diff --git a/research/two-sided-helper-extraction/.gitattributes b/research/two-sided-helper-extraction/.gitattributes
new file mode 100644
index 0000000000..d4d81cd1ac
--- /dev/null
+++ b/research/two-sided-helper-extraction/.gitattributes
@@ -0,0 +1,4 @@
+vendor/** -text
+data/** -text
+evidence/** -text
+allocation/** -text
diff --git a/research/two-sided-helper-extraction/ALLOCATION-PINS.json b/research/two-sided-helper-extraction/ALLOCATION-PINS.json
new file mode 100644
index 0000000000..36daf943e6
--- /dev/null
+++ b/research/two-sided-helper-extraction/ALLOCATION-PINS.json
@@ -0,0 +1,14 @@
+{
+  "allocation/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "allocation/FILL.json.gz": "d6585a3b05fb86efd08b1925c5ae0a03265c30f895f5e2c4e1cdfe91978cd3ef",
+  "allocation/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/PROFILE.json": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+  "allocation/PROVIDERS.json": "91a212677bc21d45990ad811dba16a6ce2f89fc43b61e67f75a09c35c6eace3b",
+  "allocation/RESULT.json": "5ba974e706ff58a523097693bfdc0e00935ddf4ad5d5ea467c38dc8a4fad4210",
+  "allocation/baseline/CLAIM.json": "29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30",
+  "allocation/baseline/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "allocation/baseline/PROFILE.json": "528400282a268b6e5983a5251af6040450fa0e7d9ddf7d65e4a0aa6a0b9096a6",
+  "allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e",
+  "allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e",
+  "allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461"
+}
diff --git a/research/two-sided-helper-extraction/CLAIM.json b/research/two-sided-helper-extraction/CLAIM.json
new file mode 100644
index 0000000000..4edc2cb723
--- /dev/null
+++ b/research/two-sided-helper-extraction/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/two-sided-helper-extraction/CONSTRUCTION.md b/research/two-sided-helper-extraction/CONSTRUCTION.md
new file mode 100644
index 0000000000..650131970c
--- /dev/null
+++ b/research/two-sided-helper-extraction/CONSTRUCTION.md
@@ -0,0 +1,86 @@
+# Paired input/output extraction
+
+Let M denote the complete non-target forward operator of the pinned PR2894
+word: the A gates after the entry prelude, the B gates and formal invertible
+warps, and the restore gates. Target writes are omitted in this definition;
+they are checked separately by the full independent word auditor. Operators
+are noncommuting formal symbols, so the argument uses no numerical sampling.
+
+Let H contain zero-entry helper registers which are neither existing restored
+helpers nor sources of the initial operator corrections. For a terminal
+hyperplane E, let R consist of registers whose current terminal frames lie in
+E. Seek a column y and a row alpha, supported on R, such that
+
+- v = M^-1 y is scalar and supported on H;
+- u = alpha M is scalar and supported on H;
+- alpha y = u v = 1.
+
+These are two exact nullspace conditions with a nonzero pairing. Finite-field
+linear algebra can nominate candidates, but every published identity here is
+replayed over rational coefficients in the free operator algebra.
+
+Choose an invertible dyadic input change S and output change T with
+`S e_h = v`, `u S = e_h^T`, `T y = e_h`, and `e_h^T T = alpha`.
+Then the h column and h row of `T M S` are both the corresponding identity
+column and row. Register h is restored exactly for every arbitrary dirty
+helper input and is not read by other output registers. This supplies the
+cold endpoint needed by the inverse-reverse cleanup contract.
+
+For h=408, E is the binary hyperplane perpendicular to 52, with canonical
+basis `(256,128,64,36,20,8,2,1)`. The output certificate is especially small:
+
+```
+alpha = e_408^T + (1/2)e_42^T + e_105^T
+y = 2 e_42
+
+408 += (1/2) * 42
+408 += 105
+42  -= 2 * 408
+```
+
+All three terminal additions use frame E. The 24 input gates in
+`data/TRANSFORM.json` act at frame zero. They include one scaling by 2 and
+otherwise dyadic additions. `structure.py` derives S, T, M, u, v, alpha and y
+from the literal gates and checks all seven identities, independently of the
+word producer. `verify.py` also checks both full target maps and the dual
+orientation with the inherited exact auditor.
+
+The target correction becomes `C S`. The initial operator corrections retain
+their inputs because S acts only outside their source set. Warps, the cut,
+ports, target levels, removed helpers and the entry prelude are unchanged.
+The changed sections are exactly A, restore, helper_final, compensation,
+report and cleanup. Inverse-reverse cleanup is regenerated and checked from
+the full new word; its new private buffer is allocated, cleared and charged.
+
+The complete per-call profile changes from
+`{1:2404,2:642,3:262,4:128,5:26,8:8}` to
+`{1:2407,2:640,3:262,4:128,5:26,8:8}`. Helper408 changes width 9 to 8;
+there remain 408 live helpers and 632 independent inputs, with **73** private
+zero buffers instead of 72.
+
+# Owner allocation and cost
+
+Keeping PR2894's fill is worse despite the local improvement. The shipped fill
+starts from that literal T74 allocation, makes 545 same-call width exchanges,
+then 222 whole-role relocations. The exchanges preserve the set of physical
+owner families at each call. Every relocation explicitly checks the owner
+window and rejects a family already used in the call; the final independent
+auditor rechecks all 271,728 roles, compact offsets, capacity, chronology and
+family distinctness. These are discovery heuristics, with no optimality claim.
+
+The actual paid profile is
+`{1:1620344,2:426241,3:180732,4:85248,5:25700,6:120,7:1,8:5328,23:1,32:14,48:26837}`.
+Its rank mass is exactly `65088*74`. It includes every unused owner remainder.
+The complete physical stock is `66304 + 408 + 8 + 73 + 2 = 66795`.
+The inherited owner-only checker has a historical 72-buffer display field;
+our wrapper explicitly replaces that field and labels its provenance. The
+complete rebind, block-norm certificate and outer invoice independently check
+the actual 73-buffer namespace, endpoints, stock and prefix reserve.
+
+The admission adapter preserves all inherited tests, with the new source pin
+and buffer constants bound explicitly. In particular, the dimension-72
+symplectic-group stock factor is unchanged: it is not a private-buffer count.
+The old source/parent artifacts are read-only. Both new providers run the full
+five native stages; retained providers and the 16-stage retained parent may be
+reused only through exact complete-cache/source/claim receipts, and the replay
+records this distinction.
diff --git a/research/two-sided-helper-extraction/CREDITS.md b/research/two-sided-helper-extraction/CREDITS.md
new file mode 100644
index 0000000000..4233009b6a
--- /dev/null
+++ b/research/two-sided-helper-extraction/CREDITS.md
@@ -0,0 +1,39 @@
+# Credit and scope
+
+Jeremy Diviney, with substantial OpenAI Codex assistance, contributed the
+paired input/output subspace search, the explicit helper408 extraction, the
+exact structural certificate, the owner-width exchange/relocation repair,
+and the source-bound 73-buffer integration. No independent human review is
+claimed. This is a new application of ordinary exact linear algebra to these
+literal words, not a claim to have invented nullspace or basis-change methods.
+
+The immediate parent is Jeremy Kothe / `jeremykothe2`, PR2894 at
+`18d03c447886895ef9abf888398178e0428533ca`. Its two preload-resynthesized quartets,
+T74 owner order and fill, reconstruction, and complete admission remain
+credited. `vendor/preload_move.py` is unchanged from that package.
+
+The construction inherits Yiyang Lu / `Lyy-iiis`'s PR2857 staged shared kernels
+and source-bound overlay/native/release tooling; Dugongue's PR2863 packing;
+Marius-Paul Dumitrean's PR2843/PR2802 pattern-flow and retired-helper lineage;
+Jeremy Kothe's PR2833 dirt-entry supplier; and Philippe Van Velzen's PR2853
+cost and block-energy lineage. Tekalign's PR2751/PR2839 owner audit and
+admission lineage is retained in the corresponding code headers. The exact
+moment auditor is PR2894's `tools/audit_moment2857.py`, changing only the
+comparison pin and label to PR2894.
+
+The independently written exact scalar/frame auditor retains its original
+icekylinx attribution. The fast native package is copied byte-for-byte from
+PR2833's `new/fastnative`; it retains the PR2768 sparse engine and all nested
+PR2226 Clifford/operator notices. The copied material, including its original
+line endings, is pinned in `PINS.json`.
+
+The new terminal recovery changes literal gates and adds a cold endpoint.
+PR2904's fixed-gate dirty-entry/refit negative census does not cover this
+operation. The initial compensation-kernel search failed before this pivot;
+it is not presented as a new universal obstruction. Advisory overlap was
+checked against open PRs and Discussion bodies before discovery and again
+before submission. That coverage is not a novelty guarantee.
+
+The selected repository result is not changed. A passing finite release uses
+the inherited all-size/compiler/outer hypotheses and does not establish an
+unconditional integer-multiplication theorem.
diff --git a/research/two-sided-helper-extraction/MANIFEST.json b/research/two-sided-helper-extraction/MANIFEST.json
new file mode 100644
index 0000000000..b69fc6eaa2
--- /dev/null
+++ b/research/two-sided-helper-extraction/MANIFEST.json
@@ -0,0 +1,105 @@
+{
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+  "CLAIM.json": "2406680a07b43a69b0f12f8462cc43f3616f3c8cb0a46bc767541b45945cd2bf",
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diff --git a/research/two-sided-helper-extraction/PINS.json b/research/two-sided-helper-extraction/PINS.json
new file mode 100644
index 0000000000..2125095d52
--- /dev/null
+++ b/research/two-sided-helper-extraction/PINS.json
@@ -0,0 +1,52 @@
+{
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diff --git a/research/two-sided-helper-extraction/README.md b/research/two-sided-helper-extraction/README.md
new file mode 100644
index 0000000000..87f1421e9e
--- /dev/null
+++ b/research/two-sided-helper-extraction/README.md
@@ -0,0 +1,90 @@
+# Two-sided helper extraction on PR2894
+
+The explicit input/output basis change isolates helper408 as an additional
+restored cold helper. Its width drops from 9 to 8, with one additional private
+zero buffer. Both changed providers pass exact 632-input forward/dual audits
+and the full five-stage native chain. A repaired T74 owner allocation gives
+
+**κ = 0.001720398337354237885931 − 10⁻⁴⁶ − 10⁻⁷⁰**, conditional on the inherited
+supplier/outer theorem hypotheses. This is **+2.13808976768352857×10⁻⁷**
+(about **0.0124%**) over [PR2894](https://github.com/CrocSwap/integer-mult-bounds/pull/2894)
+at `18d03c447886895ef9abf888398178e0428533ca`. The selected repository result
+is not changed. The exact headline and full release receipt are bound in
+`CLAIM.json` and `evidence/`.
+
+This changes the local gate word and the cold-helper endpoint; the subsequent
+owner repair is necessary to realize a gain. Keeping the old fill loses.
+[CONSTRUCTION.md](CONSTRUCTION.md) explains the paired-nullspace identity and
+complete cost changes. The method uses standard exact linear algebra; no
+claim of a new general mathematical theorem or packing optimum is made.
+
+Credit: Jeremy Kothe's PR2894/2833 supplier and allocation, Yiyang Lu's PR2857
+shared-kernel/native/overlay work, Dugongue's PR2863 packing, Marius-Paul
+Dumitrean's PR2843/2802 lineage, Philippe Van Velzen's PR2853 cost work,
+Tekalign's admission/owner checkers, and the retained exact/native authors.
+Our contribution is the helper408 extraction, independent structural
+certificate, actual allocation repair and explicit 73-buffer integration.
+See [CREDITS.md](CREDITS.md). Substantial OpenAI Codex assistance; no independent
+human review is claimed.
+
+## Reproduce
+
+Tested on Linux, Python 3.12.3. The registered replay needs NumPy 2.5.4 and
+runs the exact construction, semantic controls, both fresh native chains,
+owner checks and rational moment. It authenticates the stored full-release
+chain; it does not rerun complete integrated admission.
+
+```sh
+python3.12 scripts/research_package.py --package research/two-sided-helper-extraction --check-only
+python3.12 scripts/research_package.py --package research/two-sided-helper-extraction
+```
+
+For a direct local-only check (standard library, fresh output directory):
+
+```sh
+python3.12 -B research/two-sided-helper-extraction/verify.py --work /tmp/helper408-local
+python3.12 -B research/two-sided-helper-extraction/check_allocation.py --work /tmp/helper408-owners
+```
+
+For complete source/native/physical/outer admission, first obtain the exact
+upstream Git objects. The driver exports them without changing the checkout
+and verifies the complete predecessor manifest before executing its code.
+
+```sh
+git fetch https://github.com/CrocSwap/integer-mult-bounds.git \
+  18d03c447886895ef9abf888398178e0428533ca \
+  e9307b48d7d1b690939935ecef0f8e524e6d92f4
+nice -n 15 env OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 \
+  python3.12 -B research/two-sided-helper-extraction/reproduce.py \
+  --repo . --work /tmp/helper408-complete
+```
+
+Use the numerical dependencies recorded in `evidence/ENVIRONMENT.json` for the
+complete inherited replay. Outputs must be fresh and external. The default
+rebuilds the retained native/parent evidence. `--retained /path/to/prior-run`
+explicitly reuses that run's `native-cache` and `NATIVE-RECEIPT.json`, only after
+full source/claim/cache and all 16 parent stages are authenticated. The recorded
+run reused retained evidence from our previous complete replay, and freshly
+replayed both changed providers. It does not claim all retained work was fresh.
+`--dry-run` only exports/authenticates PR2894 and writes the recipe.
+
+The integrated certificate uses 74 replicas, 666 calls, 271,728 helper roles,
+66,304 live families and **66,795 physical families**, including all **73**
+private zero buffers. The exact paid histogram includes every residual owner
+child. All inherited phase, cleanup, prefix, stock, geometry, rejection and
+outer checks remain required. No fractional packing estimate is used as a
+certificate.
+
+## Open next questions
+
+1. Can a second independent paired input/output direction be extracted while
+   preserving helper408? Repeat the exact nullspace construction on the new
+   word, then charge its actual native and owner costs. A modular nominee or
+   local width reduction is insufficient.
+2. Can a better literal allocation approach the new inventory's relaxation?
+   Start from the shipped feasible fill and test bounded exchanges or
+   relocations. Full exact admission remains mandatory for any higher claim.
+
+The structured questions, stopping rule and original task card are in
+[TASK.json](TASK.json). Initial failed screens, solver timeouts and the
+successful deterministic repair are summarized in `evidence/SEARCH.json`.
diff --git a/research/two-sided-helper-extraction/SOURCES.json b/research/two-sided-helper-extraction/SOURCES.json
new file mode 100644
index 0000000000..b9b9a1d41d
--- /dev/null
+++ b/research/two-sided-helper-extraction/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "572207084e5c2c21958969cc2e4c58fd4df8afb6",
+  "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/two-sided-helper-extraction/TASK.json b/research/two-sided-helper-extraction/TASK.json
new file mode 100644
index 0000000000..b5d6ee5e3f
--- /dev/null
+++ b/research/two-sided-helper-extraction/TASK.json
@@ -0,0 +1,72 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-new-helper-inventory",
+  "priority_revision": 5,
+  "base_commit": "572207084e5c2c21958969cc2e4c58fd4df8afb6",
+  "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": "Two-sided dyadic basis changes extracting one additional cold helper from the PR2894 non-target operator; exact local/native audits, actual T74 hosting and complete outer accounting.",
+  "scope_change_reason": "Direct compensation-kernel/first-frame screens yielded no admissible extension; allowing a coupled input/output basis change changes the local helper endpoint and literal gate word outside fixed-gate entry/refit screens.",
+  "bottleneck_link": "A smaller helper width alone is not profitable: the full budget includes local delta3H1-2H2, an additional private zero buffer, actual owner residuals and all outer costs.",
+  "budget_minutes": 60,
+  "stop_rule": "Promote only if exact local/native/owner/outer checks all pass and the fully charged value beats pinned PR2894; otherwise publish the scoped construction and unresolved admission.",
+  "outcome": "completed",
+  "evidence": "CLAIM.json, evidence/ADMISSION-RESULT.json, RELEASE-RECEIPT.json, FULL-NATIVE-RECEIPT.json, EXACT-OWNER-MOMENT.json; registered and full replay commands in README.",
+  "author": "Jeremy Diviney",
+  "ai_assistance": "Substantial OpenAI Codex assistance for exact algebra, optimized NumPy/SciPy nomination, deterministic owner repair, implementation and verification. No subagents used.",
+  "open_questions": [
+    {
+      "question": "Can a second independent input/output channel be isolated without spoiling the first?",
+      "why_it_matters": "The exact subspace screen retains more than one paired direction; an additional recovered helper could further change the paid profile.",
+      "first_step": "Repeat the exact paired-nullspace construction after helper408, then compare the complete local and actual idle budgets.",
+      "blocked_by": "Both provider native checks and a newly charged owner/stock/outer certificate for any composed word."
+    },
+    {
+      "question": "How much of the new inventory packing relaxation can be attained?",
+      "why_it_matters": "The exhibited repair leaves residues and does not claim optimality.",
+      "first_step": "Use the shipped literal fill as a feasible seed for bounded width exchanges/relocations; recheck actual windows and families.",
+      "blocked_by": "Any candidate needs complete exact outer admission; a fractional root alone is not a new bound."
+    }
+  ]
+}
diff --git a/research/two-sided-helper-extraction/VERIFY.json b/research/two-sided-helper-extraction/VERIFY.json
new file mode 100644
index 0000000000..6643b2df33
--- /dev/null
+++ b/research/two-sided-helper-extraction/VERIFY.json
@@ -0,0 +1,12 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": ["numpy==2.5.4"],
+  "inputs": [],
+  "commands": [{
+    "argv": ["{python}", "-B", "{package}/run_registered.py"],
+    "timeout_seconds": 300,
+    "checks": "Complete package/vendor/data pins; exact source-stage and two-sided subspace identities; both 632-input abstract forward/dual audits and four semantic mutations; fresh five-stage native chains for both words (all-column, phases, cleanup, rejection controls); actual T74 owner geometry plus mutations and directed rational moment; stored complete release/native receipt chain. Full integrated outer/retained replay is a separate reproduce.py command."
+  }]
+}
diff --git a/research/two-sided-helper-extraction/allocation/DISPATCH.json b/research/two-sided-helper-extraction/allocation/DISPATCH.json
new file mode 100644
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diff --git a/research/two-sided-helper-extraction/allocation/PROFILE.json b/research/two-sided-helper-extraction/allocation/PROFILE.json
new file mode 100644
index 0000000000..916437d9e1
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/PROFILE.json
@@ -0,0 +1 @@
+{"1":1620344,"2":426241,"3":180732,"4":85248,"5":25700,"6":120,"7":1,"8":5328,"23":1,"32":14,"48":26837}
\ No newline at end of file
diff --git a/research/two-sided-helper-extraction/allocation/PROVIDERS.json b/research/two-sided-helper-extraction/allocation/PROVIDERS.json
new file mode 100644
index 0000000000..45de4bc33f
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/PROVIDERS.json
@@ -0,0 +1 @@
+{"extra":{"actual_paid_profile":{"1":2407,"2":640,"3":262,"4":128,"5":26,"8":8},"widths":[9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,9,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,4,9,4,9,8,9,9,4,9,9,9,9,9,9,9,9,4,9,4,9,8,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,9,9,9,9,9,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,7,7,7,7,7,7,7,7,9,8,8,9,8,9,8,9,9,9,9,9,9,9,9,9,8,8,7,7,7,7,8,9,8,9,7,7,7,7,7,7,9,9,9,9,8,8,8,9,8,8,9,9,9,9,8,7,7,8,9,8,8,9,9,9,9,8,8,8,7,7,7,7,7,7,7,7,8,7,7,7,7,7,7,7,7,7,7,7,8,7,8,8,9,9,9,9,8,8,8,8,7,7,7,7,9,8,9,8,8,8,8,8,7,7,9,8,9,8,7,7,7,7,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8]},"gauge44":{"actual_paid_profile":{"1":2407,"2":640,"3":262,"4":128,"5":26,"8":8},"widths":[9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,9,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,4,9,4,9,8,9,9,4,9,9,9,9,9,9,9,9,4,9,4,9,8,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,4,9,4,9,4,9,9,9,9,4,9,9,9,9,9,9,9,9,9,9,9,9,9,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,7,7,7,7,7,7,7,7,9,8,8,9,8,9,8,9,9,9,9,9,9,9,9,9,8,8,7,7,7,7,8,9,8,9,7,7,7,7,7,7,9,9,9,9,8,8,8,9,8,8,9,9,9,9,8,7,7,8,9,8,8,9,9,9,9,8,8,8,7,7,7,7,7,7,7,7,8,7,7,7,7,7,7,7,7,7,7,7,8,7,8,8,9,9,9,9,8,8,8,8,7,7,7,7,9,8,9,8,8,8,8,8,7,7,9,8,9,8,7,7,7,7,8,8,8,8,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,5,5,8,8,8,8]}}
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diff --git a/research/two-sided-helper-extraction/allocation/RESULT.json b/research/two-sided-helper-extraction/allocation/RESULT.json
new file mode 100644
index 0000000000..325169cd4c
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/RESULT.json
@@ -0,0 +1 @@
+{"calls":666,"floating_root":0.0017203983373542838,"idle":{"1":17282,"2":1,"3":6240,"5":8384,"6":120,"7":1,"23":1,"32":14,"48":26837},"live":66304,"physical":66795,"physical_scope":"actual helper408 buffer count; whole outer invoice not yet admitted","profile":{"1":1620344,"2":426241,"3":180732,"4":85248,"5":25700,"6":120,"7":1,"8":5328,"23":1,"32":14,"48":26837},"rank_mass":4816512,"replicas":74,"roles":271728,"status":"PASS_INDEPENDENT_OWNER_CHECK_FLOATING_PRICE_ONLY"}
\ No newline at end of file
diff --git a/research/two-sided-helper-extraction/allocation/baseline/CLAIM.json b/research/two-sided-helper-extraction/allocation/baseline/CLAIM.json
new file mode 100644
index 0000000000..7a0f12d1df
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/baseline/CLAIM.json
@@ -0,0 +1,39 @@
+{
+  "admission_result_sha256": "e8ec9091be8e6c20752fdc9e9904870f60303fba7194af029a16498afdc7f318",
+  "baseline_claim_sha256": "c2a04b639c86f462caef654a29817545c57b8e5ba809e37d4d476d3577f5cd6f",
+  "baseline_head": "0b2e2537b368a0cade07ce3f71452ea018ebe394",
+  "baseline_kappa": "17200966286848326009719999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "baseline_pr": 2857,
+  "calls": 666,
+  "display": "0.001720184528377469533074 - 10^-46 - 10^-70",
+  "gain_decimal_over_pr2875": "8.372296058360512999292439366446879999990E-8",
+  "gain_over_full_pr2857": "43949846318466051/500000000000000000000000",
+  "gain_over_pr2863": "8372296058360513/100000000000000000000000",
+  "gain_over_pr2875": "8372296058360512999292439366446879999990000000000000000999999990000000000000001/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "helper_roles": 271728,
+  "inherited_hypotheses": "All-size compiler; common-label/source access; mutable source; hosting; precision/tape; recovery; ordinary recursion; BIT; analytic transfer. No new Lean audit or unconditional multiplication theorem.",
+  "kappa": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017201845283774695330739999999999999999999998999999999999999999999999",
+  "live": 66304,
+  "native_receipt_sha256": "bd438796daa50d36f03cc6df6f0c4ed655ac61804e586e73056286d0bfb3127f",
+  "original_source_head": "e9307b48d7d1b690939935ecef0f8e524e6d92f4",
+  "paid_profile": {
+    "1": 1618380,
+    "2": 427572,
+    "3": 180819,
+    "4": 85248,
+    "48": 26825,
+    "5": 25863,
+    "8": 5328
+  },
+  "physical": 66794,
+  "preload_move_review_sha256": "7510f96d3c368f12dba9ffd69a8df30f68d8a23ceb6cd9792415941f04c313ab",
+  "proof_origin": "Informal proofs and exact finite computational checks, with AI assistance. No independent human peer review claimed.",
+  "release_receipt_sha256": "c96f5e285893966b8b5cd39c08461adea88f0d8985feafb9de3fad1d9d840890",
+  "replicas": 74,
+  "retained_payload": 2048,
+  "scope": "Conditional outer headline. Two more staged quartets (preload re-synthesis) on the PR2857 shared-kernel words with a residue-free T74 owner fill. No maximum or optimality claim over changed native words, inventories, geometries, controllers or multiplication algorithms.",
+  "source_manifest_entries": 553,
+  "source_manifest_sha256": "4da246899e2c509dd8c6e5af34905c6124ca17671b188e11ac37e36adf449504",
+  "status": "PASS_CONDITIONAL_T74_PRELOAD_MOVE_RELEASE"
+}
diff --git a/research/two-sided-helper-extraction/allocation/baseline/ORDER.json b/research/two-sided-helper-extraction/allocation/baseline/ORDER.json
new file mode 100644
index 0000000000..7409c4df10
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/baseline/ORDER.json
@@ -0,0 +1 @@
+[[0,0],[0,37],[0,1],[0,38],[0,2],[0,39],[0,3],[0,40],[0,4],[0,41],[1,0],[1,37],[0,5],[0,42],[1,1],[1,38],[0,6],[0,43],[1,2],[1,39],[0,7],[0,44],[1,3],[1,40],[0,8],[0,45],[1,4],[1,41],[0,9],[0,46],[2,0],[2,37],[1,5],[1,42],[0,10],[0,47],[2,1],[2,38],[1,6],[1,43],[0,11],[0,48],[2,2],[2,39],[1,7],[1,44],[0,12],[0,49],[2,3],[2,40],[1,8],[1,45],[0,13],[0,50],[2,4],[2,41],[1,9],[1,46],[3,0],[3,37],[0,14],[0,51],[2,5],[2,42],[1,10],[1,47],[3,1],[3,38],[0,15],[0,52],[2,6],[2,43],[1,11],[1,48],[3,2],[3,39],[0,16],[0,53],[2,7],[2,44],[1,12],[1,49],[3,3],[3,40],[0,17],[0,54],[2,8],[2,45],[1,13],[1,50],[3,4],[3,41],[0,18],[0,55],[2,9],[2,46],[4,0],[4,37],[1,14],[1,51],[3,5],[3,42],[0,19],[0,56],[2,10],[2,47],[4,1],[4,38],[1,15],[1,52],[3,6],[3,43],[0,20],[0,57],[2,11],[2,48],[4,2],[4,39],[1,16],[1,53],[3,7],[3,44],[0,21],[0,58],[2,12],[2,49],[4,3],[4,40],[1,17],[1,54],[3,8],[3,45],[0,22],[0,59],[2,13],[2,50],[4,4],[4,41],[1,18],[1,55],[3,9],[3,46],[0,23],[0,60],[5,0],[5,37],[2,14],[2,51],[4,5],[4,42],[1,19],[1,56],[3,10],[3,47],[0,24],[0,61],[5,1],[5,38],[2,15],[2,52],[4,6],[4,43],[1,20],[1,57],[3,11],[3,48],[0,25],[0,62],[5,2],[5,39],[2,16],[2,53],[4,7],[4,44],[1,21],[1,58],[3,12],[3,49],[0,26],[0,63],[5,3],[5,40],[2,17],[2,54],[4,8],[4,45],[1,22],[1,59],[3,13],[3,50],[0,27],[0,64],[5,4],[5,41],[2,18],[2,55],[4,9],[4,46],[1,23],[1,60],[6,0],[6,37],[3,14],[3,51],[0,28],[0,65],[5,5],[5,42],[2,19],[2,56],[4,10],[4,47],[1,24],[1,61],[6,1],[6,38],[3,15],[3,52],[0,29],[0,66],[5,6],[5,43],[2,20],[2,57],[4,11],[4,48],[1,25],[1,62],[6,2],[6,39],[3,16],[3,53],[0,30],[0,67],[5,7],[5,44],[2,21],[2,58],[4,12],[4,49],[1,26],[1,63],[6,3],[6,40],[3,17],[3,54],[0,31],[0,68],[5,8],[5,45],[2,22],[2,59],[4,13],[4,50],[1,27],[1,64],[6,4],[6,41],[3,18],[3,55],[0,32],[0,69],[5,9],[5,46],[2,23],[2,60],[7,0],[7,37],[4,14],[4,51],[1,28],[1,65],[6,5],[6,42],[3,19],[3,56],[0,33],[0,70],[5,10],[5,47],[2,24],[2,61],[7,1],[7,38],[4,15],[4,52],[1,29],[1,66],[6,6],[6,43],[3,20],[3,57],[0,34],[0,71],[5,11],[5,48],[2,25],[2,62],[7,2],[7,39],[4,16],[4,53],[1,30],[1,67],[6,7],[6,44],[3,21],[3,58],[0,35],[0,72],[5,12],[5,49],[2,26],[2,63],[7,3],[7,40],[4,17],[4,54],[1,31],[1,68],[6,8],[6,45],[3,22],[3,59],[0,36],[0,73],[5,13],[5,50],[2,27],[2,64],[7,4],[7,41],[4,18],[4,55],[1,32],[1,69],[6,9],[6,46],[3,23],[3,60],[8,0],[8,37],[5,14],[5,51],[2,28],[2,65],[7,5],[7,42],[4,19],[4,56],[1,33],[1,70],[6,10],[6,47],[3,24],[3,61],[8,1],[8,38],[5,15],[5,52],[2,29],[2,66],[7,6],[7,43],[4,20],[4,57],[1,34],[1,71],[6,11],[6,48],[3,25],[3,62],[8,2],[8,39],[5,16],[5,53],[2,30],[2,67],[7,7],[7,44],[4,21],[4,58],[1,35],[1,72],[6,12],[6,49],[3,26],[3,63],[8,3],[8,40],[5,17],[5,54],[2,31],[2,68],[7,8],[7,45],[4,22],[4,59],[1,36],[1,73],[6,13],[6,50],[3,27],[3,64],[8,4],[8,41],[5,18],[5,55],[2,32],[2,69],[7,9],[7,46],[4,23],[4,60],[6,14],[6,51],[3,28],[3,65],[8,5],[8,42],[5,19],[5,56],[2,33],[2,70],[7,10],[7,47],[4,24],[4,61],[6,15],[6,52],[3,29],[3,66],[8,6],[8,43],[5,20],[5,57],[2,34],[2,71],[7,11],[7,48],[4,25],[4,62],[6,16],[6,53],[3,30],[3,67],[8,7],[8,44],[5,21],[5,58],[2,35],[2,72],[7,12],[7,49],[4,26],[4,63],[6,17],[6,54],[3,31],[3,68],[8,8],[8,45],[5,22],[5,59],[2,36],[2,73],[7,13],[7,50],[4,27],[4,64],[6,18],[6,55],[3,32],[3,69],[8,9],[8,46],[5,23],[5,60],[7,14],[7,51],[4,28],[4,65],[6,19],[6,56],[3,33],[3,70],[8,10],[8,47],[5,24],[5,61],[7,15],[7,52],[4,29],[4,66],[6,20],[6,57],[3,34],[3,71],[8,11],[8,48],[5,25],[5,62],[7,16],[7,53],[4,30],[4,67],[6,21],[6,58],[3,35],[3,72],[8,12],[8,49],[5,26],[5,63],[7,17],[7,54],[4,31],[4,68],[6,22],[6,59],[3,36],[3,73],[8,13],[8,50],[5,27],[5,64],[7,18],[7,55],[4,32],[4,69],[6,23],[6,60],[8,14],[8,51],[5,28],[5,65],[7,19],[7,56],[4,33],[4,70],[6,24],[6,61],[8,15],[8,52],[5,29],[5,66],[7,20],[7,57],[4,34],[4,71],[6,25],[6,62],[8,16],[8,53],[5,30],[5,67],[7,21],[7,58],[4,35],[4,72],[6,26],[6,63],[8,17],[8,54],[5,31],[5,68],[7,22],[7,59],[4,36],[4,73],[6,27],[6,64],[8,18],[8,55],[5,32],[5,69],[7,23],[7,60],[6,28],[6,65],[8,19],[8,56],[5,33],[5,70],[7,24],[7,61],[6,29],[6,66],[8,20],[8,57],[5,34],[5,71],[7,25],[7,62],[6,30],[6,67],[8,21],[8,58],[5,35],[5,72],[7,26],[7,63],[6,31],[6,68],[8,22],[8,59],[5,36],[5,73],[7,27],[7,64],[6,32],[6,69],[8,23],[8,60],[7,28],[7,65],[6,33],[6,70],[8,24],[8,61],[7,29],[7,66],[6,34],[6,71],[8,25],[8,62],[7,30],[7,67],[6,35],[6,72],[8,26],[8,63],[7,31],[7,68],[6,36],[6,73],[8,27],[8,64],[7,32],[7,69],[8,28],[8,65],[7,33],[7,70],[8,29],[8,66],[7,34],[7,71],[8,30],[8,67],[7,35],[7,72],[8,31],[8,68],[7,36],[7,73],[8,32],[8,69],[8,33],[8,70],[8,34],[8,71],[8,35],[8,72],[8,36],[8,73]]
\ No newline at end of file
diff --git a/research/two-sided-helper-extraction/allocation/baseline/PROFILE.json b/research/two-sided-helper-extraction/allocation/baseline/PROFILE.json
new file mode 100644
index 0000000000..a1a5cb62c3
--- /dev/null
+++ b/research/two-sided-helper-extraction/allocation/baseline/PROFILE.json
@@ -0,0 +1 @@
+{"1":1618380,"2":427572,"3":180819,"4":85248,"5":25863,"8":5328,"48":26825}
\ No newline at end of file
diff --git a/research/two-sided-helper-extraction/allocation/vendor/PLAN.json.gz b/research/two-sided-helper-extraction/allocation/vendor/PLAN.json.gz
new file mode 100644
index 0000000000..7a1db55a4d
Binary files /dev/null and b/research/two-sided-helper-extraction/allocation/vendor/PLAN.json.gz differ
diff --git a/research/two-sided-helper-extraction/allocation/vendor/TEMPLATE.json.gz b/research/two-sided-helper-extraction/allocation/vendor/TEMPLATE.json.gz
new file mode 100644
index 0000000000..114808c32b
Binary files /dev/null and b/research/two-sided-helper-extraction/allocation/vendor/TEMPLATE.json.gz differ
diff --git a/research/two-sided-helper-extraction/allocation/vendor/independent_owners.py b/research/two-sided-helper-extraction/allocation/vendor/independent_owners.py
new file mode 100644
index 0000000000..16013201b1
--- /dev/null
+++ b/research/two-sided-helper-extraction/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/two-sided-helper-extraction/check_allocation.py b/research/two-sided-helper-extraction/check_allocation.py
new file mode 100644
index 0000000000..461b32c08d
--- /dev/null
+++ b/research/two-sided-helper-extraction/check_allocation.py
@@ -0,0 +1,33 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Literal owner verification, newly charged private stock and exact moment."""
+import argparse,copy,gzip,hashlib,json,sys,types
+from pathlib import Path
+P=Path(__file__).resolve().parent
+
+def read(p):
+ b=p.read_bytes();return json.loads(gzip.decompress(b) if p.suffix=='.gz' else b)
+def load(n,p):
+ m=types.ModuleType(n);exec(compile(p.read_bytes(),str(p),'exec'),m.__dict__);return m
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--work',type=Path,required=True);a=ap.parse_args();out=a.work.resolve();assert __debug__ and not out.exists() and not out.is_relative_to(P);out.mkdir(parents=True)
+ pins=read(P/'ALLOCATION-PINS.json');assert {f.relative_to(P).as_posix():hashlib.sha256(f.read_bytes()).hexdigest() for f in (P/'allocation').rglob('*') if f.is_file()}==pins
+ owner=load('owners',P/'allocation/vendor/independent_owners.py');moment=load('moment',P/'tools/audit_moment.py');base=P/'allocation';providers={}
+ for tag,pid in [('base','gauge44'),('extra','extra')]:
+  w=read(P/f'data/WORD-{tag}.json.gz');helpers=sorted(set(range(224,704))-set(w['removed']))
+  providers[pid]={'widths':[len(w['helper_final'].get(str(h),[0]*9))-len(w['start_extra'].get(str(h),[])) for h in helpers],'actual_paid_profile':{int(r):n for r,n in w['report']['local_profile'].items()}}
+ order=read(base/'ORDER.json');fill=read(base/'FILL.json.gz');dispatch={(s,r):pid for s,r,pid in read(base/'DISPATCH.json')};profile=read(base/'PROFILE.json');plan=read(base/'vendor/PLAN.json.gz');template=read(base/'vendor/TEMPLATE.json.gz');T=len(order)//9
+ def check(f=fill):return owner.check(T,order,f,dispatch,profile,plan,template,providers)
+ result,win,_=check();assert T==74 and result['roles']==271728
+ # The credited geometry checker reports its historical 72-buffer stock.
+ # That field is not a source of physical evidence for this new word.
+ result['physical']=896*T+408+8+73+2;result['physical_source']='explicit 73-buffer local ABI; independently invoiced by complete release'
+ rejected={}
+ for name,fn in [('missing_role',lambda f:f['rows'].pop()),('duplicate_helper',lambda f:f['rows'][1].__setitem__(1,f['rows'][0][1])),('capacity_overflow',lambda f:f['rows'][0].__setitem__(5,49))]:
+  bad=copy.deepcopy(fill);fn(bad)
+  try:check(bad)
+  except ValueError as e:rejected[name]=str(e)
+  else:raise AssertionError('owner corruption accepted '+name)
+ m=moment.run(base,base/'baseline');result.update(status='PASS_HELPER408_LITERAL_OWNERS_AND_EXACT_MOMENT',controls=rejected,moment=m,scope='Exact local width-based whole-owner geometry and rational moment; full source/native/stock/outer admission separate.')
+ (out/'RESULT.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print(result['status'],m['target_decimal'],m['gain_decimal'])
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/data/PARENT-base.json.gz b/research/two-sided-helper-extraction/data/PARENT-base.json.gz
new file mode 100644
index 0000000000..0ca8149510
Binary files /dev/null and b/research/two-sided-helper-extraction/data/PARENT-base.json.gz differ
diff --git a/research/two-sided-helper-extraction/data/PARENT-extra.json.gz b/research/two-sided-helper-extraction/data/PARENT-extra.json.gz
new file mode 100644
index 0000000000..5c9e40118c
Binary files /dev/null and b/research/two-sided-helper-extraction/data/PARENT-extra.json.gz differ
diff --git a/research/two-sided-helper-extraction/data/TRANSFORM.json b/research/two-sided-helper-extraction/data/TRANSFORM.json
new file mode 100644
index 0000000000..0e81cdc3e3
--- /dev/null
+++ b/research/two-sided-helper-extraction/data/TRANSFORM.json
@@ -0,0 +1,271 @@
+{
+  "label": "n52-a0-v2-h408",
+  "helper": 408,
+  "normal": 52,
+  "profile": {
+    "1": 2407,
+    "2": 640,
+    "3": 262,
+    "4": 128,
+    "5": 26,
+    "8": 8
+  },
+  "inventory": {
+    "4": 26,
+    "5": 2,
+    "7": 62,
+    "8": 87,
+    "9": 231
+  },
+  "delta": {
+    "1": 3,
+    "2": -2
+  },
+  "pessimistic_local_plus_idle": 0.004766521998909923,
+  "before": [
+    [
+      "add",
+      226,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      227,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      230,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      231,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      233,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      234,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      236,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      239,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      401,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      402,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      403,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "add",
+      407,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      410,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      411,
+      408,
+      -1,
+      2,
+      []
+    ],
+    [
+      "add",
+      414,
+      408,
+      1,
+      2,
+      []
+    ],
+    [
+      "scale",
+      408,
+      2,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      401,
+      2,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      402,
+      -1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      403,
+      1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      404,
+      1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      405,
+      -1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      409,
+      1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      414,
+      -1,
+      1,
+      []
+    ],
+    [
+      "add",
+      408,
+      415,
+      1,
+      1,
+      []
+    ]
+  ],
+  "after": [
+    [
+      "add",
+      408,
+      42,
+      1,
+      2,
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ]
+    ],
+    [
+      "add",
+      408,
+      105,
+      1,
+      1,
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ]
+    ],
+    [
+      "add",
+      42,
+      408,
+      -2,
+      1,
+      [
+        256,
+        128,
+        64,
+        36,
+        20,
+        8,
+        2,
+        1
+      ]
+    ]
+  ]
+}
diff --git a/research/two-sided-helper-extraction/data/WORD-base.json.gz b/research/two-sided-helper-extraction/data/WORD-base.json.gz
new file mode 100644
index 0000000000..6303cfd847
Binary files /dev/null and b/research/two-sided-helper-extraction/data/WORD-base.json.gz differ
diff --git a/research/two-sided-helper-extraction/data/WORD-extra.json.gz b/research/two-sided-helper-extraction/data/WORD-extra.json.gz
new file mode 100644
index 0000000000..38af2b6ea7
Binary files /dev/null and b/research/two-sided-helper-extraction/data/WORD-extra.json.gz differ
diff --git a/research/two-sided-helper-extraction/evidence/ADAPTER-DERIVATION.json b/research/two-sided-helper-extraction/evidence/ADAPTER-DERIVATION.json
new file mode 100644
index 0000000000..f7c47d4eb2
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/ADAPTER-DERIVATION.json
@@ -0,0 +1,19 @@
+{
+  "source_manifest": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "source_count": 610,
+  "upstream_admit_sha256": "e7b11f72ab0d96d1c097b17967492c3f154ae419347c88d09518d46e11329d64",
+  "derived_admit_sha256": "a62c21eac4e0df502cbfb78c88b19a763fd351cde3c11c0588874f84db6992bf",
+  "upstream_blocknorm_sha256": "e5bfbad8e8e6cb4206f7ba92d333780f423918d8f217b474302346169e991f92",
+  "derived_blocknorm_sha256": "b53ebd53e3948f658c6da4f487a9ea10c9cb0a6acf2435750a32d6efeb9869c0",
+  "blocknorm_changes": {
+    "len(allocated)==72": "len(allocated)==73",
+    "all72 private": "all73 private",
+    "zero_buffers_allocated_and_cleared':72": "zero_buffers_allocated_and_cleared':73",
+    "r['zero_buffers_returned_to_zero']==72": "r['zero_buffers_returned_to_zero']==73",
+    "physical==live+8+408+72+2": "physical==live+8+408+73+2",
+    "'zero_buffers':[live+416,live+488], 'coefficient':[live+488,live+490]": "'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]",
+    "len(mp)==72": "len(mp)==73",
+    "72distinct private": "73distinct private"
+  },
+  "scope": "Explicit 72-to-73 buffer accounting; unchanged dimension72 symplectic stock, helper count408, columns632, phases/native and every retained outer guard."
+}
diff --git a/research/two-sided-helper-extraction/evidence/ADMISSION-RESULT.json b/research/two-sided-helper-extraction/evidence/ADMISSION-RESULT.json
new file mode 100644
index 0000000000..2d18261ade
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/ADMISSION-RESULT.json
@@ -0,0 +1,386 @@
+{
+  "actual_expected_helpers": 408,
+  "comparison_claim_sha256": "29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30",
+  "comparison_head": "18d03c447886895ef9abf888398178e0428533ca",
+  "comparison_kappa": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "comparison_pr": 2894,
+  "complex_lower": "1720398337354237885931/1000000000000000000000000",
+  "dispatch_sha256": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+  "external_input_sha256": {
+    "/home/jeremydiviney/intmult/build/contribution/t74-shared-kernel-search/channel_blocknorm.py": "b53ebd53e3948f658c6da4f487a9ea10c9cb0a6acf2435750a32d6efeb9869c0",
+    "/home/jeremydiviney/intmult/build/contribution/t74-shared-kernel-search/research/shared-kernel-packing/CLAIM.json": "29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30",
+    "/home/jeremydiviney/intmult/build/contribution/t74-shared-kernel-search/research/shared-kernel-packing/vendor/pr2857/vendor/pr2839/lift_parent.py": "9a1edd7d4ab4a2f2ac8d15b42b7e40f93653d65026bac59e4c1ce80b486bd60e",
+    "/home/jeremydiviney/intmult/build/contribution/t74-shared-kernel-search/research/shared-kernel-packing/vendor/pr2857/vendor/pr2839/reconstruct_replica.py": "5472811c24aef3852dc7e189dff5060076a6c0b25bfde928da50dcfe9b5bdc15",
+    "/home/jeremydiviney/intmult/build/contribution/t74-shared-kernel-search/research/shared-kernel-packing/vendor/pr2857/vendor/pr2839/replica_parent.py": "48bdbf28f59d80edb266803ec61bf5e22e8fb5e5a0e2b88004b6039147589bd4",
+    "/tmp/intmult-channel408-relocate/DISPATCH.json": "65e435bd68e97243c003677271b88485a29d4d0fae2dff1354100404a145e74c",
+    "/tmp/intmult-channel408-relocate/FILL.json.gz": "d6585a3b05fb86efd08b1925c5ae0a03265c30f895f5e2c4e1cdfe91978cd3ef",
+    "/tmp/intmult-channel408-relocate/ORDER.json": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1"
+  },
+  "fill_sha256": "d6585a3b05fb86efd08b1925c5ae0a03265c30f895f5e2c4e1cdfe91978cd3ef",
+  "gain": "213808976768352857/1000000000000000000000000",
+  "kappa": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017203983373542378859309999999999999999999998999999999999999999999999",
+  "native_receipt_sha256": "3280682ab975f412ab25e8ec433b2e52d8d3b6226db712ccabbbd2babcc2b84d",
+  "order_sha256": "519d1d5dbb997a219fcfcad34c0b03e7838bef24199784d7e964fa10090f66e1",
+  "package_manifest_sha256": "a6d0e45723ea87f43ed8026758306adbf44b5cfc8473464c77acb57f32530783",
+  "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": "8b4cae2a3c7bebfee704c820e6235063940e52d323fedc2dbb7508ad06729f7a",
+      "before_sha256": "63140c78372e088b3f34bc22549b169fd56bed8c66af9871281297bb8455b395",
+      "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": "6e994250794f792338b0edef391393cdf2a775e3d72d0c44e7753245027bdf6b",
+      "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=73,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": "64525e5eb1a6a928fe7c715f87d6174ce1b82b2a7a81d655fc2489bf5530e153",
+      "before_sha256": "8b4cae2a3c7bebfee704c820e6235063940e52d323fedc2dbb7508ad06729f7a",
+      "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": 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 construction and modern outer arithmetic. Exact inherited theorem obligations remain. Both native providers explicitly reused from authenticated fresh five-stage runs.",
+  "source_commit": "two-sided-helper408-pr2894",
+  "source_file_count": 610,
+  "source_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "source_profile": "channel408",
+  "source_upstream_head": "18d03c447886895ef9abf888398178e0428533ca",
+  "stages": [
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/reconstruct.py",
+        "--out",
+        "/tmp/intmult-channel408-full/candidate/owners"
+      ],
+      "exit_code": 0,
+      "log_sha256": "6374948b328a22bdf0e44ae3b1275235e0404f951dca3e1f1b53f972fd896874",
+      "name": "owners",
+      "script_sha256": "5472811c24aef3852dc7e189dff5060076a6c0b25bfde928da50dcfe9b5bdc15",
+      "seconds": 3.729256538907066
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/lift_parent.py",
+        "--package",
+        "/tmp/intmult-channel408-full/candidate/package",
+        "--owners",
+        "/tmp/intmult-channel408-full/candidate/owners",
+        "--out",
+        "/tmp/intmult-channel408-full/candidate/parent-data"
+      ],
+      "exit_code": 0,
+      "log_sha256": "7b6249a123ca39fae7b7a6339dd9e8ae8777b081f4336418f2cc101704b70644",
+      "name": "parent-lift",
+      "script_sha256": "9a1edd7d4ab4a2f2ac8d15b42b7e40f93653d65026bac59e4c1ce80b486bd60e",
+      "seconds": 8.420303886989132
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/new/rebind.py",
+        "/tmp/intmult-channel408-full/candidate/package",
+        "/tmp/intmult-channel408-full/native/native-cache/3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local",
+        "/tmp/intmult-channel408-full/native/native-cache/b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487/local",
+        "/tmp/intmult-channel408-full/candidate/rebound"
+      ],
+      "exit_code": 0,
+      "log_sha256": "0db47c51e66c5aa76ec69eb7d28a70742aa71df3a35c4ef620a773bc62cdb4f1",
+      "name": "rebind",
+      "script_sha256": "52f8b4cec2dab69cbe590e1fd0f7a68e1b35de5a540bd22fd2adfce07a92b46b",
+      "seconds": 0.6750722089782357
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/layout/packing74/replay.py",
+        "--data",
+        "/tmp/intmult-channel408-full/candidate/layout/packing74/candidate",
+        "--work",
+        "/tmp/intmult-channel408-full/candidate/discovery",
+        "--local",
+        "/tmp/intmult-channel408-full/native/native-cache/3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local",
+        "--discover"
+      ],
+      "exit_code": 0,
+      "log_sha256": "129d0b39b2b096454114e1ba074c0a0006c70c796096f7b96d212e612ad6d847",
+      "name": "discovery",
+      "script_sha256": "cda0f3a63c5c92c0ff45f7f3a200567d7931fd421836e72ea3b8534f6ee24dcc",
+      "seconds": 90.9474641638808
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/outer/check_ledger.py"
+      ],
+      "exit_code": 0,
+      "log_sha256": "4b24583a5d1f50c8cc98ea4910ef1b51a7bd2d4fe968a5a71b0a624c3480a12d",
+      "name": "outer-check_ledger.py",
+      "script_sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98",
+      "seconds": 0.06847563898190856
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/outer/independent_check.py"
+      ],
+      "exit_code": 0,
+      "log_sha256": "e0eee1092e06d735a8c1e4414549286c174d86d69e8ed9295c10d62354d1e9c1",
+      "name": "outer-independent_check.py",
+      "script_sha256": "a5a0361539ec7cae9eb6c0371f857919335a1720040f22af291aa3e34fc864c7",
+      "seconds": 0.06007747910916805
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/candidate/package/verify_release.py",
+        "--main",
+        "/tmp",
+        "--work",
+        "/tmp/intmult-channel408-full/candidate/release",
+        "--native-cache",
+        "/tmp/intmult-channel408-full/native/native-cache",
+        "--jobs",
+        "1"
+      ],
+      "exit_code": 0,
+      "log_sha256": "7b3371e50c95c5ee9136ece6ebd771957c69890bc9c51374f28decce2d9da9c2",
+      "name": "release",
+      "script_sha256": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b",
+      "seconds": 252.0952024848666
+    }
+  ],
+  "status": "PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE"
+}
diff --git a/research/two-sided-helper-extraction/evidence/AUDIT-base.json b/research/two-sided-helper-extraction/evidence/AUDIT-base.json
new file mode 100644
index 0000000000..3b45be5769
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/AUDIT-base.json
@@ -0,0 +1,40 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_BORROWING_WORD",
+  "input_file": "WORD-base.json.gz",
+  "content_sha256": "8d7f24d329db696be203e84c459f220f8de061fcc8681b5ab74a7a902d01bcd3",
+  "compressed_sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "removed_helpers": 72,
+  "independent_inputs": 632,
+  "warps": 72,
+  "corrections": 36,
+  "restored_cold": 73,
+  "zero_buffers": 73,
+  "entering": 134,
+  "local_profile": {
+    "1": 2407,
+    "2": 640,
+    "3": 262,
+    "4": 128,
+    "5": 26,
+    "8": 8
+  },
+  "local_mass": 5179,
+  "width_inventory": {
+    "4": 26,
+    "5": 2,
+    "7": 62,
+    "8": 87,
+    "9": 231
+  },
+  "orientations": {
+    "forward": "PASS",
+    "dual": "PASS"
+  },
+  "base": null,
+  "checked_columns": 632,
+  "elapsed_seconds": 0.45817074505612254,
+  "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."
+}
diff --git a/research/two-sided-helper-extraction/evidence/AUDIT-extra.json b/research/two-sided-helper-extraction/evidence/AUDIT-extra.json
new file mode 100644
index 0000000000..989035dc2c
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/AUDIT-extra.json
@@ -0,0 +1,40 @@
+{
+  "status": "PASS_INDEPENDENT_EXACT_BORROWING_WORD",
+  "input_file": "WORD-extra.json.gz",
+  "content_sha256": "97ac8c367548702f2510b450c251248944bb2c81e0e74b10cca250d3f2e957c1",
+  "compressed_sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
+  "v": 112,
+  "h": 9,
+  "R": 480,
+  "removed_helpers": 72,
+  "independent_inputs": 632,
+  "warps": 72,
+  "corrections": 36,
+  "restored_cold": 73,
+  "zero_buffers": 73,
+  "entering": 134,
+  "local_profile": {
+    "1": 2407,
+    "2": 640,
+    "3": 262,
+    "4": 128,
+    "5": 26,
+    "8": 8
+  },
+  "local_mass": 5179,
+  "width_inventory": {
+    "4": 26,
+    "5": 2,
+    "7": 62,
+    "8": 87,
+    "9": 231
+  },
+  "orientations": {
+    "forward": "PASS",
+    "dual": "PASS"
+  },
+  "base": null,
+  "checked_columns": 632,
+  "elapsed_seconds": 0.45386952022090554,
+  "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."
+}
diff --git a/research/two-sided-helper-extraction/evidence/ENVIRONMENT.json b/research/two-sided-helper-extraction/evidence/ENVIRONMENT.json
new file mode 100644
index 0000000000..c19662e10d
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/ENVIRONMENT.json
@@ -0,0 +1,13 @@
+{
+  "assertions_enabled": true,
+  "dependency_versions": {
+    "gmpy2": null,
+    "mpmath": "1.3.0",
+    "numpy": "2.5.4",
+    "psutil": null,
+    "scipy": "1.18.1",
+    "sympy": "1.14.0"
+  },
+  "executable": "/tmp/intmult-contribution-venv/bin/python",
+  "python": "3.12.3"
+}
diff --git a/research/two-sided-helper-extraction/evidence/EXACT-OWNER-MOMENT.json b/research/two-sided-helper-extraction/evidence/EXACT-OWNER-MOMENT.json
new file mode 100644
index 0000000000..613b49e409
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/EXACT-OWNER-MOMENT.json
@@ -0,0 +1,78 @@
+{
+  "calls": 666,
+  "controls": {
+    "capacity_overflow": "bin capacity",
+    "duplicate_helper": "duplicate helper",
+    "missing_role": "complete role count"
+  },
+  "idle": {
+    "1": 17282,
+    "2": 1,
+    "3": 6240,
+    "5": 8384,
+    "6": 120,
+    "7": 1,
+    "23": 1,
+    "32": 14,
+    "48": 26837
+  },
+  "live": 66304,
+  "moment": {
+    "W": 66304,
+    "baseline_claim_sha256": "29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30",
+    "baseline_profile_sha256": "528400282a268b6e5983a5251af6040450fa0e7d9ddf7d65e4a0aa6a0b9096a6",
+    "controls": [
+      "zero log/exp identities",
+      "overstated endpoint",
+      "added rank32 charge"
+    ],
+    "gain": "213808976768352857/1000000000000000000000000",
+    "gain_decimal": "2.13808976768352857E-7",
+    "lower": "5376244804231993393537/3125000000000000000000000",
+    "method": "Independent 128-term atanh / degree24 exponential with explicit positive tails and outward 192-bit dyadic rounding",
+    "new_moment_at_full_prior": [
+      "6277097906672672224441481878202510471791466988689607208709/6277101735386680763835789423207666416102355444464034512896",
+      "6277097906672672224441481878202510471791466988689607208711/6277101735386680763835789423207666416102355444464034512896"
+    ],
+    "normalized_profile_delta": {
+      "1": 130221056,
+      "2": -88250624,
+      "3": -5768448,
+      "5": -10807552,
+      "6": 7956480,
+      "7": 66304,
+      "23": 66304,
+      "32": 928256,
+      "48": 795648
+    },
+    "oldW": 66304,
+    "outer_endpoint": "1720398337354237885931/1000000000000000000000000",
+    "previous": "17201845283774695330739999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "profile_sha256": "ab0840eda08fa501d444be22c7298bf38b70061b91964ad1b9dd9db388720199",
+    "scope": "Complete paid histogram and exact moment only; full native/physical/outer release is separate.",
+    "status": "PASS_SEPARATE_EXACT_RATIONAL_FRONTIER_MOMENT",
+    "target": "17203983373542378859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "target_decimal": "0.0017203983373542378859309999999999999999999998999999999999999999999999",
+    "upper": "34407966747084757718637/20000000000000000000000000"
+  },
+  "physical": 66795,
+  "physical_source": "explicit 73-buffer local ABI; independently invoiced by complete release",
+  "profile": {
+    "1": 1620344,
+    "2": 426241,
+    "3": 180732,
+    "4": 85248,
+    "5": 25700,
+    "6": 120,
+    "7": 1,
+    "8": 5328,
+    "23": 1,
+    "32": 14,
+    "48": 26837
+  },
+  "rank_mass": 4816512,
+  "replicas": 74,
+  "roles": 271728,
+  "scope": "Exact local width-based whole-owner geometry and rational moment; full source/native/stock/outer admission separate.",
+  "status": "PASS_HELPER408_LITERAL_OWNERS_AND_EXACT_MOMENT"
+}
diff --git a/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RECEIPT.json b/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RECEIPT.json
new file mode 100644
index 0000000000..960a8b9654
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RECEIPT.json
@@ -0,0 +1,113 @@
+{
+  "cache_files": {
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/CACHE.json": "a998411dd7ae5156b437b1b4a7a261fedd959fb3bff546143ca8f23db72eb0e8",
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/STEPS.json": "ebbf4886c10411bc32a25a142fc73538a30951f295e79df0ba5ccd24807a7afe",
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local/CANONICAL-WORD.json.gz": "ac219a0a33ed98050d33840034c1906cd0b3755b587dff0ea0a56809360d1538",
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local/CLIFFORD-RECIPES.json": "e462ddfa9d374a0306c830db3dd8a52c6579af22ae8517ca2ebf41bc93414091",
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local/CLIFFORD-REVIEW.json": "511dceafa822f5ec5186e81bdbd9d98260650a477c798b2c69f39daa5b843f9c",
+    "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local/FULL-WORD.json.gz": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
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+  "reused_retained_native_count": 2,
+  "reused_retained_parent": true,
+  "source_commit": "two-sided-helper408-pr2894",
+  "status": "PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE"
+}
diff --git a/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RESULT.json b/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RESULT.json
new file mode 100644
index 0000000000..309db026aa
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/FULL-NATIVE-RESULT.json
@@ -0,0 +1,41 @@
+{
+  "environment_sha256": "8c22d637dd3951151e5b7764536851f6147b805a49a418651ac84a647137384d",
+  "native_receipt_sha256": "3280682ab975f412ab25e8ec433b2e52d8d3b6226db712ccabbbd2babcc2b84d",
+  "preparer_sha256": "4d207b9bbe3e0b8a86d10ad5d5f329a81da0cf56dce6c03e6fdd5b78e581ce91",
+  "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": 64.03585839597508,
+  "source_manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "stages": [
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/source/new/fastnative/run_native.py",
+        "/tmp/intmult-channel408-full/source/new/borrow/words/BORROW-WORD-43base.json.gz",
+        "/tmp/intmult-channel408-full/native/fresh-base"
+      ],
+      "exit_code": 0,
+      "log_sha256": "2f678854ac9d7def30ff1cd86eb753167f6d97e70fb311c19b7e26660c1960cd",
+      "name": "fresh-current-base",
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+      "script_sha256": "a7bfe110fe5098f6ef8bde3c43ecf15e8d1e06149abf7321a4c945383dcc2627",
+      "seconds": 31.8839402589947
+    },
+    {
+      "command": [
+        "/tmp/intmult-contribution-venv/bin/python",
+        "-B",
+        "/tmp/intmult-channel408-full/source/new/fastnative/run_native.py",
+        "/tmp/intmult-channel408-full/source/new/borrow/words/BORROW-WORD-43extra.json.gz",
+        "/tmp/intmult-channel408-full/native/fresh-extra"
+      ],
+      "exit_code": 0,
+      "log_sha256": "e31d206e7874b1d0bbf013100766025348b07f605b9232a4da1ac05081d33cdd",
+      "name": "fresh-current-extra",
+      "result_sha256": "8ade0389bac3973f812d98bf5fd111415a6f4fb143636f9326688f574299fa1e",
+      "script_sha256": "a7bfe110fe5098f6ef8bde3c43ecf15e8d1e06149abf7321a4c945383dcc2627",
+      "seconds": 32.08049960108474
+    }
+  ],
+  "status": "PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE"
+}
diff --git a/research/two-sided-helper-extraction/evidence/FULL-PACKAGE-MANIFEST.json b/research/two-sided-helper-extraction/evidence/FULL-PACKAGE-MANIFEST.json
new file mode 100644
index 0000000000..ec58ceda94
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/FULL-PACKAGE-MANIFEST.json
@@ -0,0 +1,616 @@
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+  "vendor/pr1786/FINE-PRIME-PADDING.md": "47d1b1b4df28aadda3cd6bdeb1fbc47290595e9208cd09c1a1f338520d33fdce",
+  "vendor/pr1786/NOTICE.md": "dcc1adb2461aa93ca62b6a912dbd8b215599e6af8053dfbacb7423b544dd659a",
+  "verify.py": "64525e5eb1a6a928fe7c715f87d6174ce1b82b2a7a81d655fc2489bf5530e153",
+  "verify_manifest.py": "723d726dbbe5b65a49caecae0f1aab664a1413fb639abfd3e826a5a538e14e5b",
+  "verify_release.py": "6cfefe80c02a6c0f243f50ca9e146e1ab1440b84a033d8a71d42be5a5fa27f6b"
+}
diff --git a/research/two-sided-helper-extraction/evidence/FULL-STAGES.json b/research/two-sided-helper-extraction/evidence/FULL-STAGES.json
new file mode 100644
index 0000000000..e424d88871
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/FULL-STAGES.json
@@ -0,0 +1,113 @@
+[
+  {
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+      "/tmp/intmult-contribution-venv/bin/python",
+      "-B",
+      "/tmp/intmult-channel408-full/candidate/package/reconstruct.py",
+      "--out",
+      "/tmp/intmult-channel408-full/candidate/owners"
+    ],
+    "exit_code": 0,
+    "log_sha256": "6374948b328a22bdf0e44ae3b1275235e0404f951dca3e1f1b53f972fd896874",
+    "name": "owners",
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+      "--package",
+      "/tmp/intmult-channel408-full/candidate/package",
+      "--owners",
+      "/tmp/intmult-channel408-full/candidate/owners",
+      "--out",
+      "/tmp/intmult-channel408-full/candidate/parent-data"
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+      "/tmp/intmult-channel408-full/candidate/package",
+      "/tmp/intmult-channel408-full/native/native-cache/3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3/local",
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+      "/tmp/intmult-channel408-full/candidate/layout/packing74/candidate",
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+      "--discover"
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+    "name": "outer-independent_check.py",
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+      "/tmp/intmult-contribution-venv/bin/python",
+      "-B",
+      "/tmp/intmult-channel408-full/candidate/package/verify_release.py",
+      "--main",
+      "/tmp",
+      "--work",
+      "/tmp/intmult-channel408-full/candidate/release",
+      "--native-cache",
+      "/tmp/intmult-channel408-full/native/native-cache",
+      "--jobs",
+      "1"
+    ],
+    "exit_code": 0,
+    "log_sha256": "7b3371e50c95c5ee9136ece6ebd771957c69890bc9c51374f28decce2d9da9c2",
+    "name": "release",
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+    "seconds": 252.0952024848666
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diff --git a/research/two-sided-helper-extraction/evidence/LOCAL-REPLAY.json b/research/two-sided-helper-extraction/evidence/LOCAL-REPLAY.json
new file mode 100644
index 0000000000..4a25294d0b
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/LOCAL-REPLAY.json
@@ -0,0 +1,315 @@
+{
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+          "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.",
+        "status": "PASS_EXACT_TWO_SIDED_SUBSPACE_CERTIFICATE",
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+        "status": "PASS_INDEPENDENT_EXACT_BORROWING_WORD",
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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"
+        ],
+        "scope": "Exact free-operator identities before target writes; full target correctness checked separately.",
+        "status": "PASS_EXACT_TWO_SIDED_SUBSPACE_CERTIFICATE",
+        "u": {
+          "401": "-1",
+          "402": "1/2",
+          "403": "-1/2",
+          "404": "-1/2",
+          "405": "1/2",
+          "408": "1/2",
+          "409": "-1/2",
+          "414": "1/2",
+          "415": "-1/2"
+        },
+        "v": {
+          "226": "1/2",
+          "227": "1/2",
+          "230": "-1/2",
+          "231": "-1/2",
+          "233": "-1/2",
+          "234": "-1/2",
+          "236": "1/2",
+          "239": "1/2",
+          "401": "-1/2",
+          "402": "1/2",
+          "403": "1/2",
+          "407": "-1/2",
+          "408": "1/2",
+          "410": "-1/2",
+          "411": "-1/2",
+          "414": "1/2"
+        },
+        "y": {
+          "42": "2"
+        }
+      },
+      "word_sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487"
+    }
+  },
+  "scope": "Exact local construction only; no owner allocation or higher kappa admitted. Extra private buffer is mandatory.",
+  "semantic_controls": {
+    "omit_new_private_buffer": "explicit cleanup differs from derived inverse-reverse at FULL",
+    "stale_compensation": "pre-wrapper touch of residual helper",
+    "wrong_input_scale": "target map failed 3",
+    "wrong_output_cancellation": "restored cold input still read by 408"
+  },
+  "status": "PASS_TWO_SIDED_HELPER408_LOCAL_CONSTRUCTION"
+}
diff --git a/research/two-sided-helper-extraction/evidence/NATIVE-base.json b/research/two-sided-helper-extraction/evidence/NATIVE-base.json
new file mode 100644
index 0000000000..08b8b25086
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/NATIVE-base.json
@@ -0,0 +1,55 @@
+{
+  "status": "PASS_COMPLETE_T74_NATIVE_REPLAY",
+  "engine": "sparse",
+  "word_sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3",
+  "source_sha256": {
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+    "accelerators/SPARSE-PROOF.md": "d73e4522602404caba8e7f247005a45c8a8cd26ffd2a70d65f4f9556a391d053",
+    "accelerators/sparse_state.py": "e91210ecd5085cf9add872f40bb434806838da488e12152c63c86e51fb5a7a37",
+    "accelerators/tables.py": "2fe087ba4558bd21ca49945dbedaa4047e4170e8fd4e2280701bb2f0481811b5",
+    "native/new/code/borrow/NOTICE-PR2226.md": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a",
+    "native/new/code/borrow/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce",
+    "native/new/code/borrow/bw_audit_local.py": "08d5864d9b77902fc5ab5a062a8ea843fe1e572243b8c580abb0a421b2e46d07",
+    "native/new/code/borrow/bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19",
+    "native/new/code/borrow/bw_emit.py": "99b59a6fa3feda86785e4225157dcb1a6169d256cec4f5e0acc9cea7a701df76",
+    "native/new/code/borrow/bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb",
+    "native/new/code/borrow/bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e",
+    "native/new/code/borrow/bw_tamper.py": "eab4b026965b9796eee92239660e1fb1fa629f6d9db44bc27b13911a018a6ee9",
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+    "native/new/code/borrow/vendor/pr2226_operators.py": "b37b67a04681c776dafcdc6c9af0e8a2dbfa9893b02e0fa2d77ccc9182a87988",
+    "native/new/code/borrow/vendor/pr2226_replay.py": "0f9a47cdaeed0e22938c63251c232d6f23aeee2b62b0b1223cd4473c5428bcf7",
+    "native/new/run_native_borrow.py": "8ec7db430f4f4771c06bdcfc31736193614f6ec209d57b63d4e2b75f17fb3ac8"
+  },
+  "steps": [
+    {
+      "step": "native",
+      "exit_code": 0,
+      "seconds": 0.48818629095330834
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+    {
+      "step": "ledgers",
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+      "seconds": 0.5708757441025227
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+      "step": "local-replay",
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+      "seconds": 14.670437809079885
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+    {
+      "step": "wrappers",
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+      "seconds": 0.7637620011810213
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+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 16.218504957156256
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+  ],
+  "seconds": 32.721344058867544,
+  "python": "3.12.3",
+  "scope": "Full five-stage native replay including independent all-column warp recipes and original rejection controls; supplier/outer admission separate."
+}
diff --git a/research/two-sided-helper-extraction/evidence/NATIVE-extra.json b/research/two-sided-helper-extraction/evidence/NATIVE-extra.json
new file mode 100644
index 0000000000..13ac26e613
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/NATIVE-extra.json
@@ -0,0 +1,55 @@
+{
+  "status": "PASS_COMPLETE_T74_NATIVE_REPLAY",
+  "engine": "sparse",
+  "word_sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487",
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+    "native/new/code/borrow/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce",
+    "native/new/code/borrow/bw_audit_local.py": "08d5864d9b77902fc5ab5a062a8ea843fe1e572243b8c580abb0a421b2e46d07",
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+    "native/new/code/borrow/bw_emit.py": "99b59a6fa3feda86785e4225157dcb1a6169d256cec4f5e0acc9cea7a701df76",
+    "native/new/code/borrow/bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb",
+    "native/new/code/borrow/bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e",
+    "native/new/code/borrow/bw_tamper.py": "eab4b026965b9796eee92239660e1fb1fa629f6d9db44bc27b13911a018a6ee9",
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+    "native/new/run_native_borrow.py": "8ec7db430f4f4771c06bdcfc31736193614f6ec209d57b63d4e2b75f17fb3ac8"
+  },
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+    {
+      "step": "native",
+      "exit_code": 0,
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+    {
+      "step": "ledgers",
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+    {
+      "step": "wrappers",
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+    {
+      "step": "phases",
+      "exit_code": 0,
+      "seconds": 16.12868695310317
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+  ],
+  "seconds": 32.22324956511147,
+  "python": "3.12.3",
+  "scope": "Full five-stage native replay including independent all-column warp recipes and original rejection controls; supplier/outer admission separate."
+}
diff --git a/research/two-sided-helper-extraction/evidence/OUTER-INDEPENDENT.json b/research/two-sided-helper-extraction/evidence/OUTER-INDEPENDENT.json
new file mode 100644
index 0000000000..8546dcb492
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/OUTER-INDEPENDENT.json
@@ -0,0 +1,43 @@
+{
+  "status": "PASS_INDEPENDENT_BALANCE_DERIVATION",
+  "source_sha256": "ea1d62aaf07a1bd6cb84ad085449348e9c93484b0a0d487d70d491b7360a6046",
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+          "1/1000000000000",
+          "1.7203983373542378e-15"
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+  "scope": "Independent balance derivation and margin comparisons for this package's supplier endpoint; the supplier native admission is bound by verify_release.py; inherited all-size assumptions remain."
+}
diff --git a/research/two-sided-helper-extraction/evidence/OUTER-LEDGER.json b/research/two-sided-helper-extraction/evidence/OUTER-LEDGER.json
new file mode 100644
index 0000000000..688f906806
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/OUTER-LEDGER.json
@@ -0,0 +1,579 @@
+{
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+          "decimal": "0"
+        }
+      }
+    }
+  },
+  "pr1673_kappa": {
+    "rational": "1677160151714381/1000000000000000000",
+    "decimal": "0.001677160151714381"
+  },
+  "improvement_over_pr1673": {
+    "rational": "432381856398568859309999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+    "decimal": "0.0000432381856398568859309999999999999999999998999999999999999999999999"
+  },
+  "source_sha256": {
+    "new/SPEC.json": "ea1d62aaf07a1bd6cb84ad085449348e9c93484b0a0d487d70d491b7360a6046",
+    "CLAIM.json": "2c6fa6af99c1a39ffd773eab5f3ecd8626e679670439b6e35d86b48fbbdc87d7"
+  }
+}
diff --git a/research/two-sided-helper-extraction/evidence/OVERLAP.json b/research/two-sided-helper-extraction/evidence/OVERLAP.json
new file mode 100644
index 0000000000..4935a014e3
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/OVERLAP.json
@@ -0,0 +1,19 @@
+{
+  "started_main": "57220708",
+  "prepublication_main": "a98b1ebcdd6f2fe25ffdd30cd7e753ebfe319797",
+  "guidance_changed": false,
+  "start_coverage": {
+    "open_prs": 490,
+    "discussion_records": 1572,
+    "warnings": []
+  },
+  "prepublication_latest_pr": 2907,
+  "latest_titles_checked": 25,
+  "recent_discussions_checked": 12,
+  "specific_adjacent_work": [
+    "PR2894 local supplier baseline",
+    "PR2904 fixed-gate entry/refit census",
+    "Discussion2612 current accounting and changed-word lane"
+  ],
+  "scope": "Advisory body/title coverage; not arbitrary code/unpublished-work novelty certification. No Discussion post was sent."
+}
diff --git a/research/two-sided-helper-extraction/evidence/RELEASE-RECEIPT.json b/research/two-sided-helper-extraction/evidence/RELEASE-RECEIPT.json
new file mode 100644
index 0000000000..a306de9599
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/RELEASE-RECEIPT.json
@@ -0,0 +1,7 @@
+{
+  "status": "PASS_RELEASE",
+  "kappa_decimal": "0.0017203983373542378859309999999999999999999998999999999999999999999999",
+  "manifest_sha256": "a6d0e45723ea87f43ed8026758306adbf44b5cfc8473464c77acb57f32530783",
+  "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 1720398337354237885931/1000000... brackets the ledger's b = 172039833735423788593099999999999999999999999999999999999999999999999999999999999999999999999999999999/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000. 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 0.0017203983373542378859309999999999999999999998999999999999999999999999 (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": 251.99
+}
diff --git a/research/two-sided-helper-extraction/evidence/RUNTIME-PATCHES.json b/research/two-sided-helper-extraction/evidence/RUNTIME-PATCHES.json
new file mode 100644
index 0000000000..35223808ef
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/RUNTIME-PATCHES.json
@@ -0,0 +1,225 @@
+[
+  {
+    "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": "8b4cae2a3c7bebfee704c820e6235063940e52d323fedc2dbb7508ad06729f7a",
+    "before_sha256": "63140c78372e088b3f34bc22549b169fd56bed8c66af9871281297bb8455b395",
+    "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": "6e994250794f792338b0edef391393cdf2a775e3d72d0c44e7753245027bdf6b",
+    "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=73,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": "64525e5eb1a6a928fe7c715f87d6174ce1b82b2a7a81d655fc2489bf5530e153",
+    "before_sha256": "8b4cae2a3c7bebfee704c820e6235063940e52d323fedc2dbb7508ad06729f7a",
+    "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)"
+      ]
+    ]
+  }
+]
diff --git a/research/two-sided-helper-extraction/evidence/SEARCH.json b/research/two-sided-helper-extraction/evidence/SEARCH.json
new file mode 100644
index 0000000000..32a7ac2605
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/SEARCH.json
@@ -0,0 +1,42 @@
+{
+  "date_utc": "2026-10-16",
+  "scope": "Search history only; no universal obstruction or optimality claim. Complete certificate is separate.",
+  "initial_screens": [
+    "Sparse compensation kernels with common first-frame constraints: no eligible extension found.",
+    "Single-helper terminal and last-touch Schur screens: no admissible candidate."
+  ],
+  "changed_hypothesis": "Paired input/output subspaces of the complete non-target operator, changing literal gate word and cold endpoint.",
+  "nomination": "135 finite-field role groups, 7 nominated intersections, 38 exact dyadic words; selected helper408. Nomination ranks are not used as proof.",
+  "exact_structural_check": "structure.py verifies all seven identities over rational free-operator algebra; full word auditor checks 632 independent columns forward and dual.",
+  "packing_attempts": [
+    {
+      "method": "T37 exact optimal pattern/time flow CP-SAT",
+      "seconds": 240,
+      "status": "UNKNOWN; no candidate"
+    },
+    {
+      "method": "same target HiGHS MILP",
+      "seconds": 90,
+      "status": "time limit; no candidate"
+    },
+    {
+      "method": "relaxed pattern set CP-SAT",
+      "seconds": 180,
+      "status": "feasible inherited-quality candidate, no useful gain"
+    },
+    {
+      "method": "same-call exchanges on PR2894 literal T74 fill",
+      "swaps": 545,
+      "floating_root": 0.001720177665171618,
+      "status": "owner-valid, below parent"
+    },
+    {
+      "method": "whole-role relocations with time/family/capacity constraints",
+      "moves": 222,
+      "status": "owner-valid and complete exact release subsequently passed"
+    }
+  ],
+  "optimization": "NumPy/SciPy modular/rational nomination, sparse exact native engine, deterministic bounded repair. At most two heavy single-thread processes, nice15 and idle IO.",
+  "important_failed_check": "Obsolete reference-native driver inherited an inapplicable centre-descent mutation and raised StopIteration. The unchanged current pinned sparse-native driver passed all five stages and its corrected original rejection controls. No failed control was removed by this contribution.",
+  "next": "A second extraction has nominees but no promoted composed word or higher claim in this package."
+}
diff --git a/research/two-sided-helper-extraction/evidence/SOURCE-DERIVATION.json b/research/two-sided-helper-extraction/evidence/SOURCE-DERIVATION.json
new file mode 100644
index 0000000000..5737286744
--- /dev/null
+++ b/research/two-sided-helper-extraction/evidence/SOURCE-DERIVATION.json
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+{
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+    },
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+    },
+    "new/rebuild_borrow.py": {
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+    },
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+      "before": "26f0f22b796afc82e48498203978f51c19df4e8d2cf8569bf3e1726805f7f922"
+    }
+  },
+  "manifest_sha256": "56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83",
+  "parent_manifest_sha256": "4da246899e2c509dd8c6e5af34905c6124ca17671b188e11ac37e36adf449504",
+  "source_file_count": 610,
+  "status": "PASS_SOURCE_BOUND_TWO_SIDED_HELPER408_OVERLAY",
+  "words": {
+    "base": {
+      "parent_sha256": "c20a470aec0f3e61833cb41fe190639eb358f58017143d2336c55c80fba265eb",
+      "word_sha256": "3657ad53ebe5f156f307a903479e919f2fe812811ce5d5f15e72c3aaf68dfde3"
+    },
+    "extra": {
+      "parent_sha256": "db34e39876241087b581ed9374c53e9cd393e3e86ef6103bfb54f3077c3d2761",
+      "word_sha256": "b975492ff4cbec0d619cdf2da34f55ce3b20c8a541132e4339cc6c8ae3b2e487"
+    }
+  }
+}
diff --git a/research/two-sided-helper-extraction/extract.py b/research/two-sided-helper-extraction/extract.py
new file mode 100644
index 0000000000..37796726d4
--- /dev/null
+++ b/research/two-sided-helper-extraction/extract.py
@@ -0,0 +1,52 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Two-sided dirty-helper extraction on the pinned PR2894 providers.
+
+Jeremy Diviney with OpenAI Codex assistance. Exact frame accounting and inverse
+cleanup are credited to Jeremy Kothe's preload_move.py (PR2894). This producer
+is pure; the independent auditor derives the endpoint from its literal gates.
+"""
+import collections
+import copy
+from fractions import Fraction as Q
+import preload_move as pm
+
+ALLOWED = {'A', 'restore', 'helper_final', 'compensation', 'report', 'cleanup'}
+PROFILE = {'1':2407,'2':640,'3':262,'4':128,'5':26,'8':8}
+INVENTORY = {'4':26,'5':2,'7':62,'8':87,'9':231}
+
+def apply(word, transform):
+    h = transform['helper']
+    before, after = transform['before'], transform['after']
+    pm.require(h == 408 and str(h) not in word['helper_final'], 'fresh helper408')
+    pm.require(str(h) not in word['start_extra'], 'zero entrance')
+    pm.require(len(before)==24 and len(after)==3, 'declared literal gate counts')
+    frame = after[0][-1]
+    pm.require(pm.basis(frame)==(256,128,64,36,20,8,2,1), 'hyperplane52')
+    protected = set(map(int,word['helper_final'])) | set(map(int,word['start_extra'])) | {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), 'only available unprotected helpers')
+    for g in after:
+        pm.require(g[0]=='add' and g[-1]==frame, 'declared terminal frame')
+    x=copy.deepcopy(word);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)]=list(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])
+    # The preceding compensation becomes C*S; reverse literal gate order
+    # computes right multiplication without trusting stored endpoint rows.
+    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];c=Q(g[3],g[4])
+            for target,a in C[t].items():C[s][target]=C[s].get(target,Q(0))+c*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 helper has no target compensation')
+    profile,inventory=pm.frame_report(x)
+    pm.require(profile==PROFILE and inventory==INVENTORY, 'actual local profile/inventory')
+    x['report']['local_profile']=profile;x['report']['width_inventory']=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
diff --git a/research/two-sided-helper-extraction/reproduce.py b/research/two-sided-helper-extraction/reproduce.py
new file mode 100644
index 0000000000..09442f1a3a
--- /dev/null
+++ b/research/two-sided-helper-extraction/reproduce.py
@@ -0,0 +1,69 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Pinned local Git export, declared stages, native chains and complete release.
+
+No network fetch is performed. Fresh retained bootstrap is the default;
+--retained explicitly reuses a fully authenticated prior parent/native cache.
+The preparation/release mechanisms derive from PR2894/2857/2839 with credit.
+"""
+import argparse,hashlib,io,json,os,shutil,subprocess,sys,tarfile,time
+from pathlib import Path,PurePosixPath
+from fractions import Fraction as Q
+P=Path(__file__).resolve().parent
+HEAD='18d03c447886895ef9abf888398178e0428533ca'
+UPSTREAM_MANIFEST='3cb842b93dd3b0707ceea825bef2afeaa68f8df0d554867761b4752b69077293'
+DERIVED_MANIFEST='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'
+RECORDED_RETAINED='dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def read(p):return json.loads(p.read_bytes())
+def save(p,v):p.write_text(json.dumps(v,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/shared-kernel-packing')
+ 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 ar:
+  for f in ar.getmembers():
+   p=PurePosixPath(f.name);assert not p.is_absolute() and '..' not in p.parts and '\\' not in f.name
+   if f.isdir() and (p==prefix or p in prefix.parents):continue
+   assert p.is_relative_to(prefix);rel=p.relative_to(prefix);assert f.isfile() or f.isdir()
+   q=out/rel
+   if f.isdir():q.mkdir(parents=True,exist_ok=True)
+   else:q.parent.mkdir(parents=True,exist_ok=True);q.write_bytes(ar.extractfile(f).read())
+ assert sha(out/'MANIFEST.json')==UPSTREAM_MANIFEST and tree(out)==read(out/'MANIFEST.json')
+
+def main():
+ ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--repo',type=Path,required=True);ap.add_argument('--work',type=Path,required=True);ap.add_argument('--retained',type=Path);ap.add_argument('--dry-run',action='store_true');a=ap.parse_args()
+ assert __debug__;work=a.work.resolve();assert not work.exists() and not work.is_relative_to(P) and not P.is_relative_to(work)
+ assert tree(P)==read(P/'MANIFEST.json'),'complete public package inventory'
+ work.mkdir(parents=True);upstream=work/'pr2894';export(a.repo.resolve(),upstream);core=upstream/'vendor/pr2857';source=work/'pr2833';source4=work/'source4';pm=work/'source-pm';final=work/'source';native=work/'native';candidate=work/'candidate';bound=work/'prepare-native-bound.py'
+ retained=a.retained.resolve() if a.retained else work/'retained'
+ if a.retained:assert not retained.is_relative_to(work) and not work.is_relative_to(retained)
+ py=[sys.executable,'-B'];recipe=[('export-pr2833',py+[upstream/'tools/materialize_source.py','--repo',a.repo.resolve(),'--out',source])]
+ if not a.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',source4]),('preload-stage',py+[upstream/'vendor/pm/build_pm_overlay.py','--overlay',source4,'--pm-dir',upstream/'vendor/pm','--out',pm]),('two-sided-stage',py+[P/'tools/build_channel_overlay.py','--source',pm,'--local-package',P,'--out',final]),('fresh-current-native',py+[bound,'--source',final,'--retained-cache',retained/'native-cache','--retained-receipt',retained/'NATIVE-RECEIPT.json','--out',native,'--jobs','1']),('complete-admission',py+[P/'tools/admit_channel408.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',P/'tools/channel_blocknorm.py','--comparison-claim',upstream/'CLAIM.json','--source-profile','channel408','--comparison-profile','pr2894','--jobs','1'])]
+ if a.dry_run:
+  save(work/'PREFLIGHT.json',{'status':'SOURCE_EXPORT_AND_RECIPE_ONLY_NOT_A_REPLAY','commands':[[n,list(map(str,c))] for n,c in recipe]});print('PASS_PINNED_PR2894_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 n in ['PYTHONOPTIMIZE','PYTHONPATH','WITNESS_SPEC','WITNESS_RECORD','WITNESS_DISCOVER']:env.pop(n,None)
+ stages=[]
+ for name,cmd in recipe:
+  if name=='fresh-current-native':
+   assert sha(final/'MANIFEST.json')==DERIVED_MANIFEST
+   text=(P/'tools/prepare_channel_native.py').read_text();old='OLD_RECEIPT_SHA='+repr(RECORDED_RETAINED);assert text.count(old)==1
+   new=sha(retained/'NATIVE-RECEIPT.json');bound.write_text(text.replace(old,'OLD_RECEIPT_SHA='+repr(new)))
+   save(work/'RETAINED-BINDING.json',{'recorded_receipt_sha256':RECORDED_RETAINED,'this_receipt_sha256':new,'bound_script_sha256':sha(bound),'explicit_reuse':bool(a.retained),'scope':'Only this receipt identity is rebound; complete cache, parent source/claim and 16 stages are still authenticated by the unchanged strict checks.'})
+  log=work/(name+'.log');start=time.monotonic()
+  with log.open('w') as f:r=subprocess.run(list(map(str,cmd)),env=env,cwd=work,stdin=subprocess.DEVNULL,stdout=f,stderr=subprocess.STDOUT)
+  stages.append({'stage':name,'exit_code':r.returncode,'seconds':time.monotonic()-start,'log_sha256':sha(log)});save(work/'STAGES.json',stages)
+  assert r.returncode==0,'failed '+name+'; see '+str(log);print('PASS',name,flush=True)
+ result=read(candidate/'RESULT.json');receipt=read(candidate/'release/RELEASE-RECEIPT.json');claim=read(P/'CLAIM.json')
+ assert result['status']=='PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE' and receipt['status']=='PASS_RELEASE'
+ assert Q(result['kappa'])==Q(receipt['kappa_decimal'])==Q(claim['kappa'])
+ assert result['release_receipt_sha256']==sha(candidate/'release/RELEASE-RECEIPT.json') and result['package_manifest_sha256']==receipt['manifest_sha256']
+ assert tree(P)==read(P/'MANIFEST.json') and tree(upstream)==read(upstream/'MANIFEST.json')
+ save(work/'RESULT.json',{'status':'PASS_TWO_SIDED_HELPER408_COMPLETE_REPLAY','kappa':result['kappa'],'native_receipt_sha256':sha(native/'NATIVE-RECEIPT.json'),'admission_result_sha256':sha(candidate/'RESULT.json'),'explicit_retained_reuse':bool(a.retained),'fresh_retained_bootstrap':not bool(a.retained),'stages':stages,'scope':'Conditional finite supplier/outer result; inherited all-size theorem obligations remain.'})
+ print('PASS_TWO_SIDED_HELPER408_COMPLETE_REPLAY',result['kappa'],flush=True)
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/run_registered.py b/research/two-sided-helper-extraction/run_registered.py
new file mode 100644
index 0000000000..f608249d96
--- /dev/null
+++ b/research/two-sided-helper-extraction/run_registered.py
@@ -0,0 +1,30 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Bounded local/native/owner/moment replay with stored full-release binding."""
+import hashlib,json,os,subprocess,sys,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 main():
+ assert __debug__;pins=read(P/'MANIFEST.json')
+ actual={f.relative_to(P).as_posix():sha(f) for f in P.rglob('*') if f.is_file() and f!=P/'MANIFEST.json'}
+ assert not any(f.is_symlink() for f in P.rglob('*')) and actual==pins
+ with tempfile.TemporaryDirectory(prefix='helper408-replay-') as temp:
+  out=Path(temp);env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1');env.pop('PYTHONOPTIMIZE',None)
+  for script,args in [('verify.py',['--native','--work',str(out/'local')]),('check_allocation.py',['--work',str(out/'owners')])]:
+   log=out/(script+'.log')
+   with log.open('w') as f:r=subprocess.run([sys.executable,'-B',str(P/script),*args],stdout=f,stderr=subprocess.STDOUT,env=env)
+   if r.returncode:print(log.read_text()[-4000:]);raise SystemExit(r.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-RESULT.json')
+  assert local['native_replayed'] and set(local['native'])=={'base','extra'}
+  assert admit['status']=='PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE' and release['status']=='PASS_RELEASE'
+  assert Q(owner['moment']['target'])==Q(claim['kappa'])==Q(admit['kappa'])==Q(release['kappa_decimal'])
+  assert claim['release_receipt_sha256']==admit['release_receipt_sha256']==sha(P/'evidence/RELEASE-RECEIPT.json')
+  assert claim['native_receipt_sha256']==admit['native_receipt_sha256']==native['native_receipt_sha256']==sha(P/'evidence/FULL-NATIVE-RECEIPT.json')
+  assert {f.relative_to(P).as_posix():sha(f) for f in P.rglob('*') if f.is_file() and f!=P/'MANIFEST.json'}==pins
+  print('PASS_TWO_SIDED_HELPER408_REGISTERED_LOCAL_NATIVE_OWNER_MOMENT',claim['kappa'])
+  print('Full integrated admission is authenticated stored evidence here; reproduce.py reruns it. Inherited all-size assumptions remain.')
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/structure.py b/research/two-sided-helper-extraction/structure.py
new file mode 100644
index 0000000000..8d5bd544ee
--- /dev/null
+++ b/research/two-sided-helper-extraction/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/two-sided-helper-extraction/tools/admit_channel408.py b/research/two-sided-helper-extraction/tools/admit_channel408.py
new file mode 100644
index 0000000000..dbc974a289
--- /dev/null
+++ b/research/two-sided-helper-extraction/tools/admit_channel408.py
@@ -0,0 +1,415 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Prepare and fully admit a changed-replica literal order/fill derivative.
+
+PR2833 extension by Yiyang Lu with OpenAI Codex assistance: add the exact
+immutable dirt-entry source profile and exact full outer-claim comparisons to
+PR2833 and the newer PR2843 T124 allocation. All
+inherited native, owner, invoice, block-norm, controls and release checks retained.
+
+Research runtime only: native providers must already have passed freshly and
+are authenticated by --native-receipt. --prepare-only stops before discovery.
+Default complete admission preserves the original verify.py and release stages.
+Source inputs and the native cache are read-only; all output uses fresh --work.
+"""
+import argparse
+from fractions import Fraction as Q
+import gzip
+import hashlib
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tarfile
+import time
+
+SOURCE_COMMIT = 'local-joint12-refit393'
+SOURCE_MANIFEST = '1e75eabffe1ce311cc3bddc05e76118cbdedfc806200a906c57fbc5a5dd213eb'
+PARENT_MANIFEST = 'e0eefc96567fbb45e19e6de0ca295381dbe0e686c08ddc783639b065c7c791d4'
+PRECISION = dict(endpoint_digits=24, grid_digits=18, margin_digits=28, bootstrap_steps=12)
+COMPARISON_SHA = '252b7bbdbef293f643633ff95ba7d1eabbe83e1eebcd1cb06f51834256bde1f3'
+COMPARISON_HEAD = 'e8b771ba132fe632796b28c1742a8d096c04519f'
+NATIVE_STAGES = ['native', 'ledgers', 'local-replay', 'wrappers', 'phases']
+# Supported immutable source versions; CLI selection never accepts arbitrary hashes.
+SOURCE_PROFILES = {
+    'channel408': dict(commit='two-sided-helper408-pr2894',manifest='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83',helpers=408,source_file_count=610,upstream_head='18d03c447886895ef9abf888398178e0428533ca'),
+    'shared-four': dict(commit='shared-four-kernel-pr2833', manifest='54dc42f25c1d8b85adcf593c4bf6c0f83f7351388af857812790b8a0b4c3d869', helpers=408, source_file_count=547, upstream_head='e9307b48d7d1b690939935ecef0f8e524e6d92f4'),
+    'preload-move': dict(commit='preload-move-pr2857', manifest='4da246899e2c509dd8c6e5af34905c6124ca17671b188e11ac37e36adf449504', helpers=408, source_file_count=553, upstream_head='e9307b48d7d1b690939935ecef0f8e524e6d92f4'),
+    'pr2833': dict(commit='pr2833-dirtentry', manifest='c8ec4d1b7be08d2ad30730a07392ad9cb6d0222f2c35bef43c9a80a39b16e41f', helpers=408, source_file_count=541, upstream_head='e9307b48d7d1b690939935ecef0f8e524e6d92f4'),
+    'pr2766': dict(commit='local-joint12-refit393', manifest='1e75eabffe1ce311cc3bddc05e76118cbdedfc806200a906c57fbc5a5dd213eb', helpers=415, source_file_count=491, upstream_head='e6df920cd0110e4b629e2ad84eddcb539001e174'),
+    'pr2802': dict(commit='local-joint12-pr2733', manifest='9c72b4301057a6c204c40bb6584eb74b779e06618bcd98d706d726c3e2c92451', helpers=408, source_file_count=506, upstream_head='17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd'),
+}
+COMPARISONS = {
+    'pr2894': dict(pr=2894,head='18d03c447886895ef9abf888398178e0428533ca',sha256='29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30',field='kappa'),
+    'pr2857': dict(pr=2857, head='0b2e2537b368a0cade07ce3f71452ea018ebe394', sha256='c2a04b639c86f462caef654a29817545c57b8e5ba809e37d4d476d3577f5cd6f', field='kappa'),
+    'pr2848': dict(pr=2848, head='c50d12e4720cd1fef2b5a65e337e37de9731879a', sha256='aceb1394b3e8f3abcc9b1a0dc82756ab937ffbefc2f37305a229a00ccc5137e9', field='kappa'),
+    'pr2843': dict(pr=2843, head='47a7227c044cd0cabb1432a06c61dd5d60c07f5a', sha256='0adc0edfade0260c65e79867b6c8b96f58dfe29d38aa30cfb8f3d5e9c7e828d9', field='kappa'),
+    'pr2833': dict(pr=2833, head='e9307b48d7d1b690939935ecef0f8e524e6d92f4', sha256='6f2c4195f0226c5a7f9ba604bc038cfd4100ba3caeeac8ed2defb6fb00632b70', field='kappa_rational'),
+    'pr2767': dict(pr=2767, head='e8b771ba132fe632796b28c1742a8d096c04519f', sha256='252b7bbdbef293f643633ff95ba7d1eabbe83e1eebcd1cb06f51834256bde1f3', field='kappa_rational'),
+    'pr2802': dict(pr=2802, head='17b2ee6ef3cf1468e78a6267f0ecbc9a0e6f60dd', sha256='a2fcbc8a3ad3095ecbd310a26c02e9d11c28e4d105669a08bbdfb39d7704db51', field='kappa'),
+}
+
+
+
+# Discovery records are shared by parallel mutation-audit processes on Windows.
+# Only discovery bookkeeping changes; strict pin comparison below it is untouched.
+DISCOVERY_APPEND_OLD = "   with open(os.environ['WITNESS_RECORD'],'a')as f:f.write(json.dumps([key,got],default=str)+chr(10))"
+DISCOVERY_APPEND_NEW = r'''   import time as _wr_time
+   _wr_path=Path(os.environ['WITNESS_RECORD'])
+   _wr_lock=_wr_path.with_name(_wr_path.name+'.append.lock')
+   _wr_deadline=_wr_time.monotonic()+60
+   _wr_fd=None
+   while _wr_fd is None:
+    try:_wr_fd=os.open(_wr_lock,os.O_CREAT|os.O_EXCL|os.O_WRONLY)
+    except FileExistsError:
+     if _wr_time.monotonic()>=_wr_deadline:raise TimeoutError('discovery record lock timeout; existing lock preserved')
+     _wr_time.sleep(.005)
+   try:
+    with _wr_path.open('a',encoding='utf-8',newline='\n')as _wr_out:
+     _wr_out.write(json.dumps([key,got],default=str)+chr(10))
+     _wr_out.flush()
+   finally:
+    os.close(_wr_fd)
+    _wr_lock.unlink()'''
+
+
+def need(ok, why):
+    if not ok:
+        raise RuntimeError(why)
+
+
+def sha(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def read(path):
+    body = path.read_bytes()
+    return json.loads(gzip.decompress(body) if path.suffix == '.gz' else body)
+
+
+def write(path, value):
+    # All output targets belong to this fresh work tree; never unlink an open lock.
+    lock = path.with_name(path.name + '.lock')
+    descriptor = os.open(lock, os.O_CREAT | os.O_EXCL | os.O_WRONLY)
+    try:
+        os.write(descriptor, str(os.getpid()).encode())
+        os.close(descriptor)
+        descriptor = None
+        path.write_text(json.dumps(value, sort_keys=True, indent=2) + '\n', encoding='utf-8', newline='\n')
+    finally:
+        if descriptor is not None:
+            os.close(descriptor)
+        lock.unlink()
+
+
+def tree(root, exclude=()):
+    result = {}
+    for path in sorted(root.rglob('*')):
+        need(not path.is_symlink(), 'unbound symlink: ' + str(path))
+        name = path.relative_to(root).as_posix()
+        if path.is_file() and name not in exclude:
+            result[name] = sha(path)
+    return result
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    for name in ('source', 'fill', 'order', 'dispatch', 'native-cache', 'native-receipt', 'work', 'replica-helper-dir', 'reconstructor', 'comparison-claim', 'blocknorm-checker'):
+        ap.add_argument('--' + name, type=Path, required=True)
+    ap.add_argument('--jobs', type=int, default=4)
+    ap.add_argument('--prepare-only', action='store_true')
+    ap.add_argument('--source-profile', choices=['channel408'], default='channel408')
+    ap.add_argument('--comparison-profile', choices=['pr2894'], default='pr2894')
+    a = ap.parse_args()
+    global SOURCE_COMMIT, SOURCE_MANIFEST, COMPARISON_SHA, COMPARISON_HEAD
+    source_profile = SOURCE_PROFILES[a.source_profile]
+    comparison = COMPARISONS[a.comparison_profile]
+    SOURCE_COMMIT, SOURCE_MANIFEST = source_profile['commit'], source_profile['manifest']
+    COMPARISON_SHA, COMPARISON_HEAD = comparison['sha256'], comparison['head']
+    expected_helpers, comparison_pr = source_profile['helpers'], comparison['pr']
+    need(not sys.flags.optimize and a.jobs > 0, 'enabled assertions and positive jobs required')
+    source, cache, work = a.source.resolve(), a.native_cache.resolve(), a.work.resolve()
+    need(not work.exists() and not work.is_relative_to(source) and not work.is_relative_to(cache),
+         'fresh external work required')
+    need(sha(source / 'MANIFEST.json') == SOURCE_MANIFEST, 'COMPOSED manifest pin')
+    source_files = read(source / 'MANIFEST.json')
+    need(len(source_files) == source_profile['source_file_count'] and tree(source, ('MANIFEST.json',)) == source_files,
+         'complete COMPOSED source inventory and hashes')
+    helper_dir = a.replica_helper_dir.resolve()
+    helper_paths = [helper_dir / n for n in ('lift_parent.py', 'replica_parent.py')] + [a.reconstructor.resolve()]
+    external_hashes = {str(p): sha(p) for p in helper_paths + [a.fill.resolve(), a.order.resolve(), a.dispatch.resolve(), a.comparison_claim.resolve(), a.blocknorm_checker.resolve()]}
+    need(sha(a.comparison_claim) == COMPARISON_SHA, 'exact pinned frontier headline comparison')
+    comparison_claim = read(a.comparison_claim)
+    need('headline_kappa_source' not in comparison_claim and comparison['field'] in comparison_claim,
+         'comparison must be full headline outer claim, not supplier-only CLAIM')
+    previous = Q(comparison_claim[comparison['field']])
+    need(previous == Q(comparison_claim['kappa']), 'comparison rational/decimal equality')
+    order_input = read(a.order)
+    need(order_input and all(isinstance(x,list) and len(x)==2 and all(type(v)is int for v in x) for x in order_input), 'literal integer call order')
+    T = 1 + max(r for st,r in order_input)
+    need(T > 0 and len(order_input)==9*T and set(map(tuple,order_input))=={(st,r) for st in range(9) for r in range(T)}, 'complete new replica coverage')
+    need(all([st for st,r in order_input if r==rep]==list(range(9)) for rep in range(T)), 'source stage projection')
+    dispatch_input = read(a.dispatch)
+    need(len(dispatch_input)==9*T and {(st,r) for st,r,pid in dispatch_input}==set(map(tuple,order_input)), 'complete explicit dispatch')
+    native_receipt = read(a.native_receipt)
+    need(native_receipt['status'] == 'PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE'
+         and native_receipt['source_commit'] == SOURCE_COMMIT
+         and native_receipt['manifest_sha256'] == SOURCE_MANIFEST, 'native receipt source binding')
+    need(tree(cache) == native_receipt['cache_files'], 'complete native/parent cache hashes')
+    old = source / 'vendor/pr1297'
+    need(sha(old / 'MANIFEST.json') == PARENT_MANIFEST, 'retained parent pin')
+    parent_receipt = cache / '_receipts' / PARENT_MANIFEST / 'RECEIPT.json'
+    need(sha(parent_receipt) == native_receipt['retained_parent_receipt_sha256'], 'parent receipt pin')
+    pr = read(parent_receipt)
+    need(pr['vendor_manifest_sha256'] == PARENT_MANIFEST and pr['claim_sha256'] == sha(old / 'CLAIM.json'),
+         'parent receipt claim binding')
+    for name, digest in pr['files'].items():
+        need(sha(parent_receipt.parent / name) == digest, 'parent receipt file')
+    parent_result = read(parent_receipt.parent / 'RESULT.json')
+    need(parent_result['status'] == 'PASS_GLOBAL_MIXED_X54_FUSIONS_NATIVE_AND_STRICT_ADMISSION'
+         and parent_result['kappa'] == read(old / 'CLAIM.json')['kappa'], 'retained parent completed admission')
+    natives = {}
+    for tag in ('base', 'extra'):
+        word = source / ('new/borrow/words/BORROW-WORD-43' + tag + '.json.gz')
+        entry = cache / sha(word)
+        binding = native_receipt['providers'][tag]
+        need(binding['word_sha256'] == sha(word)
+             and tree(entry, ('CACHE.json',)) == binding['complete_native_files'], 'native full-tree binding')
+        need(read(entry / 'local/FULL-WORD.json.gz') == read(word), 'native complete word')
+        stages = read(entry / 'STEPS.json')
+        need([s['step'] for s in stages] == NATIVE_STAGES and all(s['exit_code'] == 0 for s in stages),
+             'native five-stage coverage')
+        checks = read(entry / 'local/LOCAL-CHECKS.json')
+        need(all(checks[o]['paid_profile'] == read(word)['report']['local_profile'] for o in ('forward', 'backward')),
+             'native actual paid profiles')
+        natives[tag] = entry
+    work.mkdir(parents=True)
+    package = work / 'package'
+    shutil.copytree(source, package)
+    # Only the fresh external clone changes. Immutable source/cache inventories remain pinned.
+    for hp in helper_paths[:2]:
+        shutil.copy2(hp, package / hp.name)
+        need(sha(package / hp.name)==external_hashes[str(hp)], 'helper copy hash')
+    shutil.copy2(a.blocknorm_checker, package / 'blocknorm_certificate.py')
+    shutil.copy2(a.blocknorm_checker, package / 'code/blocknorm_certificate.py')
+    need(sha(package / 'blocknorm_certificate.py') == external_hashes[str(a.blocknorm_checker.resolve())], 'block-norm checker exact source binding')
+    shutil.copy2(a.reconstructor, package / 'reconstruct.py')
+    need(sha(package / 'reconstruct.py')==external_hashes[str(a.reconstructor.resolve())], 'reconstructor copy hash')
+    # The original subprocesses also write generated hash-bound source. Windows
+    # callers use a process-scoped LF adapter; no system configuration is changed.
+    lf_probe = work / '.lf-preflight.txt'
+    lf_probe.write_text('LF\n', encoding='utf-8')
+    need(lf_probe.read_bytes()==b'LF\n', 'process-scoped LF output required on Windows')
+    lf_probe.unlink()
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0',
+               OPENBLAS_NUM_THREADS='1', OMP_NUM_THREADS='1', AUDIT_FAST_SHARDS=str(a.jobs))
+    for name in ('PYTHONOPTIMIZE', 'WITNESS_SPEC', 'WITNESS_DISCOVER', 'WITNESS_RECORD'):
+        env.pop(name, None)
+    stages, patches = [], []
+
+    def run(name, script, *args):
+        start = time.monotonic()
+        command = [sys.executable, '-B', str(script), *map(str, args)]
+        log = work / (name + '.log')
+        with log.open('w') as output:
+            result = subprocess.run(command, env=env, cwd=work, stdin=subprocess.DEVNULL,
+                                    stdout=output, stderr=subprocess.STDOUT)
+        stages.append(dict(name=name, exit_code=result.returncode, seconds=time.monotonic() - start,
+                           script_sha256=sha(script), log_sha256=sha(log), command=command))
+        write(work / 'STAGES.json', stages)
+        need(result.returncode == 0, 'failed ' + name + '; see ' + str(log))
+        print('PASS', name, flush=True)
+
+    def patch(name, replacements):
+        path = package / name
+        before = sha(path)
+        body = path.read_text()
+        for old_text, new_text in replacements:
+            need(body.count(old_text) == 1, 'exact patch preimage: ' + name + ': ' + old_text[:80])
+            body = body.replace(old_text, new_text)
+        path.write_text(body)
+        patches.append(dict(path=name, before_sha256=before, after_sha256=sha(path), replacements=replacements))
+
+    # PR2530's already checked correction: restored zero buffers occupy physical
+    # rows. COMPOSED's shipped SPEC includes them; its rebound SPEC omitted them.
+    patch('new/rebind.py', [
+        ("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()))")])
+    # At T37 the historical fixed333 mutant is a no-op. Preserve the
+    # undercharge test by subtracting one from both actual charges, and
+    # require every geometry mutant to differ before the unchanged assembly.
+    patch('geometry_controls.py', [
+        (" 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")])
+    # Preserve the exact fixed-grid-maximum equality while deriving precision
+    # from the same SPEC read by both independent outer arithmetic checkers.
+    patch('verify_release.py', [
+        ('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")])
+    # Keep the native dimension and paid moment ledger fixed; bind replica
+    # width to both the checked source geometry and the independent B invoice.
+    patch('outer/check_ledger.py', [
+        ('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']")])
+    patch('code/witness.py', [(DISCOVERY_APPEND_OLD, DISCOVERY_APPEND_NEW)])
+    patch('verify.py', [
+        ("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')")])
+    # A sharper local reserve is certified against actual scalar/Horner
+    # prefixes of BOTH orientations and BOTH providers. All sweep and physical
+    # row charges remain unchanged; this never omits an invocation or bridge.
+    patch('code/witness.py', [
+        ("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()")])
+    patch('code/invoice_allcold.py', [
+        ("    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")])
+    patch('independent_core.py', [
+        ("    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()")])
+    patch('code/invoice_allcold.py', [
+        ("        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.")])
+    patch('independent_core.py', [
+        ("    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")])
+    patch('audit_mixed.py', [
+        ("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)")])
+    patch('code/assemble.py', [
+        (" 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=73,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")])
+    patch('code/assembly_controls.py', [
+        ("        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)),")])
+    patch('freeze_spec.py', [
+        ("spec['expected']['assembly_controls_rejected'] = 32 + sum(", "spec['expected']['assembly_controls_rejected'] = 37 + sum(")])
+    patch('replay.py', [
+        ("len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==114", "len(rd(work/'ADMISSION-CONTROLS.json')['rejected_controls'])==119")])
+    patch('verify.py', [
+        ("['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)")])
+    write(work / 'RUNTIME-PATCHES.json', patches)
+    shutil.copy2(a.fill, package / 'new/borrow-fill/FILL.json.gz')
+    shutil.copy2(a.order, package / 'new/borrow-fill/ORDER.json')
+    shutil.copy2(a.dispatch, package / 'new/borrow-fill/DISPATCH.json')
+    run('owners', package / 'reconstruct.py', '--out', work / 'owners')
+    run('parent-lift', package / 'lift_parent.py', '--package', package, '--owners', work / 'owners', '--out', work / 'parent-data')
+    for name in ('PLAN.json', 'OWNERS.json.gz', 'DISPATCH.json', 'PROFILE.json', 'CONSTRUCTION.json',
+                 'GLOBAL-TEMPLATE.json.gz', 'SPEC.json'):
+        shutil.copy2(work / 'parent-data' / name, package / name)
+    shutil.copy2(work / 'owners/ORDER.json', package / 'ORDER.json')
+    spec = read(package / 'SPEC.json')
+    spec['outer_refinement'] = PRECISION
+    spec['expected']['live'] = 896*T
+    # COMPOSED's pre-life mechanism changes which helper labels retain width8.
+    # Preserve its declared spot set; rebind and the original strict verifier
+    # still check the actual native widths, including every other helper.
+    source_spots = read(source / 'new/SPEC.json')['width_spot_helpers']
+    need(source_spots == [278, 281, 284, 289], 'COMPOSED source spot-width pins')
+    spec['width_spot_helpers'] = source_spots
+    write(package / 'new/SPEC.json', spec)
+    run('rebind', package / 'new/rebind.py', package, natives['base'] / 'local',
+        natives['extra'] / 'local', work / 'rebound')
+    spec = read(work / 'rebound/SPEC.json')
+    for tag in ('base', 'extra'):
+        c = read(natives[tag] / 'local/CANONICAL-WORD.json.gz')
+        need(c['R']==expected_helpers and len(c['centers'])==8 and len(c.get('zero_buffers',[]))==73, 'helper408 physical ABI including all 73 private buffers')
+    need(spec['expected']['physical'] == 896*T+expected_helpers+8+73+2, 'complete physical cost including all actual helpers and 73 buffers')
+    layout = work / 'layout'
+    layout.mkdir()
+    with tarfile.open(old / 'upstream-layout.tar.gz') as archive:
+        need(all(m.isfile() and not Path(m.name).is_absolute() and '..' not in Path(m.name).parts
+                 for m in archive.getmembers()), 'retained archive paths')
+        archive.extractall(layout, filter='data')
+    runtime = layout / 'packing74'
+    runtime.mkdir()
+    for name in ('replay.py', 'freeze_spec.py', 'audit_mixed.py', 'independent_core.py', 'geometry_controls.py', 'audit_fast.py', 'blocknorm_certificate.py'):
+        shutil.copy2(package / name, runtime / name)
+    for name in ('code', 'construction', 'inputs'):
+        shutil.copytree(package / name, runtime / name)
+    shutil.copytree(work / 'rebound', runtime / 'candidate')
+    shutil.copytree(natives['extra'], runtime / 'native-extra')
+    data = runtime / 'candidate'
+    result = dict(status='PREPARED_REPLICA_SAME_WORD_DERIVATIVE_NOT_ADMITTED', source_commit=SOURCE_COMMIT,
+                  source_manifest_sha256=SOURCE_MANIFEST, native_receipt_sha256=sha(a.native_receipt),
+                  fill_sha256=sha(package / 'new/borrow-fill/FILL.json.gz'),
+                  order_sha256=sha(package / 'new/borrow-fill/ORDER.json'), dispatch_sha256=sha(package / 'new/borrow-fill/DISPATCH.json'), replicas=T, source_profile=a.source_profile, source_file_count=source_profile['source_file_count'], source_upstream_head=source_profile['upstream_head'], actual_expected_helpers=expected_helpers, comparison_pr=comparison_pr, comparison_head=COMPARISON_HEAD, comparison_claim_sha256=COMPARISON_SHA, comparison_kappa=str(previous), external_input_sha256=external_hashes, profile=read(work / 'rebound/PROFILE.json'),
+                  patches=patches, scope='Prepared only; source/native/parent inputs authenticated and literal owner fill reconstructed.')
+    write(work / 'RESULT.json', result)
+    # Preparation still authenticates every read-only input at its end.
+    need(tree(source, ('MANIFEST.json',))==source_files and tree(cache)==native_receipt['cache_files'], 'read-only inputs changed during preparation')
+    need(all(sha(Path(p))==h for p,h in external_hashes.items()), 'external candidate/helper inputs changed')
+    if a.prepare_only:
+        print(result['status'], flush=True)
+        return
+    run('discovery', runtime / 'replay.py', '--data', data, '--work', work / 'discovery',
+        '--local', natives['base'] / 'local', '--discover')
+    supplier = read(work / 'discovery/RESULT.json')
+    for name in ('PLAN.json', 'PROFILE.json', 'SPEC.json'):
+        shutil.copy2(data / name, package / 'new' / name)
+    spec = read(package / 'new/SPEC.json')
+    original_claim = read(source / 'CLAIM.json')
+    claim = dict(status='CONDITIONAL_CANDIDATE_EXPECTED_BY_REPLAY', kappa=supplier['kappa'],
+                 kappa_decimal=supplier['kappa_decimal'], baseline_pr=comparison_pr, baseline_head=COMPARISON_HEAD,
+                 baseline_kappa=str(previous), outer_refinement=PRECISION,
+                 scope=original_claim['scope'], kappa_layers=original_claim['kappa_layers'],
+                 headline_kappa_source='outer/OUTER-CLAIM.json',
+                 verification='Candidate discovered from literal fill; full original verification must pass separately.')
+    write(package / 'CLAIM.json', claim)
+    C = Q(spec['expected']['complex_lower'])
+    write(package / 'outer/B.json', dict(b=str(C-Q(1,10**104)), b_above_endpoint=str(C+Q(1,10**24)),
+                                        profile=spec['expected']['global_profile'], live=spec['expected']['live']))
+    for name in ('check_ledger.py', 'independent_check.py'):
+        run('outer-' + name, package / 'outer' / name)
+    ledger = read(package / 'outer/LEDGER.json')
+    row = ledger['rows']['struct_boundary_radix_union']['kappa']
+    kappa = Q(row['rational'])
+    need(kappa == C-Q(1,10**70)-Q(1,10**46) and kappa > previous,
+         'candidate must strictly improve full exact pinned frontier headline before full release')
+    outer_claim = read(source / 'outer/OUTER-CLAIM.json')
+    outer_claim.update(kappa=row['decimal'], kappa_rational=row['rational'],
+                       baseline_head=COMPARISON_HEAD, baseline_kappa=str(previous), gain=str(kappa-previous),
+                       b='certified complex_lower - 1e-104 (outer/B.json)',
+                       retuned_slacks='Endpoint precision24; free gaps follow outer/check_ledger.py from the frozen SPEC.',
+                       fixed_grid_maximum='kappa=C-10^-70-10^-46 exactly; same fixed-grid-maximum proof at precision24.')
+    write(package / 'outer/OUTER-CLAIM.json', outer_claim)
+    (package / 'provenance').mkdir(exist_ok=True)
+    shutil.copy2(a.comparison_claim, package / ('provenance/PR' + str(comparison_pr) + '-HEADLINE-CLAIM.json'))
+    write(package / 'MANIFEST.json', tree(package, ('MANIFEST.json',)))
+    run('release', package / 'verify_release.py', '--main', source.parents[1], '--work', work / 'release',
+        '--native-cache', cache, '--jobs', a.jobs)
+    receipt = read(work / 'release/RELEASE-RECEIPT.json')
+    need(receipt['status'] == 'PASS_RELEASE' and Q(receipt['kappa_decimal']) == kappa
+         and receipt['manifest_sha256'] == sha(package / 'MANIFEST.json'), 'complete release binding')
+    need(sha(source / 'MANIFEST.json') == SOURCE_MANIFEST
+         and tree(source, ('MANIFEST.json',)) == source_files and tree(cache) == native_receipt['cache_files'],
+         'read-only source/cache inputs changed')
+    need(all(sha(Path(p))==h for p,h in external_hashes.items()), 'external candidate/helper inputs changed during admission')
+    result.update(status='PASS_REPLICA_ORDER_FILL_DERIVATIVE_COMPLETE_RELEASE',
+                  complex_lower=str(C), kappa=str(kappa), kappa_decimal=row['decimal'],
+                  gain=str(kappa-previous), release_receipt_sha256=sha(work / 'release/RELEASE-RECEIPT.json'),
+                  package_manifest_sha256=sha(package / 'MANIFEST.json'), stages=stages,
+                  scope='Conditional finite construction and modern outer arithmetic. Exact inherited theorem obligations remain. Both native providers explicitly reused from authenticated fresh five-stage runs.')
+    write(work / 'RESULT.json', result)
+    print(result['status'], row['decimal'], flush=True)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/two-sided-helper-extraction/tools/audit_moment.py b/research/two-sided-helper-extraction/tools/audit_moment.py
new file mode 100644
index 0000000000..0d96586a00
--- /dev/null
+++ b/research/two-sided-helper-extraction/tools/audit_moment.py
@@ -0,0 +1,79 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Independent dyadic interval moment auditor, atlas D020.
+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()=='29cd4aa92059a561437d7670b574c51ae4e1cfeaaf6feb6cc318d915869e6d30','exact pinned PR2894 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/two-sided-helper-extraction/tools/build_channel_overlay.py b/research/two-sided-helper-extraction/tools/build_channel_overlay.py
new file mode 100644
index 0000000000..5b9ab21a63
--- /dev/null
+++ b/research/two-sided-helper-extraction/tools/build_channel_overlay.py
@@ -0,0 +1,53 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Append the declared two-sided helper408 stage to immutable PR2894 source."""
+import argparse,gzip,hashlib,json,shutil,sys,types
+from pathlib import Path
+sys.dont_write_bytecode=True
+PARENT='4da246899e2c509dd8c6e5af34905c6124ca17671b188e11ac37e36adf449504'
+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=a.source.resolve();out=a.out.resolve();p=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/channel408';local.mkdir()
+ for n in ['PINS.json','verify.py','extract.py','structure.py',*pins]:
+  dest=local/n;dest.parent.mkdir(parents=True,exist_ok=True);shutil.copy2(p/n,dest)
+ shutil.copy2(p/'extract.py',out/'new/borrow/channel_extract.py')
+ prov=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/PM-WORD-{tag}.json.gz');shutil.copy2(p/f'data/WORD-{tag}.json.gz',q)
+  w=read(q);hs=sorted(set(range(224,704))-set(w['removed']))
+  prov[pid]={'widths':[len(w['helper_final'].get(str(h),[0]*9))-len(w['start_extra'].get(str(h),[])) for h in hs],'actual_paid_profile':w['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',prov)
+ 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="""    # Explicit two-sided input/output change; the extra cold helper is charged.
+    import channel_extract
+    channel_parent=json.loads(gzip.decompress((D/'inputs'/f'PM-WORD-{wt}.json.gz').read_bytes()))
+    assert chain[-1]==channel_parent
+    channel_transform=json.loads((D/'channel408/data/TRANSFORM.json').read_text())
+    channel_word=channel_extract.apply(chain[-1],channel_transform)
+    assert set(k_ for k_ in chain[-1] if chain[-1][k_]!=channel_word[k_])==channel_extract.ALLOWED
+    chain.append(channel_word);steps.append('two-sided-helper408')
+"""
+ 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('preload-move-independent-review'"))
+ new=line.replace("P/'new/borrow/words/BORROW-WORD-43base.json.gz'","P/'new/borrow/inputs/PM-WORD-base.json.gz'").replace("P/'new/borrow/words/BORROW-WORD-43extra.json.gz'","P/'new/borrow/inputs/PM-WORD-extra.json.gz'")
+ new+="\nrun('two-sided-helper408-review',P/'new/borrow/channel408/verify.py','--work',work/'two-sided-helper408-review')"
+ assert text.count(line)==1;path.write_text(text.replace(line,new))
+ before=tree(src);after=tree(out);save(out/'MANIFEST.json',after)
+ 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/channel_extract.py'}|{f'new/borrow/words/BORROW-WORD-43{tag}.json.gz' for tag in ('base','extra')}|{f'new/borrow/inputs/PM-WORD-{tag}.json.gz' for tag in ('base','extra')}|{'new/borrow/channel408/'+n for n in ['PINS.json','verify.py','extract.py','structure.py',*pins]}
+ assert set(changes)==expected and tree(src)==before
+ result={'status':'PASS_SOURCE_BOUND_TWO_SIDED_HELPER408_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))
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/tools/channel_blocknorm.py b/research/two-sided-helper-extraction/tools/channel_blocknorm.py
new file mode 100644
index 0000000000..20afc31774
--- /dev/null
+++ b/research/two-sided-helper-extraction/tools/channel_blocknorm.py
@@ -0,0 +1,268 @@
+"""Physical-owner boundary certificate; retains the completed native phase audit.
+
+certify(hosted, local_dirs) is a finite premise checker for the separate universal
+block-energy lemma. It does not replace frame/phase/primitive or release checks.
+"""
+import gzip, hashlib, json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def require(ok, message):
+    if not ok:
+        raise AssertionError('blocknorm: ' + message)
+
+
+def digest(path):
+    return hashlib.sha256(Path(path).read_bytes()).hexdigest()
+
+
+def read(path):
+    path = Path(path)
+    raw = gzip.decompress(path.read_bytes()) if path.suffix == '.gz' else path.read_bytes()
+    return json.loads(raw)
+
+
+def replay_endpoint(events, v, helpers, back):
+    """Exact rows in the free warp algebra, plus private first-write discipline.
+
+    Frame transports/centre children retain the separately audited native
+    coordinate interfaces. A warp prefixes a formal invertible operator; only
+    adjacent inverse pairs cancel. Thus no numerical sampling is used.
+    """
+    n = 2*v + helpers
+    rows = {('L', i): {(i, ()): Q(1)} for i in range(n)}
+    live_z, allocated, freed, cleared_c = set(), set(), set(), Counter()
+    tags = {'phase', 'scalar', 'warp', 'center', 'climb', 'adapter', 'residual_adapter', 'zero_buffer'}
+    for index, event in enumerate(events):
+        tag = event[0]
+        require(tag in tags, 'unknown native event')
+        if tag == 'zero_buffer':
+            _, action, z = event
+            r = ('Z', z)
+            if action == 'alloc':
+                require(z not in allocated and r not in rows, 'zero buffer duplicate allocation')
+                allocated.add(z); live_z.add(z); rows[r] = {}
+            else:
+                require(action == 'free' and z in live_z and not rows[r], 'zero buffer release nonzero/unallocated')
+                live_z.remove(z); freed.add(z)
+        elif tag == 'scalar':
+            e = event[1]; op = e[0]; target = tuple(e[1])
+            require(op in ('clear','copy','scale','add'), 'unknown scalar')
+            source = tuple(e[2]) if op in ('copy','add') else None
+            for r in [target] + ([source] if source else []):
+                require(r[0] in ('L','C','Z'), 'unknown register class')
+                if r[0] == 'L': require(0 <= r[1] < n, 'live role range')
+                if r[0] == 'C': require(0 <= r[1] < 8, 'centre role range')
+                if r[0] == 'Z': require(r[1] in live_z, 'zero buffer read/write before alloc or after free')
+            if op == 'clear':
+                rows[target] = {}
+                if target[0] == 'C': cleared_c[target[1]] += 1
+            elif op == 'copy':
+                require(source in rows, 'source read before initialization')
+                # First private write must be an explicit clear, even if copy overwrites.
+                require(target in rows, 'private copy before first clear')
+                rows[target] = dict(rows[source])
+            elif op == 'scale':
+                require(target in rows, 'scale before first clear')
+                q = Q(e[2], e[3]); rows[target] = {j:q*x for j,x in rows[target].items() if q*x}
+            else:
+                require(target in rows and source in rows, 'add read before first clear')
+                q = Q(e[3],e[4]); dest=rows[target]
+                require(target != source, 'aliased scalar add')
+                for j,x in rows[source].items():
+                    y=dest.get(j,Q(0))+q*x
+                    if y: dest[j]=y
+                    else: dest.pop(j,None)
+        elif tag == 'warp':
+            r, op = tuple(event[1]), event[2]
+            require(r in rows and (r[0] != 'Z' or r[1] in live_z), 'warp before initialization')
+            require(isinstance(op,int) and op != 0, 'invalid formal warp')
+            rows[r] = {(i, word[1:] if word and word[0] == -op else (op,)+word): x
+                       for (i,word),x in rows[r].items()}
+        elif tag == 'center':
+            require(('C',event[1]) in rows, 'centre child before first clear')
+    require(not live_z and allocated == freed and len(allocated)==73, 'all73 private zero buffers released')
+    require(set(cleared_c)==set(range(8)) and all(cleared_c[k]==2 for k in range(8)), 'each centre first and terminal clear')
+    require(all(not row for r,row in rows.items() if r[0] in ('C','Z')), 'private work nonzero at boundary')
+    for i in range(n):
+        want={(i,()):Q(1)}
+        if back and i<v: want[(v+i,())]=Q(-1)
+        if not back and v<=i<2*v: want[(i-v,())]=Q(1)
+        require(rows['L',i] == want, 'all-column endpoint mismatch row '+str(i))
+    return {'all_arbitrary_columns':n,'helper_to_data_response_zero':True,
+            'centres_first_clear_and_terminal_zero':8,'zero_buffers_allocated_and_cleared':73,
+            'coefficient_work_contract':'unchanged audited clear-before-and-after Horner macro'}
+
+
+
+def certify_providers(registry, local_dirs):
+    endpoint={}; localbits=0
+    for pid,p in registry.items():
+        base=Path(local_dirs[pid]); cp=base/'CANONICAL-WORD.json.gz'; pp=base/'LOCAL-PROGRAMS.json.gz'
+        replay=read(base/'INDEPENDENT-LOCAL-REPLAY.json'); checks=read(base/'LOCAL-CHECKS.json'); programs=read(pp)
+        require(replay['status']=='PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY', 'completed native endpoint replay')
+        require(digest(cp)==p['canonical_word_sha256']==replay['canonical_word_sha256'], 'canonical hash')
+        require(digest(pp)==p['local_programs_sha256']==replay['local_programs_sha256'], 'program hash')
+        require(programs==p['local_programs'] and checks==p['local_program_checks'], 'actual registry programs/checks')
+        require(digest(base/'CLIFFORD-RECIPES.json')==p['exact_local_clifford_recipe_sha256'], 'phase recipe binding')
+        require(digest(base/'RESIDUAL-ADAPTERS.json')==p['residual_adapter_sha256'], 'residual adapter binding')
+        require((p['v'],p['R'],p['h'])==(112,408,9), 'actualR408 ABI')
+        endpoint[pid]={}
+        for direction in ('forward','backward'):
+            r=replay['local'][direction]; c=checks[direction]
+            require(r['all_exact_columns']==632 and r['private_work_erased'] and r['zero_buffers_returned_to_zero']==73, 'native all-column/private endpoint')
+            require(c['private_centers_cleared'] and c['private_coefficient_stream_cleared_after_each_macro'], 'native private macro contract')
+            localbits=max(localbits,r['prefix_bits_upper'])
+            endpoint[pid][direction]=replay_endpoint(programs[direction],112,408,direction=='backward')
+    return endpoint, localbits
+
+
+def full_stock_l2(physical):
+    """Conservative ambient conversion includes every symplectic cover vertex."""
+    require(isinstance(physical,int) and 0<physical<=2**20, 'bounded complete physical stock')
+    group=2**(36*36)
+    for j in range(1,37): group *= 2**(2*j)-1
+    stock=group*physical
+    bits=(stock.bit_length()+1)//2
+    require(bits<=1330, 'full stock l2 cap1330')
+    return stock.bit_length(), bits
+
+
+def certify(hosted, local_dirs):
+    """Return depth18/full-stock norm only after actual finite premise checks.
+
+    local_dirs maps every provider id to its actual local/ artifact directory.
+    Caller MUST also run the unchanged native frame/phase and physical primitive
+    audits and full invoice; this checker neither fabricates nor replaces them.
+    """
+    d = hosted
+    require(d['m']==73, '73-dimensional address space')
+    live, physical = d['live'],d['physical']
+    require(isinstance(live,int) and live>0 and live%896==0, 'live896T')
+    T=live//896
+    stock_bits, stock_l2_bits=full_stock_l2(physical)
+    require(physical==live+8+408+73+2 and physical <= 2**20, 'physical stock bound')
+    ns=d['private_namespace']
+    require(ns=={'centers':[live,live+8], 'reserved_tableau':[live+8,live+416],
+                 'zero_buffers':[live+416,live+489], 'coefficient':[live+489,live+491]}, 'private namespaces')
+    registry=d['local_providers']; require(set(local_dirs)==set(registry), 'complete provider directory map')
+    endpoint, localbits = certify_providers(registry, local_dirs)
+    require(localbits<=128, 'local prefix128 reserve')
+    calls=d['calls']; require(len(calls)==9*T, '9T calls')
+    bycall={}; stages=[Counter() for _ in range(T)]; foreign=0
+    pairs=[0,0,0,1,1,2,2,3,3]; backwards={1,3,5,7}
+    for call in calls:
+        r,s=call['replica'],call['stage']; pid=call['provider_id']
+        require(isinstance(r,int) and 0<=r<T and isinstance(s,int) and 0<=s<9, 'call replica/stage')
+        require(call['pair']==pairs[s] and call['orientation']==('backward' if s in backwards else 'forward'), 'actual9-stage recipe')
+        require(pid in registry, 'registered provider'); p=registry[pid]; ori=call['orientation']
+        require(call['local_program_sha256']==p['local_program_checks'][ori]['sha256'], 'call actual program hash')
+        owners=call['owners']; families=[x[0] for x in owners]
+        require(len(families)==632 and len(set(families))==632 and all(isinstance(f,int) and 0<=f<live for f in families), 'distinct live-family embedding')
+        want=[896*r+(2*pairs[s]+side)*112+port for side in range(2) for port in range(112)]
+        require(families[:224]==want, 'caller data block')
+        for j,(f,route) in enumerate(owners):
+            if j<224:
+                require(route==[1,s,j%112], 'exact data phase route')
+            else:
+                width=p['widths'][j-224]
+                require(route[0] in (3,4) and 0<=route[1]<20 and isinstance(route[2],int) and route[2]>=0, 'family-local helper route')
+                if route[0]==3: require(width==9 and len(route)==3, 'full-width helper route')
+                else: require(len(route)==5 and route[3]==width and len(route[4])==9-width and len(set(route[4]))==9-width and all(0<=x<9 for x in route[4]), 'residual spectator permutation')
+                foreign += (f//896 != r)
+        require(call['time'] not in bycall, 'serialized call times'); bycall[call['time']]=call
+        stages[r][s]+=1
+    require(all(c==Counter(range(9)) for c in stages), 'every replica9 calls exactly')
+    kinds={'local_cover_sweep','idle_cover_sweep','bridge','terminal','terminal_Y_translations','bank_padding_cover_sweep','translate_every_live_family'}
+    seq=[[] for _ in range(T)]; active=[0]*T; bridges=[0]*T; globals_seen=[]
+    for event in d['execution_schedule']:
+        kind=event['kind']; require(kind in kinds, 'known schedule event')
+        if kind in ('bank_padding_cover_sweep','translate_every_live_family'):
+            globals_seen.append(kind); require(event['families']==([live,live] if kind=='bank_padding_cover_sweep' else [0,live]), 'family-local global sweep')
+            continue
+        r=event['replica']; require(0<=r<T and event['replicas']==[r], 'single replica event')
+        seq[r].append(event['source_event'])
+        if kind=='local_cover_sweep':
+            call=bycall.get(event['time']); require(call and (call['replica'],call['stage'],call['provider_id'])==(r,event['stage'],event['provider_id']), 'schedule actual call')
+            active[r]+=1
+        elif kind=='bridge':
+            require(0<=event['src']<4 and 0<=event['dst']<4 and event['src']!=event['dst'] and event['coefficient'] in (-1,1), 'within-replica disjoint shear pair bridge')
+            bridges[r]+=1
+        elif kind=='idle_cover_sweep': require(0<=event['pair']<4 and all(0<=x<20 for x in event['child_indices']), 'within-family idle child')
+        elif kind=='terminal': require(event['pairs']==4, '4 within-replica terminal exchanges')
+        elif kind=='terminal_Y_translations': require(event['pairs']==list(range(4)), '4 within-family Y translations')
+    require(all(s==list(range(30)) for s in seq), 'literal per-replica source-event projection0..29')
+    require(active==[9]*T and bridges==[9]*T, '9active9bridges per block')
+    require(globals_seen==['bank_padding_cover_sweep','translate_every_live_family'] and not d['bank_padding']['children'] and not d['bank_padding']['families'], 'only family-local terminal sweeps')
+    for child in d['idle_children']:
+        require(child['family']//896==child['replica'] and child['replicas']==1 and 0<=child['family']<live, 'idle child stays owner block')
+    zb=d['private_zero_buffer_lowering']; require(zb['allocation']==zb['release']=='clear' and zb['families']==ns['zero_buffers'], 'physical zero buffer clear ABI')
+    require(set(zb['provider_maps'])==set(registry), 'complete private Z provider mapping')
+    for pid,mp in zb['provider_maps'].items():
+        require(pid in registry and len(mp)==73 and set(mp.values())==set(range(*ns['zero_buffers'])), '73distinct private Z slots')
+    return {'status':'PASS_TENSOR_BLOCK_NORM_CERTIFICATE','replicas':T,
+            'physical_families':physical,'live_families':live,'block_width_families':896,
+            'active_calls_per_block':9,'bridges_per_block':9,'boundary_depth_bits':18,'max_active_depth':18,
+            'stocknorm_bits':stock_l2_bits,'stock_l2_bits':stock_l2_bits,'physical_stock_bits':stock_bits,'partial_cover_bits':1,'stocknorm_condition':'sqrt(|Sp(72,2)| * physical_families) <= 2^stock_l2_bits',
+            'input_l2_bits':37,'local_actual_prefix_bits':localbits,'local_reserve_bits':128,
+            'actual_prefix_bits':localbits+37+18+stock_l2_bits+1+4,'required_reserve_bits':128+37+18+stock_l2_bits+1+4,'retained_payload_bits':2048,
+            'foreign_helper_roles_checked':foreign,'endpoint_replay':endpoint,
+            '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.'}
+
+
+
+def certify_context(context, roles, local_dirs, *, source_parent):
+    """Independent pre-emission owner chart; source_parent is mandatory.
+
+    make_context's exact per-replica source projection is rechecked from its
+    order, while the concrete source recipe supplies the nine same-replica
+    bridges. check_roles must still validate all literal windows and charts.
+    """
+    c=context; order=c['order']; require(len(order)%9==0 and order, 'context9T calls')
+    T=len(order)//9; live=896*T; physical=live+490
+    stock_bits, stock_l2_bits=full_stock_l2(physical)
+    require(physical<=2**20, 'context physical stock bound')
+    require(len(set(map(tuple,order)))==9*T and set(map(tuple,order))=={(s,r) for r in range(T) for s in range(9)}, 'context full stage inventory')
+    require(all([s for s,r in order if r==rr]==list(range(9)) for rr in range(T)), 'context per-replica9stage order')
+    require(c['at']=={tuple(key):t for t,key in enumerate(order)}, 'context time map')
+    require(c['event_count']==30*T and c['bridges']==9*T, 'context source projection count')
+    require(c['stage_pair']==dict(enumerate([0,0,0,1,1,2,2,3,3])), 'context actual pair recipe')
+    recipe=source_parent['recipe']
+    expected_bridges=[(1,0,1),(1,0,-1),(2,1,1),(2,1,-1),(3,2,1),(3,2,-1),(2,3,1),(1,2,1),(0,1,1)]
+    require([(e['src'],e['dst'],e['coefficient']) for e in recipe if e['kind']=='bridge']==expected_bridges, 'source nine within-replica bridge pairs')
+    source=source_parent['execution_schedule']
+    require(len(source)==32 and [e['kind'] for e in source[-2:]]==['bank_padding_cover_sweep','translate_every_live_family'], 'source30 plus2global')
+    require(sum(e['kind']=='bridge' for e in source)==9 and sum(e['kind']=='local_cover_sweep' for e in source)==9, 'source9local9bridge')
+    require(all(0<=e['src']<4 and 0<=e['dst']<4 and e['src']!=e['dst'] and e['coefficient'] in (-1,1) for e in source if e['kind']=='bridge'), 'source bridge physical pair range')
+    registry={}
+    for pid,base in local_dirs.items():
+        base=Path(base); w=read(base/'CANONICAL-WORD.json.gz'); pg=read(base/'LOCAL-PROGRAMS.json.gz')
+        registry[pid]={'v':w['v'],'R':w['R'],'h':w['h'],
+           'canonical_word_sha256':digest(base/'CANONICAL-WORD.json.gz'),
+           'local_programs_sha256':digest(base/'LOCAL-PROGRAMS.json.gz'),
+           'local_programs':pg,'local_program_checks':read(base/'LOCAL-CHECKS.json'),
+           'exact_local_clifford_recipe_sha256':digest(base/'CLIFFORD-RECIPES.json'),
+           'residual_adapter_sha256':digest(base/'RESIDUAL-ADAPTERS.json')}
+    endpoint,localbits=certify_providers(registry,local_dirs)
+    require(localbits<=128 and c['max_local_prefix']==localbits, 'context actual local prefix')
+    require(len(roles)==9*T*408, 'context complete helper roles')
+    bycall={tuple(key):set() for key in order}; seenhelpers={tuple(key):set() for key in order};foreign=0
+    for z in roles:
+        key=(z['stage'],z['replica']);f=z['family'];r=z['replica'];s=z['stage'];owner=z['owner_replica'];port=z['port'];child=z['child']
+        require(key in bycall and z['time']==c['at'][key], 'context actual role call')
+        require(0<=owner<T and 0<=port<112 and child in c['child_pair'], 'context owner role coordinates')
+        require(f==896*owner+(2*c['child_pair'][child]+c['side'][child])*112+port and 0<=f<live, 'context physical owner block')
+        require(f//224!=4*r+c['stage_pair'][s], 'context helper/data alias')
+        require(f not in bycall[key] and z['helper'] not in seenhelpers[key], 'context helper/family alias')
+        bycall[key].add(f);seenhelpers[key].add(z['helper']);foreign+=(owner!=r)
+    require(all(v==set(range(408)) for v in seenhelpers.values()), 'context every helper exactly once')
+    return {'status':'PASS_TENSOR_BLOCK_NORM_CERTIFICATE','replicas':T,
+        'physical_families':physical,'live_families':live,'max_active_depth':18,
+        'boundary_depth_bits':18,'stock_l2_bits':stock_l2_bits,'stocknorm_bits':stock_l2_bits,'physical_stock_bits':stock_bits,
+        'partial_cover_bits':1,'local_actual_prefix_bits':localbits,'local_reserve_bits':128,
+        'input_l2_bits':37,'actual_prefix_bits':localbits+37+18+stock_l2_bits+1+4,
+        'required_reserve_bits':128+37+18+stock_l2_bits+1+4,'retained_payload_bits':2048,'foreign_helper_roles_checked':foreign,
+        'endpoint_replay':endpoint,
+        'scope':'Pre-emission finite premises only. Caller must retain exact source projection, actual phase/primitive audits, check_roles windows/charts and complete release.'}
diff --git a/research/two-sided-helper-extraction/tools/prepare_channel_native.py b/research/two-sided-helper-extraction/tools/prepare_channel_native.py
new file mode 100644
index 0000000000..c8edae101d
--- /dev/null
+++ b/research/two-sided-helper-extraction/tools/prepare_channel_native.py
@@ -0,0 +1,76 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Two fresh changed-word native chains; explicit authenticated parent reuse.
+Yiyang (@Lyy-iiis), with substantial OpenAI Codex assistance.
+Derived from the PR2839/PR2848 native preparation lineage, retaining validators.
+"""
+from pathlib import Path
+from concurrent.futures import ThreadPoolExecutor
+from importlib import metadata
+import argparse,hashlib,json,gzip,os,platform,shutil,subprocess,sys,time
+sys.dont_write_bytecode=True
+SOURCE_SHA='56cf455752722051d598a7da1e5ee700637fbaef09189f534413dbe6e0525a83'
+SOURCE_FILES=610
+SOURCE_COMMIT='two-sided-helper408-pr2894'
+PARENT_SHA='e0eefc96567fbb45e19e6de0ca295381dbe0e686c08ddc783639b065c7c791d4'
+OLD_RECEIPT_SHA='dd36443f2789ffa6deca7210c76ada781e2b9b7e622a546b366f51a475faff3e'
+def need(ok,why):
+ if not ok:raise ValueError(why)
+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 write(p,v):p.write_text(json.dumps(v,sort_keys=True,indent=2)+'\n')
+def tree(p,exclude=()):
+ out={}
+ for f in sorted(p.rglob('*')):
+  need(not f.is_symlink(),'no cache/source symlinks')
+  if f.is_file()and f.relative_to(p).as_posix()not in exclude:out[f.relative_to(p).as_posix()]=sha(f)
+ return out
+
+def main():
+ ap=argparse.ArgumentParser()
+ for n in ['source','retained-cache','retained-receipt','out']:ap.add_argument('--'+n,type=Path,required=True)
+ ap.add_argument('--jobs',type=int,default=2);a=ap.parse_args();source=a.source.resolve();out=a.out.resolve();oldcache=a.retained_cache.resolve()
+ need(not sys.flags.optimize and 1<=a.jobs<=2,'assertions enabled and max2 jobs')
+ need(sha(source/'MANIFEST.json')==SOURCE_SHA and len(read(source/'MANIFEST.json'))==SOURCE_FILES and tree(source,('MANIFEST.json',))==read(source/'MANIFEST.json'),'complete immutable derived source')
+ need(not list(source.rglob('__pycache__'))and not list(source.rglob('*.pyc')),'source free of bytecode and cache folders')
+ before=tree(source);oldreceipt=read(a.retained_receipt)
+ need(sha(a.retained_receipt)==OLD_RECEIPT_SHA and tree(oldcache)==oldreceipt['cache_files'],'complete PR2848 retained native/cache evidence')
+ old=source/'vendor/pr1297';need(sha(old/'MANIFEST.json')==PARENT_SHA and tree(old,('MANIFEST.json',))==read(old/'MANIFEST.json'),'unchanged retained source')
+ prdir=oldcache/'_receipts'/PARENT_SHA;need(sha(prdir/'RECEIPT.json')==oldreceipt['retained_parent_receipt_sha256'],'retained parent receipt identity');pr=read(prdir/'RECEIPT.json')
+ need(pr['vendor_manifest_sha256']==PARENT_SHA and pr['claim_sha256']==sha(old/'CLAIM.json'),'retained parent source claim')
+ for name,h in pr['files'].items():need(sha(prdir/name)==h,'retained parent result binding')
+ need(read(prdir/'RESULT.json')['status']=='PASS_GLOBAL_MIXED_X54_FUSIONS_NATIVE_AND_STRICT_ADMISSION' and read(prdir/'RESULT.json')['kappa']==read(old/'CLAIM.json')['kappa'],'retained full parent admission')
+ pstages=read(prdir/'STAGES.json');need(len(pstages)==16 and all(s['exit_code']==0 for s in pstages),'all16 retained parent stages')
+ need(not out.exists()and not out.is_relative_to(source)and not out.is_relative_to(oldcache),'fresh external native work');out.mkdir(parents=True);cache=out/'native-cache';cache.mkdir()
+ steps=['native','ledgers','local-replay','wrappers','phases']
+ for tag,name in [('base','gauge44-word.json.gz'),('extra','extra-word.json.gz')]:
+  word=old/name;key=sha(word);need(pr['words'][tag]==key,'retained word hash');entry=oldcache/key
+  need(read(entry/'local/FULL-WORD.json.gz')==read(word),'retained complete literal word');st=read(entry/'STEPS.json');need([s['step']for s in st]==steps and all(s['exit_code']==0 for s in st),'retained native five stages')
+  cj=read(entry/'CACHE.json');need(cj['word_sha256']==key and cj['files']==tree(entry,('CACHE.json',)),'retained full native files')
+  shutil.copytree(entry,cache/key)
+ shutil.copytree(prdir,cache/'_receipts'/PARENT_SHA)
+ versions={}
+ for name in ['numpy','scipy','sympy','mpmath','psutil','gmpy2']:
+  try:versions[name]=metadata.version(name)
+  except metadata.PackageNotFoundError:versions[name]=None
+ write(out/'ENVIRONMENT.json',dict(python=platform.python_version(),executable=sys.executable,dependency_versions=versions,assertions_enabled=True))
+ env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0',OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1')
+ for k in ['PYTHONOPTIMIZE','WITNESS_SPEC','WITNESS_DISCOVER','WITNESS_RECORD']:env.pop(k,None)
+ driver=source/'new/fastnative/run_native.py';start=time.monotonic();stages=[];words={t:source/('new/borrow/words/BORROW-WORD-43'+t+'.json.gz')for t in ['base','extra']}
+ def fresh(tag):
+  word=words[tag];work=out/('fresh-'+tag);cmd=[sys.executable,'-B',str(driver),str(word),str(work)];log=out/('native-'+tag+'.log');begin=time.monotonic()
+  with log.open('w')as f:r=subprocess.run(cmd,cwd=out,env=env,stdin=subprocess.DEVNULL,stdout=f,stderr=subprocess.STDOUT)
+  need(r.returncode==0,'fresh native '+tag+' failed; '+str(log));res=read(work/'RESULT.json');need(res['status']=='PASS_COMPLETE_T74_NATIVE_REPLAY'and res['word_sha256']==sha(word),'fresh native result')
+  entry=cache/sha(word);shutil.copytree(work/'native',entry);need(read(entry/'local/FULL-WORD.json.gz')==read(word),'fresh complete literal word')
+  st=read(entry/'STEPS.json');need([s['step']for s in st]==steps and all(s['exit_code']==0 for s in st),'fresh native five stages')
+  checks=read(entry/'local/LOCAL-CHECKS.json');can=read(entry/'local/CANONICAL-WORD.json.gz')
+  need(can['R']==408 and len(can['centers'])==8 and len(can['zero_buffers'])==73,'complete physical ABI')
+  for orientation in ['forward','backward']:need(checks[orientation]['all_columns']==632 and checks[orientation]['paid_profile']==read(word)['report']['local_profile'],'actual all-column native profile')
+  write(entry/'CACHE.json',dict(word_sha256=sha(word),files=tree(entry)))
+  rec=dict(name='fresh-current-'+tag,exit_code=0,command=cmd,script_sha256=sha(driver),log_sha256=sha(log),result_sha256=sha(work/'RESULT.json'),seconds=time.monotonic()-begin);print('PASS',rec['name'],flush=True);return rec
+ with ThreadPoolExecutor(max_workers=a.jobs)as pool:stages=list(pool.map(fresh,['base','extra']))
+ need(tree(source)==before and tree(oldcache)==oldreceipt['cache_files']and sha(a.retained_receipt)==OLD_RECEIPT_SHA,'read-only input drift')
+ rec=dict(status='PASS_COMPOSED_FRESH_NATIVE_PROVIDERS_AND_AUTHENTICATED_CACHE',source_commit=SOURCE_COMMIT,manifest_sha256=SOURCE_SHA,providers={t:dict(word_sha256=sha(w),complete_native_files=tree(cache/sha(w),('CACHE.json',)))for t,w in words.items()},retained_parent_receipt_sha256=sha(cache/'_receipts'/PARENT_SHA/'RECEIPT.json'),cache_files=tree(cache),fresh_current_provider_count=2,fresh_retained_native_count=0,reused_retained_native_count=2,fresh_retained_parent=False,reused_retained_parent=True,retained_reuse_receipt_sha256=OLD_RECEIPT_SHA)
+ write(out/'NATIVE-RECEIPT.json',rec);write(out/'STAGES.json',stages);write(out/'RESULT.json',dict(status='PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE',source_manifest_sha256=SOURCE_SHA,native_receipt_sha256=sha(out/'NATIVE-RECEIPT.json'),preparer_sha256=sha(Path(__file__)),environment_sha256=sha(out/'ENVIRONMENT.json'),stages=stages,seconds=time.monotonic()-start,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.'))
+ print('PASS_TWO_FRESH_SHARED_KERNEL_NATIVE_CHAINS_AUTHENTICATED_PARENT_REUSE',flush=True)
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/vendor/audit_local.py b/research/two-sided-helper-extraction/vendor/audit_local.py
new file mode 100644
index 0000000000..8224873d04
--- /dev/null
+++ b/research/two-sided-helper-extraction/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/two-sided-helper-extraction/vendor/fastnative/.gitattributes b/research/two-sided-helper-extraction/vendor/fastnative/.gitattributes
new file mode 100644
index 0000000000..e6d60b4a58
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/.gitattributes
@@ -0,0 +1,3 @@
+# Source pins bind original bytes, including inherited CRLF line endings.
+vendor/** -text -whitespace
+fixtures/*.gz binary
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/EXPECTED.json b/research/two-sided-helper-extraction/vendor/fastnative/EXPECTED.json
new file mode 100644
index 0000000000..24a65daada
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/EXPECTED.json
@@ -0,0 +1,84 @@
+{
+  "base": {
+    "normalized_sha256": "72152474a7c1f65f8bddec3197a9661d035e2ef0edfd08751a19038c470f654f",
+    "recipe_bytes_sha256": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3",
+    "reference_files": {
+      "CANONICAL-WORD.json.gz": "dd1f277eafbde7fbc68c51fad396a64e8afe389a8529bbe61e187014a8a48215",
+      "CLIFFORD-RECIPES.json": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3",
+      "CLIFFORD-REVIEW.json": "255cf6f3d1105e9c60e2b589e3445a6b7e69af575abcfe4f6a0aba971fdb4195",
+      "FULL-WORD.json.gz": "ae8b6b4d62a9da29331062fae1bd68b0341edf83152f5a5ef50c5109ba578f9a",
+      "INDEPENDENT-LOCAL-REPLAY.json": "26adad9d1cd317e8e6c2f5db0f42e5f35ef4220e84280c80ac273aa2a329903a",
+      "LOCAL-CHECKS.json": "91d4117ece180666bcbda47204aad48c6b1d16f9d16bbc75f7b25493ae51674f",
+      "LOCAL-PROGRAMS.json.gz": "63e43ef535377b6e44cd264f126d8aded95441bd263e0d047eb168d6c46409bf",
+      "RESIDUAL-ADAPTERS.json": "6a807c59d857faed1140f9d7dd4dee863553f7a00a95ddd4601ef4dc8ea93b12",
+      "SCALAR-FRAME-AUDIT.json": "10347acf893d70592ca4af8ee1cdf58a06510a444992feffcddf5c03bdf63e42",
+      "WARP-RECIPE-CHECKS.json": "95bc1e29bae8210542423d7b0d6b4c07b29d3948a2c987507a97cf085f963252",
+      "WRAPPER-CHECKS.json": "508fe304ad6bd06c2c80b93b724cbd94368330f1f06f597f20fbcf2db9b4d771"
+    },
+    "coverage": {
+      "status": "PASS_WARP_RECIPES_EXACT_ON_ALL_512_COLUMNS",
+      "canonical_word_sha256": "db6955899dffd8bab29e566e4cecc5a2ef51dba21aa64db1a9076a96fbed69f6",
+      "recipe_sha256": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3",
+      "warp_classes": 166,
+      "operators": 65,
+      "columns_each": 512,
+      "controls_rejected": [
+        "recipe: wrong global phase",
+        "recipe: wrong translation",
+        "recipe: wrong linear phase",
+        "recipe: wrong quadratic form",
+        "recipe: wrong matrix",
+        "recipe: wrong G (still invertible)",
+        "recipe: non-invertible G",
+        "recipe: inverse warp recipe used for the forward warp",
+        "recipe: recipe of another warp class",
+        "recipe: swapped from/to frames",
+        "recipe: missing warp class",
+        "logical: wrong G",
+        "logical: wrong phase"
+      ]
+    },
+    "reference": "Fresh PR2751 native run; receipts and file hashes bound by PR2751 REUSE-PINS.json."
+  },
+  "extra": {
+    "normalized_sha256": "ae9e09a9a806c75f1ff444470e44e6543807e673c0292b6772a8b5dcdf5a4072",
+    "recipe_bytes_sha256": "a9641c6cbc4e05677e7559bf1764468f3dbcd9efe0ae710205590c381f6b5f08",
+    "reference_files": {
+      "CANONICAL-WORD.json.gz": "dacaaa72961e8bcfefa5f5125aa79b2bae33d4faead01a651bd44a8ea5ab2412",
+      "CLIFFORD-RECIPES.json": "a9641c6cbc4e05677e7559bf1764468f3dbcd9efe0ae710205590c381f6b5f08",
+      "CLIFFORD-REVIEW.json": "9622789fd43d2c3e14d98ae3df48765d1faeb8f5664136f48384dcd603e215fe",
+      "FULL-WORD.json.gz": "1bb44a73d5841afb954b49ae94dba2e0c536b1eea9436ae5d89de87d8a04e127",
+      "INDEPENDENT-LOCAL-REPLAY.json": "1ca177b1b78a0faaaaeeb05d44ccef50810d20d9f5607b3fa7dd493067f69ef1",
+      "LOCAL-CHECKS.json": "91d4117ece180666bcbda47204aad48c6b1d16f9d16bbc75f7b25493ae51674f",
+      "LOCAL-PROGRAMS.json.gz": "63e43ef535377b6e44cd264f126d8aded95441bd263e0d047eb168d6c46409bf",
+      "RESIDUAL-ADAPTERS.json": "c4dd3cf0ce67c9ef6ab86b051026c0d884c3548dfc6118f047d6f56bb7331352",
+      "SCALAR-FRAME-AUDIT.json": "abbfa5baf5228072679d6ac08b873115ef3a00c39e6632e110d1f94a5f7657da",
+      "WARP-RECIPE-CHECKS.json": "32c3480dd0f953237f567a5e1c66eb15de9cee5b57c219b571bcc9cb993042dd",
+      "WRAPPER-CHECKS.json": "508fe304ad6bd06c2c80b93b724cbd94368330f1f06f597f20fbcf2db9b4d771"
+    },
+    "coverage": {
+      "status": "PASS_WARP_RECIPES_EXACT_ON_ALL_512_COLUMNS",
+      "canonical_word_sha256": "e20375d1bb82dc7fad688357e81e135c7386b2f46d85c7a2c393d30b72ea44df",
+      "recipe_sha256": "a9641c6cbc4e05677e7559bf1764468f3dbcd9efe0ae710205590c381f6b5f08",
+      "warp_classes": 166,
+      "operators": 65,
+      "columns_each": 512,
+      "controls_rejected": [
+        "recipe: wrong global phase",
+        "recipe: wrong translation",
+        "recipe: wrong linear phase",
+        "recipe: wrong quadratic form",
+        "recipe: wrong matrix",
+        "recipe: wrong G (still invertible)",
+        "recipe: non-invertible G",
+        "recipe: inverse warp recipe used for the forward warp",
+        "recipe: recipe of another warp class",
+        "recipe: swapped from/to frames",
+        "recipe: missing warp class",
+        "logical: wrong G",
+        "logical: wrong phase"
+      ]
+    },
+    "reference": "Fresh PR2751 native run; receipts and file hashes bound by PR2751 REUSE-PINS.json."
+  }
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/FRESHNESS.json b/research/two-sided-helper-extraction/vendor/fastnative/FRESHNESS.json
new file mode 100644
index 0000000000..81a3a1dff3
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/FRESHNESS.json
@@ -0,0 +1,124 @@
+{
+  "checked_at": "2026-10-15T20:49:44.952707+00:00",
+  "scientific_base_commit": "2d3af1ba7e28b74248b47381768e5b116078ba1c",
+  "fetched_canonical_main": "936fac15b1b1b59dc5285c713a77f9f3c07b2906",
+  "priority_revision": 5,
+  "unchanged_since_base": [
+    "AGENTS.md",
+    "CONTRIBUTING.md",
+    "autoresearch.md",
+    "docs/research/agent-task-catalog.json",
+    "certificates/selected-result.json",
+    "scripts/research_package.py",
+    "docs/research/research-family-status.md",
+    "all executed native and accelerator dependency sources"
+  ],
+  "reviewed_updates": "Ledger dispositions, P104/P112 mechanisms, generic recursive packets, exact Gaussian recovery and QQ16 contract navigation; no changed native/accelerator dependency or applicable scope restriction. Keep scientific pins unchanged.",
+  "overlap": {
+    "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE",
+    "searched_at": "2026-10-15T20:47:33.782571+00:00",
+    "terms": [
+      "bw_phases",
+      "zero_state",
+      "T74 native",
+      "sparse native"
+    ],
+    "coverage": {
+      "open_prs": {
+        "fetched_at": "2026-10-15T20:46:20.897437+00:00",
+        "complete_pagination": true,
+        "records": 710
+      },
+      "discussions": {
+        "fetched_at": "2026-10-15T20:28:04.284423+00:00",
+        "complete_pagination": true,
+        "records": 1389
+      }
+    },
+    "local_records": 38,
+    "warnings": [
+      "discussions: refresh failed; using old data if available: Post \"https://api.github.com/graphql\": dial tcp 140.82.121.5:443: i/o timeout\n"
+    ],
+    "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.",
+    "matches_total": 5,
+    "matches": [
+      {
+        "kind": "pr",
+        "number": 2329,
+        "title": "Tooling: 3.15\u00d7 faster production Clifford zero_state via gate tables with identical receipts",
+        "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2329",
+        "head": "68a7161a610f175dc8e7b22f95acd033191450d9",
+        "updated_at": "2026-10-15T20:35:01Z",
+        "draft": false,
+        "state": "open",
+        "matched_terms": [
+          "zero_state"
+        ],
+        "score": 3,
+        "excerpt": "n/phase evaluation with identical cold617 helper-interface receipts. This PR wires that equivalent `zero_state` into the **production** multicold evaluator used by `scripts/verify_cold617_interface.py`.\n\nPath: `research/complex-multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/vendor/clifford/clifford_exact.py`.\n\nNo certificate \u03ba pins change. Same-tip provenance hygiene:\n- `research/clifford-state-performance/` vendors pairwise-era bytes as `baseline.py` and demotes the live pairwise "
+      },
+      {
+        "kind": "local-readme",
+        "title": "research/t74-native-fast/README.md",
+        "path": "research/t74-native-fast/README.md",
+        "sha256": "9dec97c3e9b79beeeb986e5bbbecb71fe29b4de4e0990eef9cee4d7563b8b5eb",
+        "matched_terms": [
+          "zero_state",
+          "t74 native"
+        ],
+        "score": 2,
+        "excerpt": "# Complete T74 native replay with exact sparse state evaluation\n\n**Tooling improvement; no new \u03ba.** This opt-in runner applies the existing\nPR1029 sparse evaluator and PR662 exact gate tables to the current T74\nClifford wrappers and phase lowering. It runs the complete five-stage native\npipeline, including the unchanged independent warp-recipe checker. No previous\nnative result is reused. The benchmark compares the original and accelerated\nrunners on the same PR2751 base word; both provider word"
+      },
+      {
+        "kind": "local-task",
+        "title": "research/t74-native-fast/TASK.json",
+        "path": "research/t74-native-fast/TASK.json",
+        "sha256": "12d011122b6f47589ee41101b6d73bcd50fdbebd2c837ac3c3509fb857c5d442",
+        "matched_terms": [
+          "t74 native",
+          "sparse native"
+        ],
+        "score": 2,
+        "excerpt": "evaluation with PR662 gate tables into both Clifford-using stages of the complete warp-aware PR2751 T74 native replay. Benchmark complete five-stage runs against the unchanged driver.\",\n  \"scope_change_reason\": \"The earlier U8 fast runners omit the present T74 independent warp-recipe stage. This scope keeps that stage and all other native controls.\",\n  \"task_classification\": \"Explicit engineering override after comparing three narrow candidates; retained assignment seed2, no new random novelty c"
+      },
+      {
+        "kind": "local-readme",
+        "title": "research/phase-recipes-parallel/README.md",
+        "path": "research/phase-recipes-parallel/README.md",
+        "sha256": "d74022ec200b13e600bbd4a60472d749efd712026f68d471905985275c34b6f4",
+        "matched_terms": [
+          "zero_state"
+        ],
+        "score": 1,
+        "excerpt": "xact state evaluator\n(`research/clifford-state-performance/fast_state.py`, pinned by digest) as `Op.zero_state` in every\nprocess, the same substitution PR662's own `run.py` makes. The parallel layer composes with any\nper-edge evaluator.\n\n## Benchmark (same input, same machine)\n\n| Runner | Wall time | Speedup |\n|---|---:|---:|\n| pinned serial `phases_full.py` via `run_portable.py` | 92.2 s | 1\u00d7 |\n| `phases_parallel.py --jobs 4`, reference engine | 33.0 s (separate run) | 2.8\u00d7 |\n| `phases_parallel"
+      },
+      {
+        "kind": "pr",
+        "number": 2398,
+        "title": "Research: extra factors do not lower the fixed P112 COPY-power optimum",
+        "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2398",
+        "head": "8051d99dfd91a788d25bfc92c3863a33c658a5a9",
+        "updated_at": "2026-10-15T13:21:06Z",
+        "draft": false,
+        "state": "open",
+        "matched_terms": [
+          "t74 native"
+        ],
+        "score": 1,
+        "excerpt": "blem are different matrices/interfaces. The other active helper-inventory scope concerns PR #2339's T74 native compensation.\n- **Coordination:** [canonical claim in discussion #2006](https://github.com/CrocSwap/integer-mult-bounds/discussions/2006#discussioncomment-18942846). Final offline overlap queries used all terms `2321` + `terms`, and path `research/p112-overcomplete-factor-spaces/*`. Snapshot coverage: 587 open PRs including drafts at `2026-10-15T07:07:38.026722Z`, 1,116 Discussion recor"
+      }
+    ]
+  },
+  "recent_discussion_fallback": {
+    "count": 40,
+    "full_pagination": false,
+    "updated_descending": true,
+    "comments_per_discussion": 5,
+    "snapshot_sha256": "8f77f8a598759e291ed37aae3412fff725dfd86c0919c99e55a40655f4354dd3",
+    "scope": "40 most recently updated discussions and last5 comments each. No new duplicate scope found; not all historical comments.",
+    "own_claim": 2755
+  },
+  "decision": "Continue the bounded integration; credit PR662/1029 and related PR1041/2329. Do not claim a novel evaluator, new kappa or changed selected frontier.",
+  "submission_parent_commit": "936fac15b1b1b59dc5285c713a77f9f3c07b2906",
+  "local_sync": "Isolated branch fast-forwarded to fetched canonical main. Package restored through sparse-checkout add; all source pins rechecked. Scientific provenance base remains2d3af1b."
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/LICENSE b/research/two-sided-helper-extraction/vendor/fastnative/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
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+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
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+      where such license applies only to those patent claims licensable
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+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
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+      or a Contribution incorporated within the Work constitutes direct
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+
+   4. Redistribution. You may reproduce and distribute copies of the
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+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
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+      (d) If the Work includes a "NOTICE" text file as part of its
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+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
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+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
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+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
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+   8. Limitation of Liability. In no event and under no legal theory,
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+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
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+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
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+      To apply the Apache License to your work, attach the following
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+   Copyright [yyyy] [name of copyright owner]
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+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
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+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
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diff --git a/research/two-sided-helper-extraction/vendor/fastnative/NATIVE-LINEAGE-NOTICE b/research/two-sided-helper-extraction/vendor/fastnative/NATIVE-LINEAGE-NOTICE
new file mode 100644
index 0000000000..380e979f0e
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/NATIVE-LINEAGE-NOTICE
@@ -0,0 +1,14 @@
+Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls.
+
+New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained.
+Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance.
+
+T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance.
+
+PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged.
+
+Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance.
+
+The preceding paragraphs are inherited source notices, not attribution of this derivative.
+This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed.
+Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/PINS.json b/research/two-sided-helper-extraction/vendor/fastnative/PINS.json
new file mode 100644
index 0000000000..7c83dc5432
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/PINS.json
@@ -0,0 +1,22 @@
+{
+  "vendor/accelerators/SPARSE-NOTICE.md": "3da80a5155c625bff907a42a82c65bfcf92854d2c960bcea4537c19c99efd4f2",
+  "vendor/accelerators/SPARSE-PROOF.md": "d73e4522602404caba8e7f247005a45c8a8cd26ffd2a70d65f4f9556a391d053",
+  "vendor/accelerators/sparse_state.py": "e91210ecd5085cf9add872f40bb434806838da488e12152c63c86e51fb5a7a37",
+  "vendor/accelerators/tables.py": "2fe087ba4558bd21ca49945dbedaa4047e4170e8fd4e2280701bb2f0481811b5",
+  "vendor/native/new/code/borrow/NOTICE-PR2226.md": "6b6730303818f6edc2a253eb4d05471eee58f28b5815fb250c32ae376f774c8a",
+  "vendor/native/new/code/borrow/bw_adapters.py": "c5907050a9a7fa36d4fcba3ad4fe440d1bec2063360c095013891785ba65c3ce",
+  "vendor/native/new/code/borrow/bw_audit_local.py": "08d5864d9b77902fc5ab5a062a8ea843fe1e572243b8c580abb0a421b2e46d07",
+  "vendor/native/new/code/borrow/bw_check_recipes.py": "d600b959a0ac462dc28deb8c0d5d8f9e0c76d7f7d7b6f92a296c5ef9e0a1de19",
+  "vendor/native/new/code/borrow/bw_emit.py": "99b59a6fa3feda86785e4225157dcb1a6169d256cec4f5e0acc9cea7a701df76",
+  "vendor/native/new/code/borrow/bw_gauss.py": "0884b14d6d77cde419a3c773ad9b21d0d18de1e6e20e6b6d5add458ed32ba4cb",
+  "vendor/native/new/code/borrow/bw_phases.py": "9d1a620e26715f4c42fd0347ecc14ef5a4a9031867869b64e8bae4d8526a821e",
+  "vendor/native/new/code/borrow/bw_tamper.py": "eab4b026965b9796eee92239660e1fb1fa629f6d9db44bc27b13911a018a6ee9",
+  "vendor/native/new/code/borrow/bw_transport.py": "9818e08b819310b40f1441b89be8c4369584a5b3fa5dfe9b86b1df9a7f5d6a76",
+  "vendor/native/new/code/borrow/vendor/PR2226-NOTICE.md": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422",
+  "vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "vendor/native/new/code/borrow/vendor/pr2226_operators.py": "b37b67a04681c776dafcdc6c9af0e8a2dbfa9893b02e0fa2d77ccc9182a87988",
+  "vendor/native/new/code/borrow/vendor/pr2226_replay.py": "0f9a47cdaeed0e22938c63251c232d6f23aeee2b62b0b1223cd4473c5428bcf7",
+  "vendor/native/new/run_native_borrow.py": "8ec7db430f4f4771c06bdcfc31736193614f6ec209d57b63d4e2b75f17fb3ac8",
+  "fixtures/WORD-base.json.gz": "ae8b6b4d62a9da29331062fae1bd68b0341edf83152f5a5ef50c5109ba578f9a",
+  "fixtures/WORD-extra.json.gz": "1bb44a73d5841afb954b49ae94dba2e0c536b1eea9436ae5d89de87d8a04e127"
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/README.md b/research/two-sided-helper-extraction/vendor/fastnative/README.md
new file mode 100644
index 0000000000..1ca40309bd
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/README.md
@@ -0,0 +1,161 @@
+# Complete T74 native replay with exact sparse state evaluation
+
+**Tooling improvement; no new κ.** This opt-in runner applies the existing
+PR1029 sparse evaluator and PR662 exact gate tables to the current T74
+Clifford wrappers and phase lowering. It runs the complete five-stage native
+pipeline, including the unchanged independent warp-recipe checker. No previous
+native result is reused. The benchmark compares the original and accelerated
+runners on the same PR2751 base word; both provider words are replayed in CI.
+
+The contribution is integration, coverage-preserving comparison and reproducible
+complete-native benchmarking. The sparse evaluator and gate tables are copied
+unchanged from their credited predecessors. Older U8 fast runners do not include
+this T74 warp-aware pipeline. PR2329 concerns a different multicold production
+checker; it is not a dependency of this package.
+
+## Result and scope
+
+Three alternating pairs measured **3.57× faster complete native replay**,
+with median **306.7s → 85.9s** (72.0% less wall time). These are Python 3.12.14 /
+numpy 2.2.6 measurements on this shared Linux host, specific to this fixture.
+
+| Stage | Original median (s) | Sparse median (s) |
+|---|---:|---:|
+| native | 1.20 | 1.19 |
+| ledgers | 1.44 | 1.41 |
+| local-replay | 38.21 | 37.70 |
+| wrappers | 5.76 | 2.15 |
+| phases | 259.39 | 43.40 |
+
+`phases` includes unchanged independent warp-recipe verification. Stage medians
+do not necessarily sum to the median total. Every sample and stage is retained
+in `evidence/BENCHMARK.json`. Every sample uses a fresh subprocess and
+fresh output directory. There is no saved-result cache. In-process caches hold
+only exact, immutable gate tables, with the predecessor's bounded cache sizes.
+
+The five stages are transport, ledgers, independent local replay, wrappers, and
+phase lowering followed by independent warp-recipe verification. The last audit
+checks 166 warp classes on all 512 columns, including global phase, and retains
+all thirteen recipe mutations. All other original native checks remain enabled.
+The full paid supplier, physical hosting and outer inequalities are **outside
+this benchmark**. This is neither a whole-project speedup nor a faster integer
+multiplication algorithm. The selected certificate remains unchanged.
+
+`compare.py` reads every field in all eleven native artifacts. It removes only
+the two documented top-level elapsed-time fields. Before normalizing compressed
+container hashes to decompressed hashes, it verifies the actual container
+bindings. Recipe hashes remain hashes of the original serialized bytes. A changed
+control list, a missing file, an invalid binding or a different recipe fails.
+`EXPECTED.json` records the complete normalized reference digest and exact recipe
+hash for each provider; original receipt hashes trace to PR2751's `REUSE-PINS.json`.
+
+`stage.py` substitutes only `Op.zero_state` inside a fresh process, then executes
+the pinned wrappers or phase script unchanged. Tableaux, lowering, rank checks,
+off-support checks, denominators and global-phase comparisons remain. The
+independent numpy warp checker is a separate unchanged process. The retained
+`SPARSE-PROOF.md` proves the predecessor's evaluator equivalence; its compiler
+integration section describes PR1029, whereas this package uses the explicit
+process-local substitution above.
+
+The current exact algebra's original dense evaluator is also compared with the
+sparse evaluator for dimensions 1–5, twelve length-20 circuits per dimension, both
+adjoints, and every input basis column (1,488 comparisons, deterministic seed 2).
+This finite check supplements the predecessor's proof; it is not a formal proof
+of the complete multiplication theorem.
+
+## Reproduce
+
+From repository root, in a Python 3.12 environment with `numpy==2.2.6`:
+
+```sh
+python3.12 scripts/research_package.py --package research/t74-native-fast
+```
+
+Expected: `PASS_T74_NATIVE_FAST_REFERENCE_AND_CONTROLS base` and `extra`, then
+`PASS_REGISTERED_RESEARCH_PACKAGE`. Each provider starts a fresh complete native
+replay; the extra run uses a Git-free package copy in a path with spaces.
+The base run also exercises 18 boundary controls: source digest/inventory/
+symlink changes, altered benchmark fixture, optimized Python, output reuse, singular warp and incorrect
+paid profile in both engines, actual emitted recipe mutations, and changed
+receipt coverage/bindings. Source drift is rejected before any vendored import.
+A failed stage cannot produce the runner's success receipt.
+
+To use the runner on another word under the **same pinned native source version**:
+
+```sh
+python3.12 -I -B research/t74-native-fast/run_native.py WORD.json.gz /tmp/t74-fresh
+```
+
+The output directory must not exist. Add `--engine reference` to invoke the
+unchanged original driver. This standalone command needs no Git or network;
+its sources are authenticated and copied into the output directory before use.
+Logs, `COMMANDS.json`, the original native artifacts, and `RESULT.json` are kept.
+It does not authenticate an arbitrary input as a known construction; it checks
+that input through the native pipeline. The fixture verifier above additionally
+requires exact fixture and reference-output pins.
+
+To repeat the controlled benchmark (several minutes per reference run):
+
+```sh
+python3.12 -I -B research/t74-native-fast/benchmark.py --pairs 3 --provider base --work /tmp/t74-benchmark-fresh
+```
+
+Expected: `PASS_COMPLETE_T74_NATIVE_BENCHMARK` and three
+`PASS_ALL_NATIVE_OUTPUTS_IDENTICAL` comparisons. Order alternates
+reference/sparse, sparse/reference, reference/sparse. OS caches are not flushed;
+this shared-host timing is descriptive, with no timing threshold in CI.
+
+## Sources and coverage boundary
+
+Scientific base: `2d3af1ba7e28b74248b47381768e5b116078ba1c`, priority revision 5.
+Submission parent after canonical sync: `936fac15b1b1b59dc5285c713a77f9f3c07b2906`.
+The relevant dependencies and selected record are unchanged; see `FRESHNESS.json`.
+The exact source closure and fixture hashes are in `PINS.json`. File-by-file
+origins, dependency heads and transformations are in `SOURCE-PROVENANCE.json`.
+The native closure is PR2679 at `2e2cf56521df8a2b816b2689144765ee00b69a24`
+with PR2751's published native-audit overlay at
+`4cfbb0cc8314d7fb4e8e754545a49a42eb590a69`. Its bytes are unchanged here,
+including the repaired incomplete-centre negative control. Existing frozen
+packages and `upstream/` are untouched.
+
+The runner supports this specific closure, not arbitrary future native versions.
+There is no result-cache invalidation problem: every invocation recomputes the
+native evidence. Changing a vendored dependency requires an explicit source pin
+update, new before/after comparison and review. Generic package CI reruns both
+providers whenever this package changes. Main-line documentation pins are
+historical provenance, not admission of pending PR2751.
+
+Inherited all-size/compiler, source-access, hosting, precision/tape, recovery and
+analytic obligations remain with the original construction. Exact finite replay
+does not discharge them. Source hashes protect against accidental drift; they
+are not a security boundary against someone editing both code and its pins.
+
+## Open next questions
+
+The next measured bottlenecks are the independent local replay and all-column
+warp matrices. Profile them before choosing an exact representation change;
+preserve arbitrary-input, both-orientation and phase-sensitive coverage.
+A separate maintainer decision could adopt this entry point for future T74
+construction work after independent replay and source-inventory review. This
+package makes no automatic migration. Structured first steps and blockers are
+in `TASK.json`.
+
+## Credit
+
+Prepared by Tekalign (@tekuuu), with substantial OpenAI Codex assistance in
+profiling, integration, verification, review and documentation. No independent
+human review is claimed. Apache-2.0; see `LICENSE` and retained notices.
+
+- Charles Bethin (@cbethin), PR662: exact bounded gate tables.
+- Ali Romman (@aliromman), PR1029: exact sparse state propagation and its proof.
+- Sagar Thakrar (@thakrarsagar), PR1041: prior complete U8 phase benchmarking
+  and parallel runner; the present runner does not use its parallelization.
+- Victor Li (@VictorLiwentao), PR2329: related pending production integration
+  for the multicold helper checker, independently useful overlap.
+- Cinna Davis (@1337isnot1337), PR2226: anticipatory dirty borrowing and exact
+  warp operators; Rohan Arun and the native lineage: T74 native realization.
+- Philippe Van Velzen, PR2679: pre-life hosts, refit/alias and source snapshot;
+  PR2751 by Tekalign supplies the current two provider words and audit overlay.
+  Jeremy Kothe, zxv, Mason Hale, Marius-Paul Dumitrean, icekylinx,
+  DreamingOfClouds and the remaining predecessor contributions are retained in
+  `NATIVE-LINEAGE-NOTICE` and the native source notices.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/SOURCE-PROVENANCE.json b/research/two-sided-helper-extraction/vendor/fastnative/SOURCE-PROVENANCE.json
new file mode 100644
index 0000000000..07cd8a7880
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/SOURCE-PROVENANCE.json
@@ -0,0 +1,214 @@
+{
+  "schema_version": 1,
+  "base_commit": "2d3af1ba7e28b74248b47381768e5b116078ba1c",
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+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/code/borrow/bw_transport.py"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "vendor/native/new/code/borrow/vendor/PR2226-NOTICE.md",
+      "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422",
+      "origin": {
+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/PR2226-NOTICE.md"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py",
+      "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+      "origin": {
+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/clifford/clifford_exact.py"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "vendor/native/new/code/borrow/vendor/pr2226_operators.py",
+      "sha256": "b37b67a04681c776dafcdc6c9af0e8a2dbfa9893b02e0fa2d77ccc9182a87988",
+      "origin": {
+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/pr2226_operators.py"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "vendor/native/new/code/borrow/vendor/pr2226_replay.py",
+      "sha256": "0f9a47cdaeed0e22938c63251c232d6f23aeee2b62b0b1223cd4473c5428bcf7",
+      "origin": {
+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/code/borrow/vendor/pr2226_replay.py"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "vendor/native/new/run_native_borrow.py",
+      "sha256": "8ec7db430f4f4771c06bdcfc31736193614f6ec209d57b63d4e2b75f17fb3ac8",
+      "origin": {
+        "repository": "philippeVV/integer-mult-bounds",
+        "commit": "2e2cf56521df8a2b816b2689144765ee00b69a24",
+        "path": "research/gmx-t74-borrow43-handoff/new/run_native_borrow.py"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "fixtures/WORD-base.json.gz",
+      "sha256": "ae8b6b4d62a9da29331062fae1bd68b0341edf83152f5a5ef50c5109ba578f9a",
+      "origin": {
+        "commit": "4cfbb0cc8314d7fb4e8e754545a49a42eb590a69",
+        "path": "research/t74-joint-twelve/inputs/WORD-base.json.gz"
+      },
+      "transformation": "byte copy"
+    },
+    {
+      "local": "fixtures/WORD-extra.json.gz",
+      "sha256": "1bb44a73d5841afb954b49ae94dba2e0c536b1eea9436ae5d89de87d8a04e127",
+      "origin": {
+        "commit": "4cfbb0cc8314d7fb4e8e754545a49a42eb590a69",
+        "path": "research/t74-joint-twelve/inputs/WORD-extra.json.gz"
+      },
+      "transformation": "byte copy"
+    }
+  ],
+  "predecessors": {
+    "PR662": "458744109003e0958798f27c1f04be78f03663ce",
+    "PR1029": "ff4d7b9ac97a584275fe0653f226f4ce2ffc6086",
+    "PR1041": "9576c644a4cafd2cfac309689a19342451702f81",
+    "PR2329": "68a7161a610f175dc8e7b22f95acd033191450d9",
+    "PR2751": "4cfbb0cc8314d7fb4e8e754545a49a42eb590a69"
+  },
+  "reference_receipts": {
+    "commit": "4cfbb0cc8314d7fb4e8e754545a49a42eb590a69",
+    "path": "research/t74-joint-twelve/REUSE-PINS.json",
+    "sha256": "c33bf92fccb63f4d9a3ff6f7e025ac831ad012dd92d236b0f046bc4b1c6a29b2"
+  },
+  "license": "Apache-2.0; retained notices accompany code."
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/SOURCES.json b/research/two-sided-helper-extraction/vendor/fastnative/SOURCES.json
new file mode 100644
index 0000000000..aa25e09d27
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/SOURCES.json
@@ -0,0 +1,56 @@
+{
+  "schema_version": 1,
+  "base_commit": "2d3af1ba7e28b74248b47381768e5b116078ba1c",
+  "files": [
+    {
+      "path": "AGENTS.md",
+      "usage": "provenance",
+      "git_blob": "00c96932e109c701310f4910057bae2d6cec0c0f",
+      "sha256": "2d47ee25f6900efa3bac76f66f59cc6d6e077ed1e7301497ab332668ad288d4c"
+    },
+    {
+      "path": "CONTRIBUTING.md",
+      "usage": "provenance",
+      "git_blob": "e51435543687f1bd88ab22248082dc689ce8b853",
+      "sha256": "df5b5646602f42cb5da5844f04ac925182ddcd0f627b9de1c96a5095bb7a277a"
+    },
+    {
+      "path": "autoresearch.md",
+      "usage": "provenance",
+      "git_blob": "0515a31cd888a18e5830987da12d4051f552c8cc",
+      "sha256": "e3e85885c27919c4f603954ef25339e9c1be4bd107f829921078b8134b366044"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "889b95d936746df124872133ae1e7cc339adcb92",
+      "sha256": "7d185cd8c2af35988d638d969748ad7b670f902606444dbfc748e4402c340df6"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/current-status.md",
+      "usage": "provenance",
+      "git_blob": "d73b4ff9da41f044e793422db4318be17e234a6c",
+      "sha256": "adb54af005eb11edaf84d782fe729338680ff908f6d4fbf39ba1062d2e7d8a77"
+    },
+    {
+      "path": "docs/research/pr-ledger.md",
+      "usage": "provenance",
+      "git_blob": "a8863ed429a4c0e7e701a2fadd96201cfc879920",
+      "sha256": "0147d16503fe779b32249ba66e23469cda9ecaa62e06c2c925e2fd4575109a56"
+    },
+    {
+      "path": "docs/research/community-batch1099-review.md",
+      "usage": "provenance",
+      "git_blob": "6cb6ec061a071a06a2d18cd4dc3e9a2b05d28099",
+      "sha256": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb"
+    }
+  ],
+  "dependency_manifest": "SOURCE-PROVENANCE.json",
+  "scope": "Main selected result is provenance only. All executed dependencies are vendored, exact-pinned and separate from selected supplier admission."
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/TASK.json b/research/two-sided-helper-extraction/vendor/fastnative/TASK.json
new file mode 100644
index 0000000000..6235ec0568
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/TASK.json
@@ -0,0 +1,75 @@
+{
+  "schema_version": 1,
+  "task_id": "replay-runtime",
+  "priority_revision": 5,
+  "base_commit": "2d3af1ba7e28b74248b47381768e5b116078ba1c",
+  "original_card": {
+    "id": "replay-runtime",
+    "question": "Can one measured replay bottleneck be sped up without dropping coverage?",
+    "starting_points": [
+      "scripts/run_isolated_tests.py",
+      "scripts/verify_replay_coverage.py",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Profile one isolated replay and optimize the measured bottleneck.",
+      "Design source-bound reuse with explicit dependency invalidation and negative controls."
+    ],
+    "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.",
+    "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.",
+    "allowed_variations": [
+      "Profile one stage or design one source-bound cache boundary."
+    ],
+    "scope_change_triggers": [
+      "Skipping coverage or comparing different fixtures to claim speedup."
+    ],
+    "overlap_terms": [
+      "replay runtime",
+      "cache invalidation",
+      "isolated tests"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Integrate PR1029 sparse exact state evaluation with PR662 gate tables into both Clifford-using stages of the complete warp-aware PR2751 T74 native replay. Benchmark complete five-stage runs against the unchanged driver.",
+  "scope_change_reason": "The earlier U8 fast runners omit the present T74 independent warp-recipe stage. This scope keeps that stage and all other native controls.",
+  "task_classification": "Explicit engineering override after comparing three narrow candidates; retained assignment seed2, no new random novelty claim.",
+  "assignment_seed": 2,
+  "candidate_tasks": [
+    "Further source aliases: limited fixed-word headroom after PR2751.",
+    "Common-prefix mutation replay: higher coverage/invalidation risk.",
+    "Complete T74 sparse native integration: measured phase lowering bottleneck, chosen."
+  ],
+  "bottleneck_link": "Reducing the cost of fresh exact native admission lets changed-word candidates and independent reviewers iterate sooner.",
+  "budget_minutes": 60,
+  "stop_rule": "One source snapshot and two PR2751 provider words; three alternating paired base benchmarks, complete extra replay, output equivalence and boundary controls. No wider algorithmic search.",
+  "outcome": "completed",
+  "evidence": "Three alternating paired complete base native runs: median306.7496s reference versus85.8840s sparse (3.57167x). Every field of all11 native artifacts matches after only declared normalization; phase recipes byte-identical. Registered Python3.12/numpy2.2.6 replay passes both providers, Git-free relocation,1488 exact dense/sparse columns and18 boundary controls;84 inherited controls retained. See evidence/BENCHMARK.json, COVERAGE.json and VALIDATION.json.",
+  "author": "Tekalign (@tekuuu)",
+  "ai_assistance": "Substantial OpenAI Codex assistance in profiling, integration, verification, review and documentation. No independent human review claimed.",
+  "coordination": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2755",
+  "open_questions": [
+    {
+      "question": "Can the unchanged exact native local replay be accelerated next?",
+      "why_it_matters": "After exact state lowering is cheaper, independent local replay and warp matrices become a larger part of total time.",
+      "first_step": "Profile one complete fresh native run and price an exact representation change against the current all-column implementation.",
+      "blocked_by": "Must retain arbitrary-input, both-orientation and phase-sensitive checks; counting checks is not evidence of equivalent coverage."
+    },
+    {
+      "question": "Should the opt-in runner become a maintained upstream native entry point?",
+      "why_it_matters": "Future construction authors could verify changed words faster without copying a full dependency tree.",
+      "first_step": "Independently replay this package and review its closed source inventory, output equivalence and failure controls.",
+      "blocked_by": "Maintainer approval and a migration plan for other native source versions. This snapshot does not auto-upgrade."
+    }
+  ]
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/VERIFY.json b/research/two-sided-helper-extraction/vendor/fastnative/VERIFY.json
new file mode 100644
index 0000000000..17384abdd2
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/VERIFY.json
@@ -0,0 +1,36 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [
+    "numpy==2.2.6"
+  ],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py",
+        "--provider",
+        "base"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Fresh complete five-stage base native replay, including independent all512-column warp recipes and all inherited controls; compare every native field to pinned reference. Also reject altered source, singular warp, paid profile, recipe, receipt, optimized execution and output reuse."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py",
+        "--provider",
+        "extra",
+        "--relocate"
+      ],
+      "timeout_seconds": 600,
+      "checks": "Fresh complete five-stage extra native replay, including independent all512-column warp recipes and all inherited controls; compare every native field to pinned reference.  Execute from a Git-free relocated package in a path with spaces."
+    }
+  ]
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/benchmark.py b/research/two-sided-helper-extraction/vendor/fastnative/benchmark.py
new file mode 100644
index 0000000000..93b2622759
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/benchmark.py
@@ -0,0 +1,42 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Alternating fresh complete native runs; same fixture and no result caching."""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import platform
+import statistics
+import subprocess
+import sys
+import time
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+from common import HERE, need, source_bytes
+from compare import compare
+
+def main():
+ need(__debug__, 'assertions must remain enabled')
+ p=argparse.ArgumentParser(description=__doc__);p.add_argument('--pairs',type=int,default=3);p.add_argument('--provider',choices=('base','extra'),default='base');p.add_argument('--work',type=Path,required=True);a=p.parse_args()
+ need(a.pairs>=1 and not a.work.exists(),'positive pairs and fresh work required')
+ source_bytes(HERE/'vendor');word=HERE/f'fixtures/WORD-{a.provider}.json.gz'
+ pins=json.loads((HERE/'PINS.json').read_text())
+ need(hashlib.sha256(word.read_bytes()).hexdigest()==pins[word.relative_to(HERE).as_posix()],'fixture digest')
+ a.work.mkdir(parents=True)
+ samples=[];comparisons=[];env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1');env.pop('PYTHONOPTIMIZE',None)
+ for i in range(a.pairs):
+  paths={}
+  for engine in (('reference','sparse') if i%2==0 else ('sparse','reference')):
+   out=a.work/f'pair{i}-{engine}';cmd=[sys.executable,'-I','-B',str(HERE/'run_native.py'),str(word),str(out),'--engine',engine]
+   start=time.monotonic()
+   with (a.work/f'pair{i}-{engine}.log').open('w') as log:r=subprocess.run(cmd,env=env,stdout=log,stderr=subprocess.STDOUT,timeout=900)
+   elapsed=time.monotonic()-start;need(r.returncode==0,'native benchmark run failed '+str(out))
+   receipt=json.loads((out/'RESULT.json').read_text());need(receipt['status']=='PASS_COMPLETE_T74_NATIVE_REPLAY','native receipt')
+   samples.append({'pair':i,'engine':engine,'wall_seconds':elapsed,'steps':receipt['steps']});paths[engine]=out/'native/local'
+   (a.work/'SAMPLES.json').write_text(json.dumps(samples,indent=2)+'\n');print('PASS sample',i,engine,round(elapsed,3),flush=True)
+  result=compare(paths['reference'],paths['sparse']);comparisons.append(result);print(result['status'],i,flush=True)
+ medians={e:statistics.median(s['wall_seconds'] for s in samples if s['engine']==e) for e in ('reference','sparse')}
+ result={'status':'PASS_COMPLETE_T74_NATIVE_BENCHMARK','provider':a.provider,'pairs':a.pairs,'samples':samples,'comparisons':comparisons,'median_wall_seconds':medians,'speedup':medians['reference']/medians['sparse'],'python':platform.python_version(),'platform':platform.platform(),'cpu_count':os.cpu_count(),'input_sha256':hashlib.sha256(word.read_bytes()).hexdigest(),'scope':'Fresh sequential subprocesses; all five stages and independent warp recipe check run each time. No cached result reuse. Shared host; OS caches not flushed. Timings descriptive, not a correctness threshold.'}
+ (a.work/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n');print(result['status'],result['speedup'],flush=True)
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/common.py b/research/two-sided-helper-extraction/vendor/fastnative/common.py
new file mode 100644
index 0000000000..9ed8d88b97
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/common.py
@@ -0,0 +1,26 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Authenticate the closed source snapshot before importing any vendored code."""
+import hashlib
+import json
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+
+def need(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+def sha(body):
+    return hashlib.sha256(body).hexdigest()
+
+def source_bytes(vendor):
+    pins = json.loads((HERE / 'PINS.json').read_text())
+    expected = {p.removeprefix('vendor/'): h for p, h in pins.items() if p.startswith('vendor/')}
+    paths = list(vendor.rglob('*'))
+    need(not vendor.is_symlink() and all(not p.is_symlink() for p in paths), 'source symlink')
+    actual = {p.relative_to(vendor).as_posix(): p.read_bytes() for p in paths if p.is_file()}
+    need(set(actual) == set(expected), 'complete source path inventory')
+    for name, body in actual.items():
+        need(sha(body) == expected[name], 'source digest: ' + name)
+    return actual
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/compare.py b/research/two-sided-helper-extraction/vendor/fastnative/compare.py
new file mode 100644
index 0000000000..f3c60c6133
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/compare.py
@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Compare all native mathematical outputs; only two elapsed fields are omitted.
+Gzip container hashes are independently checked before semantic normalization.
+"""
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import sys
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from common import need
+FILES = {
+ 'CANONICAL-WORD.json.gz', 'FULL-WORD.json.gz', 'LOCAL-PROGRAMS.json.gz',
+ 'CLIFFORD-RECIPES.json', 'CLIFFORD-REVIEW.json', 'INDEPENDENT-LOCAL-REPLAY.json',
+ 'LOCAL-CHECKS.json', 'RESIDUAL-ADAPTERS.json', 'SCALAR-FRAME-AUDIT.json',
+ 'WARP-RECIPE-CHECKS.json', 'WRAPPER-CHECKS.json',
+}
+def sha(data):
+ return hashlib.sha256(data).hexdigest()
+def canonical(value):
+ return json.dumps(value,sort_keys=True,separators=(',',':')).encode()
+def normalized(directory):
+ need({p.name for p in directory.iterdir()}==FILES, 'complete native output inventory')
+ raw={n:(directory/n).read_bytes() for n in FILES}
+ data={n:gzip.decompress(b) if n.endswith('.gz') else b for n,b in raw.items()}
+ values={n:json.loads(b) for n,b in data.items()}
+ # Preserve and validate every hash's binding. Only container-dependent hashes
+ # are replaced by the digest of the actual decompressed artifact for comparison.
+ for n in ('INDEPENDENT-LOCAL-REPLAY.json','CLIFFORD-REVIEW.json','WARP-RECIPE-CHECKS.json'):
+  need(values[n]['canonical_word_sha256']==sha(raw['CANONICAL-WORD.json.gz']), 'canonical container binding '+n)
+  values[n]['canonical_word_sha256']=sha(data['CANONICAL-WORD.json.gz'])
+ for n in ('CLIFFORD-REVIEW.json','WARP-RECIPE-CHECKS.json'):
+  need(values[n]['recipe_sha256']==sha(raw['CLIFFORD-RECIPES.json']), 'recipe byte binding '+n)
+ need(values['INDEPENDENT-LOCAL-REPLAY.json']['local_programs_sha256']==sha(raw['LOCAL-PROGRAMS.json.gz']), 'program container binding')
+ values['INDEPENDENT-LOCAL-REPLAY.json']['local_programs_sha256']=sha(data['LOCAL-PROGRAMS.json.gz'])
+ audit=values['SCALAR-FRAME-AUDIT.json']
+ need(audit['input_content_sha256']==sha(data['FULL-WORD.json.gz']), 'full word binding')
+ need(audit['canonical_content_sha256']==sha(data['CANONICAL-WORD.json.gz']), 'canonical content binding')
+ for n in ('SCALAR-FRAME-AUDIT.json','CLIFFORD-REVIEW.json'):
+  seconds=values[n].pop('seconds')
+  need(type(seconds) in (float,int) and seconds>=0, 'valid elapsed field '+n)
+ return values
+
+def compare(first,second):
+ a,b=normalized(first),normalized(second)
+ need(a==b,'native outputs differ: '+str([n for n in FILES if a[n]!=b[n]]))
+ return {'status':'PASS_ALL_NATIVE_OUTPUTS_IDENTICAL','files':len(FILES),
+         'normalized_sha256':sha(canonical(a)),
+         'recipe_bytes_sha256':sha((first/'CLIFFORD-RECIPES.json').read_bytes())}
+
+if __name__=='__main__':
+ print(json.dumps(compare(Path(sys.argv[1]),Path(sys.argv[2])),indent=2))
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/controls.py b/research/two-sided-helper-extraction/vendor/fastnative/controls.py
new file mode 100644
index 0000000000..5877dead77
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/controls.py
@@ -0,0 +1,192 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Rejection controls at source, word, emitted recipe and receipt boundaries."""
+import copy
+import gzip
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tempfile
+import random
+
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from common import HERE, need, source_bytes
+from compare import compare
+
+
+def evaluator_check():
+    """Finite differential check against this snapshot's original dense algebra.
+
+    Seed2, dimensions1..5, twelve length20 circuits per dimension, every input
+    basis column. Covers all five gate kinds, both C signs and adjoints. This
+    supplements the predecessor proof; it is not a full formal proof.
+    """
+    from stage import module
+    source_bytes(HERE / 'vendor')
+    algebra = module('clifford_exact', HERE / 'vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py')
+    tables = module('test_exact_tables', HERE / 'vendor/accelerators/tables.py')
+    sparse = module('test_exact_sparse', HERE / 'vendor/accelerators/sparse_state.py')
+    rng = random.Random(2)
+    columns = 0
+    for n in range(1, 6):
+        for _ in range(12):
+            op = algebra.ident(n)
+            for j in range(20):
+                if j % 5 == 0:
+                    rows = [1 << i for i in range(n)]
+                    if n > 1:
+                        for _ in range(2 * n):
+                            a, b = rng.sample(range(n), 2)
+                            rows[a] ^= rows[b]
+                    gate = algebra.perm(n, rows)
+                elif j % 5 == 1:
+                    rows = [0] * n
+                    for a in range(n):
+                        for b in range(a, n):
+                            if rng.randrange(2):
+                                rows[a] |= 1 << b
+                                rows[b] |= 1 << a
+                    alpha = [((rows[i] >> i) & 1) + 2 * rng.randrange(2) for i in range(n)]
+                    gate = algebra.diag(n, rows, alpha)
+                elif j % 5 == 2:
+                    gate = algebra.cgate(n, rng.randrange(1 << n), rng.choice((-1, 1)))
+                elif j % 5 == 3:
+                    gate = algebra.xgate(n, rng.randrange(1 << n))
+                else:
+                    gate = algebra.ident(n)
+                    gate.circuit.append(('phase', rng.randrange(4)))
+                op = op.then(gate)
+            for candidate in (op, op.adjoint()):
+                for basis in range(1 << n):
+                    need(candidate.zero_state(basis) == sparse.zero_state(candidate, tables, basis),
+                         'dense/sparse exact state mismatch')
+                    columns += 1
+    print('PASS_T74_EXACT_STATE_DIFFERENTIAL', columns, 'columns')
+
+
+def reject(argv, message):
+    result = subprocess.run([sys.executable, '-I', '-B', *map(str, argv)],
+                            stdout=subprocess.PIPE, stderr=subprocess.STDOUT, timeout=45)
+    text = result.stdout.decode(errors='replace')
+    need(result.returncode != 0 and message in text, 'expected rejection: ' + message + '\n' + text[-2000:])
+
+
+def check(local):
+    evaluator_check()
+    controls = []
+    with tempfile.TemporaryDirectory(prefix='t74-negative-') as temporary:
+        root = Path(temporary)
+        # Authenticate before loading even the first vendored import. A sentinel
+        # would be created if tampered code were executed before rejection.
+        for mutation in ('digest', 'extra', 'missing', 'symlink'):
+            vendor = root / mutation
+            shutil.copytree(HERE / 'vendor', vendor)
+            target = vendor / 'accelerators/tables.py'
+            if mutation == 'digest':
+                sentinel = root / 'EXECUTED'
+                target.write_text('from pathlib import Path\nPath(' + repr(str(sentinel)) + ').touch()\n')
+                message = 'source digest'
+            elif mutation == 'extra':
+                (vendor / 'unlisted.py').write_text('raise RuntimeError("unlisted")\n')
+                message = 'complete source path inventory'
+            elif mutation == 'missing':
+                target.unlink()
+                message = 'complete source path inventory'
+            else:
+                target.unlink()
+                target.symlink_to(HERE / 'vendor/accelerators/tables.py')
+                message = 'source symlink'
+            reject([HERE / 'stage.py', '--vendor', vendor, '--script', 'bw_phases.py', root / 'unused'], message)
+            controls.append('source:' + mutation)
+        need(not (root / 'EXECUTED').exists(), 'tampered source executed')
+        package = root / 'changed fixture package'
+        shutil.copytree(HERE, package, ignore=shutil.ignore_patterns('__pycache__'))
+        fixture = package / 'fixtures/WORD-base.json.gz'
+        fixture.write_bytes(fixture.read_bytes() + b'changed')
+        unused = root / 'benchmark-must-not-start'
+        reject([package / 'benchmark.py', '--pairs', 1, '--work', unused], 'fixture digest')
+        need(not unused.exists(), 'invalid benchmark fixture created outputs')
+        controls.append('benchmark-fixture')
+        for script in ('run_native.py', 'stage.py', 'verify.py'):
+            reject(['-O', HERE / script], 'assertions must remain enabled')
+            controls.append('optimized:' + script)
+        existing = root / 'existing'
+        existing.mkdir()
+        (existing / 'preserve').write_text('do not overwrite')
+        reject([HERE / 'run_native.py', HERE / 'fixtures/WORD-base.json.gz', existing], 'fresh work directory required')
+        need(list(existing.iterdir()) == [existing / 'preserve'] and
+             (existing / 'preserve').read_text() == 'do not overwrite', 'existing output changed')
+        controls.append('existing-output')
+
+        word = json.loads(gzip.decompress((HERE / 'fixtures/WORD-base.json.gz').read_bytes()))
+        for mutation in ('singular-warp', 'paid-profile'):
+            bad = copy.deepcopy(word)
+            if mutation == 'singular-warp':
+                bad['warps'][0][2][1] = bad['warps'][0][2][0]
+                message = 'non-invertible G'
+            else:
+                key = next(iter(bad['report']['local_profile']))
+                bad['report']['local_profile'][key] += 1
+                message = 'paid profile differs'
+            path = root / (mutation + '.json')
+            path.write_text(json.dumps(bad))
+            for engine in ('reference', 'sparse'):
+                out = root / (mutation + '-' + engine)
+                reject([HERE / 'run_native.py', path, out, '--engine', engine], 'stage failed')
+                log = out / ('reference-driver.log' if engine == 'reference' else 'native-bw_transport.py.log')
+                need(message in log.read_text(), 'wrong rejection reason for ' + str(out))
+                need(not (out / 'RESULT.json').exists(), 'failed native run wrote success')
+                controls.append('word:' + mutation + ':' + engine)
+
+        # Exercise the independent checker on mutated FILES, in addition to its
+        # thirteen retained internal matrix-mutation controls in every full run.
+        for mutation in ('phase', 'missing-class'):
+            out = root / ('recipe-' + mutation)
+            shutil.copytree(local, out)
+            path = out / 'CLIFFORD-RECIPES.json'
+            recipes = json.loads(path.read_text())
+            if mutation == 'phase':
+                left = recipes['warps'][0]['left']
+                left['phase'] = (left['phase'] + 1) % 4
+                message = 'warp recipe is not the exact column product'
+            else:
+                recipes['warps'].pop()
+                message = 'recipe classes differ'
+            path.write_text(json.dumps(recipes))
+            reject([HERE / 'vendor/native/new/code/borrow/bw_check_recipes.py', out], message)
+            controls.append('recipe-file:' + mutation)
+
+        for mutation in ('coverage', 'missing-file', 'container-binding'):
+            out = root / ('receipt-' + mutation)
+            shutil.copytree(local, out)
+            if mutation == 'missing-file':
+                (out / 'LOCAL-CHECKS.json').unlink()
+                message = 'complete native output inventory'
+            else:
+                path = out / 'WARP-RECIPE-CHECKS.json'
+                receipt = json.loads(path.read_text())
+                if mutation == 'coverage':
+                    receipt['controls_rejected'].pop()
+                    message = 'native outputs differ'
+                else:
+                    receipt['canonical_word_sha256'] = '0' * 64
+                    message = 'canonical container binding'
+                path.write_text(json.dumps(receipt))
+            try:
+                compare(local, out)
+            except ValueError as error:
+                need(message in str(error), 'wrong comparison failure')
+            else:
+                raise AssertionError('altered native outputs accepted: ' + mutation)
+            controls.append('comparison:' + mutation)
+    print('PASS_T74_NATIVE_FAST_BOUNDARY_CONTROLS', len(controls), json.dumps(controls))
+    return controls
+
+
+if __name__ == '__main__':
+    need(__debug__, 'assertions must remain enabled')
+    source_bytes(HERE / 'vendor')
+    check(Path(sys.argv[1]))
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/evidence/BENCHMARK.json b/research/two-sided-helper-extraction/vendor/fastnative/evidence/BENCHMARK.json
new file mode 100644
index 0000000000..53c0d77ab3
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/evidence/BENCHMARK.json
@@ -0,0 +1,249 @@
+{
+  "status": "PASS_COMPLETE_T74_NATIVE_BENCHMARK",
+  "provider": "base",
+  "pairs": 3,
+  "samples": [
+    {
+      "pair": 0,
+      "engine": "reference",
+      "wall_seconds": 304.12705635900784,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.2277613850019407
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4153370510030072
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 38.20502878499974
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 5.7440066569979535
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 257.3918046769977
+        }
+      ]
+    },
+    {
+      "pair": 0,
+      "engine": "sparse",
+      "wall_seconds": 85.88402091899479,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.189789870986715
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4454092910018517
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 37.58784284500871
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 2.166318774994579
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 43.39858223599731
+        }
+      ]
+    },
+    {
+      "pair": 1,
+      "engine": "sparse",
+      "wall_seconds": 85.56597218499519,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.1618483210040722
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4005460170010338
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 37.7024452869955
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 2.0632049500127323
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 43.14079914300237
+        }
+      ]
+    },
+    {
+      "pair": 1,
+      "engine": "reference",
+      "wall_seconds": 308.15912566099723,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.1598684070049785
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4444775400043
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 37.1472855930042
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 5.759292622999055
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 262.5130987189914
+        }
+      ]
+    },
+    {
+      "pair": 2,
+      "engine": "reference",
+      "wall_seconds": 306.74960786000884,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.204015570008778
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4606356029980816
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 38.59787878699717
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 5.9340596520050894
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 259.39262297499226
+        }
+      ]
+    },
+    {
+      "pair": 2,
+      "engine": "sparse",
+      "wall_seconds": 87.2939048440021,
+      "steps": [
+        {
+          "step": "native",
+          "exit_code": 0,
+          "seconds": 1.208094222994987
+        },
+        {
+          "step": "ledgers",
+          "exit_code": 0,
+          "seconds": 1.4107751400006237
+        },
+        {
+          "step": "local-replay",
+          "exit_code": 0,
+          "seconds": 38.536898468999425
+        },
+        {
+          "step": "wrappers",
+          "exit_code": 0,
+          "seconds": 2.150425133993849
+        },
+        {
+          "step": "phases",
+          "exit_code": 0,
+          "seconds": 43.88330491501256
+        }
+      ]
+    }
+  ],
+  "comparisons": [
+    {
+      "status": "PASS_ALL_NATIVE_OUTPUTS_IDENTICAL",
+      "files": 11,
+      "normalized_sha256": "72152474a7c1f65f8bddec3197a9661d035e2ef0edfd08751a19038c470f654f",
+      "recipe_bytes_sha256": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3"
+    },
+    {
+      "status": "PASS_ALL_NATIVE_OUTPUTS_IDENTICAL",
+      "files": 11,
+      "normalized_sha256": "72152474a7c1f65f8bddec3197a9661d035e2ef0edfd08751a19038c470f654f",
+      "recipe_bytes_sha256": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3"
+    },
+    {
+      "status": "PASS_ALL_NATIVE_OUTPUTS_IDENTICAL",
+      "files": 11,
+      "normalized_sha256": "72152474a7c1f65f8bddec3197a9661d035e2ef0edfd08751a19038c470f654f",
+      "recipe_bytes_sha256": "3fad1a9ae138ddb89442753cb2ef3c0666c58f40d5488d503fbf75f7f480d4d3"
+    }
+  ],
+  "median_wall_seconds": {
+    "reference": 306.74960786000884,
+    "sparse": 85.88402091899479
+  },
+  "speedup": 3.5716726415188793,
+  "python": "3.12.14",
+  "platform": "Linux-7.2.8-200.fc44.x86_64-x86_64-with-glibc2.43",
+  "cpu_count": 16,
+  "input_sha256": "ae8b6b4d62a9da29331062fae1bd68b0341edf83152f5a5ef50c5109ba578f9a",
+  "scope": "Fresh sequential subprocesses; all five stages and independent warp recipe check run each time. No cached result reuse. Shared host; OS caches not flushed. Timings descriptive, not a correctness threshold.",
+  "numpy_version": "2.2.6",
+  "stage_median_seconds": {
+    "reference": {
+      "native": 1.204015570008778,
+      "ledgers": 1.4444775400043,
+      "local-replay": 38.20502878499974,
+      "wrappers": 5.759292622999055,
+      "phases": 259.39262297499226
+    },
+    "sparse": {
+      "native": 1.189789870986715,
+      "ledgers": 1.4107751400006237,
+      "local-replay": 37.7024452869955,
+      "wrappers": 2.150425133993849,
+      "phases": 43.39858223599731
+    }
+  },
+  "whole_native_time_reduction_percent": 72.00191337874843,
+  "launch_command": "python3.12 -I -B research/t74-native-fast/benchmark.py --pairs 3 --provider base --work FRESH_DIRECTORY",
+  "source_pin_manifest_sha256": "f619e8e1c163078fb70c6fc3b98a498a671b8c02927b91d6cc253af2a775b6c9"
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/evidence/COVERAGE.json b/research/two-sided-helper-extraction/vendor/fastnative/evidence/COVERAGE.json
new file mode 100644
index 0000000000..6ccc53ea51
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/evidence/COVERAGE.json
@@ -0,0 +1,106 @@
+{
+  "scope": "Coverage summary extracted from the complete original base replay. All eleven complete native outputs are compared separately, not merely this summary.",
+  "arbitrary_live_columns_each_orientation": 639,
+  "warp_replay": {
+    "status": "PASS_EXACT_MONOMIAL_WARP_COLUMNS_ALL_512_BOTH_ORIENTATIONS",
+    "warps": 65,
+    "event_classes_checked_on_all_512_columns": 202,
+    "zero_buffers": 72
+  },
+  "local_controls": [
+    "wrong_scale",
+    "missing_center",
+    "wrong_common_frame",
+    "wrong_child_rank",
+    "missing_pre_wrapper",
+    "missing_post_wrapper",
+    "wrapper_with_wrong_frame",
+    "wrapper_in_wrong_phase",
+    "wrapper_on_a_data_register",
+    "wrapper_on_a_target_register",
+    "wrapper_on_a_centre_register",
+    "centre_step_not_nested",
+    "centre_descent_incomplete",
+    "hpe_pre_wrapper_resolved_to_full_recipe",
+    "hpe_post_wrapper_without_terminal_frame",
+    "hpe_post_wrapper_wrong_terminal_frame",
+    "hpe_tail_gate_at_full_frame",
+    "hpe_tail_climb_dropped",
+    "hpe_helper_exit_adapter_to_full",
+    "hpe_tail_gate_moved_into_full_cleanup",
+    "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+    "cold_hpe_pre_wrapper_dropped",
+    "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+    "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+    "cold_hpe_wrapper_with_nonzero_entrance",
+    "cold_hpe_post_wrapper_wrong_terminal_frame",
+    "cold_hpe_premix_gate_before_pre_wrapper",
+    "warp_missing_inverse_at_full_cleanup",
+    "warp_missing_forward",
+    "warp_frame_mismatch",
+    "warp_to_frame_not_carried_by_G",
+    "warp_wrong_sign",
+    "warp_wrong_operator",
+    "warp_inverse_moved_before_use",
+    "warp_inverse_wrong_frame",
+    "warp_rank_changing",
+    "warp_phase_B_dropped_gate_after_warp",
+    "zero_buffer_not_freed",
+    "zero_buffer_gate_outside_cleanup",
+    "zero_buffer_garbage_left",
+    "zero_buffer_replaced_by_restored_register_at_full",
+    "warp_wrong_G_invertible_not_carrying_frame",
+    "warp_noninvertible_G",
+    "warp_zero_column_G",
+    "warp_operator_dropped_from_table",
+    "warp_wrong_quadratic_phase_of_K"
+  ],
+  "wrapper_controls": [
+    "wrong global phase",
+    "wrong translation",
+    "wrong quadratic form",
+    "sides swapped",
+    "wrong width",
+    "hpe: U-wrapper decoded against a FULL ending",
+    "hpe: width misreported as 9 - dim E",
+    "hpe: wrong terminal hyperplane",
+    "hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}",
+    "hpe: wrong global phase",
+    "cold hpe: identity pre wrapper instead of R_{0,U}",
+    "cold hpe: identity post wrapper instead of L_{0,U}",
+    "cold hpe: no wrappers (cold FULL convention L = R = I)",
+    "cold hpe: U-wrapper decoded against a FULL ending",
+    "cold hpe: width misreported as 9",
+    "cold hpe: wrong terminal hyperplane",
+    "cold hpe: wrong global phase",
+    "warp: wrong global phase",
+    "warp: wrong translation",
+    "warp: wrong linear phase",
+    "warp: wrong quadratic form",
+    "warp: recipe of another operator",
+    "warp: inverse recipe used as the warp",
+    "warp: wrong G (frame-changed column)",
+    "warp: non-invertible G"
+  ],
+  "recipe_controls": [
+    "recipe: wrong global phase",
+    "recipe: wrong translation",
+    "recipe: wrong linear phase",
+    "recipe: wrong quadratic form",
+    "recipe: wrong matrix",
+    "recipe: wrong G (still invertible)",
+    "recipe: non-invertible G",
+    "recipe: inverse warp recipe used for the forward warp",
+    "recipe: recipe of another warp class",
+    "recipe: swapped from/to frames",
+    "recipe: missing warp class",
+    "logical: wrong G",
+    "logical: wrong phase"
+  ],
+  "recipe_warp_classes": 166,
+  "recipe_columns_each": 512,
+  "phase_frames": 1076,
+  "directed_edges": 2940,
+  "endpoint_adapters": 224,
+  "all_child_equalities_include_global_phase": true
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/evidence/REGISTERED.log b/research/two-sided-helper-extraction/vendor/fastnative/evidence/REGISTERED.log
new file mode 100644
index 0000000000..dd419f7dee
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/evidence/REGISTERED.log
@@ -0,0 +1,20 @@
+CHECK Fresh complete five-stage base native replay, including independent all512-column warp recipes and all inherited controls; compare every native field to pinned reference. Also reject altered source, singular warp, paid profile, recipe, receipt, optimized execution and output reuse.
+PASS native
+PASS ledgers
+PASS local-replay
+PASS wrappers
+PASS phases
+PASS_COMPLETE_T74_NATIVE_REPLAY sparse 86.818
+PASS_T74_EXACT_STATE_DIFFERENTIAL 1488 columns
+PASS_T74_NATIVE_FAST_BOUNDARY_CONTROLS 18 ["source:digest", "source:extra", "source:missing", "source:symlink", "benchmark-fixture", "optimized:run_native.py", "optimized:stage.py", "optimized:verify.py", "existing-output", "word:singular-warp:reference", "word:singular-warp:sparse", "word:paid-profile:reference", "word:paid-profile:sparse", "recipe-file:phase", "recipe-file:missing-class", "comparison:coverage", "comparison:missing-file", "comparison:container-binding"]
+PASS_T74_NATIVE_FAST_REFERENCE_AND_CONTROLS base
+CHECK Fresh complete five-stage extra native replay, including independent all512-column warp recipes and all inherited controls; compare every native field to pinned reference.  Execute from a Git-free relocated package in a path with spaces.
+PASS native
+PASS ledgers
+PASS local-replay
+PASS wrappers
+PASS phases
+PASS_COMPLETE_T74_NATIVE_REPLAY sparse 87.385
+PASS_T74_NATIVE_FAST_REFERENCE_AND_CONTROLS extra
+PASS_T74_NATIVE_FAST_GIT_FREE_RELOCATION extra
+PASS_REGISTERED_RESEARCH_PACKAGE research/t74-native-fast outcome=partial
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/evidence/VALIDATION.json b/research/two-sided-helper-extraction/vendor/fastnative/evidence/VALIDATION.json
new file mode 100644
index 0000000000..9848bae05c
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/evidence/VALIDATION.json
@@ -0,0 +1,44 @@
+{
+  "status": "PASS_COMPLETE_T74_NATIVE_FAST_VALIDATION",
+  "checked_at": "2026-10-15T20:57:23.935468+00:00",
+  "command": "python3.12 scripts/research_package.py --package research/t74-native-fast",
+  "python": "3.12.14",
+  "numpy": "2.2.6",
+  "registered_exit_code": 0,
+  "providers": [
+    "base",
+    "extra"
+  ],
+  "extra_git_free_relocation": true,
+  "dense_sparse_columns": 1488,
+  "boundary_controls_rejected": 18,
+  "inherited_controls_per_provider": {
+    "local": 46,
+    "wrappers": 25,
+    "recipes": 13
+  },
+  "benchmark_pairs": 3,
+  "outputs_compared_per_pair": 11,
+  "registered_log_sha256": "78a49def69d0465f4318b9e24613246ba5fb6de19441e54b88fb50dfe823f149",
+  "code_sha256": {
+    "benchmark.py": "3e544453c89310281d745a37e861cbd79065b1740d90f1ec883fc200b189a557",
+    "common.py": "8f04e08b99a370fa82115fc46fbb3af4ab44f4facd47de07b01e1a2499a94914",
+    "compare.py": "ebf877a6f47ef1fd2b797fd6077bd45d132d8cb56ab7553044bae3d86e238e45",
+    "controls.py": "03131f4dc6a1830f10e35fb837ada456f060ca510994d250c5c2666a6342c23a",
+    "run_native.py": "a7bfe110fe5098f6ef8bde3c43ecf15e8d1e06149abf7321a4c945383dcc2627",
+    "stage.py": "3cce27dd5a359ebc4dc70d4aab994aee52bc0a12e59db7da3f902257f876cffe",
+    "verify.py": "6dbdc56ca6cfde987869e12990a495d7eded78dd1887fb3fdf2d196060220fcc"
+  },
+  "pin_manifest_sha256": "f619e8e1c163078fb70c6fc3b98a498a671b8c02927b91d6cc253af2a775b6c9",
+  "notes": [
+    "The registered log reports outcome=partial because metadata was finalized only after both provider checks succeeded; the complete outcome is recorded now.",
+    "After timing, benchmark.py gained a fixture-digest guard before any timed subprocess. Its corruption control passes. Timed run_native.py, stage.py, common.py and vendored execution sources are unchanged.",
+    "Initial sparse-checkout metadata failures were resolved by materializing package paths before the successful full replay. They were not mathematical failures."
+  ],
+  "not_claimed": [
+    "new kappa",
+    "complete supplier or outer replay in this round",
+    "whole-project speedup",
+    "formal verification of the multiplication theorem"
+  ]
+}
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-base.json.gz b/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-base.json.gz
new file mode 100644
index 0000000000..f1fc67a6ea
Binary files /dev/null and b/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-base.json.gz differ
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-extra.json.gz b/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-extra.json.gz
new file mode 100644
index 0000000000..f06e80c4dd
Binary files /dev/null and b/research/two-sided-helper-extraction/vendor/fastnative/fixtures/WORD-extra.json.gz differ
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/requirements.txt b/research/two-sided-helper-extraction/vendor/fastnative/requirements.txt
new file mode 100644
index 0000000000..aaa34fa3b2
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/requirements.txt
@@ -0,0 +1 @@
+numpy==2.2.6
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/run_native.py b/research/two-sided-helper-extraction/vendor/fastnative/run_native.py
new file mode 100644
index 0000000000..64ef0eb83f
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/run_native.py
@@ -0,0 +1,96 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Complete T74 native replay; fresh source snapshot, no result cache.
+
+Uses the unchanged T74 transport, emitter, local audit, adapters, phase lowering
+and independent warp-recipe audit. Only Op.zero_state in the two Clifford-using
+stages changes to the previously published exact sparse evaluator.
+"""
+import argparse
+import json
+import os
+from pathlib import Path
+import platform
+import subprocess
+import sys
+import time
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from common import HERE, need, sha, source_bytes
+
+STEPS = ('native', 'ledgers', 'local-replay', 'wrappers', 'phases')
+
+def main():
+    need(__debug__, 'assertions must remain enabled')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('word', type=Path)
+    parser.add_argument('work', type=Path)
+    parser.add_argument('--engine', choices=('reference', 'sparse'), default='sparse')
+    args = parser.parse_args()
+    started = time.monotonic()
+    blobs = source_bytes(HERE / 'vendor')
+    original = args.word.resolve()
+    need(original.is_file(), 'input word missing')
+    body = original.read_bytes()
+    work = args.work.resolve()
+    need(not work.exists(), 'fresh work directory required')
+    work.mkdir(parents=True)
+    vendor = work / 'source'
+    for name, contents in blobs.items():
+        target = vendor / name
+        target.parent.mkdir(parents=True, exist_ok=True)
+        target.write_bytes(contents)
+    word = work / ('INPUT.json.gz' if original.suffix == '.gz' else 'INPUT.json')
+    word.write_bytes(body)
+    native = vendor / 'native/new/code/borrow'
+    output = work / 'native'
+    env = dict(os.environ, PYTHONDONTWRITEBYTECODE='1', PYTHONUTF8='1', PYTHONINTMAXSTRDIGITS='0')
+    env.pop('PYTHONOPTIMIZE', None)
+    commands = []
+    def run(name, command, cwd):
+        before = time.monotonic()
+        with (work / (name + '.log')).open('w') as log:
+            result = subprocess.run(command, cwd=cwd, env=env, stdin=subprocess.DEVNULL,
+                                    stdout=log, stderr=subprocess.STDOUT)
+        entry = {'step': name, 'exit_code': result.returncode,
+                 'seconds': time.monotonic()-before, 'command': command}
+        commands.append(entry)
+        (work / 'COMMANDS.json').write_text(json.dumps(commands, indent=2)+'\n')
+        need(result.returncode == 0, 'stage failed: '+name+'; see '+str(work/(name+'.log')))
+        return entry
+    if args.engine == 'reference':
+        run('reference-driver', [sys.executable, '-I', '-B', str(vendor/'native/new/run_native_borrow.py'), str(word), str(output)], native)
+        steps = json.loads((output/'STEPS.json').read_text())
+    else:
+        output.mkdir()
+        local = output/'local'
+        plan = [
+            ('native', [('bw_transport.py', [word, local])]),
+            ('ledgers', [('bw_emit.py', [local])]),
+            ('local-replay', [('bw_audit_local.py', [local])]),
+            ('wrappers', [('bw_adapters.py', [local/'CANONICAL-WORD.json.gz', local/'RESIDUAL-ADAPTERS.json', local/'WRAPPER-CHECKS.json'])]),
+            ('phases', [('bw_phases.py', [local]), ('bw_check_recipes.py', [local])]),
+        ]
+        steps = []
+        for label, scripts in plan:
+            before = time.monotonic()
+            for script, arguments in scripts:
+                if script in ('bw_adapters.py', 'bw_phases.py'):
+                    command = [sys.executable, '-I', '-B', str(HERE/'stage.py'), '--vendor', str(vendor), '--script', script]
+                else:
+                    command = [sys.executable, '-I', '-B', str(native/script)]
+                run(label+'-'+script, command + list(map(str, arguments)), native)
+            steps.append({'step':label,'exit_code':0,'seconds':time.monotonic()-before})
+            (output/'STEPS.json').write_text(json.dumps(steps,indent=2)+'\n')
+            print('PASS', label, flush=True)
+    need([s['step'] for s in steps] == list(STEPS) and all(s['exit_code']==0 for s in steps), 'complete native stage coverage')
+    need(source_bytes(vendor) == blobs and word.read_bytes() == body, 'source or input modified')
+    result = {'status':'PASS_COMPLETE_T74_NATIVE_REPLAY', 'engine':args.engine,
+              'word_sha256':sha(body), 'source_sha256':{k:sha(v) for k,v in sorted(blobs.items())},
+              'steps':steps, 'seconds':time.monotonic()-started, 'python':platform.python_version(),
+              'scope':'Full five-stage native replay including independent all-column warp recipes and original rejection controls; supplier/outer admission separate.'}
+    (work/'RESULT.json').write_text(json.dumps(result,indent=2)+'\n')
+    print(result['status'], args.engine, round(result['seconds'],3), flush=True)
+
+if __name__ == '__main__':
+    main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/stage.py b/research/two-sided-helper-extraction/vendor/fastnative/stage.py
new file mode 100644
index 0000000000..9ecc54bca4
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/stage.py
@@ -0,0 +1,40 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Run an unchanged pinned T74 script with PR1029/PR662 exact state evaluation."""
+import argparse
+import importlib.util
+from pathlib import Path
+import runpy
+import sys
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from common import need, source_bytes
+
+def module(name, path):
+    spec = importlib.util.spec_from_file_location(name, path)
+    result = importlib.util.module_from_spec(spec)
+    sys.modules[name] = result
+    spec.loader.exec_module(result)
+    return result
+
+def main():
+    need(__debug__, 'assertions must remain enabled')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--vendor', type=Path, required=True)
+    parser.add_argument('--script', choices=('bw_adapters.py', 'bw_phases.py'), required=True)
+    parser.add_argument('arguments', nargs='+')
+    args = parser.parse_args()
+    vendor = args.vendor.resolve()
+    source_bytes(vendor)
+    native = vendor / 'native/new/code/borrow'
+    algebra = module('clifford_exact', native / 'vendor/clifford/clifford_exact.py')
+    tables = module('t74_exact_tables', vendor / 'accelerators/tables.py')
+    sparse = module('t74_exact_sparse', vendor / 'accelerators/sparse_state.py')
+    tables.clear_caches()
+    algebra.Op.zero_state = lambda self, basis=0: sparse.zero_state(self, tables, basis)
+    script = native / args.script
+    sys.argv = [str(script), *args.arguments]
+    runpy.run_path(str(script), run_name='__main__')
+
+if __name__ == '__main__':
+    main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-NOTICE.md b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-NOTICE.md
new file mode 100644
index 0000000000..a3b31e157f
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-NOTICE.md
@@ -0,0 +1,33 @@
+# Attribution
+
+Prepared for Ali Romman (@aliromman) with substantial OpenAI Codex assistance.
+New code, tests and documentation use the repository's Apache-2.0 license.
+No independent human review is claimed.
+
+- Charles Bethin (@cbethin), PR662, supplied the exact permutation and phase
+  tables. This package imports those tables unchanged and compares against
+  his complete dense evaluator. PR662 head:
+  `458744109003e0958798f27c1f04be78f03663ce`.
+- The Gaussian-dyadic algebra and lowering come from the retained
+  `clifford_exact.py`. `lowering.py` adapts its `monomial` and `lower_child`
+  routines to take an evaluator argument. `run.py` adapts `phases_full.py`.
+  The latter credits icekylinx and the PR425 ancestry, with Codex assistance.
+  The PR531 license and notice remain at
+  `research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor531/`.
+  Those files retain the upstream contributor and AI-assistance notices.
+- Jonathan Capalbo's PR942 supplies the retained U8 replay archive used by
+  the benchmark. Its head is
+  `1960cfa919a0945d0ca4cb14ea96237000037903`.
+  The U8 word comes from the PR869/870 lineage, which credits NewBArch's
+  triangle-hybrid construction and ColdWitness/icekylinx's driver, on Jeremy
+  Kothe's PR799 X4 work. Chafik Boukhalfa's PR741/890 work and Hao Yan's
+  PR858 work remain credited in the retained package notices.
+
+The new contribution is the sparse state update, its explicit compiler
+entry point, and the complete U8 comparison with corruption controls and
+time/memory measurements. Sparse state propagation is an established general
+technique; this package makes no priority claim for that technique.
+
+The package does not change frozen source files, accepted certificates,
+`upstream/`, or the default selected replay. All inherited compiler,
+realization, hosting, precision, tape and analytic obligations remain.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-PROOF.md b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-PROOF.md
new file mode 100644
index 0000000000..bbd5990439
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/SPARSE-PROOF.md
@@ -0,0 +1,81 @@
+# Exact support updates
+
+This argument applies to the valid gates from the pinned `clifford_exact.py`.
+The input is a basis index `0 <= basis < 2^n`. Each state has Gaussian integer
+numerators and a common denominator `2^den`. A missing dictionary key has
+numerator zero. The output contains all `2^n` numerators, including zeros.
+
+## Induction over the circuit
+
+The initial dictionary has the one entry `basis -> (1, 0)`. It is the same
+state as the retained dense evaluator.
+
+For `P`, the validated binary matrix is invertible. Its index map is a
+permutation. Thus no two nonzero entries collide, and omitted zero entries
+contribute no value. For `X`, translation by XOR is also a permutation.
+
+For `D` and `phase`, each amplitude is multiplied by a power of `i`. The
+four rotations of `(a, b)` are `(a, b)`, `(-b, a)`, `(-a, -b)`, and `(b, -a)`.
+Zero remains zero. The `D` phases and `P` index maps use the unchanged PR662
+tables. Those tables depend on the dimension and all gate coefficients.
+They do not depend on a state or on a previous check result. The source pins
+retain their exact formulas and bounded caches.
+
+For `C`, put `y = x xor q` and let `s` be the sign. If the numerators at
+`x` and `y` are `(a, b)` and `(c, d)`, the new numerators are
+
+```text
+x: (a - s*b + c + s*d, b + s*a + d - s*c)
+y: (c - s*d + a + s*b, d + s*c + b - s*a).
+```
+
+The denominator exponent increases by one. These are the two rows of the
+retained dense update. XOR partitions the index set into pairs when `q != 0`.
+The loop visits a pair once if either entry is nonzero. If both entries are
+present, it skips the larger index. If only one entry is present, its partner
+has value zero. A pair with two zero entries contributes two zeros and need
+not be visited. Exact cancellation removes a zero output entry. When `q = 0`,
+both formulas give `(2*a, 2*b)` at the same index; the update is the identity
+after division by two.
+
+The common-factor test after `C` gives the same answer on the dictionary as
+on the dense vector: omitted entries are zero and are divisible by two.
+The other gates only permute entries or rotate their Gaussian coordinates.
+They cannot change the common power of two. Thus those gates need no further
+normalization. This proves equality of both the complete vector and `den`
+after every gate. It also covers circuits whose support shrinks after a
+`C` gate. A valid Clifford circuit cannot map a nonzero input to the zero
+state, because each gate is invertible.
+
+## The compiler checks
+
+`lowering.py` retains the algebra and checks of the pinned lowering routine.
+It passes a state evaluator through ordinary function arguments. It changes
+no retained module, method or global value. The reference mode calls the
+original lowering routine. The dense and sparse modes use the same explicit
+lowering code with their respective evaluators.
+
+Every tableau equality, off-support zero check, denominator check, and global
+phase check remains. The final comparison still checks the complete compiled
+state against the complete input state. No phase is inferred from a tableau.
+
+`run.py` retains the frame-span, frame-rank, edge-rank and endpoint-rank checks
+of `phases_full.py`. It visits every frame, every directed edge including
+center transitions, and every source and target adapter. Its public entry
+point rejects optimized Python before it loads the retained assertion-based
+algebra. It also rejects source drift and an existing output directory.
+
+## Work and storage
+
+Let `s` be the current number of nonzero amplitudes and `N = 2^n`. A state
+update now visits `s` entries, or at most `s` XOR pairs, in place of all `N`
+entries. Dictionary operations have their usual expected constant lookup
+cost. Integer arithmetic remains exact. A first use of a PR662 gate table
+still takes `O(N)` work, and the final full output also takes `O(N)` work.
+Each of the two retained table caches has at most 64 entries.
+
+This is a support-sensitive improvement. It is not a polynomial-size
+stabilizer representation: the support can be all `N` indices. The benchmark
+measures the complete selected dimension-nine phase command, including table
+construction, source admission, parsing, lowering, checks and output writing.
+It makes no claim about multiplication runtime or the full cold replay.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/sparse_state.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/sparse_state.py
new file mode 100644
index 0000000000..ca39f73494
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/sparse_state.py
@@ -0,0 +1,65 @@
+"""Evaluate exact Clifford states on their nonzero support.
+
+Gate tables are from Charles Bethin's PR662. The support update is new.
+Prepared for Ali Romman with substantial OpenAI Codex assistance.
+Apache-2.0.
+"""
+
+
+def zero_state(op, tables, basis=0):
+    """Return every Gaussian numerator and the power-of-two denominator."""
+    size = 1 << op.n
+    if not 0 <= basis < size:
+        raise IndexError(basis)
+    state = {basis: (1, 0)}
+    den = 0
+    for gate in op.circuit:
+        kind = gate[0]
+        if kind == 'P':
+            mapping = tables.permutation_table(op.n, tuple(gate[1]))
+            state = {mapping[x]: value for x, value in state.items()}
+        elif kind == 'X':
+            state = {x ^ gate[1]: value for x, value in state.items()}
+        elif kind in ('D', 'phase'):
+            phases = (tables.phase_table(op.n, tuple(gate[1]), tuple(gate[2]))
+                      if kind == 'D' else None)
+            out = {}
+            for x, (a, b) in state.items():
+                phase = phases[x] if phases is not None else gate[1] % 4
+                if phase == 0:
+                    out[x] = (a, b)
+                elif phase == 1:
+                    out[x] = (-b, a)
+                elif phase == 2:
+                    out[x] = (-a, -b)
+                else:
+                    out[x] = (b, -a)
+            state = out
+        elif kind == 'C':
+            q, sign = gate[1:]
+            out = {}
+            for x, (a, b) in state.items():
+                y = x ^ q
+                if y < x and y in state:
+                    continue
+                c, d = state.get(y, (0, 0))
+                first = (a - sign*b + c + sign*d,
+                         b + sign*a + d - sign*c)
+                second = (c - sign*d + a + sign*b,
+                          d + sign*c + b - sign*a)
+                if first != (0, 0):
+                    out[x] = first
+                if second != (0, 0):
+                    out[y] = second
+            state = out
+            den += 1
+            while den and all((a & 1) == (b & 1) == 0
+                              for a, b in state.values()):
+                state = {x: (a // 2, b // 2) for x, (a, b) in state.items()}
+                den -= 1
+        else:
+            raise AssertionError(gate)
+    vec = [(0, 0)] * size
+    for x, value in state.items():
+        vec[x] = value
+    return vec, den
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/tables.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/tables.py
new file mode 100644
index 0000000000..5d546d8a05
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/accelerators/tables.py
@@ -0,0 +1,82 @@
+"""Exact Gaussian-dyadic state evaluation with bounded, state-free gate tables.
+
+Charles Bethin, with substantial OpenAI Codex assistance. Apache-2.0.
+The gate semantics and normalization follow the pinned clifford_exact.py.
+"""
+from functools import lru_cache
+
+
+@lru_cache(maxsize=64)
+def permutation_table(n, rows):
+    """Compute Gx from G(x xor lowbit(x)) xor G(lowbit(x))."""
+    columns = [sum(((row >> j) & 1) << i for i, row in enumerate(rows))
+               for j in range(n)]
+    table = [0] * (1 << n)
+    for x in range(1, len(table)):
+        bit = x & -x
+        table[x] = table[x ^ bit] ^ columns[bit.bit_length() - 1]
+    return tuple(table)
+
+
+@lru_cache(maxsize=64)
+def phase_table(n, rows, linear):
+    """Remove the lowest bit; all remaining quadratic partners have larger indices."""
+    table = [0] * (1 << n)
+    for x in range(1, len(table)):
+        bit = x & -x
+        i, rest = bit.bit_length() - 1, x ^ bit
+        table[x] = (table[rest] + linear[i] +
+                    2 * ((rows[i] & rest).bit_count() & 1)) % 4
+    return tuple(table)
+
+
+def clear_caches():
+    permutation_table.cache_clear()
+    phase_table.cache_clear()
+
+
+def zero_state(self, basis=0):
+    """Drop-in evaluator for valid pinned Op circuits; return the full exact state."""
+    size = 1 << self.n
+    vec = [(0, 0)] * size
+    vec[basis] = (1, 0)
+    den = 0
+    for gate in self.circuit:
+        kind = gate[0]
+        if kind == 'P':
+            mapping = permutation_table(self.n, tuple(gate[1]))
+            out = [(0, 0)] * size
+            for x, value in enumerate(vec):
+                out[mapping[x]] = value
+            vec = out
+        elif kind == 'X':
+            vec = [vec[x ^ gate[1]] for x in range(size)]
+        elif kind in ('D', 'phase'):
+            phases = (phase_table(self.n, tuple(gate[1]), tuple(gate[2]))
+                      if kind == 'D' else [gate[1] % 4] * size)
+            out = []
+            for (a, b), phase in zip(vec, phases):
+                if phase == 0:
+                    out.append((a, b))
+                elif phase == 1:
+                    out.append((-b, a))
+                elif phase == 2:
+                    out.append((-a, -b))
+                else:
+                    out.append((b, -a))
+            vec = out
+        elif kind == 'C':
+            q, sign = gate[1:]
+            out = []
+            for x, (a, b) in enumerate(vec):
+                c, d = vec[x ^ q]
+                out.append((a - sign*b + c + sign*d,
+                            b + sign*a + d - sign*c))
+            vec = out
+            den += 1
+        else:
+            raise AssertionError(gate)
+        while den and all((a & 1) == (b & 1) == 0 for a, b in vec):
+            vec = [(a // 2, b // 2) for a, b in vec]
+            den -= 1
+    return vec, den
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/NOTICE-PR2226.md b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/NOTICE-PR2226.md
new file mode 100644
index 0000000000..a14b299ef5
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/NOTICE-PR2226.md
@@ -0,0 +1,21 @@
+# Credit: anticipatory dirty borrowing (PR2226)
+
+The construction realised by this native chain is **PR2226, "anticipatory dirty borrowing"**, by Cinna Davis
+(@1337isnot1337), prepared with substantial OpenAI Codex assistance (Apache-2.0): the logical reference change
+K_G of a lender register (a monomial Clifford: a permutation of the 512 columns with phase mod 4), the initial
+compensation terms c K_G z, the early cold tail, the exact cold restoration and the private zero buffers of the
+FULL-frame cleanup.  `vendor/pr2226_operators.py`, `vendor/pr2226_replay.py` and `vendor/PR2226-NOTICE.md` are byte copies
+of PR2226's `operators.py`, `replay.py` and `NOTICE.md`.  `bw_gauss.py` is a port of `operators.py` (change, monomial,
+apply_mono, coord, frame, check) and adds a decoder from a serialized `clifford_exact` monomial to its exact 512 x 512
+Gaussian matrix.
+
+What this chain adds (the P3 native realisation, with the borrowing work's explicit chronological BORROW-WORD as input):
+warp events and zero buffers in `LOCAL-PROGRAMS`, warp recipes in `CLIFFORD-RECIPES.json` (lowered with the unchanged
+`lower_child`, rank zero, then compared with the exact numpy column product), logical K_G recipes in
+`RESIDUAL-ADAPTERS.json`, an independent local replay in both orientations that checks every warp product on all 512
+columns, and the negative controls listed in `INDEPENDENT-LOCAL-REPLAY.json`, `WRAPPER-CHECKS.json`, `WARP-RECIPE-CHECKS.json`
+and `bw_tamper.py`.
+
+Lineage retained: icekylinx (PR425/433/514, scalar and wrapper machinery), DreamingOfClouds (PR458/484/593 hyperplane/cold-HPE
+extensions), the clifford_exact compiler (vendor531), and the owners named in the package README.  `vendor/clifford/clifford_exact.py`
+is a byte copy.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_adapters.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_adapters.py
new file mode 100644
index 0000000000..82beaa9c1d
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_adapters.py
@@ -0,0 +1,165 @@
+"""Paid residual wrappers for entering helpers (Lemma A): generation and independent decoding.  Apache-2.0.
+Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.  The wrapper construction follows PR #458
+(chafreaky): a helper that starts at frame E and ends at FULL has the physical residual S_E = T_FULL T_E^-1 (apply T_E^-1 first);
+S_E = L_E (C_[w] x I) R_E with R_E applied first; the wrappers  R_E^-1  before the whole local invocation and  L_E^-1  after its
+full-frame cleanup turn the residual into the coordinate factor C_[w] x I and restore the other 9 - w coordinates identically.
+usage: adapters_gk.py CANONICAL-WORD.json.gz RESIDUAL-ADAPTERS.json OUT-LEMMA-A.json
+Writes the recipes (generation uses clifford_exact.lower_child) and then DECODES the serialized monomials with the primitive
+constructors of clifford_exact (not lower_child) and checks, for every entrance frame, that  L_E^-1 S_E R_E^-1  has exactly the
+tableau and zero-state vector (global phase included) of  fourier(9, range(w)); mutated recipes (wrong phase, swapped sides, wrong
+translation, wrong width) must be rejected."""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import copy, gzip, json, sys
+from pathlib import Path
+# Package-path adaptation only; the exact wrapper mathematics is unchanged.
+HERE = Path(__file__).resolve().parent
+sys.path.insert(0, str(HERE / 'vendor/clifford'))   # BW: the pinned vendor531 clifford_exact (byte copy)
+sys.path.insert(0, str(HERE))
+from clifford_exact import canonical_frame, lower_child, fourier, diag, perm, xgate, Op, identity, transpose, inv, parity, monomial as mono_of, mv
+import bw_gauss
+n = 9; FULL = tuple(1 << i for i in range(n))
+def monomial_op(rec):
+    """decode a serialized monomial (matrix rows, quadratic rows, Z4 linear part, translation, phase)"""
+    out = diag(n, tuple(rec['quadratic_rows']), tuple(rec['linear_Z4'])).then(perm(n, tuple(rec['matrix_rows']))).then(xgate(n, rec['offset']))
+    return out.then(Op(n, identity(n), [('phase', rec['phase'])]))
+def S_of(U, END=FULL):
+    # HPE: a helper that starts at E=U and ends at END has residual T_END T_E^-1 (END = FULL is the inherited case)
+    return canonical_frame(n, tuple(U)).adjoint().then(canonical_frame(n, tuple(END)))
+def wrapped_ok(U, rec, END=FULL):
+    """exactly: L^-1 S R^-1 = C_[w] x I  (apply order: R^-1, S, L^-1), w = dim END - dim E"""
+    w = len(END) - len(U); S = S_of(U, END); Rm = monomial_op(rec['right']); Lm = monomial_op(rec['left'])
+    net = Rm.adjoint().then(S).then(Lm.adjoint()); target = fourier(n, range(w))
+    return rec['rank'] == w and net.tab == target.tab and net.zero_state() == target.zero_state()
+def _contains(a, b):
+    a = list(a)
+    for x in b:
+        for y in sorted(a, reverse=True):
+            if x >> (y.bit_length() - 1) & 1: x ^= y
+        if x: return False
+    return True
+def Kop(G_cols):
+    """BW: K_G = perm(G) then diag(Q), Q = I + G^-T G^-1: PR2226's monomial() and the conjugator inside clifford_exact.canonical_frame."""
+    G = transpose(tuple(G_cols), n); gi = inv(G, n)
+    Q = tuple((1 << i) ^ sum(parity(gi_i & gi_j) << j for j, gi_j in enumerate(transpose(gi, n))) for i, gi_i in enumerate(transpose(gi, n)))
+    return perm(n, G).then(diag(n, Q))
+def numeric_K(G_cols):
+    import numpy as np
+    pv, ph = bw_gauss.monomial(list(G_cols), n)
+    N = 1 << n; re = np.zeros((N, N), dtype=np.int64); im = np.zeros((N, N), dtype=np.int64)
+    unit = [(1, 0), (0, 1), (-1, 0), (0, -1)]
+    for x in range(N): re[pv[x], x], im[pv[x], x] = unit[ph[x]]
+    return re, im, 0
+def warp_ok(G_cols, rec):
+    """BW: the serialized monomial equals PR2226's exact numpy K_G on all 512 columns (indep. decode) and its op decodes to K_G exactly."""
+    m = bw_gauss.recipe_matrix(rec, n)
+    if not bw_gauss.equal_scaled(numeric_K(G_cols), m): return False
+    dec = monomial_op(rec); ref = Kop(G_cols)
+    return dec.tab == ref.tab and dec.zero_state() == ref.zero_state()
+
+def main():
+    c = json.load(gzip.open(sys.argv[1])); frames = c['frames']; v = c['v']
+    starts = sorted({c['start'][r] for r in range(2 * v, len(c['start'])) if c['start'][r] != 0 and c['final'][r] == 1})
+    # HPE: (entrance, terminal) pairs of helpers ending at a proper subspace; key 'E:U'.  Inherited words have none.
+    ends = sorted({(c['start'][r], c['final'][r]) for r in range(2 * v, len(c['start'])) if c['final'][r] != 1})
+    # COLD-HPE: e == 0 (a cold helper, entrance = bottom, T_0 = I) is allowed: the (0, U) recipe is keyed '0:U'
+    assert all(len(frames[u]) < n and _contains(frames[u], frames[e]) for e, u in ends)
+    cold_ends = [(e, u) for e, u in ends if e == 0]
+    recipes = {}
+    for f in starts:
+        U = frames[f]; rec, compiled = lower_child(S_of(U))
+        recipes[str(f)] = dict(frame=f, vectors=list(U), entrance_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    for e, u in ends:
+        E, U = frames[e], frames[u]; rec, compiled = lower_child(S_of(E, U))
+        recipes['%d:%d' % (e, u)] = dict(frame=e, terminal=u, vectors=list(E), terminal_vectors=list(U), entrance_rank=len(E),
+                                         terminal_rank=len(U), rank=rec['rank'], left=rec['left'], right=rec['right'])
+    # BW: monomial recipes of the warps K_G (anticipatory dirty borrowing, PR2226): one per operator, serialized like a wrapper monomial
+    warp_recipes = {}
+    for w in c.get('warps', []):
+        _, rec_k = mono_of(Kop(w['G_columns']))
+        warp_recipes[str(w['op'])] = dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], G_columns=list(w['G_columns']), K=rec_k)
+    Path(sys.argv[2]).write_text(json.dumps(dict(status='RESIDUAL_ADAPTER_RECIPES', recipes=recipes, warps=warp_recipes), sort_keys=True, separators=(',', ':')) + '\n')
+    # ---- independent decode of the serialized file
+    data_all = json.loads(Path(sys.argv[2]).read_text()); data = data_all['recipes']
+    dot = lambda a, b: bin(a & b).count('1') & 1
+    detail = []
+    for f in starts:
+        rec = data[str(f)]; U = frames[f]
+        assert wrapped_ok(U, rec), ('wrapper product is not C_[w] x I', f)
+        detail.append(dict(frame=f, entrance_rank=len(U), residual_width=n - len(U), vectors=list(U), all_even_weight=all(bin(x).count('1') % 2 == 0 for x in U),
+                           totally_isotropic=all(dot(a, b) == 0 for a in U for b in U)))
+    hdetail = []
+    for e, u in ends:   # HPE: independent decode, residual width = dim U - dim E
+        rec = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u]
+        assert wrapped_ok(E, rec, U), ('HPE wrapper product is not C_[w] x I', e, u)
+        hdetail.append(dict(frame=e, terminal=u, entrance_rank=len(E), terminal_rank=len(U), residual_width=len(U) - len(E)))
+    controls = []
+    def reject(name, fn):
+        f = starts[0]; rec = copy.deepcopy(data[str(f)]); fn(rec)
+        if wrapped_ok(frames[f], rec): raise AssertionError('mutated wrapper accepted: ' + name)
+        controls.append(name)
+    reject('wrong global phase', lambda r: r['right'].__setitem__('phase', (r['right']['phase'] + 1) % 4))
+    reject('wrong translation', lambda r: r['left'].__setitem__('offset', r['left']['offset'] ^ 1))
+    reject('wrong quadratic form', lambda r: r['right'].__setitem__('quadratic_rows', [x ^ 2 if i == 0 else x for i, x in enumerate(r['right']['quadratic_rows'])]) if False else r['right']['linear_Z4'].__setitem__(0, (r['right']['linear_Z4'][0] + 2) % 4))
+    reject('sides swapped', lambda r: (r.__setitem__('left', r['right']), r.__setitem__('right', r['left'])))
+    reject('wrong width', lambda r: r.__setitem__('rank', r['rank'] + 1))
+    if ends:   # HPE controls on the first (E, U) pair
+        e, u = next((p for p in ends if p[0] != 0), ends[0]); rec0 = data['%d:%d' % (e, u)]   # COLD-HPE: an entering pair if any (= ends[0] without cold ends)
+        def hreject(name, ok):
+            if ok: raise AssertionError('HPE mutation accepted: ' + name)
+            controls.append(name)
+        hreject('hpe: U-wrapper decoded against a FULL ending', wrapped_ok(frames[e], rec0))
+        hreject('hpe: width misreported as 9 - dim E', wrapped_ok(frames[e], dict(rec0, rank=n - len(frames[e])), frames[u]))
+        other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u]) and _contains(frames[f], frames[e]))
+        hreject('hpe: wrong terminal hyperplane', wrapped_ok(frames[e], rec0, frames[other]))
+        fe = next(((e2, u2) for e2, u2 in ends if str(e2) in data), None)
+        if fe:   # an entrance shared with FULL-ended helpers: R_{E,FULL} must not serve as R_{E,U}
+            r2 = data['%d:%d' % fe]
+            hreject('hpe: pre wrapper resolved to the FULL recipe R_{E,FULL}', wrapped_ok(frames[fe[0]], dict(r2, right=data[str(fe[0])]['right']), frames[fe[1]]))
+        hreject('hpe: wrong global phase', wrapped_ok(frames[e], dict(rec0, left=dict(rec0['left'], phase=(rec0['left']['phase'] + 1) % 4)), frames[u]))
+    if cold_ends:   # COLD-HPE controls on the first cold pair (0, U): factor_iff_pre says only R_{0,U} itself may precede
+        e, u = cold_ends[0]; recc = data['%d:%d' % (e, u)]; E, U = frames[e], frames[u]
+        ID = dict(matrix_rows=[1 << i for i in range(n)], offset=0, quadratic_rows=[0] * n, linear_Z4=[0] * n, phase=0)
+        assert monomial_op(ID).tab == identity(n)   # the control's wrapper really is the identity
+        def creject(name, ok):
+            if ok: raise AssertionError('cold HPE mutation accepted: ' + name)
+            controls.append(name)
+        creject('cold hpe: identity pre wrapper instead of R_{0,U}', wrapped_ok(E, dict(recc, right=ID), U))
+        creject('cold hpe: identity post wrapper instead of L_{0,U}', wrapped_ok(E, dict(recc, left=ID), U))
+        creject('cold hpe: no wrappers (cold FULL convention L = R = I)', wrapped_ok(E, dict(recc, left=ID, right=ID), U))
+        creject('cold hpe: U-wrapper decoded against a FULL ending', wrapped_ok(E, recc))
+        creject('cold hpe: width misreported as 9', wrapped_ok(E, dict(recc, rank=n), U))
+        other = next(f for f in range(len(frames)) if f != u and len(frames[f]) == len(frames[u]))
+        creject('cold hpe: wrong terminal hyperplane', wrapped_ok(E, recc, frames[other]))
+        creject('cold hpe: wrong global phase', wrapped_ok(E, dict(recc, right=dict(recc['right'], phase=(recc['right']['phase'] + 1) % 4)), U))
+        ent = next((p for p in ends if p[0] != 0 and p[1] == u), None)
+        same = lambda x, y: monomial_op(x).tab == monomial_op(y).tab and monomial_op(x).zero_state() == monomial_op(y).zero_state()
+        if ent and not same(data['%d:%d' % ent]['right'], recc['right']):   # an entering helper ending at the same U: its R_{E,U} must not serve as R_{0,U}
+            creject('cold hpe: pre wrapper resolved to an entering recipe R_{E,U}', wrapped_ok(E, dict(recc, right=data['%d:%d' % ent]['right']), U))
+    wdetail = []
+    for w in c.get('warps', []):   # BW: independent decode of every warp recipe, then mutation controls on the first warp
+        rec = data_all['warps'][str(w['op'])]
+        assert rec['G_columns'] == w['G_columns']
+        assert warp_ok(w['G_columns'], rec['K']), ('warp recipe differs from the exact monomial K_G', w['op'])
+        wdetail.append(dict(op=w['op'], from_frame=w['from_frame'], to_frame=w['to_frame'], columns_checked=1 << n))
+    if c.get('warps'):
+        w0 = c['warps'][0]; k0 = data_all['warps'][str(w0['op'])]['K']
+        def wreject(name, ok):
+            if ok: raise AssertionError('warp mutation accepted: ' + name)
+            controls.append(name)
+        wreject('warp: wrong global phase', warp_ok(w0['G_columns'], dict(k0, phase=(k0['phase'] + 1) % 4)))
+        wreject('warp: wrong translation', warp_ok(w0['G_columns'], dict(k0, offset=k0['offset'] ^ 1)))
+        wreject('warp: wrong linear phase', warp_ok(w0['G_columns'], dict(k0, linear_Z4=[(k0['linear_Z4'][0] + 2) % 4] + k0['linear_Z4'][1:])))
+        wreject('warp: wrong quadratic form', warp_ok(w0['G_columns'], dict(k0, quadratic_rows=[k0['quadratic_rows'][0] ^ 2, k0['quadratic_rows'][1] ^ 1] + k0['quadratic_rows'][2:])))
+        wreject('warp: recipe of another operator', warp_ok(w0['G_columns'], data_all['warps'][str(c['warps'][1]['op'])]['K']))
+        wreject('warp: inverse recipe used as the warp', warp_ok(w0['G_columns'], mono_of(Kop(w0['G_columns']).adjoint())[1]))
+        G2 = list(w0['G_columns']); G2[0] ^= G2[1]
+        wreject('warp: wrong G (frame-changed column)', warp_ok(G2, k0))
+        sing = list(w0['G_columns']); sing[1] = sing[0]
+        try: Kop(sing); raise SystemExit('non-invertible G accepted')
+        except (AssertionError, StopIteration, ValueError): controls.append('warp: non-invertible G')
+    res = dict(status='PASS_RESIDUAL_WRAPPERS_ARE_EXACT', frames=len(detail), **({'hyperplane_end_pairs': hdetail} if ends else {}), **({'cold_hyperplane_end_pairs': len(cold_ends)} if cold_ends else {}), wrappers_reject=controls, all_even_weight=all(d['all_even_weight'] for d in detail), **({'warp_recipes_exact_on_all_512_columns': wdetail} if wdetail else {}),
+               all_totally_isotropic=all(d['totally_isotropic'] for d in detail), detail=detail)
+    Path(sys.argv[3]).write_text(json.dumps(res, indent=1) + '\n')
+    print('Lemma A (exact): L^-1 S_E R^-1 = C_[w] x I for', len(detail), 'entrance frames, global phase included;', len(controls), 'wrapper mutations rejected; all-even-weight:', res['all_even_weight'])
+if __name__ == '__main__': main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_audit_local.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_audit_local.py
new file mode 100644
index 0000000000..912a0c447c
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_audit_local.py
@@ -0,0 +1,289 @@
+# Local independent replay of the attributed PR514 / PR433 checker (icekylinx with OpenAI Codex assistance), extended (BW) with
+# monomial warps and private zero buffers for anticipatory dirty borrowing (PR2226, Cinna Davis @1337isnot1337, with OpenAI
+# Codex assistance, Apache-2.0).  The exact Gaussian column products below are a port of PR2226's operators.py (change /
+# monomial / apply_mono / coord / frame / check); they use only numpy and share no code with the emitter or with the
+# clifford_exact phase compiler.  Every edit is marked "BW:".  The complete inherited checker and its controls are retained.
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import copy,gzip,hashlib,json,sys,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+import numpy as np
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+OUT=Path(sys.argv[1])
+c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'))
+ir={'local_programs':json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))}
+v,R,h=c['v'],c['R'],c['h'];n=2*v+R;frames=c['frames']
+levels={int(t):f for t,f in c.get('target_levels',{}).items()}
+entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+plain={r for r in range(n) if r not in set(entering)}
+
+def contains(a,b):
+    for x in a:
+        for y in b:
+            if x>>(y.bit_length()-1)&1:x^=y
+        if x:return False
+    return True
+hpe={r for r in range(2*v,n) if c['final'][r]!=1}
+assert all(len(frames[c['final'][r]])<h for r in hpe)
+cold=sorted(hpe-set(entering));wrapped=sorted(set(entering)|hpe);plain={r for r in range(n) if r not in set(wrapped)}
+zb=list(c.get('zero_buffers',[]))
+assert set(zb)==hpe,'every hyperplane-ended helper is replaced by a zero buffer in the FULL cleanup, and only those'
+
+from bw_gauss import *   # BW: exact Gaussian column products (PR2226 operators.py port), numpy only
+WARPCACHE={}
+def warp_columns(op,f0,f1,G,qmut=None,table=None):
+    """all 512 columns of  T_f0^-1 K_G^{+-1} T_f1  (the physical rank-zero product of the warp), exactly, both orientations."""
+    key=(op,f0,f1,tuple(G),qmut)
+    if key in WARPCACHE:return WARPCACHE[key]
+    assert len(G)==h and f2rank(G)==h,'non-invertible G'
+    U,E=frames[f0],frames[f1]
+    if op>0:assert sorted(lin(G,x) for x in span(U))==sorted(span(E)),'G does not carry the from frame onto the to frame'
+    else:assert sorted(lin(G,x) for x in span(E))==sorted(span(U)),'G^-1 does not carry the from frame onto the to frame'
+    z=warp_product(G,U,E,op,h,qmut)
+    fwd=check_mono(z)
+    bre,bim,bexp=z                                   # inverse-transpose of a (scaled) unitary monomial is its entrywise conjugate
+    bwd=check_mono((bre,-bim,bexp))
+    WARPCACHE[key]=(fwd,bwd);return WARPCACHE[key]
+# ---------------------------------------------------------------------------------------------------------------------------
+def add_row(row,src,q):
+    for j,x in src.items():
+        z=row.get(j,Q(0))+q*x
+        if z:row[j]=z
+        else:row.pop(j,None)
+def warp_row(row,op):
+    out={}
+    for (var,word),x in row.items():
+        word=word[1:] if word and word[0]==-op else (op,)+word
+        out[var,word]=x
+    return out
+
+def local(events,back,table=None,qmut=None):
+    table=c['warps'] if table is None else table
+    G_of={w['op']:w['G_columns'] for w in table}
+    rows={('L',r):{(r,()):Q(1)} for r in range(n)}
+    norm={('L',r):Q(1) for r in range(n)};prefix=Q(1);cur=c['start'].copy();private={}
+    hist=Counter();phases=[];entry=[];exit=[];centers=[];chain={};wrappers=[]
+    wset=set(wrapped);pre_seen=set();post_seen=set();zlive=set();warp_hashes=[];nwarp=0
+    allowed=['zero_frame_precondition','entry_adapters','A','centers','B']+(['cleanup_tail'] if c.get('tail') else [])+['final','exit_adapters','full_frame_cleanup','done']
+    for event in events:
+        tag=event[0]
+        if tag=='phase':
+            phases.append(event[1]);assert phases==allowed[:len(phases)]
+            if event[1]=='A':assert entry==[(r,f) for r,f in enumerate(c['start']) if r in plain] and sorted(r for k_,r,f_ in wrappers if k_=='pre')==wrapped
+            if event[1]=='centers':assert all(cur[r]==levels.get(r-v,0) for r in range(v,2*v))
+            if event[1]=='full_frame_cleanup':assert cur==c['final'] and exit==[(r,f) for r,f in enumerate(c['final']) if r not in hpe]
+            assert not private
+        elif tag=='residual_adapter':
+            _,kind,r,f,*end=event;assert r in wrapped and f==c['start'][r] and kind in ('pre','post')
+            assert end==([c['final'][r]] if r in hpe else [])
+            if end and kind=='post':assert cur[r]==end[0]
+            assert (kind=='pre' and phases[-1]=='entry_adapters') or (kind=='post' and phases[-1]=='full_frame_cleanup')
+            assert (kind,r) not in {(k,x) for k,x,_ in wrappers};wrappers.append((kind,r,f))
+            (pre_seen if kind=='pre' else post_seen).add(r)
+        elif tag=='adapter':
+            assert event[3]==(c['start'] if event[1]=='old_to_new' else c['final'])[event[2]]
+            (entry if event[1]=='old_to_new' else exit).append((event[2],event[3]))
+        elif tag=='climb':
+            _,part,r,a,b,rank=event
+            assert not private and phases[-1]==part and cur[r]==a
+            assert contains(frames[a],frames[b]) and rank==len(frames[b])-len(frames[a])>0
+            hist[rank]+=1;cur[r]=b
+        elif tag=='zero_buffer':   # BW: private FULL-frame zero buffers of the cleanup; allocated empty, returned empty
+            _,kind,z=event;assert phases[-1]=='full_frame_cleanup' and z in zb
+            if kind=='alloc':
+                assert z not in zlive and ('Z',z) not in rows;zlive.add(z);rows['Z',z]={};norm['Z',z]=Q(0)
+            else:
+                assert kind=='free' and z in zlive and not rows['Z',z];zlive.remove(z)
+        elif tag=='warp':          # BW: monomial logical reference change, rank zero, exact on all 512 columns
+            _,r,op,f0,f1=event;nwarp+=1
+            assert op and abs(op) in G_of and phases[-1] in ('zero_frame_precondition','A','B','cleanup_tail','full_frame_cleanup')
+            assert not private
+            if r[0]=='L':
+                assert cur[r[1]]==f0,('warp frame mismatch',r,cur[r[1]],f0)
+                assert r[1] not in wset or (r[1] in pre_seen and r[1] not in post_seen),('warp wrapper order',r)
+            else:
+                assert r[0]=='Z' and r[1] in zlive and f0==f1==1
+            assert len(frames[f0])==len(frames[f1]),'a warp is rank zero: equal dimensions'
+            warp_hashes.append(warp_columns(op,f0,f1,G_of[abs(op)],qmut))
+            rows[tuple(r)]=warp_row(rows[tuple(r)],op)
+            if r[0]=='L':cur[r[1]]=f1
+        elif tag=='center':
+            _,k,a,b,rank=event
+            assert phases[-1]=='centers' and private=={('C',k):a}
+            cf=c['center_frames'][k];cr=len(frames[cf])
+            assert contains(frames[a],frames[b]) if back else contains(frames[b],frames[a])
+            assert rank==abs(len(frames[a])-len(frames[b]))>0
+            chain.setdefault(k,[]).append((a,b))
+            private['C',k]=b;hist[rank]+=1;centers.append(k)
+        elif tag=='scalar':
+            _,e,f=event;op=e[0];target=tuple(e[1]);source=tuple(e[2]) if op in ('copy','add') else None
+            if target[0]=='C' and op=='clear':
+                assert private.get(target,f)==f
+                private.pop(target,None)
+            else:
+                for r in (target,source):
+                    if r is None:continue
+                    if r[0]=='L':assert cur[r[1]]==f and (r[1] not in wset or (r[1] in pre_seen and r[1] not in post_seen)),('common frame / wrapper order',r,cur[r[1]],f)
+                    elif r[0]=='Z':   # BW: a zero buffer lives only inside the FULL-frame cleanup, at FULL
+                        assert r[1] in zlive and f==1 and phases[-1]=='full_frame_cleanup',('zero buffer misuse',r)
+                    else:
+                        if r==target and r not in private:private[r]=f
+                        assert private[r]==f
+            if op=='clear':rows[target]={};norm[target]=Q(0)
+            elif op=='copy':rows[target]=dict(rows[source]);norm[target]=norm[source]
+            elif op=='scale':
+                q=Q(e[2],e[3]);a,b=abs(q.numerator),q.denominator
+                assert a&(a-1)==0 and b&(b-1)==0
+                rows[target]={j:q*x for j,x in rows[target].items()};norm[target]*=abs(q)
+            else:
+                q=Q(e[3],e[4]);a,b=abs(q.numerator),q.denominator
+                assert source!=target and b&(b-1)==0
+                w=0
+                for bit in bin(a)[2:]:w=2*w+int(bit)
+                assert Q(w,b)*(1 if q>0 else -1)==q
+                prefix=max(prefix,Q(a)*norm[source])
+                norm[target]=norm.get(target,Q(0))+abs(q)*norm[source]
+                row=rows.setdefault(target,{})
+                add_row(row,rows[source],q)
+            prefix=max(prefix,norm[target])
+        else:raise AssertionError(tag)
+    assert phases==allowed and set(centers)==set(range(len(c['centers']))) and not private and not zlive
+    assert sorted(r for k,r,_ in wrappers if k=='pre')==wrapped and sorted(r for k,r,_ in wrappers if k=='post')==wrapped
+    for k,st in chain.items():
+        cf=c['center_frames'][k]
+        if back:assert st[-1][1]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+        else:assert st[0][0]==cf and all(st[i][1]==st[i+1][0] for i in range(len(st)-1))
+    assert all(not row for reg,row in rows.items() if reg[0] in 'CZ')
+    assert cur==c['final']
+    for r in range(n):
+        expected={(r,()):Q(1)}
+        if back and r<v:expected[(v+r,())]=Q(-1)
+        elif not back and v<=r<2*v:expected[(r-v,())]=Q(1)
+        assert rows['L',r]==expected,('column mismatch',back,r)
+    assert prefix<2**192
+    return hist,{'all_exact_columns':n,'prefix_l1_upper':str(prefix),
+                 'prefix_bits_upper':prefix.numerator.bit_length()-prefix.denominator.bit_length()+1,
+                 'charged_payload_bits':192,'private_work_erased':True,'zero_buffers_returned_to_zero':len(zb),
+                 'warp_events':nwarp,'warp_columns_each_exact':1<<h,'warp_product_sha256':hashlib.sha256(json.dumps(warp_hashes).encode()).hexdigest()}
+
+t0=time.monotonic()
+profiles={};checks={}
+for name in ('forward','backward'):
+    profiles[name],checks[name]=local(ir['local_programs'][name],name=='backward')
+    assert dict(profiles[name])=={int(r):z for r,z in c['local_profile'].items()}
+    print('independent emitted replay PASS',name,flush=True)
+controls=[];reasons={}
+def ev_index(es,pred,start=0):return next(i for i in range(start,len(es)) if pred(es[i]))
+def phase_at(es,name):return es.index(['phase',name])
+def first_warp(es,sign=1,start=0):return ev_index(es,lambda e:e[0]=='warp' and (e[2]>0)==(sign>0),start)
+def cleanup_warp(es):return first_warp(es,-1,phase_at(es,'full_frame_cleanup'))
+def incomplete_centre_descent(es):
+    # Split paths lose an intermediate step. An unsplit path is truncated at
+    # an actual nested rank-one frame, with its child rank repriced correctly.
+    # Thus the control cannot fail merely because a split no longer exists.
+    indices=[i for i,e in enumerate(es) if e[0]=='center' and e[3]!=0]
+    if indices:
+        es.pop(indices[0]);return
+    e=next(e for e in es if e[0]=='center')
+    stop=next(f for f in range(len(frames)) if len(frames[f])==1 and contains(frames[f],frames[e[2]]))
+    e[3]=stop;e[4]=len(frames[e[2]])-1
+
+mutations=[
+    ('wrong_scale',lambda es:next(e for e in es if e[0]=='scalar' and e[1][0]=='scale')[1].__setitem__(2,3)),
+    ('missing_center',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='center'))),
+    ('wrong_common_frame',lambda es:next(e for e in es if e[0]=='scalar' and e[2]!=0).__setitem__(2,0)),
+    ('wrong_child_rank',lambda es:next(e for e in es if e[0]=='climb').__setitem__(5,99)),
+]+([
+    ('missing_pre_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre'))),
+    ('missing_post_wrapper',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post'))),
+    ('wrapper_with_wrong_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[2] in entering).__setitem__(3,0)),
+    ('wrapper_in_wrong_phase',lambda es:es.insert(es.index(['phase','A']),es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post')))),
+    ('wrapper_on_a_data_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,3)),
+    ('wrapper_on_a_target_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,v+3)),
+    ('wrapper_on_a_centre_register',lambda es:next(e for e in es if e[0]=='residual_adapter').__setitem__(2,['C',0])),
+] if entering else [])+([
+    ('centre_step_not_nested',lambda es:next(e for e in es if e[0]=='center').__setitem__(3,next(f for f in range(len(frames)) if not contains(frames[f],frames[next(e for e in es if e[0]=='center')[2]]) and not contains(frames[next(e for e in es if e[0]=='center')[2]],frames[f])))),
+    ('centre_descent_incomplete',incomplete_centre_descent),
+] if levels else [])+([
+    ('hpe_pre_wrapper_resolved_to_full_recipe',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and len(e)==5).pop()),
+    ('hpe_post_wrapper_without_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and len(e)==5).pop()),
+    ('hpe_post_wrapper_wrong_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and len(e)==5).__setitem__(4,1)),
+    ('hpe_tail_gate_at_full_frame',lambda es:next(e for e in es[es.index(['phase','cleanup_tail']):] if e[0]=='scalar').__setitem__(2,1)),
+    ('hpe_tail_climb_dropped',lambda es:es.pop(next(i for i in range(es.index(['phase','cleanup_tail']),len(es)) if es[i][0]=='climb'))),
+    ('hpe_helper_exit_adapter_to_full',lambda es:es.insert(es.index(['phase','full_frame_cleanup']),['adapter','new_to_old',min(hpe),1])),
+    ('hpe_tail_gate_moved_into_full_cleanup',lambda es:(lambda x:(x.__setitem__(2,1),es.insert(es.index(['phase','full_frame_cleanup'])+1,x)))(es.pop(next(i for i in range(es.index(['phase','cleanup_tail']),len(es)) if es[i][0]=='scalar')))),
+] if hpe else [])+([
+    ('cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter',lambda es:(lambda i:es.__setitem__(i,['adapter','old_to_new',cold[0],0]))(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]))),
+    ('cold_hpe_pre_wrapper_dropped',lambda es:es.pop(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]))),
+    ('cold_hpe_post_wrapper_replaced_by_exit_adapter',lambda es:(lambda i:es.__setitem__(i,['adapter','new_to_old',cold[0],c['final'][cold[0]]]))(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='post' and e[2]==cold[0]))),
+    ('cold_hpe_pre_wrapper_resolved_to_cold_full_convention',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]).pop()),
+    ('cold_hpe_wrapper_with_nonzero_entrance',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]).__setitem__(3,1)),
+    ('cold_hpe_post_wrapper_wrong_terminal_frame',lambda es:next(e for e in es if e[0]=='residual_adapter' and e[1]=='post' and e[2]==cold[0]).__setitem__(4,1)),
+    ('cold_hpe_premix_gate_before_pre_wrapper',lambda es:(lambda ev:es.insert(next(i for i,e in enumerate(es) if e[0]=='residual_adapter' and e[1]=='pre' and e[2]==cold[0]),ev))(es.pop(next(i for i,e in enumerate(es) if e[0]=='scalar' and (('L',cold[0]) in [tuple(e[1][1])]+([tuple(e[1][2])] if e[1][0] in ('add','copy') else []))))) ),
+] if cold else [])
+# BW: mutations of the warp / zero-buffer events (each must be rejected by the literal replay)
+if c.get('warps'):
+    def other_frame(es,i):   # a frame of the same dimension that is not the event's own to-frame
+        e=es[i];return next(f for f in range(len(frames)) if f not in (e[3],e[4]) and len(frames[f])==len(frames[e[4]]) and f!=0)
+    mutations+=[
+    ('warp_missing_inverse_at_full_cleanup',lambda es:es.pop(cleanup_warp(es))),
+    ('warp_missing_forward',lambda es:es.pop(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_frame_mismatch',lambda es:(lambda i:es[i].__setitem__(3,other_frame(es,i)))(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_to_frame_not_carried_by_G',lambda es:(lambda i:es[i].__setitem__(4,other_frame(es,i)))(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_wrong_sign',lambda es:(lambda i:es[i].__setitem__(2,-es[i][2]))(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_wrong_operator',lambda es:(lambda i:es[i].__setitem__(2,es[i][2]%len(c['warps'])+1))(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_inverse_moved_before_use',lambda es:es.insert(first_warp(es,1,phase_at(es,'B')),es.pop(cleanup_warp(es)))),
+    ('warp_inverse_wrong_frame',lambda es:es[cleanup_warp(es)].__setitem__(3,0)),
+    ('warp_rank_changing',lambda es:(lambda i:es[i].__setitem__(4,0))(first_warp(es,1,phase_at(es,'B')))),
+    ('warp_phase_B_dropped_gate_after_warp',lambda es:es.pop(ev_index(es,lambda e:e[0]=='scalar',first_warp(es,1,phase_at(es,'B'))))),
+    ]
+if zb:
+    mutations+=[
+    ('zero_buffer_not_freed',lambda es:es.pop(ev_index(es,lambda e:e[0]=='zero_buffer' and e[1]=='free'))),
+    ('zero_buffer_gate_outside_cleanup',lambda es:es.insert(phase_at(es,'full_frame_cleanup')-1,['scalar',['add',['Z',zb[0]],['L',0],1,1],1])),
+    ('zero_buffer_garbage_left',lambda es:es.pop(ev_index(es,lambda e:e[0]=='scalar' and e[1][0]=='add' and e[1][1]==['Z',zb[0]] ,phase_at(es,'full_frame_cleanup')))),
+    ]
+def mutate_gate_to_L(es):
+    i=ev_index(es,lambda e:e[0]=='scalar' and ['Z',zb[0]] in [e[1][1]]+([e[1][2]] if e[1][0]=='add' else []),phase_at(es,'full_frame_cleanup'))
+    g=es[i][1];es[i][1]=[g[0]]+[(['L',zb[0]] if x==['Z',zb[0]] else x) for x in g[1:3]]+list(g[3:])
+if zb:
+    mutations.append(('zero_buffer_replaced_by_restored_register_at_full',mutate_gate_to_L))
+for name,mut in mutations:
+    es=copy.deepcopy(ir['local_programs']['forward']);mut(es)   # a mutation that cannot be built is an error, not a rejection
+    try:local(es,False)
+    except (AssertionError,KeyError) as exc:controls.append(name);reasons[name]=repr(exc.args)[:160]
+    else:raise AssertionError('mutation accepted: '+name)
+# BW: table / operator tampering of the warps themselves
+def tampered(name,table_fn,qmut=None):
+    t=copy.deepcopy(c['warps']);table_fn(t)
+    try:local(ir['local_programs']['forward'],False,table=t,qmut=qmut)
+    except (AssertionError,KeyError) as exc:controls.append(name);reasons[name]=repr(exc.args)[:160]
+    else:raise AssertionError('tampered warp operator accepted: '+name)
+if c.get('warps'):
+    def wrongG(t):
+        U=frames[t[0]['from_frame']];E=frames[t[0]['to_frame']]
+        G=list(t[0]['G_columns']);outside=next(x for x in range(1,1<<h) if x not in span(U))
+        # replace a column so that G is still invertible but a frame vector no longer lands in the to frame
+        for i in range(h):
+            for j in range(h):
+                if i!=j:
+                    G2=list(G);G2[i]^=G2[j]
+                    if f2rank(G2)==h and sorted(lin(G2,x) for x in span(U))!=sorted(span(E)):t[0]['G_columns']=G2;return
+        raise AssertionError('no column tamper found')
+    tampered('warp_wrong_G_invertible_not_carrying_frame',wrongG)
+    tampered('warp_noninvertible_G',lambda t:t[0]['G_columns'].__setitem__(1,t[0]['G_columns'][0]))
+    tampered('warp_zero_column_G',lambda t:t[0]['G_columns'].__setitem__(0,0))
+    tampered('warp_operator_dropped_from_table',lambda t:t.pop(0))
+    tampered('warp_wrong_quadratic_phase_of_K',lambda t:None,qmut=(0,2))
+result={'status':'PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY',   # lineage label kept: the warp replay below is a strict superset
+'warp_replay':{'status':'PASS_EXACT_MONOMIAL_WARP_COLUMNS_ALL_512_BOTH_ORIENTATIONS','warps':len(c.get('warps',[])),'event_classes_checked_on_all_512_columns':len(WARPCACHE),'zero_buffers':len(zb)},
+'canonical_word_sha256':hashlib.sha256((OUT/'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+'local_programs_sha256':hashlib.sha256((OUT/'LOCAL-PROGRAMS.json.gz').read_bytes()).hexdigest(),
+'v':v,'helpers':R,'local':checks,'paid_profiles':{name:dict(H) for name,H in profiles.items()},
+'entering_helpers':len(entering),**({'cold_hyperplane_ended_helpers':len(cold)} if cold else {}),
+'negative_controls_rejected':controls,'negative_control_reasons':reasons,
+'scope':'Literal forward and inverse-transpose replay on every arbitrary data/helper column in the free warp operator algebra, physical frame incidence, ordered paid wrappers, every warp product checked exactly on all 512 columns incl. scalar phases, cleared private work and zero buffers, prefix coefficients. Global hosting and outer exponent are separate.'}
+(OUT/'INDEPENDENT-LOCAL-REPLAY.json').write_text(json.dumps(result,indent=2)+'\n')
+print(result['status'],result['warp_replay']['status'],len(controls),'controls rejected',flush=True)
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_check_recipes.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_check_recipes.py
new file mode 100644
index 0000000000..6db8ad50eb
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_check_recipes.py
@@ -0,0 +1,81 @@
+"""Independent recheck of the emitted warp recipes against the emitted programs (numpy only, no clifford_exact).
+
+Every warp event class (sign, operator, from frame, to frame) used by LOCAL-PROGRAMS in either orientation must have a recipe in
+CLIFFORD-RECIPES.json whose serialized monomial equals, on all 512 columns exactly (global phase included), the product
+T_to K_G^{+-1} T_from^-1 recomputed here from the canonical word's G and frames (port of PR2226's operators.py).  The logical
+K_G recipe of RESIDUAL-ADAPTERS.json must equal the exact K_G.  Mutated recipes (phase, translation, quadratic form, wrong G,
+inverse used for the forward warp, a missing class, swapped frames) must all be rejected.  usage: bw_check_recipes.py OUT_DIR
+"""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import copy,gzip,hashlib,json,sys,time
+from pathlib import Path
+import numpy as np
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import bw_gauss as g
+OUT=Path(sys.argv[1]);t0=time.monotonic()
+c=json.load(gzip.open(OUT/'CANONICAL-WORD.json.gz'));h=c['h'];frames=c['frames']
+progs=json.load(gzip.open(OUT/'LOCAL-PROGRAMS.json.gz'))
+rec_all=json.loads((OUT/'CLIFFORD-RECIPES.json').read_text())
+res_all=json.loads((OUT/'RESIDUAL-ADAPTERS.json').read_text())
+G_of={w['op']:w['G_columns'] for w in c.get('warps',[])}
+used=set()
+for orientation in ('forward','backward'):
+    for e in progs[orientation]:
+        if e[0]=='warp':used.add((1 if e[2]>0 else -1,abs(e[2]),e[3],e[4]))
+assert used==set(map(tuple,c.get('warp_edges',[]))),'emitted warp classes differ from the word'
+by={(w['sign'],w['op'],w['old'],w['new']):w for w in rec_all.get('warps',[])}
+assert set(by)==used,('recipe classes differ from the emitted warp classes',len(set(by)^used))
+def numeric_K(G):
+    pv,ph=g.monomial(list(G),h);N=1<<h;re=np.zeros((N,N),dtype=np.int64);im=np.zeros((N,N),dtype=np.int64)
+    unit=[(1,0),(0,1),(-1,0),(0,-1)]
+    for x in range(N):re[pv[x],x],im[pv[x],x]=unit[ph[x]]
+    return re,im,0
+def product_ok(sign,op,f0,f1,left,G=None):
+    G=G_of[op] if G is None else G
+    if left is None:return False
+    try:Z=g.warp_product(G,frames[f0],frames[f1],sign*op,h)
+    except AssertionError:return False
+    return g.equal_scaled(Z,g.recipe_matrix(left,h))
+def logical_ok(op,rec,G=None):
+    G=G_of[op] if G is None else G
+    return g.equal_scaled(numeric_K(G),g.recipe_matrix(rec,h))
+for key,w in sorted(by.items()):
+    sign,op,f0,f1=key
+    assert w['rank']==0 and w['right'] is None and w['G_columns']==G_of[op],key
+    assert product_ok(sign,op,f0,f1,w['left']),('warp recipe is not the exact column product',key)
+for w in c.get('warps',[]):
+    r=res_all['warps'][str(w['op'])]
+    assert r['G_columns']==w['G_columns'] and (r['from_frame'],r['to_frame'])==(w['from_frame'],w['to_frame'])
+    assert logical_ok(w['op'],r['K']),('logical K_G recipe is not exact',w['op'])
+controls=[]
+def reject(name,ok):
+    if ok:raise AssertionError('mutation accepted: '+name)
+    controls.append(name)
+if by:
+    key=next(k for k in sorted(by) if k[0]>0 and k[2]!=k[3]);w=by[key];sign,op,f0,f1=key;left=w['left'];Gx=G_of[op]
+    reject('recipe: wrong global phase',product_ok(*key,dict(left,phase=(left['phase']+1)%4)))
+    reject('recipe: wrong translation',product_ok(*key,dict(left,offset=left['offset']^1)))
+    reject('recipe: wrong linear phase',product_ok(*key,dict(left,linear_Z4=[(left['linear_Z4'][0]+2)%4]+left['linear_Z4'][1:])))
+    reject('recipe: wrong quadratic form',product_ok(*key,dict(left,quadratic_rows=[left['quadratic_rows'][0]^2,left['quadratic_rows'][1]^1]+left['quadratic_rows'][2:])))
+    reject('recipe: wrong matrix',product_ok(*key,dict(left,matrix_rows=[left['matrix_rows'][1],left['matrix_rows'][0]]+left['matrix_rows'][2:])))
+    G2=list(Gx);G2[0]^=G2[1]
+    reject('recipe: wrong G (still invertible)',product_ok(*key,left,G=G2))
+    sing=list(Gx);sing[1]=sing[0]
+    reject('recipe: non-invertible G',product_ok(*key,left,G=sing))
+    reject('recipe: inverse warp recipe used for the forward warp',product_ok(sign,op,f0,f1,next(x for k,x in by.items() if k[0]==-sign and k[1]==op)['left']) if any(k[0]==-sign and k[1]==op for k in by) else False)
+    # frame mismatch: the recipe of this class used for a class with another frame
+    other=next((k for k in by if k!=key and k[0]==sign and k[1]!=op),None)
+    reject('recipe: recipe of another warp class',product_ok(*key,by[other]['left']) if other else False)
+    reject('recipe: swapped from/to frames',product_ok(sign,op,f1,f0,left))
+    # a class missing from the recipe file
+    try:
+        miss=copy.copy(by);miss.pop(key);assert set(miss)==used
+    except AssertionError:controls.append('recipe: missing warp class')
+    else:raise AssertionError('missing class accepted')
+    reject('logical: wrong G',logical_ok(op,res_all['warps'][str(op)]['K'],G=G2))
+    reject('logical: wrong phase',logical_ok(op,dict(res_all['warps'][str(op)]['K'],phase=(res_all['warps'][str(op)]['K']['phase']+1)%4)))
+out=dict(status='PASS_WARP_RECIPES_EXACT_ON_ALL_512_COLUMNS',canonical_word_sha256=hashlib.sha256((OUT/'CANONICAL-WORD.json.gz').read_bytes()).hexdigest(),
+  recipe_sha256=hashlib.sha256((OUT/'CLIFFORD-RECIPES.json').read_bytes()).hexdigest(),warp_classes=len(by),operators=len(c.get('warps',[])),
+  columns_each=1<<h,controls_rejected=controls)
+(OUT/'WARP-RECIPE-CHECKS.json').write_text(json.dumps(out,indent=2)+'\n');print(out['status'],len(by),'classes',len(controls),'controls rejected',flush=True)
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_emit.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_emit.py
new file mode 100644
index 0000000000..6d47f63ab7
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_emit.py
@@ -0,0 +1,192 @@
+# Warp-aware copy of hpe_emit_local.py (GK / PR #433 lineage: icekylinx with Codex assistance; DreamingOfClouds with Claude Opus 5.5).
+# BW: every change for anticipatory dirty borrowing (PR2226, Cinna Davis @1337isnot1337, with OpenAI Codex assistance) is marked "BW:".
+# On a word without warps / zero buffers / twisted additions the behaviour equals hpe_emit_local.py.
+"""Emit both local programs of a BORROW canonical word: scalar macros, climbs, centres, wrappers, monomial warps, zero buffers.
+
+A warp event ['warp', r, op, f0, f1] is the rank-zero logical reference change K_G^{+-1} of register r moving it from
+frame f0 to frame f1 (G(f0) = f1 for op > 0, G^-1(f0) = f1 for op < 0).  The same event stream serves both orientations:
+the inverse-transpose of a monomial K_G is the monomial conj(K_G) (same permutation, conjugated phases), a different
+formal symbol of the free operator algebra, and the exact column check of the physical product is run for both.
+"""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import sys as _sys, os as _os; _sys.path.insert(0, _os.path.dirname(_os.path.abspath(__file__)))
+import gzip,hashlib,json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+OUT=Path(_sys.argv[1]);cp=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(cp))
+frames=c['frames'];v,R,h=c['v'],c['R'],c['h'];n=2*v+R
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+def basis(vs):
+    b={}
+    for x in vs:
+        for p in sorted(b,reverse=True):
+            if x>>p&1:x^=b[p]
+        if x:
+            p=x.bit_length()-1
+            for q in b:
+                if b[q]>>p&1:b[q]^=x
+            b[p]=x
+    return tuple(b[p] for p in sorted(b,reverse=True))
+def reg(x):return list(x) if isinstance(x,list) else ['L',x]   # BW: ['Z', c] is a private zero buffer
+def dual(e):
+    e=list(e)
+    if e[0]=='add':e[1],e[2]=e[2],e[1];e[3]*=-1
+    else:e[2],e[3]=e[3],e[2]
+    return e
+def scalar(e,back):
+    e=dual(e) if back else list(e)
+    if e[0]=='add':return ['add',reg(e[1]),reg(e[2]),e[3],e[4]]
+    return ['scale',reg(e[1]),e[2],e[3]]
+def primitive_bound(e):
+    if e[0] in ('clear','copy'):return 1
+    q=Q(e[3],e[4]) if e[0]=='add' else Q(e[2],e[3])
+    a,b=abs(q.numerator),q.denominator
+    assert b&(b-1)==0
+    if e[0]=='scale':
+        assert a&(a-1)==0
+        return abs(a.bit_length()-b.bit_length())+int(q<0)
+    return 3+(a.bit_length()-1)+a.bit_count()+(b.bit_length()-1)
+def lregs(e):return [r for r in ([e[1]]+([e[2]] if e[0]=='add' else [])) if not isinstance(r,list)]
+
+def expand(e):
+    """BW: a twisted addition t += c*W(s) at frame zero: warp s by W, add, unwarp (all rank zero at frame 0)."""
+    if e[0]!='tadd':return [e]
+    _,t,s,word,a,b,f=e
+    return [['warp',s,op,0,0] for op in reversed(word)]+[['add',t,s,a,b,0]]+[['warp',s,-op,0,0] for op in word]
+
+def emit(back):
+    out=[];cur=c['start'].copy()
+    def event(e):out.append(e)
+    def scal(e,f):event(['scalar',e,f])
+    def warp(e):
+        _,r,op,f0,f1=e
+        if isinstance(r,list):assert r[0]=='Z' and f0==f1==1
+        else:
+            assert cur[r]==f0,('warp frame mismatch',r,cur[r],f0);cur[r]=f1
+        event(['warp',reg(r),op,f0,f1])
+    event(['phase','zero_frame_precondition'])
+    for e0 in c['precondition']+c['compensation']:
+        for e in expand(e0):
+            if e[0]=='warp':warp(e);continue
+            regs=lregs(e)
+            assert all(c['start'][r]==0 for r in regs)
+            scal(scalar(e,back),0)
+    event(['phase','entry_adapters'])
+    entering=[r for r,f in enumerate(c['start']) if r>=2*v and f!=0]
+    hpe={r for r in range(2*v,n) if c['final'][r]!=1}
+    wrapped=sorted(set(entering)|hpe)
+    for r,f in enumerate(c['start']):
+        if r in wrapped:event(['residual_adapter','pre',r,f]+([c['final'][r]] if c['final'][r]!=1 else []))
+        else:event(['adapter','old_to_new',r,f])
+    def climb(r,f,part):
+        old=cur[r]
+        if old==f:return
+        assert basis(frames[old]+frames[f])==tuple(frames[f])
+        rank=len(frames[f])-len(frames[old]);assert rank>0
+        event(['climb',part,r,old,f,rank]);cur[r]=f
+    for part in ('A','centers','B')+(('cleanup_tail',) if c.get('tail') else ())+('final',):
+        event(['phase',part])
+        if part in ('A','B','cleanup_tail'):
+            for e in (c['tail'] if part=='cleanup_tail' else c[part]):
+                if e[0]=='warp':warp(e);continue    # BW: monomial reference change, no climb
+                for r in lregs(e):climb(r,e[-1],part)
+                scal(scalar(e,back),e[-1])
+        elif part=='centers':
+            lv=lambda r:c.get('target_levels',{}).get(str(r-v),0)
+            assert all(cur[r]==lv(r) for r in range(v,2*v))
+            for k,r in enumerate(c['centers']):
+                cf=c['center_frames'][k];assert cur[r]==cf
+                terms=[e for e in c['cut'] if e[2]==r]
+                path=[cf]+sorted({lv(e[1]) for e in terms}-{cf},key=lambda x:-len(frames[x]))
+                C=['C',k]
+                if not back:
+                    scal(['clear',C],cf);scal(['copy',C,['L',r]],cf)
+                    for a in range(len(path)):
+                        if a>0:event(['center',k,path[a-1],path[a],len(frames[path[a-1]])-len(frames[path[a]])])
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',['L',e[1]],C,e[3],e[4]],path[a])
+                    scal(['clear',C],path[-1])
+                else:
+                    scal(['clear',C],path[-1])
+                    for a in range(len(path)-1,-1,-1):
+                        for e in terms:
+                            if lv(e[1])==path[a]:scal(['add',C,['L',e[1]],e[3],e[4]],path[a])
+                        if a>0:event(['center',k,path[a],path[a-1],len(frames[path[a-1]])-len(frames[path[a]])])
+                    scal(['add',['L',r],C,-1,1],cf);scal(['clear',C],cf)
+        else:
+            for r,f in enumerate(c['final']):climb(r,f,part)
+    event(['phase','exit_adapters'])
+    for r,f in enumerate(c['final']):
+        if r not in hpe:event(['adapter','new_to_old',r,f])
+    event(['phase','full_frame_cleanup'])
+    zb=c.get('zero_buffers',[])
+    for z in zb:event(['zero_buffer','alloc',z])             # BW: private FULL-frame zero buffers stand in for the restored (hyperplane-ended) helpers
+    for e in c['cleanup']:
+        if e[0]=='warp':warp(e);continue
+        regs=lregs(e)
+        assert all(c['final'][r]==1 for r in regs)
+        assert all(r[0]=='Z' and r[1] in zb for r in [e[1]]+([e[2]] if e[0]=='add' else []) if isinstance(r,list))
+        scal(scalar(e,back),1)
+    for z in zb:event(['zero_buffer','free',z])
+    for r in wrapped:event(['residual_adapter','post',r,c['start'][r]]+([c['final'][r]] if r in hpe else []))
+    event(['phase','done'])
+    return out
+
+def add_row(dst,src,q):
+    for j,x in src.items():
+        z=dst.get(j,Q(0))+q*x
+        if z:dst[j]=z
+        else:dst.pop(j,None)
+def warp_row(row,op):
+    out={}
+    for (var,word),x in row.items():
+        word=word[1:] if word and word[0]==-op else (op,)+word
+        out[var,word]=x
+    return out
+
+def check_local(events,back):
+    # BW: literal scalar replay of the emitted stream in the free warp algebra (rows over (register, warp word)), centres and zero buffers.
+    state={('L',r):{(r,()):Q(1)} for r in range(n)};live=[];paid=Counter();prims=0;macros=0;zlive=set();nwarp=0
+    for e in events:
+        if e[0]=='climb':assert not live;paid[e[5]]+=1
+        elif e[0]=='center':assert live==[e[1]];paid[e[4]]+=1
+        elif e[0]=='zero_buffer':
+            z=e[2]
+            if e[1]=='alloc':assert z not in zlive;zlive.add(z);state['Z',z]={}
+            else:assert not state['Z',z] and z in zlive;zlive.remove(z)
+        elif e[0]=='warp':
+            t=tuple(e[1]);nwarp+=1;state[t]=warp_row(state[t],e[2])
+        elif e[0]=='scalar':
+            op=e[1];tag=op[0];t=tuple(op[1]);macros+=1;prims+=2*primitive_bound(op)
+            if tag=='clear':
+                state[t]={}
+                if t[0]=='C' and t[1] in live:live.remove(t[1])
+            elif tag=='copy':state[t]={(var,w):x for (var,w),x in state.get(tuple(op[2]),{}).items()};live.append(t[1])
+            elif tag=='scale':state[t]={j:Q(op[2],op[3])*x for j,x in state[t].items()}
+            else:
+                s=tuple(op[2]);q=Q(op[3],op[4]);row=state.setdefault(t,{})
+                if t[0]=='C' and t[1] not in live:live.append(t[1])
+                add_row(row,state.get(s,{}),q)
+    assert not live and not zlive and all(not row for r,row in state.items() if r[0] in 'CZ')
+    for r in range(n):
+        expected={(r,()):Q(1)}
+        if back and r<v:expected[(v+r,())]=Q(-1)
+        elif not back and v<=r<2*v:expected[(r-v,())]=Q(1)
+        assert state['L',r]==expected,('emitted column mismatch',back,r)
+    assert dict(paid)=={int(r):z for r,z in c['local_profile'].items()}
+    return {'sha256':digest(events),'events':len(events),'scalar_macros':macros,'warp_events':nwarp,
+            'real_component_primitive_bound':prims,'paid_profile':dict(sorted(paid.items())),
+            'all_columns':n,'private_centers_cleared':True,'private_coefficient_stream_cleared_after_each_macro':True,
+            'zero_buffers_returned_to_zero':len(c.get('zero_buffers',[]))}
+
+programs={};checks={}
+for name,back in [('forward',False),('backward',True)]:
+    programs[name]=emit(back);checks[name]=check_local(programs[name],back)
+    print('PASS emitted',name,checks[name]['events'],'events',flush=True)
+
+(OUT/'LOCAL-PROGRAMS.json.gz').write_bytes(gzip.compress(json.dumps(programs,sort_keys=True,separators=(',',':')).encode(),mtime=0))
+(OUT/'LOCAL-CHECKS.json').write_text(json.dumps(checks,indent=2)+'\n')
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_gauss.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_gauss.py
new file mode 100644
index 0000000000..1ff29dfb24
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_gauss.py
@@ -0,0 +1,114 @@
+"""Exact Gaussian column products of monomial warps (numpy only).
+
+Port of PR2226's operators.py (Cinna Davis, @1337isnot1337, with OpenAI Codex assistance; Apache-2.0): change / monomial /
+apply_mono / coord / frame / check.  Shares no code with the clifford_exact phase compiler or the emitter.  Matrices are
+(re, im, exp) with entries (re + i im) / 2^exp-scaled: a product of frames and warps is *exact* when every row and column has
+one support entry of magnitude exactly 2^exp.
+"""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import hashlib
+import numpy as np
+def lin(cols,x):
+    out=0
+    for i,col in enumerate(cols):
+        if x>>i&1:out^=col
+    return out
+def f2rank(xs):
+    b={}
+    for x in xs:
+        while x:
+            i=x.bit_length()
+            if i not in b:b[i]=x;break
+            x^=b[i]
+    return len(b)
+def extend(xs,hh):
+    out=list(xs)
+    for i in range(hh):
+        if f2rank(out+[1<<i])>len(out):out.append(1<<i)
+    assert len(out)==hh
+    return out
+def f2inverse(cols,hh):
+    perm=[lin(cols,x) for x in range(1<<hh)];back=[0]*len(perm)
+    assert len(set(perm))==len(perm),'non-invertible G'
+    for i,j in enumerate(perm):back[j]=i
+    return [back[1<<i] for i in range(hh)]
+def change(source,target,hh):
+    a=extend(source,hh);b=extend(target,hh);ai=f2inverse(a,hh)
+    return [lin(b,x) for x in ai]
+def monomial(cols,hh,qmut=None):
+    gi=f2inverse(cols,hh)
+    git=[sum(((gi[j]>>i)&1)<<j for j in range(hh)) for i in range(hh)]
+    M=[(1<<j)^lin(git,gi[j]) for j in range(hh)]
+    if qmut:M[qmut[0]]^=qmut[1]; M[qmut[1].bit_length()-1]^=1<<qmut[0]   # BW control hook: a wrong (still symmetric) quadratic form
+    assert all((M[j]>>i&1)==(M[i]>>j&1) for i in range(hh) for j in range(hh))
+    permv=np.array([lin(cols,x) for x in range(1<<hh)],dtype=np.int64)
+    phase=np.array([sum(((M[i]>>i)&1)*(x>>i&1) for i in range(hh))+
+       2*sum(((M[j]>>i)&1)*(x>>i&1)*(x>>j&1) for i in range(hh) for j in range(i+1,hh))
+       for x in permv],dtype=np.int64)%4
+    return permv,phase
+def apply_mono(z,recipe,sign=1):
+    re,im,exp=z;perm,phase=recipe;rr=np.empty_like(re);ii=np.empty_like(im)
+    if sign==1:
+        for p in range(4):
+            mask=phase==p;r=re[mask];i=im[mask]
+            if p==0:a,b=r,i
+            elif p==1:a,b=-i,r
+            elif p==2:a,b=-r,-i
+            else:a,b=i,-r
+            rr[perm[mask]]=a;ii[perm[mask]]=b
+    else:
+        r=re[perm];i=im[perm]
+        for p in range(4):
+            mask=phase==p
+            if p==0:a,b=r[mask],i[mask]
+            elif p==1:a,b=i[mask],-r[mask]
+            elif p==2:a,b=-r[mask],-i[mask]
+            else:a,b=-i[mask],r[mask]
+            rr[mask]=a;ii[mask]=b
+    return rr,ii,exp
+def coord(z,axes,sign=1):
+    re,im,exp=z
+    for j in axes:
+        p=np.array([x for x in range(len(re)) if not(x>>j&1)]);q=p^(1<<j)
+        a,b,cc,d=re[p].copy(),im[p].copy(),re[q].copy(),im[q].copy()
+        if sign==1:
+            re[p]=a-b+cc+d;im[p]=a+b+d-cc
+            re[q]=a+b+cc-d;im[q]=b-a+cc+d
+        else:
+            re[p]=a+b+cc-d;im[p]=b-a+cc+d
+            re[q]=a-b+cc+d;im[q]=a+b+d-cc
+        exp+=1
+    return re,im,exp
+def span(b):
+    s={0}
+    for x in b:s|={t^x for t in s}
+    return s
+def frame(z,bas,hh,sign=1):
+    G=change([1<<i for i in range(len(bas))],bas,hh);K=monomial(G,hh)
+    return apply_mono(coord(apply_mono(z,K,-1),range(len(bas)),sign),K,1)
+def check_mono(z):
+    re,im,exp=z;support=(re!=0)|(im!=0)
+    assert np.all(support.sum(axis=0)==1) and np.all(support.sum(axis=1)==1),'not a monomial matrix'
+    rr=re[support];ii=im[support];unit=1<<exp
+    assert np.all(((np.abs(rr)==unit)&(ii==0))|((rr==0)&(np.abs(ii)==unit))),'entries are not unit Gaussian phases'
+    return hashlib.sha256(re.astype('<i8',copy=False).tobytes()+im.astype('<i8',copy=False).tobytes()+str(exp).encode()).hexdigest()
+def eye(hh):return (np.eye(1<<hh,dtype=np.int64),np.zeros((1<<hh,1<<hh),dtype=np.int64),0)
+def warp_product(G,U,E,op,hh,qmut=None):
+    """Z = T_E K_G^{+-1} T_U^{-1} as an exact Gaussian matrix (apply T_U^{-1} first), for a warp of sign(op) from frame U to frame E."""
+    K=monomial(G,hh,qmut)
+    z=frame(eye(hh),U,hh,-1);z=apply_mono(z,K,1 if op>0 else -1);return frame(z,E,hh,1)
+def recipe_matrix(rec,hh):
+    """Dense exact matrix (re, im, exp=0) of a serialized clifford_exact monomial (matrix_rows, quadratic_rows, linear_Z4, offset, phase):
+    |x> -> i^(qvalue(x)+phase) |G x ^ offset>,  qvalue = sum alpha_i x_i + 2 sum_{i in x} parity((Q_i >> (i+1)) & (x >> (i+1)))."""
+    N=1<<hh;re=np.zeros((N,N),dtype=np.int64);im=np.zeros((N,N),dtype=np.int64)
+    rows,Q,alpha,b,ph=rec['matrix_rows'],rec['quadratic_rows'],rec['linear_Z4'],rec['offset'],rec['phase']
+    unit=[(1,0),(0,1),(-1,0),(0,-1)]
+    for x in range(N):
+        y=sum(((rows[i]&x).bit_count()&1)<<i for i in range(hh))^b
+        q=(sum(alpha[i] for i in range(hh) if x>>i&1)+2*sum(((Q[i]>>(i+1))&(x>>(i+1))).bit_count()&1 for i in range(hh) if x>>i&1)+ph)%4
+        re[y,x],im[y,x]=unit[q]
+    return re,im,0
+def equal_scaled(z,m):
+    """z (scaled by 2^exp) equals m (exp 0) entrywise exactly"""
+    re,im,exp=z;return bool(np.array_equal(re,m[0]<<exp) and np.array_equal(im,m[1]<<exp))
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_phases.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_phases.py
new file mode 100644
index 0000000000..99f351785e
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_phases.py
@@ -0,0 +1,59 @@
+# Warp-aware copy of phases_full.py (PR425 / icekylinx with Codex assistance, heterogeneous centres).
+# BW: exact lowering of every anticipatory-dirty-borrowing warp (PR2226, Cinna Davis @1337isnot1337, with OpenAI Codex assistance):
+# each distinct physical warp product T_to K_G^{+-1} T_from^-1 is lowered with the unchanged lower_child and must have rank ZERO
+# (a monomial Clifford); its serialized monomial is then compared with an independent exact numpy column product on all 512 columns.
+"""Exact phase-aware lowering of every used edge of a BORROW canonical word, warps included.  usage: bw_phases.py OUT_DIR"""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import gzip,hashlib,json,sys,time
+from collections import Counter
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE/'vendor/clifford'));sys.path.insert(0,str(HERE))
+from clifford_exact import *
+import bw_gauss
+from bw_adapters import Kop
+
+OUT=Path(sys.argv[1]);P=OUT/'CANONICAL-WORD.json.gz'
+c=json.load(gzip.open(P));n=c['h'];frames=c['frames'];start=time.monotonic();ops=[]
+for U in frames:
+    op=canonical_frame(n,U)
+    L=[u|(u<<n) for u in U]+[v<<n for v in nullspace(U,n)]
+    pre=[x|(z<<n) for x,z,p in inverse(op.tab)[n:]]
+    assert rank(L)==n and rank(L+pre)==n
+    assert rank([x for x,z,p in op.tab[n:]])==len(U)
+    ops.append(op)
+edges=set(map(tuple,c['edges']))|{(a,b) for f in c['center_frames'] for a,b in ((f,0),(0,f))};recipes=[];hist=Counter()
+for i,(a,b) in enumerate(sorted(edges)):
+    op=ops[a].adjoint().then(ops[b]);rec,compiled=lower_child(op)
+    assert rec['rank']==abs(len(frames[a])-len(frames[b]))
+    hist[rec['rank']]+=1;recipes.append({'old':a,'new':b,**rec})
+    if i%200==0:print('exact phase edges',i,'/',len(edges),'seconds',time.monotonic()-start,flush=True)
+adapters=[];F=fourier(n)
+for i,q in enumerate(c['ports']):
+    for role,old,f in [('source',cgate(n,q),c['start'][i]),
+                       ('target',cgate(n,q).adjoint().then(F),c['final'][c['v']+i])]:
+        rec,compiled=lower_child(old.adjoint().then(ops[f]));assert rec['rank']==0
+        adapters.append({'port':i,'role':role,'frame':f,**rec})
+# BW: warps.  Edge classes are (sign, operator, from frame, to frame); the physical product is T_to K^{+-1} T_from^-1.
+G_of={w['op']:w['G_columns'] for w in c.get('warps',[])}
+warps=[]
+for sign,op_id,f0,f1 in sorted(map(tuple,c.get('warp_edges',[]))):
+    G=G_of[op_id];K=Kop(G);Ks=K if sign>0 else K.adjoint()
+    op=ops[f0].adjoint().then(Ks).then(ops[f1]);rec,compiled=lower_child(op)
+    assert rec['rank']==0 and rec['right'] is None,('warp is not a monomial Clifford',sign,op_id,f0,f1)
+    Z=bw_gauss.warp_product(G,frames[f0],frames[f1],sign*op_id,n)
+    assert bw_gauss.equal_scaled(Z,bw_gauss.recipe_matrix(rec['left'],n)),('recipe differs from the exact column product',sign,op_id,f0,f1)
+    hist['warp']+=1;warps.append({'sign':sign,'op':op_id,'old':f0,'new':f1,'G_columns':G,**rec})
+raw=json.dumps({'children':recipes,'endpoint_adapters':adapters,'warps':warps},sort_keys=True,separators=(',',':')).encode()
+(OUT/'CLIFFORD-RECIPES.json').write_bytes(raw)
+result={'status':'PASS_NEW_WORD_EXACT_LOCAL_PHASE_RECIPES',
+        'canonical_word_sha256':hashlib.sha256(P.read_bytes()).hexdigest(),
+        'frames':len(frames),'directed_edges':len(edges),'ranks':{str(k):x for k,x in hist.items()},
+        'endpoint_adapters':len(adapters),'warp_recipes':len(warps),'warp_recipes_rank_zero':all(w['rank']==0 for w in warps),
+        'warp_recipes_equal_exact_512_column_product':True,
+        'all_child_equalities_include_global_phase':True,
+        'recipe_sha256':hashlib.sha256(raw).hexdigest(),'seconds':time.monotonic()-start,
+        'scope':'Every local frame, centre transition and warp. Expanded scalar-interface integration and global emitted program are separate obligations.'}
+(OUT/'CLIFFORD-REVIEW.json').write_text(json.dumps(result,indent=2)+'\n')
+print('PASS exact local phases',result['seconds'],'seconds',flush=True)
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_tamper.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_tamper.py
new file mode 100644
index 0000000000..a519863fd8
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_tamper.py
@@ -0,0 +1,58 @@
+"""Tamper controls of the native borrow chain.  Every tampered BORROW-WORD / emitted artifact must be REJECTED by the chain.
+usage: bw_tamper.py BORROW-WORD.json.gz NATIVE_LOCAL_DIR WORK_DIR [--files]   (--files also reruns the heavier file-level stages)"""
+import copy,gzip,json,os,shutil,subprocess,sys,time
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+word_path=Path(sys.argv[1]).resolve();local=Path(sys.argv[2]).resolve();work=Path(sys.argv[3]).resolve();work.mkdir(parents=True,exist_ok=True)
+flags=(0x00000040|0x08000000) if os.name=='nt' and os.environ.get('BW_IDLE','1')=='1' else 0
+def run(script,*args):
+    p=subprocess.run([sys.executable,'-B',str(HERE/script),*map(str,args)],stdout=subprocess.PIPE,stderr=subprocess.STDOUT,cwd=HERE,creationflags=flags)
+    return p.returncode,p.stdout.decode(errors='replace')
+W=json.loads(gzip.decompress(word_path.read_bytes()))
+results=[];t0=time.monotonic()
+def word_tamper(name,fn,expect):
+    w=copy.deepcopy(W);fn(w);p=work/(name+'.json.gz');p.write_bytes(gzip.compress(json.dumps(w).encode()))
+    out=work/('out-'+name)
+    if out.exists():shutil.rmtree(out)
+    rc,log=run('bw_transport.py',p,out)
+    ok=rc!=0 and expect in log
+    results.append(dict(name=name,rejected=rc!=0,expected_reason=expect,reason_matches=expect in log,last_line=log.strip().splitlines()[-1][:200] if log.strip() else ''))
+    assert ok,(name,rc,log[-600:])
+def sw(g,i,j):g[i],g[j]=g[j],g[i]
+first_cleanup_warp=lambda w:next(i for i,e in enumerate(w['cleanup']) if e[0]=='warp')
+word_tamper('wrong_G_not_carrying_frame',lambda w:w['warps'][0].__setitem__(2,[w['warps'][0][2][0]^w['warps'][0][2][1]]+w['warps'][0][2][1:]),'G does not map the from frame onto the to frame')
+word_tamper('non_invertible_G',lambda w:w['warps'][0][2].__setitem__(1,w['warps'][0][2][0]),'non-invertible G')
+word_tamper('missing_inverse_warp_in_cleanup',lambda w:w['cleanup'].pop(first_cleanup_warp(w)),'arbitrary-input endpoint')
+word_tamper('missing_forward_warp',lambda w:w['warps'].pop(0),'')
+word_tamper('frame_mismatch_from_basis',lambda w:w['warps'][0].__setitem__(3,next(x[3] for x in w['warps'] if sorted(x[3])!=sorted(w['warps'][0][3]) and len(x[3])==len(w['warps'][0][3]))),'')
+word_tamper('inverse_warp_sign_flipped',lambda w:w['cleanup'].__setitem__(first_cleanup_warp(w),['warp',w['cleanup'][first_cleanup_warp(w)][1],abs(w['cleanup'][first_cleanup_warp(w)][2]),w['cleanup'][first_cleanup_warp(w)][3]]),'arbitrary-input endpoint')
+word_tamper('inverse_warp_wrong_operator',lambda w:w['cleanup'].__setitem__(first_cleanup_warp(w),['warp',w['cleanup'][first_cleanup_warp(w)][1],-(abs(w['cleanup'][first_cleanup_warp(w)][2])%len(w['warps'])+1),w['cleanup'][first_cleanup_warp(w)][3]]),'arbitrary-input endpoint')
+word_tamper('inverse_warp_on_wrong_register',lambda w:w['cleanup'].__setitem__(first_cleanup_warp(w),['warp',(w['cleanup'][first_cleanup_warp(w)][1]+1)%(w['report']['v']*2),w['cleanup'][first_cleanup_warp(w)][2],w['cleanup'][first_cleanup_warp(w)][3]]),'arbitrary-input endpoint')
+word_tamper('warp_moved_after_its_first_use',lambda w:w['warps'][0].__setitem__(0,w['warps'][0][0]+5),'')
+if W['initial_corrections']:
+    word_tamper('initial_correction_sign_flipped',lambda w:w['initial_corrections'][0].__setitem__('coefficient',str(-__import__('fractions').Fraction(w['initial_corrections'][0]['coefficient']))),'arbitrary-input endpoint')
+    word_tamper('initial_correction_dropped',lambda w:w['initial_corrections'].pop(0),'arbitrary-input endpoint')
+    word_tamper('initial_correction_wrong_operator',lambda w:w['initial_corrections'][0].__setitem__('operator_word',[w['initial_corrections'][0]['operator_word'][0]%len(w['warps'])+1]),'arbitrary-input endpoint')
+word_tamper('zero_buffer_gate_dropped',lambda w:w['cleanup'].pop(next(i for i,e in enumerate(w['cleanup']) if e[0]=='add' and e[1]>=2*w['report']['v']+w['report']['R'])),'arbitrary-input endpoint')
+if '--files' in sys.argv:
+    def file_tamper(name,script,files,mutate,expect_fail=True):
+        d=work/('files-'+name)
+        if d.exists():shutil.rmtree(d)
+        shutil.copytree(local,d);mutate(d)
+        rc,log=run(script,d,*[]) if script!='bw_adapters.py' else run(script,d/'CANONICAL-WORD.json.gz',d/'RESIDUAL-ADAPTERS.json',d/'WRAPPER-CHECKS.json')
+        results.append(dict(name=name,rejected=rc!=0,last_line=log.strip().splitlines()[-1][:200] if log.strip() else ''));assert rc!=0,(name,log[-400:])
+    def edit_json(path,fn,gz=False):
+        d=json.loads(gzip.decompress(path.read_bytes()) if gz else path.read_text());fn(d)
+        path.write_bytes(gzip.compress(json.dumps(d,sort_keys=True,separators=(',',':')).encode(),mtime=0) if gz else json.dumps(d,sort_keys=True,separators=(',',':')).encode())
+    def recipe_phase(d):edit_json(d/'CLIFFORD-RECIPES.json',lambda r:next(x for x in r['warps'] if x['sign']>0 and x['old']!=x['new'])['left'].__setitem__('phase',(next(x for x in r['warps'] if x['sign']>0 and x['old']!=x['new'])['left']['phase']+1)%4))
+    def recipe_drop_inverse(d):edit_json(d/'CLIFFORD-RECIPES.json',lambda r:r['warps'].pop(next(i for i,x in enumerate(r['warps']) if x['sign']<0)))
+    def recipe_swap_G(d):edit_json(d/'CLIFFORD-RECIPES.json',lambda r:next(x for x in r['warps'] if x['sign']>0).__setitem__('G_columns',next(x for x in r['warps'] if x['sign']>0)['G_columns'][::-1]))
+    def prog_drop_warp(d):edit_json(d/'LOCAL-PROGRAMS.json.gz',lambda p:p['forward'].pop(next(i for i,e in enumerate(p['forward']) if e[0]=='warp' and e[2]<0 and i>len(p['forward'])//2)),gz=True)
+    def prog_wrong_G(d):edit_json(d/'CANONICAL-WORD.json.gz',lambda c:c['warps'][0].__setitem__('G_columns',c['warps'][0]['G_columns'][::-1]),gz=True)
+    file_tamper('recipe_phase_tampered','bw_check_recipes.py',None,recipe_phase)
+    file_tamper('recipe_inverse_missing','bw_check_recipes.py',None,recipe_drop_inverse)
+    file_tamper('recipe_G_tampered','bw_check_recipes.py',None,recipe_swap_G)
+    file_tamper('program_missing_inverse_warp','bw_audit_local.py',None,prog_drop_warp)
+    file_tamper('word_G_reversed','bw_audit_local.py',None,prog_wrong_G)
+(work/'TAMPER-RESULTS.json').write_text(json.dumps(dict(status='PASS_ALL_TAMPERS_REJECTED',tampers=results,seconds=time.monotonic()-t0),indent=1)+'\n')
+print('PASS all',len(results),'tampers rejected in',round(time.monotonic()-t0,1),'s')
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_transport.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_transport.py
new file mode 100644
index 0000000000..08248542b1
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/bw_transport.py
@@ -0,0 +1,416 @@
+"""Transport an explicit BORROW-WORD to the native canonical frame-id form, with warps, and replay it exactly.
+
+Anticipatory dirty borrowing is the construction of PR2226 (Cinna Davis, @1337isnot1337, with OpenAI Codex
+assistance; Apache-2.0): a retiring helper's register is lent to a later helper through a monomial Clifford
+logical reference change K_G ("warp"), the retired field's value being replaced by K_G z. The explicit
+chronological BORROW-WORD (canonical coordinates, literal frames, warps, cold restoration, inverse cleanup
+with private zero buffers) is the builder output of the borrowing work (P1/P2).  This script is the
+transport stage of the native chain (the analogue of hpe_audit_and_transport.py): it never trusts the builder.
+It replays the program in the free operator algebra generated by the warps over every arbitrary input,
+in BOTH orientations (forward and inverse-transpose), checks every frame chain and the paid profile, compacts
+the helper registers to R' = R - k, and writes the native CANONICAL-WORD.
+
+usage: bw_transport.py BORROW-WORD.json[.gz] OUT_DIR
+"""
+if not __debug__:
+    raise RuntimeError('assertions must remain enabled')   # every check of this stage is an assert
+import argparse
+import copy
+import gzip
+import hashlib
+import json
+import sys
+import time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def read(path):
+    data = path.read_bytes()
+    return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data)
+
+
+def basis(vs):
+    pivots = {}
+    for x in vs:
+        for k in sorted(pivots, reverse=True):
+            if x >> k & 1:
+                x ^= pivots[k]
+        if x:
+            k = x.bit_length() - 1
+            for j in pivots:
+                if pivots[j] >> k & 1:
+                    pivots[j] ^= x
+            pivots[k] = x
+    return tuple(pivots[k] for k in sorted(pivots, reverse=True))
+
+
+def span(b):
+    s = {0}
+    for x in b:
+        s |= {t ^ x for t in s}
+    return frozenset(s)
+
+
+def rank_of(vs):
+    return len(basis(vs))
+
+
+def solve_G(cols, h):
+    """G given as images of e_i; returns (invertible?, image-of-subspace function)."""
+    def lin(x):
+        out = 0
+        for i, c in enumerate(cols):
+            if x >> i & 1:
+                out ^= c
+        return out
+    return lin, rank_of(cols) == h
+
+
+# ---- free operator algebra over the warps ------------------------------------------------------------------
+def add_row(dst, src, c):
+    for key, value in list(src.items()):
+        z = dst.get(key, Q(0)) + c * value
+        if z:
+            dst[key] = z
+        elif key in dst:
+            del dst[key]
+
+
+def warp_row(row, op):
+    out = {}
+    for (var, word), value in row.items():
+        word = word[1:] if word and word[0] == -op else (op,) + word
+        out[var, word] = value
+    return out
+
+
+def is_dyadic(q):
+    return q.denominator & (q.denominator - 1) == 0
+
+
+def gate_regs(e):
+    if e[0] == 'add':
+        return [e[1], e[2]]
+    if e[0] == 'scale':
+        return [e[1]]
+    raise AssertionError(e[0])
+
+
+def dual(e):
+    e = list(e)
+    if e[0] == 'add':
+        e[1], e[2] = e[2], e[1]
+        e[3] = -e[3]
+    elif e[0] == 'scale':
+        e[2], e[3] = e[3], e[2]
+    return e
+
+
+def apply_gate(e, rows, back):
+    if back:
+        e = dual(e)
+    if e[0] == 'scale':
+        q = Q(e[2], e[3])
+        assert q
+        rows[e[1]] = {j: q * x for j, x in rows[e[1]].items()}
+    else:
+        assert e[1] != e[2]
+        add_row(rows[e[1]], rows[e[2]], Q(e[3], e[4]))
+
+
+def run(word_path, out):
+    t0 = time.monotonic()
+    word = read(word_path)
+    assert word['kind'] == 'BORROW-WORD'
+    v, h, R0 = word['report']['v'], word['report']['h'], word['report']['R']
+    assert h == 9 and v == 112
+    n0 = 2 * v + R0
+    removed = sorted(word['removed'])
+    assert all(2 * v <= r < n0 for r in removed) and len(set(removed)) == len(removed)
+    k = len(removed)
+    kept = [r for r in range(n0) if r not in set(removed)]
+    newid = {r: i for i, r in enumerate(kept)}
+    n = len(kept)
+    R = R0 - k
+    assert n == 2 * v + R
+    Zbase = n0                                       # builder convention: zero buffer of restored c is register n0 + c
+    ports = word['ports']
+    assert len(set(ports)) == v
+    full = tuple(1 << i for i in range(h - 1, -1, -1))
+    frames, frame_ids = [(), full], {(): 0, full: 1}
+
+    def fid(vectors):
+        frame = basis(vectors)
+        if frame not in frame_ids:
+            frame_ids[frame] = len(frames)
+            frames.append(frame)
+        return frame_ids[frame]
+
+    def R_(r):                                       # register -> new register (int) or ['Z', c]
+        if isinstance(r, list):
+            return r
+        if r >= Zbase:
+            return ['Z', newid[r - Zbase]]
+        return newid[r]
+
+    start = [fid([p]) for p in ports] + [0] * (v + R)
+    for r, frame in word['start_extra'].items():
+        assert 2 * v <= int(r) < n0 and int(r) not in set(removed)
+        start[newid[int(r)]] = fid(frame)
+    final = [1] * v + [fid(x for x in range(1, 1 << h) if (x & p).bit_count() % 2 == 0) for p in ports] + [1] * R
+    helper_final = {}
+    for r, frame in word['helper_final'].items():
+        assert 2 * v <= int(r) < n0 and int(r) not in set(removed)
+        helper_final[newid[int(r)]] = fid(frame)
+        final[newid[int(r)]] = helper_final[newid[int(r)]]
+    zero_buffers = sorted(helper_final)              # every restored (hyperplane-ended) helper is replaced by a private zero buffer in the FULL cleanup
+
+    def gate(e):
+        e = copy.deepcopy(e)
+        # Four-low lifted-target port (PR2436 mechanism): literal A-phase warp after the entry adapters.
+        if e[0] == 'warp':
+            assert len(e) == 5
+            return ['warp', R_(e[1]), e[2], fid(e[3]), fid(e[4])]
+        if e[0] == 'add':
+            e[1], e[2] = R_(e[1]), R_(e[2])
+        else:
+            e[1] = R_(e[1])
+        e[-1] = None if e[-1] is None else fid(e[-1])
+        return e
+
+    # warps: operator table; op id = position + 1; G given by images of the basis vectors
+    warps = []
+    for i, (pos, lender, G, frm, to) in enumerate(word['warps']):
+        warps.append({'op': i + 1, 'B_pos': pos, 'lender': newid[lender], 'G_columns': list(G),
+                      'from_frame': fid(frm), 'to_frame': fid(to)})
+    byp = {}
+    for w_ in warps:
+        byp.setdefault(w_['B_pos'], []).append(w_)
+
+    def warp_event(r, op, f0, f1):
+        return ['warp', r, op, f0, f1]
+
+    # compensation (zero frame): initial corrections first, as twisted additions  t += c * W(s)
+    pre = []
+    for term in word['initial_corrections']:
+        q = Q(term['coefficient'])
+        pre.append(['tadd', newid[term['target']], newid[term['source']], list(term['operator_word']),
+                    q.numerator, q.denominator, 0])
+    precondition = pre + [gate(e) for e in word['precondition']]       # the formal initial corrections come first (PR2226 order)
+    compensation = [gate(e) for e in word['compensation']]
+    A = [gate(e) for e in word['A']]
+    cut = [gate(e) for e in word['cut']]
+    B = []
+    for p in range(len(word['B']) + 1):
+        for w_ in sorted(byp.get(p, []), key=lambda x: x['op']):
+            B.append(warp_event(w_['lender'], w_['op'], w_['from_frame'], w_['to_frame']))
+        if p < len(word['B']):
+            B.append(gate(word['B'][p]))
+    assert sum(1 for e in B if e[0] == 'warp') == len(warps)
+    tail = [gate(e) for e in word['restore']]
+    cleanup = []
+    for e in word['cleanup']:
+        if e[0] == 'warp':
+            cleanup.append(warp_event(R_(e[1]), e[2], 1, 1))
+            assert basis(e[3]) == full
+        else:
+            cleanup.append(gate(e))
+    centers = [newid[r] for r in word['centers']]
+    center_frames = [fid(f) for f in word['center_frames']]
+    levels = {str(t): fid(f) for t, f in word['target_levels'].items()}
+
+    canonical = dict(h=h, v=v, R=R, ports=ports, frames=frames, start=start, final=final,
+                     precondition=precondition, compensation=compensation, A=A, cut=cut, B=B, tail=tail,
+                     cleanup=cleanup, centers=centers, center_frames=center_frames, target_levels=levels,
+                     warps=warps, zero_buffers=zero_buffers, removed=removed, helper_origin=kept[2 * v:],
+                     borrow=dict(k=k, base=word.get('base'), original_helpers=R0))
+    # ---- exact scalar replay in the free algebra over the warps (both orientations) -----------------------------------
+    nz = len(zero_buffers)
+
+    def regkey(r):
+        return tuple(r) if isinstance(r, list) else ('L', r)
+
+    def expand_tadd(e):
+        _, t, s, wordops, a, b, f = e
+        ev = [warp_event(s, op, 0, 0) for op in reversed(wordops)]
+        ev.append(['add', t, s, a, b, 0])
+        ev += [warp_event(s, -op, 0, 0) for op in wordops]
+        return ev
+
+    def program():
+        yield 'pre', [x for e in precondition + compensation for x in (expand_tadd(e) if e[0] == 'tadd' else [e])]
+        yield 'A', A
+        yield 'A', cut
+        yield 'B', B
+        yield 'tail', tail
+        yield 'cleanup', cleanup
+
+    def fullprog():
+        return [(part, e) for part, es in program() for e in es]
+    prog = fullprog()
+    for back in (False, True):
+        rows = {regkey(r): {(r, ()): Q(1)} for r in range(n)}
+        for c in zero_buffers:
+            rows[('Z', c)] = {}
+        for part, e in prog:
+            if e[0] == 'warp':
+                key = ('L', e[1]) if not isinstance(e[1], list) else tuple(e[1])
+                rows[key] = warp_row(rows[key], e[2])
+            else:
+                if e[0] == 'add':
+                    src, dst = regkey(e[2]), regkey(e[1])
+                    a, b = e[3], e[4]
+                    if back:
+                        src, dst, a = dst, src, -a
+                    assert src != dst
+                    add_row(rows[dst], rows[src], Q(a, b))
+                else:
+                    key = regkey(e[1])
+                    a, b = (e[3], e[2]) if back else (e[2], e[3])
+                    q = Q(a, b)
+                    assert q
+                    rows[key] = {j: q * x for j, x in rows[key].items()}
+        expected = {regkey(r): {(r, ()): Q(1)} for r in range(n)}
+        for t in range(v):
+            if back:
+                expected[('L', t)][(v + t, ())] = Q(-1)
+            else:
+                expected[('L', v + t)][(t, ())] = Q(1)
+        for c in zero_buffers:
+            expected[('Z', c)] = {}
+        bad = [key for key in expected if rows[key] != expected[key]]
+        assert not bad, ('arbitrary-input endpoint (free warp algebra)', back, bad[:8])
+    # dyadic primitives
+    for part, e in prog:
+        if e[0] == 'add':
+            assert is_dyadic(Q(e[3], e[4]))
+        elif e[0] == 'scale':
+            q = Q(e[2], e[3])
+            a = abs(q.numerator)
+            assert is_dyadic(q) and a and a & (a - 1) == 0
+
+    wrapped_regs = {r for r in range(2 * v, n) if start[r] != 0 or final[r] != 1}   # entering or hyperplane-ended helpers carry wrappers
+    # ---- frame chains, paid profile, edges, warps -------------------------------------------------------------------
+    contains = lambda a, b: basis(frames[a] + frames[b]) == tuple(frames[b])
+    cur = start.copy()
+    paid, edges = Counter(), set()
+    wsum = {w_['op']: w_ for w_ in warps}
+    G_of = {}
+    for w_ in warps:
+        lin, inv_ = solve_G(w_['G_columns'], h)
+        assert inv_, ('non-invertible G', w_['op'])
+        img = basis([lin(x) for x in frames[w_['from_frame']]])
+        assert img == tuple(frames[w_['to_frame']]), ('G does not map the from frame onto the to frame', w_['op'])
+        assert len(frames[w_['from_frame']]) == len(frames[w_['to_frame']])
+        G_of[w_['op']] = lin
+    warp_edges = set()
+
+    def regs_of(e):
+        return [r for r in gate_regs(e) if not isinstance(r, list)]
+
+    def climb(r, f):
+        old = cur[r]
+        assert contains(old, f), ('nonmonotone', r, old, f)
+        if old != f:
+            degree = len(frames[f]) - len(frames[old])
+            paid[degree] += 1
+            edges.add((old, f))
+            cur[r] = f
+
+    def do_warp(e):
+        _, r, op, f0, f1 = e
+        if isinstance(r, list):
+            assert r[0] == 'Z'
+            assert f0 == f1 == 1
+            return
+        assert cur[r] == f0, ('warp frame mismatch', r, op, cur[r], f0)
+        a = abs(op)
+        lin = G_of[a]
+        if op > 0:
+            ok = basis([lin(x) for x in frames[f0]]) == tuple(frames[f1])
+        else:
+            ok = basis([lin(x) for x in frames[f1]]) == tuple(frames[f0])
+        assert ok, ('warp G does not carry the frame', op, f0, f1)
+        cur[r] = f1
+        warp_edges.add((1 if op > 0 else -1, a, f0, f1))
+
+    # zero-frame phase
+    for e in precondition + compensation:
+        if e[0] == 'tadd':
+            assert start[e[2]] == 0 and start[e[1]] == 0 and e[-1] == 0 and e[2] not in set(wrapped_regs) and all(op != 0 for op in e[3])
+            for ev in expand_tadd(e):
+                if ev[0] == 'warp':
+                    do_warp(ev)                      # frame 0 -> 0: K_G itself is the physical operator
+            continue
+        for r in regs_of(e):
+            assert start[r] == 0 and e[-1] == 0, ('zero-frame precondition on a nonzero entrance', e)
+    for part in ('A', 'B'):
+        if part == 'B':
+            assert all(cur[r] == f for r, f in zip(centers, center_frames))
+            assert all(cur[v + t] == levels.get(str(t), 0) for t in range(v))
+            for r, frame in zip(centers, center_frames):
+                served = {levels.get(str(e[1] - v), 0) for e in cut if e[2] == r}
+                old = frame
+                for f in sorted(served, key=lambda f: -len(frames[f])):
+                    assert contains(f, old)
+                    if old != f:
+                        paid[len(frames[old]) - len(frames[f])] += 1
+                        edges.add((old, f))
+                        edges.add((f, old))
+                        old = f
+        for e in (A if part == 'A' else B):
+            if e[0] == 'warp':
+                do_warp(e)
+            else:
+                for r in regs_of(e):
+                    climb(r, e[-1])
+    for e in tail:
+        for r in regs_of(e):
+            climb(r, e[-1])
+    for r, f in enumerate(final):
+        climb(r, f)
+    for e in cleanup:
+        if e[0] == 'warp':
+            do_warp(e)
+            continue
+        for r in gate_regs(e):
+            if isinstance(r, list):
+                assert r[0] == 'Z' and r[1] in set(zero_buffers) and e[-1] == 1
+            else:
+                assert final[r] == 1 and e[-1] == 1, ('cleanup on a non-FULL end', e)
+    assert all(len(frames[final[r]]) < h for r in zero_buffers)
+    assert set(zero_buffers) == set(helper_final)
+    rep = word['report']
+    assert dict(paid) == {int(r): c for r, c in rep['local_profile'].items()}, ('paid profile differs', dict(paid), rep['local_profile'])
+    canonical['local_profile'] = dict(sorted(paid.items()))
+    canonical['edges'] = sorted(edges)
+    canonical['warp_edges'] = sorted(warp_edges)
+    out.mkdir(parents=True, exist_ok=False)
+    payload = json.dumps(canonical, sort_keys=True, separators=(',', ':')).encode()
+    (out / 'CANONICAL-WORD.json.gz').write_bytes(gzip.compress(payload, mtime=0))
+    raw = word_path.read_bytes()
+    (out / 'FULL-WORD.json.gz').write_bytes(gzip.compress(gzip.decompress(raw) if word_path.suffix == '.gz' else raw, mtime=0))
+    receipt = dict(status='PASS_BORROW_WORD_FREE_ALGEBRA_ALL_COLUMNS_AND_NATIVE_FRAMES',
+                   input_content_sha256=hashlib.sha256(gzip.decompress(raw) if word_path.suffix == '.gz' else raw).hexdigest(),
+                   canonical_content_sha256=hashlib.sha256(payload).hexdigest(),
+                   live_columns_each_orientation=n, helpers=R, original_helpers=R0, removed_helpers=k,
+                   zero_buffers=nz, warps=len(warps), warp_events=sum(e[0] == 'warp' for part, e in prog),
+                   initial_corrections=len(word['initial_corrections']),
+                   scalar_operations=len([1 for p, e in prog if e[0] != 'warp']),
+                   local_profile=dict(sorted(paid.items())), local_rank_mass=sum(r * z for r, z in paid.items()),
+                   widths=[len(frames[final[r]]) - len(frames[start[r]]) for r in range(2 * v, n)],
+                   frames=len(frames), directed_edges=len(edges), warp_edge_classes=len(warp_edges),
+                   seconds=time.monotonic() - t0,
+                   scope='Fresh exact forward and inverse-transpose replay over a free noncommutative warp algebra on every arbitrary input, native frame chains, dyadic primitives, zero buffers returned to zero. Physical Clifford exactness of every warp is checked by the local replay and the phase recipes.')
+    (out / 'SCALAR-FRAME-AUDIT.json').write_text(json.dumps(receipt, indent=2) + '\n')
+    print(json.dumps({k_: x for k_, x in receipt.items() if k_ != 'widths'}, indent=2), flush=True)
+
+
+if __name__ == '__main__':
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('word', type=Path)
+    ap.add_argument('out', type=Path)
+    a = ap.parse_args()
+    run(a.word, a.out)
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/PR2226-NOTICE.md b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/PR2226-NOTICE.md
new file mode 100644
index 0000000000..5ea70357a0
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/PR2226-NOTICE.md
@@ -0,0 +1,22 @@
+# Attribution and license
+
+New construction, proof text and checkers: Cinna Davis (@1337isnot1337), with
+substantial OpenAI Codex assistance, Apache-2.0.
+
+The selected complex canonical word is the PR1042 ancestry retained in PR1094.
+Jeremy Kothe, Rohan Arun, Hao Yan, Chafik Boukhalfa, icekylinx, Jonathan Capalbo
+and the source package's full provider/frame/controller lineage retain credit.
+Ali Romman supplied the source-bound fixed-block theorem and certificate;
+Thomas DiFiore supplied the earlier block discovery. The borrowing construction
+does not attribute its changed interface to those predecessor results.
+
+`price_engine.py` is an unchanged copy of the incorporated
+`research/complex-local-word-ceiling/ceiling.py`: Douglas Colkitt, with Claude
+(Anthropic) assistance; original SPDX/license context and docstring retained.
+General Clifford frame and exact Gaussian normal forms are inherited from
+`notes/general-clifford-frames.tex` and the repository's credited phase/compiler
+lineage. The package independently checks its actual local Gaussian products.
+
+Source hashes, base commits and the copied engine's Git blob are in SOURCES.json.
+No full native supplier, all-size compiler, precision theorem or new kappa is
+claimed. No independent human review is claimed.
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py
new file mode 100644
index 0000000000..166841a037
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py
@@ -0,0 +1,149 @@
+"""Small exact Gaussian-dyadic Clifford compiler, independent of gx internals.
+Paulis use i^p X^x Z^z. State vectors use integer Gaussian numerators / 2^d.
+The tableau is supplemented by a literal circuit, so global phases are kept.
+"""
+from dataclasses import dataclass
+
+def parity(x):return x.bit_count()&1
+def rank(rows):
+ p={}
+ for x in rows:
+  while x:
+   b=x.bit_length()-1
+   if b not in p:p[b]=x;break
+   x^=p[b]
+ return len(p)
+def transpose(rows,n):return tuple(sum(((rows[j]>>i)&1)<<j for j in range(n)) for i in range(n))
+def mv(rows,x):return sum(parity(r&x)<<i for i,r in enumerate(rows))
+def inv(rows,n):
+ a=[r|(1<<(n+i)) for i,r in enumerate(rows)]
+ for j in range(n):
+  k=next(i for i in range(j,n) if a[i]>>j&1);a[j],a[k]=a[k],a[j]
+  for i in range(n):
+   if i!=j and a[i]>>j&1:a[i]^=a[j]
+ assert [r&((1<<n)-1) for r in a]==[1<<i for i in range(n)]
+ return tuple(r>>n for r in a)
+def basis_extend(cols,n):
+ out=[]
+ for x in list(cols)+[1<<i for i in range(n)]:
+  if rank(out+[x])>len(out):out.append(x)
+ assert len(out)==n
+ return tuple(out)
+def nullspace(rows,n):
+ a=list(rows);p=[];k=0
+ for j in range(n):
+  t=next((i for i in range(k,len(a)) if a[i]>>j&1),None)
+  if t is None:continue
+  a[t],a[k]=a[k],a[t]
+  for i in range(len(a)):
+   if i!=k and a[i]>>j&1:a[i]^=a[k]
+  p.append(j);k+=1
+ return tuple((1<<j)|sum(((a[i]>>j)&1)<<v for i,v in enumerate(p)) for j in range(n) if j not in p)
+def pmul(a,b):
+ x,z,p=a;y,w,q=b
+ return x^y,z^w,(p+q+2*parity(z&y))%4
+def identity(n):return tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,0) for i in range(n)])
+def apply(T,p):
+ n=len(T)//2;x,z,ph=p;out=(0,0,ph)
+ for i in range(n):
+  if x>>i&1:out=pmul(out,T[i])
+ for i in range(n):
+  if z>>i&1:out=pmul(out,T[n+i])
+ return out
+def compose(A,B):return tuple(apply(A,p) for p in B)
+def inverse(T):
+ n=len(T)//2;cols=[x|(z<<n) for x,z,p in T];rows=transpose(cols,2*n);cols_inv=transpose(inv(rows,2*n),2*n);out=[]
+ for j,w in enumerate(cols_inv):
+  x=w&((1<<n)-1);z=w>>n;u,v,p=apply(T,(x,z,0));assert (u,v)==identity(n)[j][:2];out.append((x,z,(-p)%4))
+ return tuple(out)
+def qvalue(Q,alpha,x,n):
+ return (sum(alpha[i] for i in range(n) if x>>i&1)+2*sum(parity((Q[i]>>(i+1))&(x>>(i+1))) for i in range(n) if x>>i&1))%4
+def mul_i(a,p):
+ x,y=a;p%=4
+ return [(x,y),(-y,x),(-x,-y),(y,-x)][p]
+@dataclass
+class Op:
+ n:int
+ tab:tuple
+ circuit:list
+ def then(self,b):
+  assert self.n==b.n
+  return Op(self.n,compose(b.tab,self.tab),self.circuit+b.circuit)
+ def adjoint(self):
+  circ=[]
+  for e in reversed(self.circuit):
+   if e[0]=='P':circ.append(('P',inv(e[1],self.n)))
+   elif e[0]=='D':circ.append(('D',e[1],tuple((-x)%4 for x in e[2])))
+   elif e[0]=='C':circ.append(('C',e[1],-e[2]))
+   elif e[0]=='phase':circ.append(('phase',(-e[1])%4))
+   else:circ.append(e)
+  return Op(self.n,inverse(self.tab),circ)
+ def zero_state(self,basis=0):
+  N=1<<self.n;vec=[(0,0)]*N;vec[basis]=(1,0);den=0
+  for e in self.circuit:
+   if e[0]=='P':
+    v=[(0,0)]*N
+    for x,a in enumerate(vec):v[mv(e[1],x)]=a
+    vec=v
+   elif e[0]=='X':vec=[vec[x^e[1]] for x in range(N)]
+   elif e[0]=='D':vec=[mul_i(a,qvalue(e[1],e[2],x,self.n)) for x,a in enumerate(vec)]
+   elif e[0]=='phase':vec=[mul_i(a,e[1]) for a in vec]
+   elif e[0]=='C':
+    q,sgn=e[1:];v=[]
+    for x,(a,b) in enumerate(vec):
+     c,d=vec[x^q]
+     # C=(1+i)I/2+(1-i)X/2; inverse conjugates both coefficients.
+     v.append((a-sgn*b+c+sgn*d,b+sgn*a+d-sgn*c))
+    vec=v;den+=1
+   else:raise AssertionError(e)
+   while den and all((a&1)==(b&1)==0 for a,b in vec):vec=[(a//2,b//2) for a,b in vec];den-=1
+  return vec,den
+def ident(n):return Op(n,identity(n),[])
+def perm(n,G):
+ cols=transpose(G,n);gi=inv(G,n)
+ return Op(n,tuple([(a,0,0) for a in cols]+[(0,a,0) for a in gi]),[('P',tuple(G))])
+def diag(n,Q,alpha=None):
+ Q=tuple(Q);assert transpose(Q,n)==Q
+ alpha=tuple(alpha) if alpha is not None else tuple((Q[i]>>i)&1 for i in range(n))
+ assert all(alpha[i]%2==(Q[i]>>i)&1 for i in range(n))
+ return Op(n,tuple([(1<<i,Q[i],alpha[i]) for i in range(n)]+[(0,1<<i,0) for i in range(n)]),[('D',Q,alpha)])
+def cgate(n,q,sgn=1):
+ return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(q if q>>i&1 else 0,1<<i,(3*sgn)%4 if q>>i&1 else 0) for i in range(n)]),[('C',q,sgn)])
+def xgate(n,b):return Op(n,tuple([(1<<i,0,0) for i in range(n)]+[(0,1<<i,2*((b>>i)&1)) for i in range(n)]),[('X',b)])
+def fourier(n,axes=None):
+ out=ident(n)
+ for i in range(n) if axes is None else axes:out=out.then(cgate(n,1<<i))
+ return out
+def hadamard(n,axes):
+ axes=list(axes);Q=tuple(1<<i if i in axes else 0 for i in range(n));S=diag(n,Q)
+ return S.then(fourier(n,axes)).then(S)
+def canonical_frame(n,U):
+ r=len(U)
+ if r==0:return ident(n)
+ if r==n:return fourier(n)
+ G=transpose(basis_extend(U,n),n);gi=inv(G,n);Q=tuple((1<<i)^sum(parity(gi_i&gi_j)<<j for j,gi_j in enumerate(transpose(gi,n))) for i,gi_i in enumerate(transpose(gi,n)))
+ K=perm(n,G).then(diag(n,Q))
+ return K.adjoint().then(fourier(n,range(r))).then(K)
+def monomial(op):
+ n=op.n;T=op.tab;assert all(x==0 and p%2==0 for x,z,p in T[n:]);G=transpose([x for x,z,p in T[:n]],n);b=mv(G,sum((p//2)<<i for i,(x,z,p) in enumerate(T[n:])))
+ gt=transpose(G,n);cols=[mv(gt,z) for x,z,p in T[:n]];Q=transpose(cols,n);alpha=[(p-2*parity(b&z))%4 for x,z,p in T[:n]]
+ out=diag(n,Q,alpha).then(perm(n,G)).then(xgate(n,b));assert out.tab==T
+ vec,den=op.zero_state();assert den==0 and all(a==(0,0) for i,a in enumerate(vec) if i!=b);phase=[(1,0),(0,1),(-1,0),(0,-1)].index(vec[b]);out=out.then(Op(n,identity(n),[('phase',phase)]));assert out.zero_state()==op.zero_state()
+ return out,dict(matrix_rows=G,offset=b,quadratic_rows=Q,linear_Z4=alpha,phase=phase)
+def lower_child(op):
+ n=op.n;Bcols=[x for x,z,p in op.tab[n:]];r=rank(Bcols)
+ if not r:
+  mon,rec=monomial(op);return dict(rank=0,left=rec,right=None),mon
+ G=transpose(basis_extend(Bcols,n),n);A=inv(G,n);PA=perm(n,A);part=op.then(PA);Bcols=[x for x,z,p in part.tab[n:]];Dcols=[z for x,z,p in part.tab[n:]]
+ picks=[];selected=[]
+ for j,x in enumerate(Bcols):
+  if rank(selected+[x])>len(selected):picks.append(j);selected.append(x)
+ assert len(picks)==r and all(x>>r==0 for x in Bcols)
+ Br=transpose(selected,r);Bi=inv(Br,r);Dr=transpose([Dcols[j]&((1<<r)-1) for j in picks],r)
+ Qsmall=tuple(sum(parity(row&col)<<j for j,col in enumerate(transpose(Bi,r))) for row in Dr);Q=Qsmall+(0,)*(n-r);DQ=diag(n,Q)
+ V=part.then(DQ).then(hadamard(n,range(r)));assert all(x==0 for x,z,p in V.tab[n:]);Vmon,Vrec=monomial(V)
+ S=diag(n,tuple(1<<i if i<r else 0 for i in range(n)))
+ left=S.adjoint().then(DQ.adjoint()).then(PA.adjoint());right=Vmon.then(S.adjoint()).then(xgate(n,(1<<r)-1))
+ lmon,lrec=monomial(left);rmon,rrec=monomial(right);compiled=rmon.then(fourier(n,range(r))).then(lmon)
+ assert compiled.tab==op.tab and compiled.zero_state()==op.zero_state()
+ return dict(rank=r,left=lrec,right=rrec),compiled
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_operators.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_operators.py
new file mode 100644
index 0000000000..5c4fbe8cce
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_operators.py
@@ -0,0 +1,140 @@
+#!/usr/bin/env python3
+"""Exact Gaussian-integer checks of every nominated rank-zero handoff.
+
+Each complete512-column operator is evaluated with a shared power-of-two
+denominator. No floating approximation or binary-frame equality is substituted
+for the actual Gaussian operator product.
+"""
+import argparse,hashlib,json
+from pathlib import Path
+import numpy as np
+
+
+def linear(cols,x):
+    out=0
+    for i,c in enumerate(cols):
+        if x>>i&1:out^=c
+    return out
+
+
+def rank(xs):
+    b={}
+    for x in xs:
+        while x:
+            i=x.bit_length()
+            if i not in b:b[i]=x;break
+            x^=b[i]
+    return len(b)
+
+
+def extend(xs,h):
+    out=list(xs)
+    for i in range(h):
+        if rank(out+[1<<i])>len(out):out.append(1<<i)
+    assert len(out)==h
+    return out
+
+
+def inverse(cols,h):
+    perm=[linear(cols,x) for x in range(1<<h)];back=[0]*len(perm)
+    assert len(set(perm))==len(perm)
+    for i,j in enumerate(perm):back[j]=i
+    return [back[1<<i] for i in range(h)]
+
+
+def change(source,target,h):
+    a=extend(source,h);b=extend(target,h);ai=inverse(a,h)
+    return [linear(b,x) for x in ai]
+
+
+def monomial(cols,h):
+    gi=inverse(cols,h)
+    git=[sum(((gi[j]>>i)&1)<<j for j in range(h)) for i in range(h)]
+    M=[(1<<j)^linear(git,gi[j]) for j in range(h)]
+    assert all((M[j]>>i&1)==(M[i]>>j&1) for i in range(h) for j in range(h))
+    perm=np.array([linear(cols,x) for x in range(1<<h)],dtype=np.int64)
+    phase=np.array([sum(((M[i]>>i)&1)*(x>>i&1) for i in range(h))+
+       2*sum(((M[j]>>i)&1)*(x>>i&1)*(x>>j&1) for i in range(h) for j in range(i+1,h))
+       for x in perm],dtype=np.int64)%4
+    return perm,phase
+
+
+def apply_mono(z,recipe,sign=1):
+    re,im,exp=z;perm,phase=recipe;rr=np.empty_like(re);ii=np.empty_like(im)
+    if sign==1:
+        for p in range(4):
+            mask=phase==p;r=re[mask];i=im[mask]
+            if p==0:a,b=r,i
+            elif p==1:a,b=-i,r
+            elif p==2:a,b=-r,-i
+            else:a,b=i,-r
+            rr[perm[mask]]=a;ii[perm[mask]]=b
+    else:
+        r=re[perm];i=im[perm]
+        for p in range(4):
+            mask=phase==p
+            if p==0:a,b=r[mask],i[mask]
+            elif p==1:a,b=i[mask],-r[mask]
+            elif p==2:a,b=-r[mask],-i[mask]
+            else:a,b=-i[mask],r[mask]
+            rr[mask]=a;ii[mask]=b
+    return rr,ii,exp
+
+
+def coord(z,axes,sign=1):
+    re,im,exp=z
+    for j in axes:
+        p=np.array([x for x in range(len(re)) if not(x>>j&1)]);q=p^(1<<j)
+        a,b,c,d=re[p].copy(),im[p].copy(),re[q].copy(),im[q].copy()
+        if sign==1:
+            re[p]=a-b+c+d;im[p]=a+b+d-c
+            re[q]=a+b+c-d;im[q]=b-a+c+d
+        else:
+            re[p]=a+b+c-d;im[p]=b-a+c+d
+            re[q]=a-b+c+d;im[q]=a+b+d-c
+        exp+=1
+    return re,im,exp
+
+
+def frame(z,basis,h,sign=1):
+    G=change([1<<i for i in range(len(basis))],basis,h);K=monomial(G,h)
+    return apply_mono(coord(apply_mono(z,K,-1),range(len(basis)),sign),K,1)
+
+
+def check(z):
+    re,im,exp=z;support=(re!=0)|(im!=0)
+    assert np.all(support.sum(axis=0)==1) and np.all(support.sum(axis=1)==1)
+    rr=re[support];ii=im[support];unit=1<<exp
+    assert np.all(((np.abs(rr)==unit)&(ii==0))|((rr==0)&(np.abs(ii)==unit)))
+    return hashlib.sha256(re.astype('<i8',copy=False).tobytes()+im.astype('<i8',copy=False).tobytes()+str(exp).encode()).hexdigest()
+
+
+def main():
+    p=argparse.ArgumentParser();p.add_argument('--replay',type=Path,required=True)
+    p.add_argument('--output',type=Path,required=True);a=p.parse_args();data=json.loads(a.replay.read_text())
+    h=9;size=1<<h;records=[];negative_rejected=False
+    for handoff in data['symbolic_warps']:
+        U=handoff['from_basis'];E=handoff['to_basis'];assert len(U)==len(E)
+        G=change(U,E,h);K=monomial(G,h)
+        z=(np.eye(size,dtype=np.int64),np.zeros((size,size),dtype=np.int64),0)
+        z=frame(z,U,h,-1);z=apply_mono(z,K);z=frame(z,E,h,1)
+        handhash=check(z)
+        if not negative_rejected:
+            zbad=(np.eye(size,dtype=np.int64),np.zeros((size,size),dtype=np.int64),0)
+            zbad=frame(zbad,U,h,-1);zbad=frame(zbad,E,h,1)
+            try:check(zbad)
+            except AssertionError:negative_rejected=True
+        z=(np.eye(size,dtype=np.int64),np.zeros((size,size),dtype=np.int64),0)
+        z=coord(z,range(h),-1);z=apply_mono(z,K,-1);z=coord(z,range(h),1)
+        exit_hash=check(z)
+        records.append({'operator':handoff['operator'],'G_columns':G,
+          'handoff_exact_monomial_sha256':handhash,'full_exit_exact_monomial_sha256':exit_hash})
+    assert negative_rejected
+    out={'status':'PASS_EXACT_GAUSSIAN_BORROW_HANDOFFS','operators':len(records),
+      'omitted_logical_basis_map_rejected':negative_rejected,
+      'columns_per_operator':size,'physical_rank_zero_products_checked':2*len(records),
+      'records':records,'scope':'exact local adapter products only; no hosting or new kappa'}
+    a.output.write_text(json.dumps(out,indent=2)+'\n');print(json.dumps({k:x for k,x in out.items() if k!='records'}))
+
+
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_replay.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_replay.py
new file mode 100644
index 0000000000..1bbe590206
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/code/borrow/vendor/pr2226_replay.py
@@ -0,0 +1,293 @@
+#!/usr/bin/env python3
+"""Exact replay over a free operator algebra for nominated dirty borrowing.
+
+The current implementation closes cleanup at FULL on every non-target field.
+It prices that choice explicitly. This is not a hosted supplier admission.
+"""
+import argparse,gzip,json,time
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+
+def span(basis):
+    s={0}
+    for x in basis:s|={t^x for t in s.copy()}
+    return frozenset(s)
+
+
+def incident(e):return e[1:3] if e[0]=='add' else e[1:2]
+
+
+def add(dst,src,c):
+    for key,value in list(src.items()):
+        z=dst.get(key,Q(0))+c*value
+        if z:dst[key]=z
+        elif key in dst:del dst[key]
+
+
+def warp(row,op):
+    out={}
+    for (var,word),value in row.items():
+        word=word[1:] if word and word[0]==-op else (op,)+word
+        out[var,word]=value
+    return out
+
+
+def main():
+    p=argparse.ArgumentParser();p.add_argument('--word',type=Path,required=True)
+    p.add_argument('--blocks',type=Path);p.add_argument('--inventory',type=Path,required=True)
+    p.add_argument('--recover-cold',action='store_true')
+    p.add_argument('--framed-word',type=Path)
+    p.add_argument('--output',type=Path,required=True);a=p.parse_args();start=time.monotonic()
+    w=json.loads(gzip.decompress(a.word.read_bytes()));blocks=json.loads(a.blocks.read_text())['sources'][0]['blocks'] if a.blocks else []
+    inv=json.loads(a.inventory.read_text());pairs=inv['pairs']
+    assert len(pairs)==80 and sum(x['low'] for x in pairs)==32
+    assert all(x.get('handoff_paid_rank',0)==0 for x in pairs)
+    v=w['v'];n=2*v+w['R'];full=span([1<<i for i in range(w['h'])]);frames=list(map(span,w['frames']))
+    removed={x['register'] for x in pairs};active=[r for r in range(n) if r not in removed]
+    val={r:{(r,()):Q(1)} for r in active};cur={r:frames[w['start'][r]] for r in active}
+    anticipation=inv['initial_corrections']
+    for term in anticipation:
+        target=term['target'];source=term['source'];word=tuple(term['operator_word']);coefficient=Q(term['coefficient'])
+        assert v<=target<2*v and source in active and not(v<=source<2*v)
+        assert len(w['frames'][w['start'][source]])==0
+        assert all(1<=abs(op)<=len(pairs) for op in word)
+        assert coefficient.denominator&(coefficient.denominator-1)==0
+        add(val[target],{(source,word):Q(1)},coefficient)
+    mapping={};profile=Counter();reverse=[];warps=[];framed_steps=[]
+    def frame_basis(F):
+        b={}
+        for x in F:
+            while x:
+                j=x.bit_length()
+                if j not in b:b[j]=x;break
+                x^=b[j]
+        return [b[j] for j in sorted(b,reverse=True)]
+    def resolve(r):return mapping.get(r,r)
+    def climb(r,f):
+        if not cur[r]<=f:raise ValueError(('nonnested climb',r,len(cur[r]),len(f)))
+        d=(len(f).bit_length()-1)-(len(cur[r]).bit_length()-1)
+        if d:profile[d]+=1
+        cur[r]=f
+    def scalar(e,framed=True,record=True):
+        rs=[resolve(r) for r in incident(e)]
+        if any(r not in val for r in rs):raise ValueError(('unallocated borrowed field',e))
+        if framed:
+            for r in rs:climb(r,frames[e[-1]])
+            framed_steps.append(['gate',rs,frame_basis(frames[e[-1]])])
+        if e[0]=='add':
+            c=Q(e[3],e[4]);add(val[rs[0]],val[rs[1]],c)
+            if record and not(v<=rs[0]<2*v):reverse.append(('add',rs[0],rs[1],c))
+        else:
+            c=Q(e[2],e[3]);val[rs[0]]={k:c*x for k,x in val[rs[0]].items()}
+            if record and not(v<=rs[0]<2*v):reverse.append(('scale',rs[0],c))
+    original_target_levels={r:w['start'][r] for r in range(v,2*v)}
+    for e in w['precondition']+w['compensation']:
+        for r in incident(e):
+            if v<=r<2*v:original_target_levels[r]=e[-1]
+        if e[0]=='add' and e[2] in removed:continue
+        scalar(e,record=False)
+    for e in w['A']:scalar(e)
+    for r,f in original_target_levels.items():climb(r,frames[f])
+    for r,f in original_target_levels.items():framed_steps.append(['pin',r,frame_basis(frames[f])])
+    for r,f in zip(w['centers'],w['center_frames']):
+        assert cur[r]==frames[f];profile[len(w['frames'][f])]+=1
+        framed_steps.append(['pin',r,frame_basis(frames[f])])
+    for e in w['cut']:scalar(e,framed=False,record=False)
+    deferred={};skip=set()
+    for b in blocks:
+        ss=set(b['helpers']);part=[]
+        for i in range(b['first_correction'],b['first_input']):
+            e=w['B'][i]
+            if set(incident(e))<=ss:part.append(e);skip.add(i)
+        deferred[b['first_input']]=part
+    starts={}
+    for i,x in enumerate(pairs):starts.setdefault(x.get('handoff_B',x['deadline']),[]).append((i+1,x))
+    removed_early_echoes={i for x in pairs if x['low'] for i in x.get('deleted_prefix_indices',x['deleted_echo_indices'])}
+    early_rewrites={int(i):gates for x in pairs if x['low'] for i,gates in x.get('early_prefix_rewrites',{}).items()}
+    early_tail={}
+    for e in inv.get('early_tail_events',[]):early_tail.setdefault(e['before_B'],[]).append(e['gate'])
+    for i,e in enumerate(w['B']):
+        for t in early_tail.get(i,[]):scalar(t)
+        if i in starts:
+            for op,x in starts[i]:
+                old=x['borrow_from'];new=x['register'];assert x['retirement_B_event']<i
+                if x['low']:
+                    assert val[old]=={(old,()):Q(1)},'low lender is exactly its restored initial input'
+                E_basis=x.get('handoff_basis',x['common_basis'][:x['retirement_dimension']])
+                E=span(E_basis)
+                paid=abs(len(E_basis)-(len(cur[old]).bit_length()-1))
+                assert paid==x.get('handoff_paid_rank',0)
+                if paid:profile[paid]+=1
+                framed_steps.append(['warp',old,frame_basis(cur[old]),E_basis])
+                # A monomial logical K_G aligns the smaller space inside the
+                # larger one. The physical adapter pays their dimension gap;
+                # the inverse logical reference change at FULL is rank zero.
+                val[old]=warp(val[old],op);reverse.append(('warp',old,op));cur[old]=E
+                mapping[new]=old;warps.append({'operator':op,'borrow_from':old,'removed':new,
+                  'from_basis':w['frames'][x['retirement_frame']],'to_basis':E_basis,
+                  'physical_handoff_rank':paid})
+                for target,c in x.get('handoff_echo_coefficients',{}).items():
+                    target=int(target);climb(target,E);add(val[target],val[old],Q(c))
+                    framed_steps.append(['gate',[target,old],E_basis])
+        for d in deferred.get(i,[]):scalar(d)
+        for d in early_rewrites.get(i,[]):scalar(d)
+        if i not in skip and i not in removed_early_echoes:scalar(e)
+    for t in early_tail.get(len(w['B']),[]):scalar(t)
+    for r in range(v,2*v):climb(r,frames[w['final'][r]])
+    bad_y=[]
+    for r in range(v,2*v):
+        expected={(r,()):Q(1),(r-v,()):Q(1)}
+        if val[r]!=expected:bad_y.append(r)
+    if bad_y:raise ValueError(('output map failed in exact free operator algebra',bad_y[:12]))
+    cold=[r for r in active if not(v<=r<2*v) and len(w['frames'][w['final'][r]])<w['h']]
+    # A modular nomination for scalar restoration at the old cold frame.
+    # Operator words remain distinct formal coordinates in this diagnostic.
+    prime=65521;modular_cache={};cold_span_nominations=[];cold_clearable=[]
+    for c in cold:
+        V=frames[w['final'][c]]
+        pool=tuple(r for r in active if not(v<=r<2*v) and cur[r]<=V<=frames[w['final'][r]])
+        if pool not in modular_cache:
+            piv={}
+            for r in pool:
+                x={k:(q.numerator*pow(q.denominator,-1,prime))%prime for k,q in val[r].items()}
+                while x:
+                    j=min(x)
+                    if j not in piv:
+                        z=pow(x[j],-1,prime);piv[j]={k:t*z%prime for k,t in x.items()};break
+                    z=x[j]
+                    for k,t in piv[j].items():
+                        y=(x.get(k,0)-z*t)%prime
+                        if y:x[k]=y
+                        elif k in x:del x[k]
+            modular_cache[pool]=piv
+        x={(c,()):1};piv=modular_cache[pool]
+        while x:
+            j=min(x)
+            if j not in piv:break
+            z=x[j]
+            for k,t in piv[j].items():
+                y=(x.get(k,0)-z*t)%prime
+                if y:x[k]=y
+                elif k in x:del x[k]
+        if not x:
+            cold_span_nominations.append(c)
+            dependents=[r for r in active if not(v<=r<2*v) and
+                        any(var==c for var,word in val[r])]
+            if all(cur[r]<=V and all(not word for var,word in val[r] if var==c) for r in dependents):
+                cold_clearable.append(c)
+    probe={r:dict(row) for r,row in val.items()};probe_cur=cur.copy();bad_tail_incidence=[]
+    moved_tail_indices={e['old_tail_index'] for e in inv.get('early_tail_events',[])}
+    for index,e in enumerate(w['tail']):
+        if index in moved_tail_indices:continue
+        rs=[resolve(r) for r in incident(e)];f=frames[e[-1]]
+        for r in rs:
+            if not probe_cur[r]<=f:bad_tail_incidence.append((index,r))
+            probe_cur[r]=f
+        if e[0]=='add':add(probe[rs[0]],probe[rs[1]],Q(e[3],e[4]))
+        else:probe[rs[0]]={k:Q(e[2],e[3])*x for k,x in probe[rs[0]].items()}
+    cold_fail=[r for r in cold if probe[r]!={(r,()):Q(1)}]
+    full_cold_dependence=[r for r in active if not(v<=r<2*v) and r not in cold and
+                          any(var in cold for var,word in probe[r])]
+    restored=[];cold_witnesses=[]
+    def exact_combination(pool,goal):
+        piv={}
+        for r in pool:
+            x=dict(val[r]);code={r:Q(1)}
+            while x:
+                j=min(x)
+                if j not in piv:
+                    z=x[j];piv[j]=({k:t/z for k,t in x.items()},{k:t/z for k,t in code.items()});break
+                row,coeff=piv[j];z=x[j];add(x,row,-z);add(code,coeff,-z)
+        x=dict(goal);code={}
+        while x:
+            j=min(x)
+            if j not in piv:return None
+            row,coeff=piv[j];z=x[j];add(x,row,-z);add(code,coeff,z)
+        return code
+    def dyadic(q):return q.denominator&(q.denominator-1)==0
+    def unit(q):return q and dyadic(q) and abs(q.numerator)&(abs(q.numerator)-1)==0
+    def cleanup_add(d,s,c,V):
+        climb(d,V);climb(s,V);add(val[d],val[s],c);reverse.append(('add',d,s,c));framed_steps.append(['gate',[d,s],frame_basis(V)])
+    if a.recover_cold:
+        for c in sorted(cold_clearable,key=lambda r:(len(frames[w['final'][r]]),r)):
+            V=frames[w['final'][c]]
+            pool=[r for r in active if not(v<=r<2*v) and r not in restored and cur[r]<=V]
+            solution=exact_combination(pool,{(c,()):Q(1)})
+            if solution is None or not all(dyadic(z) for z in solution.values()):continue
+            pivot=c if unit(solution.get(c,Q(0))) else next((r for r,z in solution.items() if unit(z)),None)
+            if pivot is None:continue
+            # All sources are still unchanged while this one row is prepared.
+            for r in set(solution)|{c}:climb(r,V)
+            factor=solution[pivot]
+            if factor!=1:
+                val[pivot]={k:factor*z for k,z in val[pivot].items()};reverse.append(('scale',pivot,factor))
+                framed_steps.append(['gate',[pivot],frame_basis(V)])
+            for r,z in solution.items():
+                if r!=pivot:cleanup_add(pivot,r,z,V)
+            if pivot!=c:
+                val[c],val[pivot]=val[pivot],val[c];reverse.append(('swap',c,pivot))
+                framed_steps.append(['gate',[c,pivot],frame_basis(V)])
+            assert val[c]=={(c,()):Q(1)}
+            for r in active:
+                if v<=r<2*v or r==c:continue
+                assert all(not word for var,word in val[r] if var==c)
+                z=val[r].get((c,()),Q(0))
+                if z:cleanup_add(r,c,-z,V)
+            assert all(not any(var==c for var,word in val[r]) for r in active if not(v<=r<2*v) and r!=c)
+            restored.append(c);cold_witnesses.append({'register':c,'frame':w['final'][c],
+                         'preparation':{str(r):str(z) for r,z in solution.items()}})
+    for r in active:
+        if not(v<=r<2*v) and r not in restored:climb(r,full)
+    # Restored cold inputs are decoupled. Their FULL-frame substitutes are
+    # private zero buffers; no recursive child runs during this cleanup.
+    work={r:({} if r in restored else dict(row)) for r,row in val.items()}
+    negative={r:dict(work[r]) for r in active if not(v<=r<2*v)}
+    for e in reversed(reverse):
+        if e[0]=='add':
+            _,d,s,c=e;add(work[d],work[s],-c);add(negative[d],negative[s],-c)
+        elif e[0]=='scale':
+            _,d,c=e;work[d]={k:x/c for k,x in work[d].items()};negative[d]={k:x/c for k,x in negative[d].items()}
+        elif e[0]=='swap':
+            _,d,s=e;work[d],work[s]=work[s],work[d];negative[d],negative[s]=negative[s],negative[d]
+        else:
+            _,d,op=e;work[d]=warp(work[d],-op)
+    for r in active:
+        if not(v<=r<2*v) and work[r]!=({} if r in restored else {(r,()):Q(1)}):raise ValueError(('cleanup failed',r))
+    rejected=[r for r,row in negative.items() if row!=({} if r in restored else {(r,()):Q(1)})]
+    if not rejected:raise ValueError('missing inverse warp negative control did not fail')
+    mass=sum(r*c for r,c in profile.items());copy=64;noncopy=mass-copy;stock=Q(896,9);m=73
+    idle=72*stock-noncopy
+    aa=.00177
+    numerical=(sum(c*(r/m)**(1-aa) for r,c in profile.items())+float(idle)/51*(51/m)**(1-aa))/float(stock)
+    out={'status':'PASS_EXACT_FREE_OPERATOR_BORROWING_REPLAY','original_registers':n,
+       'remaining_registers':len(active),'removed_helper_registers':len(removed),
+       'independent_input_columns':len(active),'symbolic_warps':warps,'target_map':'Y+=X',
+       'all_non_target_inputs_restored':True,'omitted_inverse_warps_rejected_registers':rejected,
+       'early_tail_events':inv.get('early_tail_events',[]),
+       'initial_anticipatory_corrections':anticipation,
+       'new_cleanup':('restore selected cold rows, decouple their inputs, then reverse the non-target word at FULL using zero buffers'
+                      if restored else 'reverse every non-target scalar/warp at FULL; old tail omitted'),
+       'exact_cold_restoration':cold_witnesses,'zero_FULL_cleanup_buffers':len(restored),
+       'unchanged_cold_tail_probe':{'cold_roles':len(cold),'failed_cold_outputs':cold_fail,
+          'full_roles_still_depending_on_cold_inputs':full_cold_dependence,
+          'nonnested_tail_incidences':bad_tail_incidence,
+          'claim':'diagnostic only; unchanged cold tail is not adopted'},
+       'cold_frame_scalar_restoration_modular_nominations':cold_span_nominations,
+       'cold_clearance_modular_nominations':cold_clearable,
+       'local_profile':dict(sorted(profile.items())),'local_mass':mass,'noncopy_mass':noncopy,
+       'favorable_idle_mass_per_call':str(idle),'favorable_numerical_moment_at_a_0_00177':numerical,
+       'seconds':time.monotonic()-start,
+       'scope':'exact operator-algebra scalar replay plus proposed frame dimensions; physical Clifford recipes, both orientations, ownership, exact invoice and bit rail remain unresolved'}
+    a.output.write_text(json.dumps(out,indent=2)+'\n');print('PASS_FIXED_BORROWED_WORD columns='+str(len(active))+' removed='+str(len(removed))+' cold='+str(len(restored)))
+    if a.framed_word:
+        data={'start':{str(r):w['frames'][w['start'][r]] for r in active},
+          'final':{str(r):frame_basis(cur[r]) for r in active},'steps':framed_steps,
+          'copy_profile':dict(Counter(len(w['frames'][f]) for f in w['center_frames'])),
+          'handoff_profile':dict(Counter(x.get('physical_handoff_rank',0) for x in warps if x.get('physical_handoff_rank',0))),
+          'original_profile':dict(sorted(profile.items())),'h':w['h']}
+        a.framed_word.write_text(json.dumps(data,separators=(',',':'))+'\n')
+
+
+if __name__=='__main__':main()
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/run_native_borrow.py b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/run_native_borrow.py
new file mode 100644
index 0000000000..942310947b
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/vendor/native/new/run_native_borrow.py
@@ -0,0 +1,22 @@
+"""Native chain for a BORROW-WORD (anticipatory dirty borrowing, PR2226): transport -> emit -> independent replay -> wrappers -> phases (+ independent warp-recipe recheck).
+Same step layout and STEPS.json as the lineage replay_native.py; usage: run_native_borrow.py BORROW-WORD.json[.gz] WORK_DIR  (WORK_DIR must not exist)."""
+import json,os,subprocess,sys,time
+from pathlib import Path
+HERE=Path(__file__).resolve().parent/'code/borrow'
+word=Path(sys.argv[1]).resolve();work=Path(sys.argv[2]).resolve();work.mkdir(parents=True,exist_ok=False);local=work/'local'
+env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',PYTHONUTF8='1',PYTHONINTMAXSTRDIGITS='0');env.pop('PYTHONOPTIMIZE',None)
+flags=(0x00000040|0x08000000) if os.name=='nt' and os.environ.get('BW_IDLE','1')=='1' else 0   # windowless, IDLE priority
+steps=[]
+for label,script,args in [('native',HERE/'bw_transport.py',[word,local]),('ledgers',HERE/'bw_emit.py',[local]),
+        ('local-replay',HERE/'bw_audit_local.py',[local]),
+        ('wrappers',HERE/'bw_adapters.py',[local/'CANONICAL-WORD.json.gz',local/'RESIDUAL-ADAPTERS.json',local/'WRAPPER-CHECKS.json']),
+        ('phases',[HERE/'bw_phases.py',HERE/'bw_check_recipes.py'],[local])]:   # phases = exact lowering, then the independent warp-recipe recheck
+    t=time.monotonic();log=b''
+    for script in (script if isinstance(script,list) else [script]):
+        p=subprocess.run([sys.executable,'-B',str(script),*map(str,args)],stdout=subprocess.PIPE,stderr=subprocess.STDOUT,cwd=HERE,env=env,creationflags=flags)
+        log+=p.stdout
+        if p.returncode:break
+    (work/(label+'.log')).write_bytes(log)
+    steps.append(dict(step=label,exit_code=p.returncode,seconds=time.monotonic()-t));(work/'STEPS.json').write_text(json.dumps(steps,indent=2)+'\n')
+    assert p.returncode==0,(label,log.decode(errors='replace')[-4000:])
+    print('PASS',label,round(steps[-1]['seconds'],1),flush=True)
diff --git a/research/two-sided-helper-extraction/vendor/fastnative/verify.py b/research/two-sided-helper-extraction/vendor/fastnative/verify.py
new file mode 100644
index 0000000000..0c311cd6e7
--- /dev/null
+++ b/research/two-sided-helper-extraction/vendor/fastnative/verify.py
@@ -0,0 +1,55 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+# Tekalign (@tekuuu), with substantial OpenAI Codex assistance.
+"""Fresh complete native replay against the pinned PR2751 reference outputs."""
+import argparse
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tempfile
+
+sys.path.insert(0, str(Path(__file__).resolve().parent))
+from common import HERE, need, sha, source_bytes
+from compare import canonical, normalized
+
+
+def main():
+    need(__debug__, 'assertions must remain enabled')
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument('--provider', choices=('base', 'extra'), default='base')
+    parser.add_argument('--relocate', action='store_true', help='replay a Git-free copy in a path with spaces')
+    args = parser.parse_args()
+    if args.relocate:
+        with tempfile.TemporaryDirectory(prefix='t74-relocate-') as temporary:
+            root = Path(temporary)
+            package = root / 'package with spaces'
+            shutil.copytree(HERE, package, ignore=shutil.ignore_patterns('__pycache__'))
+            need(not (root / '.git').exists(), 'Git-free relocation')
+            subprocess.run([sys.executable, '-I', '-B', str(package / 'verify.py'),
+                            '--provider', args.provider], cwd=root, check=True)
+        print('PASS_T74_NATIVE_FAST_GIT_FREE_RELOCATION', args.provider)
+        return
+    source_bytes(HERE / 'vendor')
+    word = HERE / f'fixtures/WORD-{args.provider}.json.gz'
+    pins = json.loads((HERE / 'PINS.json').read_text())
+    need(sha(word.read_bytes()) == pins[word.relative_to(HERE).as_posix()], 'fixture digest')
+    expected = json.loads((HERE / 'EXPECTED.json').read_text())[args.provider]
+    with tempfile.TemporaryDirectory(prefix='t74-native-fast-') as temporary:
+        work = Path(temporary) / 'replay'
+        subprocess.run([sys.executable, '-I', '-B', str(HERE / 'run_native.py'),
+                        str(word), str(work)], check=True)
+        local = work / 'native/local'
+        output = normalized(local)
+        need(sha(canonical(output)) == expected['normalized_sha256'], 'all native outputs match reference')
+        need(sha((local / 'CLIFFORD-RECIPES.json').read_bytes()) == expected['recipe_bytes_sha256'], 'recipe bytes')
+        need(output['WARP-RECIPE-CHECKS.json'] == expected['coverage'], 'independent warp coverage')
+        if args.provider == 'base':
+            from controls import check
+            check(local)
+    print('PASS_T74_NATIVE_FAST_REFERENCE_AND_CONTROLS', args.provider)
+
+
+if __name__ == '__main__':
+    main()
diff --git a/research/two-sided-helper-extraction/vendor/preload_move.py b/research/two-sided-helper-extraction/vendor/preload_move.py
new file mode 100644
index 0000000000..55b435035b
--- /dev/null
+++ b/research/two-sided-helper-extraction/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/two-sided-helper-extraction/verify.py b/research/two-sided-helper-extraction/verify.py
new file mode 100644
index 0000000000..f5eb4057a1
--- /dev/null
+++ b/research/two-sided-helper-extraction/verify.py
@@ -0,0 +1,63 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Replay the local construction; optional full native replay. No global kappa claim."""
+import argparse,copy,gzip,hashlib,json,os,subprocess,sys,types
+from pathlib import Path
+P=Path(__file__).resolve().parent
+
+def need(ok,reason):
+    if not ok:raise RuntimeError(reason)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def read(p):
+    b=p.read_bytes();return json.loads(gzip.decompress(b) if b[:2]==b'\x1f\x8b' else b)
+def save(p,x):p.write_text(json.dumps(x,indent=2,sort_keys=True)+'\n')
+def word(p,x):p.write_bytes(gzip.compress(json.dumps(x,separators=(',',':')).encode(),mtime=0))
+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 main():
+    ap=argparse.ArgumentParser(description=__doc__);ap.add_argument('--work',type=Path,required=True);ap.add_argument('--native',action='store_true');a=ap.parse_args()
+    need(not sys.flags.optimize,'assertions enabled')
+    out=a.work.resolve();need(not out.exists() and not out.is_relative_to(P) and not P.is_relative_to(out),'fresh external output');out.mkdir(parents=True)
+    pins=read(P/'PINS.json');actual={f.relative_to(P).as_posix():sha(f) for d in ('vendor','data') for f in (P/d).rglob('*') if f.is_file()}
+    need(actual==pins,'exact complete vendor/data bytes')
+    pm=load('preload_move',P/'vendor/preload_move.py');gen=load('channel_extract',P/'extract.py');aud=load('independent_channel_audit',P/'vendor/audit_local.py')
+    structure=load('channel_structure',P/'structure.py')
+    transform=read(P/'data/TRANSFORM.json');rows={}
+    for tag in ('base','extra'):
+        parent=read(P/f'data/PARENT-{tag}.json.gz');got=gen.apply(parent,transform);expected=read(P/f'data/WORD-{tag}.json.gz')
+        need(got==expected,'complete literal reconstruction '+tag)
+        aud.run(P/f'data/PARENT-{tag}.json.gz',out/f'PARENT-AUDIT-{tag}.json')
+        aud.run(P/f'data/WORD-{tag}.json.gz',out/f'AUDIT-{tag}.json')
+        receipt=read(out/f'AUDIT-{tag}.json')
+        need(receipt['independent_inputs']==632 and receipt['restored_cold']==receipt['zero_buffers']==73,'charged 73 private buffers')
+        need(receipt['local_profile']==gen.PROFILE and receipt['width_inventory']==gen.INVENTORY,'independently derived profile/inventory')
+        rows[tag]={'parent_sha256':sha(P/f'data/PARENT-{tag}.json.gz'),'word_sha256':sha(P/f'data/WORD-{tag}.json.gz'),'audit':receipt,'structure':structure.check(parent,transform,aud)}
+    def bad_scale(w):
+        g=next(g for g in w['A'][w['prelude_events']:] if g[:2]==['scale',408]);g[2]=1
+    def bad_output(w):w['restore'][-1][3]=-1
+    def bad_comp(w):w['compensation']=copy.deepcopy(read(P/'data/PARENT-base.json.gz')['compensation'])
+    def bad_buffer(w):w['cleanup']=[['add',g[1]-704 if g[1]==1112 else g[1],g[2]-704 if g[2]==1112 else g[2],*g[3:]] if g[0]=='add' else g for g in w['cleanup']]
+    rejected={}
+    for name,change,regen in [('wrong_input_scale',bad_scale,True),('wrong_output_cancellation',bad_output,True),('stale_compensation',bad_comp,False),('omit_new_private_buffer',bad_buffer,False)]:
+        w=copy.deepcopy(read(P/'data/WORD-base.json.gz'));change(w)
+        need(w!=read(P/'data/WORD-base.json.gz'),'nontrivial mutant')
+        if regen:
+            profile,inventory=pm.frame_report(w);w['report']['local_profile']=profile;w['report']['width_inventory']=inventory
+            z=copy.deepcopy(w);z['A']=z['A'][z['prelude_events']:];w['cleanup']=pm.derive_cleanup(z,set(map(int,z['helper_final'])))
+        f=out/(name+'.json.gz');word(f,w)
+        try:aud.run(f,out/(name+'.json'))
+        except (AssertionError,RuntimeError,ValueError) as e:rejected[name]=str(e)
+        else:raise RuntimeError('semantic mutant accepted: '+name)
+    native={}
+    if a.native:
+        for tag in ('base','extra'):
+            dest=out/('native-'+tag);cmd=[sys.executable,'-X','pycache_prefix='+str(out/'bytecode'),'-B',str(P/'vendor/fastnative/run_native.py'),str(P/f'data/WORD-{tag}.json.gz'),str(dest),'--engine','sparse']
+            env=dict(os.environ,PYTHONDONTWRITEBYTECODE='1',OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1');env.pop('PYTHONOPTIMIZE',None)
+            with (out/('NATIVE-'+tag+'.log')).open('w') as log:subprocess.run(cmd,check=True,env=env,stdout=log,stderr=subprocess.STDOUT)
+            native[tag]=read(dest/'RESULT.json');need(native[tag]['status']=='PASS_COMPLETE_T74_NATIVE_REPLAY' and native[tag]['word_sha256']==rows[tag]['word_sha256'],'native result binding')
+    need(actual=={f.relative_to(P).as_posix():sha(f) for d in ('vendor','data') for f in (P/d).rglob('*') if f.is_file()},'source bytes unchanged')
+    result={'status':'PASS_TWO_SIDED_HELPER408_LOCAL_CONSTRUCTION','scope':'Exact local construction only; no owner allocation or higher kappa admitted. Extra private buffer is mandatory.','providers':rows,'semantic_controls':rejected,'native':native,'native_replayed':a.native}
+    save(out/'RESULT.json',result);print(result['status'],json.dumps(rejected),flush=True)
+if __name__=='__main__':main()