree(out)
+    changes = {n: {'before': before.get(n), 'after': after.get(n)} for n in set(before) | set(after)
+               if before.get(n) != after.get(n)}
+    expected = {'new/BORROW-PROVIDERS.json', 'new/rebuild_borrow.py', 'verify.py', 'new/borrow/paired_extension.py'}
+    expected |= {f'new/borrow/words/BORROW-WORD-43{tag}.json.gz' for tag in ('base', 'extra')}
+    expected |= {f'new/borrow/inputs/CHANNEL408-WORD-{tag}.json.gz' for tag in ('base', 'extra')}
+    expected |= {'new/borrow/paired-extension/' + n for n in copied}
+    assert set(changes) == expected and tree(src) == before
+    save(out / 'MANIFEST.json', after)
+    result = {'status': 'PASS_SOURCE_BOUND_PAIRED_EXTENSION_OVERLAY', 'parent_manifest_sha256': PARENT,
+              'manifest_sha256': sha(out / 'MANIFEST.json'), 'source_file_count': len(after),
+              'changes': changes, 'words': records, 'builder_sha256': sha(Path(__file__))}
+    save(out.parent / (out.name + '-DERIVATION.json'), result)
+    print(result['status'], result['manifest_sha256'], len(after), flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/paired-helper-extension/tools/derive_adapters.py b/research/paired-helper-extension/tools/derive_adapters.py
new file mode 100644
index 0000000000..67b81d6f53
--- /dev/null
+++ b/research/paired-helper-extension/tools/derive_adapters.py
@@ -0,0 +1,85 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Adapter derivation by Mason Hale with OpenAI Codex assistance; inherited
+# PR2908/2894/2857/2839 admission and native authors retain their attribution.
+"""Derive three closed-profile adapters from exact PR2908 source, with counted patches.
+No native/invoice check is removed. Source/hash arguments bind the new declared overlay;
+retained_receipt_sha binds only the explicitly reused unchanged parent cache.
+"""
+from pathlib import Path
+import argparse,gzip,hashlib,json,sys
+PARENT_HEAD='51309592971e3b5be935599eed2a95404dc7781e'
+NEW_COMMIT='paired-helper-extension-pr2908'
+FINAL_SOURCE_SHA='98d57c82a1c7318be3c330c3b66897844d57232f0aaeaea88fb4bebd0a1bedf1'
+FINAL_SOURCE_FILES=632
+OLD_SOURCE='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'
+OLD_RETAINED='dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'
+sha=lambda b:hashlib.sha256(b).hexdigest()
+
+def need(p,msg):
+ if not p:raise ValueError(msg)
+
+def tree(p):
+ need(not any(f.is_symlink()for f in p.rglob('*')),'no symlinks')
+ return {f.relative_to(p).as_posix():sha(f.read_bytes())for f in p.rglob('*')if f.is_file()and f!=p/'MANIFEST.json'}
+
+def derive(parent,source,expected,out,retained_sha):
+ manifest=json.loads((parent/'MANIFEST.json').read_bytes());need(tree(parent)==manifest,'complete exact parent manifest inventory')
+ # These pins are independent of the manifest file contents themselves.
+ need(sha((parent/'MANIFEST.json').read_bytes())=='9dba3fe371602ec023a54e26c0fd66f69eb7a74be86aab89923529083c14b36f','exact PR2908 package manifest')
+ newsha=sha((source/'MANIFEST.json').read_bytes());need(newsha==expected==FINAL_SOURCE_SHA,'exact final declared source manifest')
+ files=json.loads((source/'MANIFEST.json').read_bytes());need(len(files)==FINAL_SOURCE_FILES and tree(source)==files,'complete final source inventory')
+ for tag in ('base','extra'):
+  wp=source/f'new/borrow/words/BORROW-WORD-43{tag}.json.gz'
+  w=json.loads(gzip.decompress(wp.read_bytes()));oldword=json.loads(gzip.decompress((parent/f'data/WORD-{tag}.json.gz').read_bytes()))
+  need(set(map(int,w['helper_final']))==set(map(int,oldword['helper_final']))|{424,428,412,331,299,320,511,304,499},'exact nine extra restored helpers')
+  need(all(w['helper_final'][h]==U for h,U in oldword['helper_final'].items()),'all inherited restored endpoints retained')
+  need(len(w['helper_final'])==82 and w['report']['local_profile']=={'1':2416,'2':640,'3':280,'4':110,'5':26,'8':8},'declared82-buffer local profile')
+  need(w['report']['width_inventory']=={'4':26,'5':2,'7':62,'8':96,'9':222},'declared current helper inventory')
+ nfiles=len(files);comparison_sha=sha((parent/'CLAIM.json').read_bytes());claim=json.loads((parent/'CLAIM.json').read_bytes())
+ need('headline_kappa_source'not in claim and 'kappa'in claim,'headline outer comparison')
+ need(len(retained_sha)==64 and all(c in'0123456789abcdef'for c in retained_sha),'retained receipt SHA256')
+ out.mkdir(parents=True,exist_ok=False);changes={}
+ def adapt(oldname,newname,pairs):
+  p=parent/'tools'/oldname;body=p.read_text();oldhash=sha(p.read_bytes());applied=[]
+  for old,new in pairs:
+   need(body.count(old)==1,f'exact preimage occurrence {oldname}: {old[:120]}')
+   body=body.replace(old,new);applied.append({'old':old,'new':new})
+  q=out/newname;q.write_text(body);compile(body,str(q),'exec');changes[newname]={'source':str(p),'before_sha256':oldhash,'after_sha256':sha(q.read_bytes()),'replacements':applied}
+ adapt('prepare_channel_native.py','prepare_extension_native.py',[
+  ("SOURCE_SHA='"+OLD_SOURCE+"'","SOURCE_SHA='"+newsha+"'"),
+  ('SOURCE_FILES=610','SOURCE_FILES='+str(nfiles)),
+  ("SOURCE_COMMIT='two-sided-helper408-pr2894'","SOURCE_COMMIT='"+NEW_COMMIT+"'"),
+  ("OLD_RECEIPT_SHA='"+OLD_RETAINED+"'","OLD_RECEIPT_SHA='"+retained_sha+"'"),
+  ("len(can['zero_buffers'])==73","len(can['zero_buffers'])==82"),
+ ])
+ oldprofile="    'channel408': dict(commit='two-sided-helper408-pr2894',manifest='"+OLD_SOURCE+"',helpers=408,source_file_count=610,upstream_head='18d03c447886895ef9abf888398178e0428533ca'),"
+ newprofile="    'paired-extension': dict(commit='"+NEW_COMMIT+"',manifest='"+newsha+"',helpers=408,source_file_count="+str(nfiles)+",upstream_head='"+PARENT_HEAD+"'),"
+ adapt('admit_channel408.py','admit_extension.py',[
+  (oldprofile,newprofile),
+  ("COMPARISONS = {","COMPARISONS = {\n    'pr2908': dict(pr=2908,head='"+PARENT_HEAD+"',sha256='"+comparison_sha+"',field='kappa'),"),
+  ("ap.add_argument('--source-profile', choices=['channel408'], default='channel408')","ap.add_argument('--source-profile', choices=['paired-extension'], default='paired-extension')"),
+  ("ap.add_argument('--comparison-profile', choices=['pr2894'], default='pr2894')","ap.add_argument('--comparison-profile', choices=['pr2908'], default='pr2908')"),
+  ('zero_buffers_allocated_and_cleared=73','zero_buffers_allocated_and_cleared=82'),
+  ("len(c.get('zero_buffers',[]))==73, 'helper408 physical ABI including all 73 private buffers'","len(c.get('zero_buffers',[]))==82, 'paired extension physical ABI including all 82 private buffers'"),
+  ("896*T+expected_helpers+8+73+2, 'complete physical cost including all actual helpers and 73 buffers'","896*T+expected_helpers+8+82+2, 'complete physical cost including all actual helpers and 82 buffers'"),
+ ])
+ adapt('channel_blocknorm.py','extension_blocknorm.py',[
+  ("len(allocated)==73, 'all73 private zero buffers released'","len(allocated)==82, 'all82 private zero buffers released'"),
+  ("'zero_buffers_allocated_and_cleared':73","'zero_buffers_allocated_and_cleared':82"),
+  ("r['zero_buffers_returned_to_zero']==73","r['zero_buffers_returned_to_zero']==82"),
+  ('physical==live+8+408+73+2','physical==live+8+408+82+2'),
+  ("'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]","'zero_buffers':[live+416,live+498], 'coefficient':[live+498,live+500]"),
+  ("len(mp)==73 and set(mp.values())==set(range(*ns['zero_buffers'])), '73distinct private Z slots'","len(mp)==82 and set(mp.values())==set(range(*ns['zero_buffers'])), '82distinct private Z slots'"),
+  ('T=len(order)//9; live=896*T; physical=live+490','T=len(order)//9; live=896*T; physical=live+500'),
+ ])
+ # The native address dimension and symplectic stock factor are deliberately retained.
+ b=(out/'extension_blocknorm.py').read_text();a=(out/'admit_extension.py').read_text()
+ need("require(d['m']==73"in b and 'Sp(72,2)'in b and 'range(1,37)'in b,'retained native dimension and symplectic group')
+ need('assert m==73'in a,'retained outer dimension')
+ receipt={'status':'PASS_CHECKED_82_BUFFER_ADAPTER_DERIVATION','parent_head':PARENT_HEAD,'parent_manifest_sha256':sha((parent/'MANIFEST.json').read_bytes()),'source_commit':NEW_COMMIT,'source_manifest_sha256':newsha,'source_files':nfiles,'comparison_sha256':comparison_sha,'retained_receipt_sha256':retained_sha,'buffer_count':82,'physical_overhead':500,'changes':changes}
+ (out/'ADAPTER-DERIVATION.json').write_text(json.dumps(receipt,indent=2)+'\n');return receipt
+
+if __name__=='__main__':
+ ap=argparse.ArgumentParser();ap.add_argument('--parent-package',type=Path,required=True);ap.add_argument('--source',type=Path,required=True);ap.add_argument('--source-manifest',required=True);ap.add_argument('--retained-receipt',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args()
+ r=derive(a.parent_package,a.source,a.source_manifest,a.out,sha(a.retained_receipt.read_bytes()));print(r['status'],r['source_manifest_sha256'],r['source_files'])
diff --git a/research/paired-helper-extension/vendor/audit_local.py b/research/paired-helper-extension/vendor/audit_local.py
new file mode 100644
index 0000000000..8224873d04
--- /dev/null
+++ b/research/paired-helper-extension/vendor/audit_local.py
@@ -0,0 +1,501 @@
+"""Independent exact scalar/frame audit of the changed forward supplier.
+
+This does not import a generator, builder, stored compensation, or price.
+All claimed endpoint matrices are derived from the input word's gates.
+Optional --main checks the transported boundary against the pinned parent.
+Prepared for icekylinx with OpenAI GPT-6 Astra assistance. Apache-2.0.
+"""
+import argparse,gzip,json,hashlib,time
+from pathlib import Path
+from fractions import Fraction as F
+from collections import Counter
+
+def require(x,label):
+    if not x:raise RuntimeError(label)
+
+def basis(vs):
+    piv={}
+    for a in vs:
+        while a:
+            bit=a.bit_length()-1
+            if bit in piv:a^=piv[bit]
+            else:
+                piv[bit]=a;break
+    for k in sorted(piv):
+        for j in piv:
+            if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+    return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def registers(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+def apply(e,rows,dual=False):
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        dst=rows[t]
+        for k,x in list(rows[s].items()):
+            a=dst.get(k,F(0))+q*x
+            if a:dst[k]=a
+            else:dst.pop(k,None)
+    elif e[0]=='scale':
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+    else:raise RuntimeError('unknown scalar primitive')
+
+def invert(e):
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def check_parent_interface(word,main):
+    # Read only the retained boundary data. No builder or local checker is imported.
+    relative="research/community-k492-audit/pr622/replay/baseline558/complex-global/base/split-centres/CANONICAL-WORD.json.gz"
+    path=main/relative;raw=path.read_bytes()
+    require(hashlib.sha256(raw).hexdigest()=="66d3c3c70983224650643a0a05a21ac6c6959f84d0f4528650601016f5a76844",'parent canonical input pin')
+    parent=json.loads(gzip.decompress(raw))
+    tau=lambda x:x^(43 if (x&43).bit_count()%2 else 0)
+    ports=parent['ports'];v=word['report']['v']
+    require(len(ports)==len(set(ports))==v,'parent port count')
+    require(set(map(tau,word['ports']))==set(ports),'transported source/target ports')
+    moved={i:ports.index(tau(p)) for i,p in enumerate(word['ports'])}
+    centers=[moved.get(r,r) for r in word['centers']]
+    actual=[list(basis([tau(x) for x in frame])) for frame in word['center_frames']]
+    expected=[parent['frames'][f] for f in parent['center_frames']]
+    require(len(centers)==len(set(centers))==len(actual)==8,'eight distinct centre carriers')
+    require(actual==expected and all(len(f)==8 for f in actual),'ordered centre frame interface')
+    return dict(parent_path=relative,parent_file_sha256=hashlib.sha256(raw).hexdigest(),
+                transport_tau=43,ordered_frame_bases_match=True,all_ports_match=True,
+                transported_centers=centers,source_centers=[r for r in centers if r<v],
+                ordered_frame_bases=actual)
+
+
+def run(path,out,main=None,base=None):
+    begin=time.monotonic();data=gzip.decompress(path.read_bytes());w=json.loads(data)
+    if w.get('kind')=='BORROW-WORD':return run_borrow(path,out,main,base,w,data,begin)
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    center_interface=check_parent_interface(w,main) if main is not None else None
+    ident=lambda:[{k:F(1)} for k in range(n)]
+    main=w['A']+w['cut']+w['B']
+    for e in main+w['precondition']+w['cleanup']:
+        require(all(0<=k<n for k in registers(e)),'register out of range')
+        q=F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+        require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+        if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B'] if e[0]=='add' and not(v<=e[1]<2*v)), 'non-target reads target')
+    raw=ident()
+    for e in main:apply(e,raw)
+    dirt=[{} for _ in range(n)]
+    for y in range(v,2*v):dirt[y]={k:a for k,a in raw[y].items() if k>=2*v}
+    for e in w['precondition']:apply(e,dirt)
+    compensation=[['add',y,k,-a.numerator,a.denominator,[]] for y in range(v,2*v) for k,a in sorted(dirt[y].items())]
+    entering=set(map(int,w.get('start_extra',{})));lowends=set(map(int,w.get('helper_final',{})))
+    coldends=lowends-entering
+    require(not any(e[2] in entering for e in compensation),'nonzero entrance response')
+    require(not any(r in entering|coldends for e in w['precondition']+compensation for r in registers(e)), 'pre-wrapper touch of residual helper')
+    require(all(e[-1]==[] for e in w['precondition']+compensation),'nonzero frame precondition')
+    early=w.get('early_cleanup',[]);earlyids={i for i,U in early}
+    require(len(earlyids)==len(early),'duplicate early cleanup gate')
+    tail=[w['cleanup'][i][:-1]+[U] for i,U in early]
+    cleanup=[e for i,e in enumerate(w['cleanup']) if i not in earlyids]
+    prefix=w['precondition']+compensation+main
+    program=prefix+tail+cleanup
+    for dual in (False,True):
+        actual=ident()
+        for e in program:apply(e,actual,dual)
+        expected=ident()
+        for t in range(v):expected[t if dual else v+t][v+t if dual else t]=F(-1 if dual else 1)
+        bad=[i for i in range(n) if actual[i]!=expected[i]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        print('endpoint', 'dual' if dual else 'forward','PASS',flush=True)
+    full=basis([1<<i for i in range(h)])
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():
+        require(2*v<=int(q)<n,'non-helper entrance');start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    for section in ('A','B'):
+        if section=='B':
+            lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+            require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+            for q,U in zip(w['centers'],w['center_frames']):
+                U=basis(U);require(cur[q]==U,'center frame')
+                served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+                for T in sorted(served,key=lambda x:-len(x)):
+                    require(contained(T,U),'center path not nested')
+                    if T!=U:paid[len(U)-len(T)]+=1
+                    U=T
+        for e in w[section]:
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in tail:
+        for q in registers(e):climb(q,e[-1])
+    for q,U in enumerate(end):climb(q,U)
+    require(all(all(end[q]==full for q in registers(e)) for e in cleanup),'full cleanup reads a low end')
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch')
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n))
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch')
+    p=ident();pinv=ident()
+    for e in prefix:apply(e,p)
+    for e in reversed(prefix):apply(invert(e),pinv)
+    for q in lowends:
+        U=end[q]
+        require(all(contained(endB[k],U) for k in pinv[q]),'inverse-row cone '+str(q))
+        require(all(k==q or not p[k].get(q) or contained(endB[k],U) for k in range(n)),'dirt-column cone '+str(q))
+    report=dict(status='PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES',
+                input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),
+                parent_center_interface=center_interface,v=v,h=h,R=R,
+                entering=len(entering),lowends=len(lowends),coldends=len(coldends),
+                compensation_gates=len(compensation),local_profile=dict(sorted(paid.items())),
+                width_inventory=dict(sorted(inventory.items())),checked_columns=n,
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact rational full scalar map in both orientations; all literal native frame chains, center levels, dyadic units, entrance-zero response, wrapper exclusion and final helper row/column cones. No global owner admission or exponent repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+
+# ---------------------------------------------------------------------------------------------
+# BORROW-WORD extension (anticipatory dirty borrowing, #2226 construction on the T74 words).
+# Everything below is new; run() above is unchanged except for the dispatch on w['kind'].
+# ---------------------------------------------------------------------------------------------
+def dot(a,b):return (a&b).bit_count()&1
+
+def gmul(cols,x):
+    # G given by its columns: cols[i] = G(e_i) as a bit mask; returns G(x)
+    y=0;i=0
+    while x:
+        if x&1:y^=cols[i]
+        x>>=1;i+=1
+    return y
+
+def ginv(cols,h):
+    # inverse columns over F2 (None if singular), Gauss-Jordan on (G | I) column-wise
+    piv={};
+    for i in range(h):
+        a=cols[i];b=1<<i
+        while a:
+            t=a.bit_length()-1
+            if t in piv:a^=piv[t][0];b^=piv[t][1]
+            else:piv[t]=(a,b);break
+    if len(piv)<h:return None
+    # reduce: for each unit vector e_t find preimage
+    pre=[]
+    for t in range(h):
+        a=1<<t;b=0
+        for s in sorted(piv,reverse=True):
+            if a>>s&1:a^=piv[s][0];b^=piv[s][1]
+        if a:return None
+        pre.append(b)
+    return pre   # pre[t] = G^{-1}(e_t)
+
+def gtrans(cols,h):
+    # transpose: column j of G^T = row j of G
+    return [sum(((cols[i]>>j)&1)<<i for i in range(h)) for j in range(h)]
+
+def perp(U,h):
+    # orthogonal complement of span(U) under the standard dot product on F2^h
+    return basis([x for x in range(1,1<<h) if all(dot(x,u)==0 for u in U)]) if h<=12 else None
+
+def lagrangian(U,h):
+    # L_U={(x,z):x in U,z in x+U^perp}; vector = x | z<<h ; spanned by (u,u) and (0,p)
+    P=perp(U,h)
+    return basis([u|(u<<h) for u in U]+[p<<h for p in P])
+
+def check_warp(op,rec,h):
+    """Exact static checks of one K_G warp; raises RuntimeError. Returns dict."""
+    require(isinstance(rec,list) and len(rec)==5,'warp record shape')
+    pos,lender,cols,U,E=rec
+    require(len(cols)==h and all(isinstance(c,int) and 0<=c<(1<<h) for c in cols),'G column shape')
+    check_G_frames(cols,U,E,h)
+    return dict(position=pos,lender=lender,dim=len(U))
+
+def check_G_frames(cols,U,E,h):
+    """static K_G checks of the operator `cols` for the frame pair U -> E (used for B-phase warps and for A-phase prelude warps)"""
+    inv=ginv(cols,h);require(inv is not None,'G not invertible')
+    require(all(gmul(cols,inv[t])==1<<t for t in range(h)),'G inverse witness')
+    U=list(U);E=list(E)
+    require(len(basis(U))==len(U) and len(basis(E))==len(E),'warp frames are not bases')
+    require(len(U)==len(E),'dim(from)!=dim(to)')
+    require(all(0<=x<(1<<h) for x in U+E),'frame out of range')
+    require(basis([gmul(cols,x) for x in U])==basis(E),'G(from)!=to')
+    # symplectic form of K_G on F2^{2h}, vector = x | z<<h, columns of M: (x,z)->(Gx, (G+G^-T)x + G^-T z)
+    GiT=gtrans(inv,h)        # G^{-T}: columns j = row j of G^{-1}
+    # G^{-T}(z): via columns GiT
+    def M(vec):
+        x=vec&((1<<h)-1);z=vec>>h
+        gx=gmul(cols,x);S=gx^gmul(GiT,x)   # (G + G^{-T}) x
+        return gx|((S^gmul(GiT,z))<<h)
+    sw=lambda vec:(vec>>h)|((vec&((1<<h)-1))<<h)
+    sym=lambda a,b:dot(a,sw(b))             # omega((x,z),(x',z'))=x.z'+z.x'
+    gens=[1<<k for k in range(2*h)]
+    img=[M(g) for g in gens]
+    require(all(sym(img[a],img[b])==sym(gens[a],gens[b]) for a in range(2*h) for b in range(a+1,2*h)),'K_G not symplectic')
+    require(all(M(1<<k)==M(1<<k) for k in range(2*h)),'unreachable')
+    L0=basis([1<<k for k in range(h,2*h)]);LF=basis([(1<<k)|(1<<(k+h)) for k in range(h)])
+    require(basis([M(x) for x in [1<<k for k in range(h,2*h)]])==L0,'K_G does not fix L_0')
+    require(basis([M(x) for x in [(1<<k)|(1<<(k+h)) for k in range(h)]])==LF,'K_G does not fix L_FULL')
+    LU=lagrangian(U,h);LE=lagrangian(E,h)
+    require(len(LU)==h==len(LE),'frame Lagrangian dimension')
+    require(basis([M(x) for x in LU])==LE,'K_G(L_from)!=L_to')
+    # dual orientation uses G^{-T}: it must map from^perp to to^perp
+    require(basis([gmul(GiT,x) for x in perp(U,h)])==perp(E,h),'dual frame map')
+
+def fraction_row(e):
+    return F(e[3],e[4]) if e[0]=='add' else F(e[2],e[3])
+
+def walg_add(dst,src,c):
+    for k,x in src.items():
+        a=dst.get(k,F(0))+c*x
+        if a:dst[k]=a
+        else:dst.pop(k,None)
+
+def walg_warp(row,op):
+    # K_op acts on every stored operator word: left multiply by op, cancelling an adjacent inverse
+    out={}
+    for (var,word),x in row.items():
+        out[var,word[1:] if word and word[0]==-op else (op,)+word]=x
+    return out
+
+def walg_apply(e,rows,dual,dsym):
+    """e: scalar gate list (add/scale) or ['warp',reg,signed_op,...]; free-algebra action."""
+    if e[0]=='corr':
+        _,t,src,word,c=e
+        if not dual:
+            row=rows[src]
+            for op in reversed(word):row=walg_warp(row,op)
+            walg_add(rows[t],row,c)
+        else:
+            row=rows[t]
+            # transpose of the gate t+=c K s is s-=c K^T t, and K^T=(K^{-T})^{-1}=D^{-1}: a word K_o1..K_ok becomes D_ok^-1..D_o1^-1
+            for op in word:row=walg_warp(row,-((op>0)-(op<0))*(abs(op)+dsym))
+            walg_add(rows[src],row,-c)
+        return
+    if e[0]=='warp':
+        op=e[2];s=(op>0)-(op<0)
+        if dual:op=s*(abs(op)+dsym)     # dual orientation: K_G^{-T} is a distinct free symbol
+        rows[e[1]]=walg_warp(rows[e[1]],op);return
+    if e[0]=='add':
+        t,s=e[1:3];q=F(e[3],e[4]);require(t!=s,'self add')
+        if dual:t,s,q=s,t,-q
+        walg_add(rows[t],rows[s],q)
+    else:
+        t=e[1];q=F(e[2],e[3]);require(q!=0,'zero scale')
+        if dual:q=1/q
+        rows[t]={k:q*x for k,x in rows[t].items()}
+
+def invert_item(e,full):
+    if e[0]=='warp':return ['warp',e[1],-e[2]]
+    r=list(e)
+    if r[0]=='add':r[3]=-r[3]
+    else:r[2],r[3]=r[3],r[2]
+    return r
+
+def run_borrow(path,out,main,base,w,data,begin):
+    v,h,R=w['report']['v'],w['report']['h'],w['report']['R'];n=2*v+R
+    require((v,h)==(112,9),'wrong source geometry')
+    require(main is None,'--main parent interface is not available for coordinate-changed BORROW-WORD; use --base')
+    full=basis([1<<i for i in range(h)]);FULLB=list(full)
+    removed=set(w['removed']);require(all(2*v<=r<n for r in removed) and len(removed)==len(w['removed']),'removed must be distinct helpers')
+    live=[r for r in range(n) if r not in removed];liveset=set(live)
+    istarget=lambda r:v<=r<2*v
+    warps=w['warps'];K=len(warps)
+    # --- 1. warp records (static exact checks) ------------------------------------------------
+    for op,rec in enumerate(warps,1):
+        check_warp(op,rec,h)
+        require(rec[1] in liveset and not istarget(rec[1]),'lender must be a remaining non-target register')
+        require(0<=rec[0]<=len(w['B']),'warp position')
+    print('warps',K,'PASS static K_G checks',flush=True)
+    # --- 2. gate hygiene ----------------------------------------------------------------------
+    sections={k:w[k] for k in ('precondition','compensation','A','cut','B','restore')}
+    cleanup_given=w.get('cleanup')
+    for name,sec in list(sections.items())+([('cleanup',cleanup_given)] if cleanup_given is not None else []):
+        for e in sec:
+            if e[0]=='warp':
+                require(name in('cleanup','A'),'warp item outside cleanup list/prelude')
+                require(len(e)==(5 if name=='A' else 4),'warp item shape')
+                require(abs(e[2])<=K and e[2]!=0,'warp operator id')
+                require((e[1] in liveset or (name=='cleanup' and e[1]-n in liveset)),'warp register');continue
+            require(e[0] in('add','scale'),'unknown scalar primitive')
+            regs=registers(e)
+            if name=='cleanup':require(all((r in liveset) or (n<=r<2*n and r-n in liveset) for r in regs),'register out of range/removed')
+            else:require(all(r in liveset for r in regs),'register out of range or removed helper referenced')
+            q=fraction_row(e)
+            require(q.denominator&(q.denominator-1)==0,'non-dyadic scalar')
+            if e[0]=='scale':require(abs(q.numerator)&(abs(q.numerator)-1)==0,'non-unit scale')
+            if e[0]=='add':require(e[1]!=e[2],'self add')
+    require(all(not(v<=e[2]<2*v) for e in w['A']+w['B']+w['restore'] if e[0]=='add' and not(v<=e[1]<2*v)),'non-target reads target')
+    # wrapper / compensation sections only write targets at the zero frame
+    for e in w['precondition']+w['compensation']:
+        require(e[-1]==[] and istarget(e[1]),'wrapper gate must be a zero-frame target write')
+    require(all(e[-1] is None and istarget(e[1]) for e in w['cut']),'cut gates must be unframed target writes')
+    require(all(not istarget(e[1]) for e in w['restore']),'restoration writes only non-targets')
+    entering=set(map(int,w.get('start_extra',{})));restored=set(map(int,w.get('helper_final',{})))
+    require(all(2*v<=q<n and q in liveset for q in entering|restored),'start_extra/helper_final must name remaining helpers')
+    require(not any(e[2] in entering for e in w['compensation'] if e[0]=='add'),'nonzero entrance response')
+    require(not any(r in entering|restored for e in w['precondition']+w['compensation'] for r in registers(e)),'pre-wrapper touch of residual helper')
+    # --- 3. initial anticipatory corrections (the relaxed compensation rule) ---------------
+    corr=w['initial_corrections']
+    for t in corr:
+        word=tuple(t['operator_word']);c=F(t['coefficient'])
+        require(istarget(t['target']),'correction target')
+        s=t['source'];require(s in liveset and s>=2*v,'correction source must be a remaining helper')
+        require(s not in entering,'correction source has nonzero entrance frame')
+        require(len(word)>=1 and all(1<=abs(o)<=K for o in word),'correction operator word')
+        require(c!=0 and c.denominator&(c.denominator-1)==0,'correction coefficient')
+        # the source is the lender of the operator it is read through
+        require(all(warps[abs(o)-1][1]==s for o in word),'correction source is not the lender of its operator')
+    # --- 4. frames: literal chain, monotone, paid profile ---------------------------------------
+    end=[full]*v+[basis([x for x in range(1,1<<h) if (x&p).bit_count()%2==0]) for p in w['ports']]+[full]*R
+    for q,U in w.get('helper_final',{}).items():end[int(q)]=basis(U)
+    start=[(p,) for p in w['ports']]+[()]*(v+R)
+    for q,U in w.get('start_extra',{}).items():start[int(q)]=basis(U)
+    cur=start.copy();paid=Counter()
+    def climb(q,U):
+        U=basis(U);require(contained(cur[q],U),'frame not monotone '+str((q,cur[q],U)))
+        d=len(U)-len(cur[q])
+        if d:paid[d]+=1
+        cur[q]=U
+    npre=w.get('prelude_events',0);prelude=w['A'][:npre];Aord=w['A'][npre:]
+    require(all(e[0]=='warp' or (istarget(e[1]) and e[0] in('add','scale')) for e in prelude),'prelude items must be warps or target writes')
+    require(all(e[0]!='warp' for e in Aord),'warp item after the prelude')
+    for e in prelude:
+        if e[0]=='warp':
+            _,r_,op_,fr_,to_=e;rec_=warps[abs(op_)-1]
+            require(rec_[1]==r_ and op_!=0 and abs(op_)<=K,'prelude warp operator/lender')
+            check_G_frames(rec_[2],list(fr_) if op_>0 else list(to_),list(to_) if op_>0 else list(fr_),h)
+            require(cur[r_]==basis(fr_),'prelude warp frame mismatch '+str((r_,op_)))
+            cur[r_]=basis(to_)
+        else:
+            for q in registers(e):climb(q,e[-1])
+    for e in Aord:
+        for q in registers(e):climb(q,e[-1])
+    lev={int(t):basis(U) for t,U in w.get('target_levels',{}).items()}
+    require(all(cur[v+t]==lev.get(t,()) for t in range(v)),'target centre levels')
+    for q,U in zip(w['centers'],w['center_frames']):
+        U=basis(U);require(cur[q]==U,'center frame')
+        served={lev.get(e[1]-v,()) for e in w['cut'] if e[2]==q}
+        for T in sorted(served,key=lambda x:-len(x)):
+            require(contained(T,U),'center path not nested')
+            if T!=U:paid[len(U)-len(T)]+=1
+            U=T
+    byposition={}
+    for op,rec in enumerate(warps,1):byposition.setdefault(rec[0],[]).append(op)
+    B=w['B'];forward=[]    # chronological program of the (recorded) non-target word
+    for e in Aord:forward.append(e)
+    for p in range(len(B)+1):
+        for op in byposition.get(p,[]):
+            _,lender,cols,U,E=warps[op-1]
+            require(cur[lender]==basis(U),'warp frame mismatch '+str((op,lender,cur[lender],basis(U))))
+            cur[lender]=basis(E);forward.append(['warp',lender,op])
+        if p<len(B):
+            e=B[p];forward.append(e)
+            for q in registers(e):climb(q,e[-1])
+    endB=cur.copy()
+    for e in w['restore']:
+        for q in registers(e):climb(q,e[-1])
+        forward.append(e)
+    for q in live:climb(q,end[q])
+    require(all(cur[q]==end[q] for q in live),'end frames')
+    recorded=[e for e in forward if e[0]=='warp' or not istarget(e[1])]
+    # --- 5. derived cleanup: inverse-reverse at FULL, private zero buffers for restored inputs --------
+    buf=lambda r:r+n if r in restored else r
+    def conv(e):
+        e=invert_item(e,full)
+        if e[0]=='warp':return [e[0],buf(e[1]),e[2],FULLB]
+        if e[0]=='add':return ['add',buf(e[1]),buf(e[2]),e[3],e[4],FULLB]
+        return ['scale',buf(e[1]),e[2],e[3],FULLB]
+    derived=[conv(e) for e in reversed(recorded)]
+    if cleanup_given is not None:
+        norm=lambda c:[(list(g[:-1]),basis(g[-1])) for g in c]
+        require(norm(cleanup_given)==norm(derived),'explicit cleanup differs from derived inverse-reverse at FULL')
+    cleanup=derived if cleanup_given is None else cleanup_given
+    require(all(basis(g[-1])==full for g in cleanup),'cleanup not at FULL')
+    for g in cleanup:
+        for r in (registers(g) if g[0]!='warp' else (g[1],)):
+            require(r not in restored,'cleanup touches a restored cold input directly')
+            require(r<n or r-n in restored,'buffer for a non-restored register')
+    require(all(end[q]==full for q in live if q not in restored and not istarget(q)),'cleanup reads a low end')
+    print('frames/profile PASS',flush=True)
+    require(dict(paid)=={int(k):a for k,a in w['report']['local_profile'].items()},'paid profile mismatch '+str(dict(sorted(paid.items()))))
+    inventory=Counter(len(end[q])-len(start[q]) for q in range(2*v,n) if q in liveset)
+    require(dict(inventory)=={int(k):a for k,a in w['report']['width_inventory'].items()},'width inventory mismatch '+str(dict(sorted(inventory.items()))))
+    # --- 6. exact free-operator-algebra replay (both orientations) -----------------------------------
+    DS=10**6
+    status={}
+    corr_items=[['corr',t['target'],t['source'],tuple(t['operator_word']),F(t['coefficient'])] for t in corr]
+    program=corr_items+w['precondition']+w['compensation']+w['A']+w['cut']+[e for e in forward[len(Aord):]]
+    for dual in (False,True):
+        rows={r:{(r,()):F(1)} for r in live}
+        for c in restored:rows[c+n]={}
+        for e in program:walg_apply(e,rows,dual,DS)
+        if not dual:
+            for t in range(v):
+                require(rows[v+t]=={(v+t,()):F(1),(t,()):F(1)},'target map failed '+str(t))
+            for c in restored:
+                require(rows[c]=={(c,()):F(1)},'restored cold row is not its own input '+str(c))
+                require(all(not any(var==c for var,word in rows[r]) for r in live if r!=c),'restored cold input still read by '+str(c))
+            require(all(rows[c+n]=={} for c in restored),'buffer polluted before cleanup')
+        for e in cleanup:walg_apply(e,rows,dual,DS)
+        exp={}
+        for r in live:exp[r]={(r,()):F(1)}
+        for t in range(v):
+            if dual:exp[t]={(t,()):F(1),(v+t,()):F(-1)}
+            else:exp[v+t]={(v+t,()):F(1),(t,()):F(1)}
+        bad=[r for r in live if rows[r]!=exp[r]]
+        require(not bad,'all-column endpoint failure '+str((dual,bad[:8])))
+        require(all(rows[c+n]=={} for c in restored),'zero buffer not returned to zero '+('dual' if dual else 'forward'))
+        status['dual' if dual else 'forward']='PASS'
+        print('free-algebra','dual' if dual else 'forward','PASS',len(live),'independent inputs',flush=True)
+    # --- 7. optional pinned-base comparison ---------------------------------------------------------------------
+    base_report=None
+    if base is not None:base_report=check_base(w,base,removed)
+    report=dict(status='PASS_INDEPENDENT_EXACT_BORROWING_WORD',input_file=path.name,content_sha256=hashlib.sha256(data).hexdigest(),
+                compressed_sha256=hashlib.sha256(path.read_bytes()).hexdigest(),v=v,h=h,R=R,
+                removed_helpers=len(removed),independent_inputs=len(live),warps=K,corrections=len(corr),
+                restored_cold=len(restored),zero_buffers=len(restored),entering=len(entering),
+                local_profile=dict(sorted(paid.items())),local_mass=sum(r*c for r,c in paid.items()),
+                width_inventory=dict(sorted(inventory.items())),
+                orientations=status,base=base_report,checked_columns=len(live),
+                elapsed_seconds=time.monotonic()-begin,
+                scope='Exact free-operator-algebra replay (every remaining input is an independent column): K_G warps with G invertible, G(from)=to, symplectic form fixing L_0/L_FULL and sending L_from to L_to (rank 0), literal frame chain with warps, relaxed fixed initial compensation, derived inverse-reverse cleanup at FULL with inverse warps and private zero buffers. No Clifford phase/Gaussian product, no owner admission, no repricing.')
+    out.write_text(json.dumps(report,indent=2)+'\n');print(json.dumps(report,indent=2),flush=True)
+    return report
+
+def check_base(w,basepath,removed):
+    """Pin every unchanged section/anchor of the borrowed word to the (separately audited) canonical base word."""
+    b=json.loads(gzip.decompress(Path(basepath).read_bytes()));v=w['report']['v'];n=2*v+w['report']['R']
+    fr=lambda i:basis(b['frames'][i])
+    touch=lambda e:any(r in removed for r in registers(e))
+    nrm=lambda e:(e[0],tuple(registers(e)),fraction_row(e))
+    lit=lambda e:(nrm(e),None if e[-1] is None else basis(e[-1]))
+    litb=lambda e:(nrm(e),None if e[-1] is None else fr(e[-1]))
+    require(w['ports']==b['ports'] and w['centers']==b['centers'],'ports/centers differ from base')
+    require([basis(f) for f in w['center_frames']]==[fr(i) for i in b['center_frames']],'center frames differ from base')
+    for k in ('precondition','compensation','A','cut'):
+        exp=[litb(e) for e in b[k] if not touch(e) and not (k=='compensation' and e[0]=='add' and e[2] in removed)]
+        wk=w[k][w.get('prelude_events',0):] if k=='A' else w[k]
+        require([lit(e) for e in wk]==exp,'section differs from base minus removed-helper gates: '+k)
+    require({int(q):basis(U) for q,U in w['start_extra'].items()}=={r:fr(b['start'][r]) for r in range(2*v,n) if r not in removed and b['frames'][b['start'][r]]},'start frames differ from base')
+    for q,U in w['helper_final'].items():require(basis(U)==fr(b['final'][int(q)]),'cold end frame differs from base '+q)
+    full=basis([1<<i for i in range(w['report']['h'])])
+    require(all(fr(b['final'][r])==full for r in range(v)),'base source ends')
+    require(all(fr(b['final'][v+t])==basis([x for x in range(1,1<<w['report']['h']) if (x&w['ports'][t]).bit_count()%2==0]) for t in range(v)),'base target ends vs ports')
+    return dict(base_sha256=hashlib.sha256(Path(basepath).read_bytes()).hexdigest(),sections_match_minus_removed=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--word',type=Path,required=True,help='FULL-WORD.json.gz to check')
+    parser.add_argument('--output',type=Path,required=True,help='JSON receipt output path')
+    parser.add_argument('--main',type=Path,help='Optional pinned main checkout: also verify the transported centre/port interface')
+    parser.add_argument('--base',type=Path,help='BORROW-WORD only: canonical base word whose unchanged sections/anchors are pinned')
+    args=parser.parse_args()
+    run(args.word,args.output,args.main,args.base)
diff --git a/research/paired-helper-extension/vendor/preload_move.py b/research/paired-helper-extension/vendor/preload_move.py
new file mode 100644
index 0000000000..55b435035b
--- /dev/null
+++ b/research/paired-helper-extension/vendor/preload_move.py
@@ -0,0 +1,133 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Declared preload-move stage: two more staged quartets on the PR2857 shared-kernel words.
+
+Preload re-synthesis (quartets (456,457,466,467) and (458,459,464,465)) by Jeremy Kothe
+(jeremykothe2), with AI assistance; the staged-kernel gate shapes, frame/inverse-cleanup
+conventions and the dirt-entry supplier are credited in CREDITS.md (PR2857 Lyy-iiis, PR2863
+Dugongue, PR2833 Jeremy Kothe, PR2853 philippeVV).
+
+apply(word, patch) takes the decoded PR2857 shared-kernel word and a DECLARED patch input
+that lists every changed gate. Every listed old gate must be present at its index, no
+other gate may change, the changed sections are limited to
+{A, B, compensation, start_extra, report, cleanup}, the frame/paid profile and width
+inventory are re-derived exactly from the changed word and must equal the declaration, and
+the inverse-reverse cleanup is re-derived. The inherited exact auditor (forward and dual
+free-operator replay over every input column) is the separate semantic check.
+No file, import, process or output is touched by apply().
+"""
+import copy, hashlib, json
+from collections import Counter
+
+SOURCE_CANONICAL = {
+ 'base': 'c0af0ef7ee6282e91f046d027983b35eaed7ebcb46489134d47e07724cf664bc',
+ 'extra': '61b20fbe78fdcbca0cde0597befcc254017ee206dad0724c576672aca690c66f',
+}
+ALLOWED_SECTIONS = {'A', 'B', 'compensation', 'start_extra', 'report', 'cleanup'}
+
+def require(ok, reason):
+ if not ok:raise ValueError(str(reason))
+
+def canon(w):return hashlib.sha256(json.dumps(w,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+
+def basis(vs):
+ piv={}
+ for a in vs:
+  while a:
+   bit=a.bit_length()-1
+   if bit in piv:a^=piv[bit]
+   else:piv[bit]=a;break
+ for k in sorted(piv):
+  for j in piv:
+   if j>k and piv[j]>>k&1:piv[j]^=piv[k]
+ return tuple(piv[k] for k in sorted(piv,reverse=True))
+
+def contained(a,b):return basis(a+b)==b
+
+def restored_of(w):
+ n=2*w['report']['v']+w['report']['R']
+ return {g[1]-n for g in w['cleanup'] if g[1]>=n}|{g[2]-n for g in w['cleanup'] if g[0]=='add' and g[2]>=n}
+
+def derive_cleanup(w,restored):
+ v=w['report']['v'];n=2*v+w['report']['R'];full=list(basis([1<<i for i in range(w['report']['h'])]))
+ byp={}
+ for op,rec in enumerate(w['warps'],1):byp.setdefault(rec[0],[]).append((op,rec))
+ fw=list(w['A'])
+ for p in range(len(w['B'])+1):
+  for op,rec in byp.get(p,[]):fw.append(['warp',rec[1],op])
+  if p<len(w['B']):fw.append(w['B'][p])
+ fw+=w['restore'];buf=lambda r:r+n if r in restored else r;out=[]
+ for g in reversed([g for g in fw if g[0]=='warp' or not(v<=g[1]<2*v)]):
+  if g[0]=='warp':out.append(['warp',buf(g[1]),-g[2],full])
+  elif g[0]=='add':out.append(['add',buf(g[1]),buf(g[2]),-g[3],g[4],full])
+  else:out.append(['scale',buf(g[1]),g[3],g[2],full])
+ return out
+
+def frame_report(x):
+ """Exact paid profile and width inventory of a word, by the inherited frame rules."""
+ full=basis([1<<i for i in range(9)]);end=[full]*112+[basis([z for z in range(1,512) if(z&p).bit_count()%2==0]) for p in x['ports']]+[full]*480
+ for r,U in x['helper_final'].items():end[int(r)]=basis(U)
+ start=[(p,) for p in x['ports']]+[()]*(112+480)
+ for r,U in x['start_extra'].items():start[int(r)]=basis(U)
+ cur=start.copy();paid=Counter()
+ def climb(r,U):
+  U=basis(U);require(contained(cur[r],U),('nonmonotone frame',r,cur[r],U))
+  d=len(U)-len(cur[r])
+  if d:paid[d]+=1
+  cur[r]=U
+ def step(g):
+  if g[0]=='warp':require(cur[g[1]]==basis(g[3]),'A warp frame');cur[g[1]]=basis(g[4])
+  else:
+   for r in(g[1:3] if g[0]=='add' else g[1:2]):climb(r,g[-1])
+ for g in x['A']:step(g)
+ for r,U in zip(x['centers'],x['center_frames']):
+  require(cur[r]==basis(U),'centre frame')
+  for T in sorted({basis(x['target_levels'].get(str(g[1]-112),[])) for g in x['cut'] if g[2]==r},key=lambda t:-len(t)):
+   if basis(U)!=T:paid[len(U)-len(T)]+=1
+   U=T
+ bw={}
+ for rec in x['warps']:bw.setdefault(rec[0],[]).append(rec)
+ for p in range(len(x['B'])+1):
+  for rec in bw.get(p,[]):require(cur[rec[1]]==basis(rec[3]),'B warp frame');cur[rec[1]]=basis(rec[4])
+  if p<len(x['B']):step(x['B'][p])
+ for g in x['restore']:step(g)
+ live=set(range(704))-set(x['removed'])
+ for r in live:climb(r,end[r])
+ inv=Counter(len(end[r])-len(start[r]) for r in live if r>=224)
+ return {str(k):v for k,v in sorted(paid.items())},{str(k):v for k,v in sorted(inv.items())}
+
+def apply(word, patch):
+ """Return (changed word, ledger). Authenticates the decoded source first."""
+ require(patch.get('stage')=='preload-move','stage tag')
+ digest=canon(word);require(digest==patch['source_canonical_sha256'],'source canonical hash differs from the declared source')
+ require(patch['variant'] in SOURCE_CANONICAL and SOURCE_CANONICAL[patch['variant']]==digest,'unauthorized decoded source SHA256')
+ x=copy.deepcopy(word)
+ # A: replacements and insertions, both addressed by index in the SOURCE A (before any edit).
+ ops=patch['A_edits'];seen=set();byp={};repl={}
+ for e in ops:
+  if e['op']=='replace':
+   i=e['index'];require(i not in seen and i not in repl,('duplicate A replace',i));require(word['A'][i]==e['old'],('A old gate mismatch',i,word['A'][i]));repl[i]=e['new']
+  else:
+   require(e['op']=='insert' and 0<=e['before']<=len(word['A']),'A edit op');byp.setdefault(e['before'],[]).append(e['gate'])
+ A=[]
+ for p in range(len(word['A'])+1):
+  A.extend(copy.deepcopy(g) for g in byp.get(p,[]))
+  if p<len(word['A']):A.append(copy.deepcopy(repl.get(p,word['A'][p])))
+ x['A']=A
+ for name in ('B','compensation'):
+  idx=set()
+  for e in patch[name+'_edits']:
+   i=e['index'];require(i not in idx,(name,'duplicate index',i));idx.add(i);require(word[name][i]==e['old'],(name,'old gate mismatch',i,word[name][i]));x[name][i]=copy.deepcopy(e['new'])
+ for r,U in patch['start_extra_added'].items():
+  require(r not in x['start_extra'],('start_extra already declared',r));x['start_extra'][r]=list(U)
+ require(x['prelude_events']==word['prelude_events']+0 and len(x['A'])==len(word['A'])+len(patch['A_edits'])-len(repl),'A length bookkeeping')
+ profile,inventory=frame_report(x)
+ require(profile==patch['declared_local_profile'] and inventory==patch['declared_width_inventory'],('derived paid profile/width inventory differ from the declaration',profile,inventory))
+ x['report']['local_profile']=profile;x['report']['width_inventory']=inventory
+ t=copy.deepcopy(x);t['A']=t['A'][t['prelude_events']:];x['cleanup']=derive_cleanup(t,restored_of(x))
+ changed={k for k in word if word[k]!=x[k]}
+ require(changed<=ALLOWED_SECTIONS,('sections outside the declared stage',changed-ALLOWED_SECTIONS))
+ require(x['warps']==word['warps'] and x['helper_final']==word['helper_final'] and x['removed']==word['removed'] and x['prelude_events']==word['prelude_events'],'phase and buffer ABI unchanged')
+ require(canon(x)==patch['candidate_canonical_sha256'],'candidate canonical hash differs from the declaration')
+ ledger=dict(variant=patch['variant'],source_canonical_sha256=digest,candidate_canonical_sha256=canon(x),local_profile=profile,width_inventory=inventory,
+  changed_sections=sorted(changed),A_replaced=sorted(repl),A_inserted=sum(map(len,byp.values())),B_edits=len(patch['B_edits']),compensation_edits=len(patch['compensation_edits']),start_extra_added=sorted(patch['start_extra_added']))
+ return x,ledger
diff --git a/research/paired-helper-extension/verify.py b/research/paired-helper-extension/verify.py
new file mode 100644
index 0000000000..258c99d5c4
--- /dev/null
+++ b/research/paired-helper-extension/verify.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Independent structural identities, all-input replay and semantic controls.
+
+The free-operator auditor and structural checker are unchanged PR2908 sources.
+This check is local; native, actual owners and complete outer admission are separate.
+"""
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import sys
+import types
+from pathlib import Path
+
+P = Path(__file__).resolve().parent
+
+
+def read(p):
+    b = p.read_bytes()
+    return json.loads(gzip.decompress(b) if b[:2] == b'\x1f\x8b' else b)
+
+
+def sha(p):
+    return hashlib.sha256(p.read_bytes()).hexdigest()
+
+
+def load(name, p):
+    m = types.ModuleType(name)
+    m.__file__ = str(p)
+    sys.modules[name] = m
+    exec(compile(p.read_bytes(), str(p), 'exec'), m.__dict__)
+    return m
+
+
+def save_word(p, w):
+    p.write_bytes(gzip.compress(json.dumps(w, separators=(',', ':')).encode(), mtime=0))
+
+
+def main():
+    ap = argparse.ArgumentParser()
+    ap.add_argument('--work', type=Path, required=True)
+    a = ap.parse_args()
+    assert __debug__, 'assertions required by the independent structural checker'
+    out = a.work.resolve()
+    assert not out.exists() and not out.is_relative_to(P)
+    pins = read(P / 'PINS.json')
+    assert {f.relative_to(P).as_posix(): sha(f) for d in ('vendor', 'data')
+            for f in (P / d).rglob('*') if f.is_file()} == pins
+    out.mkdir(parents=True)
+    pm = load('preload_move', P / 'vendor/preload_move.py')
+    gen = load('paired_producer', P / 'producer.py')
+    aud = load('independent_paired_audit', P / 'vendor/audit_local.py')
+    structural = load('independent_paired_structure', P / 'structure.py')
+    transforms = [read(P / f'data/TRANSFORM-{h}.json') for h in gen.HELPERS]
+    records = {}
+    controls = {}
+    for tag in ('base', 'extra'):
+        parent = read(P / f'data/PARENT-{tag}.json.gz')
+        w = parent
+        steps = []
+        for transform in transforms:
+            steps.append(structural.check(gen.refit(w, transform), transform, aud))
+            w = gen.apply_stage(w, transform)
+            for mode in ('omit-final-output', 'wrong-final-sign'):
+                bad = copy.deepcopy(w)
+                if mode == 'omit-final-output':
+                    bad['restore'].pop()
+                else:
+                    bad['restore'][-1][3] *= -1
+                profile, inventory = pm.frame_report(bad)
+                bad['report']['local_profile'], bad['report']['width_inventory'] = profile, inventory
+                z = copy.deepcopy(bad)
+                z['A'] = z['A'][z['prelude_events']:]
+                bad['cleanup'] = pm.derive_cleanup(z, set(map(int, z['helper_final'])))
+                name = f'{tag}-{transform["helper"]}-{mode}'
+                path = out / (name + '.json.gz')
+                save_word(path, bad)
+                try:
+                    aud.run(path, out / (name + '.json'))
+                except (AssertionError, RuntimeError, ValueError) as error:
+                    controls[name] = str(error)
+                else:
+                    raise AssertionError('semantic mutant accepted: ' + name)
+        assert gen.apply(parent, transforms) == w == read(P / f'data/WORD-{tag}.json.gz')
+        audit_path = out / f'AUDIT-{tag}.json'
+        aud.run(P / f'data/WORD-{tag}.json.gz', audit_path)
+        audit = read(audit_path)
+        assert audit['independent_inputs'] == 632 and audit['restored_cold'] == audit['zero_buffers'] == gen.BUFFERS
+        assert audit['local_profile'] == gen.PROFILE and audit['width_inventory'] == gen.INVENTORY
+        records[tag] = {'parent_sha256': sha(P / f'data/PARENT-{tag}.json.gz'),
+                        'word_sha256': sha(P / f'data/WORD-{tag}.json.gz'),
+                        'structures': steps, 'audit': audit}
+    assert all(sha(P / n) == h for n, h in pins.items()), 'input drift'
+    assert len(controls) == 4 * len(gen.HELPERS)
+    result = {'status': 'PASS_NINE_ADDITIONAL_PAIRED_EXTRACTIONS', 'providers': records,
+              'semantic_controls': controls,
+              'scope': 'Exact finite local identity and invoice; full native/owner/outer checks separate.'}
+    (out / 'RESULT.json').write_text(json.dumps(result, indent=2, sort_keys=True) + '\n')
+    print(result['status'], flush=True)
+
+
+if __name__ == '__main__':
+    main()