diff --git a/research/native-center-free-code/.gitattributes b/research/native-center-free-code/.gitattributes
new file mode 100644
index 0000000000..625449502b
--- /dev/null
+++ b/research/native-center-free-code/.gitattributes
@@ -0,0 +1 @@
+* -text
diff --git a/research/native-center-free-code/ATTRIBUTION.md b/research/native-center-free-code/ATTRIBUTION.md
new file mode 100644
index 0000000000..5f6cd0d364
--- /dev/null
+++ b/research/native-center-free-code/ATTRIBUTION.md
@@ -0,0 +1,11 @@
+# Attribution and overlap
+
+Cao Yifan's canonical `research/kappa-round3-warp-20261022/` supplies the exact source payload. It changes helper entrances and shared native maps beyond his PR #4610 predecessor. Cinna Davis's PR #4470 and cumulative native/helper lineage, Dugongue's transported warp-frame lemma, zxv's native/productive/compiler work and Jacob Alan Sussman's mixed-target recursion retain credit. The exact upstream payload and replay-code precedents are pinned in SOURCES.json and ORIGINS.json; their Apache license is retained.
+
+[PR #4694](https://github.com/CrocSwap/integer-mult-bounds/pull/4694) already constructs a retained-center interface, its raw dual, and a center-free cache kernel whose old-input block is A-BR. Removing centers or observing a rank-eight defect is not claimed as new here. [PR #4698](https://github.com/CrocSwap/integer-mult-bounds/pull/4698) already isolates the eight helper observations by a legal common-chart basis and gives a conditional two-call consumer. This package instead cancels the helper part at the actual ground entrance, retains an explicit invertible main-port code, proves its exact projector/inverse/conditioning identities and emits its changed priced offer in both orientations. A general physical inverse is not assumed free.
+
+[PR #4623](https://github.com/CrocSwap/integer-mult-bounds/pull/4623) supplies the relevant border-controller and finite-precision warning. A center-deletion border was investigated here, but its recursive precision gap was not closed; it is not a multiplication result. The published construction uses fixed dyadic coefficients and no small parameter. Recent [PR #4912](https://github.com/CrocSwap/integer-mult-bounds/pull/4912) and #4918 informed the rank-saturation checks of rejected query-deletion ideas; their formal tariffs are not claimed as native gains here.
+
+The linear-algebra interpretation uses standard block elimination and orthogonal-projection identities. Local MathProof/DAG material motivated the representation; no fresh Lean/kernel verification, exhaustive search of the whole library, or priority for standard algebra is claimed. The earlier bounded-word fixed-rational implementation in [PR #4908](https://github.com/CrocSwap/integer-mult-bounds/pull/4908) is relevant to a future denominator-13 adapter, but is not invoked as a free operation here.
+
+Canonical main and priorities were refreshed during the session. The 100 most recently updated PR records were fetched, and relevant new entries and targeted source/Discussion searches were inspected; sparse source and bounded remote coverage do not establish global novelty or absence of concurrent work. The selected record remains unchanged. All checks and reviews in this package are author-side AI work, not independent human approval.
diff --git a/research/native-center-free-code/CODE-INDEPENDENT-REVIEW.json b/research/native-center-free-code/CODE-INDEPENDENT-REVIEW.json
new file mode 100644
index 0000000000..23564b801c
--- /dev/null
+++ b/research/native-center-free-code/CODE-INDEPENDENT-REVIEW.json
@@ -0,0 +1,21 @@
+{
+  "A_inverse": "I+E/13",
+  "E_square_multiple": -14,
+  "all_input_inverse_identity": true,
+  "dimension": 112,
+  "eigenvalues": {
+    "-13": 8,
+    "1": 104
+  },
+  "euclidean_condition_number": 13,
+  "native_chart_admission": false,
+  "new_kappa": null,
+  "projector_trace": "8",
+  "rank_E": 8,
+  "source_entries_sha256": "c8b1dfb9cbfccfd43e59d21cfe89de13884fea28ad03db6dab9ae18b2ce863df",
+  "symmetric": true,
+  "trace_E": "-112",
+  "public_code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0",
+  "parsed_matrix_equal": true,
+  "source_entries_note": "The source_entries hash identifies the earlier private matrix serialization. Its parsed A entries equal public CODE.json; independent.py reproduces the public Gram certificate."
+}
diff --git a/research/native-center-free-code/CODE.json b/research/native-center-free-code/CODE.json
new file mode 100644
index 0000000000..03170f4a31
--- /dev/null
+++ b/research/native-center-free-code/CODE.json
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diff --git a/research/native-center-free-code/CODED-PROOF.md b/research/native-center-free-code/CODED-PROOF.md
new file mode 100644
index 0000000000..1f28d33884
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+++ b/research/native-center-free-code/CODED-PROOF.md
@@ -0,0 +1,80 @@
+# An exact center-free native offer with an invertible eight-mode code
+
+Prepared for Dugongue with substantial OpenAI Codex assistance. Apache-2.0.
+
+Building on Cinna Davis's center-free cache kernel in PR #4694, this gives an explicit free ground-chart helper pre-compensation and an invertible eight-mode main code: all eight rank-eight center Gaussian calls disappear, all 408 independent helper jobs remain, and the main cross-transfer is an explicitly known invertible constant code. It is not the old uncoded main ABI and does not by itself prove a new κ.
+
+## The exact offer
+
+Freeze the native source payload with SHA-256 `cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. Its persistent logical rows are 112 X, 112 Y and 408 independent helpers H. The original normalized endpoint is `(X,Y,H) -> (X,Y+X,H)`. Physical entrance and exit charts remain exactly those of the frozen source.
+
+There is a completely emitted constant dyadic pre-compensation, followed by the source word with every center Gaussian operation replaced by an owned CLEAR, whose exact normalized endpoint is
+
+`X' = X;    Y' = Y + A X;    H' = H`.
+
+All 632 persistent inputs are arbitrary and independent; no helper is initialized, discarded, identified or counted twice. The literal backward construction has exact normalized endpoint
+
+`X' = X - A^T Y;    Y' = Y;    H' = H`,
+
+the raw inverse transpose of the forward endpoint. The paid profile in both directions is
+
+`{1:2201, 2:412, 3:510, 4:127, 5:40}`.
+
+The helper profile stays `{4:28,7:7,8:47,9:326}`. Relative to the source, exactly eight rank-eight children are removed and no Gaussian child is added. The pre-compensation adds 6,596 scalar ADDs with a retained scalar allowance of 32,652 primitives; all numerator magnitudes and denominators are at most 4. These finite scalar operations do not establish a better recursive exponent on their own.
+
+## Constructive proof
+
+Delete all eight center calls by replacing each with CLEAR of the owned center field in the call's destination chart. Zero has every chart, so this is a valid erasure of owned scratch, not a borrowed input overwrite. Retain every other physical instruction and every endpoint chart.
+
+The exact sparse replay over the rational free group algebra on the 72 native symbols gives
+
+`M_0 = I + S + E_X + E_H`.
+
+Here S is the original transfer X to Y. Both error blocks land only in Y. E_X reads X; E_H reads only 106 particular helpers, each with a ground entrance and full-frame exit. Every helper and every X output remains autonomous. All error terms have EMPTY native word: the errors are ordinary constant dyadic matrices, not uncomputed address-operator oracles. The 12,532 nonzero entries split into 5,936 in E_X and 6,596 in E_H.
+
+Every pairwise product of S, E_X and E_H is zero, because all three maps land in Y and none reads Y. Before executing the center-cleared word, apply `I-E_H`. Every required source and target is in the actual ground chart: the targets are Y and the sources are those 106 ground-ended helpers. The operation is the explicit list of 6,596 dyadic ADDs.
+
+Consequently
+
+`M_0 (I-E_H) = I+S+E_X`.
+
+Thus `A=I+E_X` on the 112 main port indices gives the claimed offer, with no helper contamination. Scalar operations in one common address chart have their exact owner-space action, so this is a physical fixed-template pre-compensation and not an abstract change of logical coordinates.
+
+For the backward direction, the separately emitted center-cleared source word is verified to equal `I-S^T-E_X^T-E_H^T`, with the source's distinct inverse-transpose native letters. Prepend `I+E_H^T`, again using only actual ground-chart fields. The product is `I-S^T-E_X^T`. The verifier compares all 632 independent rows in both orientations. The owned center field is empty at termination.
+
+## Explicit code, inverse and conditioning
+
+The same exact entries satisfy
+
+`E_X^T = E_X,    E_X^2 = -14 E_X,    tr(E_X) = -112`.
+
+Set `P=-E_X/14`. It is a real symmetric idempotent of trace 8, hence an orthogonal projection of rank 8. Therefore
+
+`A=I-14P`,
+
+with eigenvalue -13 on the eight-dimensional image of P and eigenvalue +1 on its 104-dimensional kernel. In particular
+
+`A^-1 = I + E_X/13`,
+
+and its Euclidean condition number is exactly 13. The complete main shear is I+N_A with N_A^2=0 and ||N_A||_2=13; both it and its inverse have norm at most 14, so its condition number is at most 196. Helpers are an independent identity block, and the physical boundary charts are unitary, so this same bound applies to the complete physical coded offer. Its inverse uses I-N_A and needs no 1/13 arithmetic; 1/13 appears only when separately inverting the main code A. Every diagonal entry of A is zero; its 5,824 nonzero off-diagonal entries are ±1/2. The exact checker verifies the degree-two polynomial entry by entry over rational arithmetic, so the spectrum and inverse are universal consequences of that identity rather than numerical eigenvalue observations.
+
+The coefficient 1/13 is part of the mathematical inverse formula. This deliverable does not call it a free dyadic SCALE, assume a division oracle, or insert A^-1 across different physical address charts without paying for the resulting adapters.
+
+## Arbitrary fiber widths
+
+The replay identities hold over Q[FreeGroup72]. Every consistently shared invertible assignment of the 72 native operators defines an evaluation homomorphism. Hence the logical word identity holds at every positive column multiplicity under the retained source native implementation. It does not rely on one-column matrix testing, erasure of central phases or tensor powers preserving sums.
+
+Every physical frame, native monomial and Gaussian child is retained from the authenticated source, except the eight deleted owned-center calls. The new instructions are only constant dyadic scalar operations at an explicitly common ground chart. No fresh nonmonomial address implementation is introduced.
+
+The exact observed maximum prefix coefficient ℓ1 norms are 457 forward and 258 backward, checked on the fixed free-symbol words. Unitary evaluation bounds intermediate exact states and perturbations at the initial input in the maximum-over-fields Euclidean fiber norm by fixed constants independent of fiber width. For discrepancies inserted at later sites, use a separate suffix bound: assign each scalar ADD or SCALE of coefficient c the bound 1+|c|, and every unitary Gaussian/monomial, owned CLEAR or owned COPY the bound 1. The product of these elementary bounds over the finite word bounds every suffix. Thus the sum of local error magnitudes times this fixed product bounds propagated rounding error; no prefix norm is substituted for a suffix norm. Entrywise infinity-norm statements require the appropriate square-root fiber-volume conversion. There is no precision-dependent epsilon and no recursive border-precision claim.
+
+## Integration boundary
+
+The old source wrapper's port-dependent entrance lines and exit hyperplanes remain. A is a constant matrix in the stated normalized logical coordinates. It must not be silently treated as a constant free recoding in every physical main chart or in a different standardized central-Q ABI. Its nonzero off-diagonal entries connect distinct entrance-line charts. A useful next step is an actual coded caller or a paid simultaneous adapter that exploits the eight-mode structure, together with complete moment, raw-dual, compiler, finite precision and outer recovery budgets. This document supplies the exact producer and its bill, not those missing consumers.
+
+## Predecessor overlap and credit
+
+Cinna Davis's PR #4694, head `2add42d1edf14a263abe90a3bcde67fc1ba30768`, already emits a center-free kernel with paid profile minus eight rank-eight calls, records its coupled cache ABI, constructs its raw dual, and proves that its 106 observed helpers start at the empty chart. The source CACHE.md was read directly. None of center deletion, the cold-helper observation or the abstract block Schur elimination is claimed here as new. PR #4698, scientific head `9079ab66ba9a1717df478a08eb957c20d84d3e61`, already emits a dyadic helper basis of 379 gates in each direction reducing observations to eight helpers, and a conditional consumer. The present deliberately dense 6,596-ADD pre-compensation is easier to audit, not a claim to a better basis count. Its changed sufficient result is the actual fixed-template helper-independent coded offer, explicit A entries, exact eight-mode spectrum/inverse/conditioning, and unchanged independent helper ABI.
+
+
+Cao Yifan / intqwq supplies the joint-helper/native-map round-three word at canonical `research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz`, commit `624de9dc66858af0945e5f8a0942488d62280d43`. Its predecessor and refreshed public lineage includes PR #4610; the exact source package and bytes, rather than an older PR headline, bind this result. Cinna Davis, the PR #4470 native/helper/controller lineage, Dugongue's exact native and complementary-provider work, DaysSky, Nick Petalas, Ryanson Jonathan, Jacob Alan Sussman, zxv and the retained scalar, Clifford, precision, compiler and outer contributors retain predecessor credit. The common-chart pre-compensation and exact eight-mode code are the present construction. Local MathProof's Schur block elimination and low-rank composition notes motivated the representation; their source-only inspection is not a fresh Lean/kernel audit or a claim of priority for elementary projection algebra.
diff --git a/research/native-center-free-code/CODED-WORDS.json.gz b/research/native-center-free-code/CODED-WORDS.json.gz
new file mode 100644
index 0000000000..935fedd9c9
Binary files /dev/null and b/research/native-center-free-code/CODED-WORDS.json.gz differ
diff --git a/research/native-center-free-code/CONTENT-HASHES.json b/research/native-center-free-code/CONTENT-HASHES.json
new file mode 100644
index 0000000000..fe66803684
--- /dev/null
+++ b/research/native-center-free-code/CONTENT-HASHES.json
@@ -0,0 +1,24 @@
+{
+  ".gitattributes": "8b9c3028d6467ff3be7c793141927841d70f47f52d0590677438f488ca154992",
+  "ATTRIBUTION.md": "7cdaf8b754a14b6bd54beb4d7d5336e36f782e2b59e6b06f286bdd8ad7126a00",
+  "CODE-INDEPENDENT-REVIEW.json": "1b7a1b1bc7d390af2e157e6100fbb205920305b99a6b9a8080ea5eb9c77790f8",
+  "CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0",
+  "CODED-PROOF.md": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01",
+  "CODED-WORDS.json.gz": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6",
+  "coded_verify.py": "ee9c29012a3163d06f59b6307b4c438805f91b5dec0c9be2408e854c7d929a71",
+  "CROSS-REVIEW.json": "d8d829b395d2943ee5adf90eda69b573a3a06f852a186c98e6e42e8cdd04ae27",
+  "EXPECTED.json": "e147122a93e3c2c5f78af42b631e1fb9410178987b9cc4ca6b5c63a5cb9dccc8",
+  "independent.py": "abaadf9beadf5e93dc7bb784f426b101463b0ad7ea5378395f1e98ea1051291a",
+  "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+  "MUTATION-CONTROLS.json": "ea6e7496a23cf172289946ed30ee7dfa7b5bf97187e272f04aec4889fc19b7a6",
+  "native_core.py": "178ff80824a012970fc9435f122152da03c7e6bdc3a7de12136fe03e05cf24fe",
+  "NOTICE": "0de30db3221dafd34a82e3347a478a73d8338edef051c054ce6f8cf404f91154",
+  "ORIGINS.json": "a07ddeccfb77d8d0d48e307c2d7bc45cf61fc27704e14e57a27b4634f7aed245",
+  "README.md": "fede7462b9f0048f8c8a8756bd2bdac6389448c2fbfa12541a564d1088198cad",
+  "SOURCE-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+  "SOURCES.json": "ba573a89af51a7c17df7d28556b82985894058d8a20e69bf7af0fb83f2891b44",
+  "TASK.json": "1c491d0692d640b2e3653c35512779eae048864faf7f3324d2b8f77703f46964",
+  "VALIDATION.md": "d8ebdfdbe2b9a913851525de7167485cb9fb6470e263ea4541a07246da74edce",
+  "VERIFY.json": "242db372594d7df8a77841f093e5afe2c0f9767a6a6b82b07277996f460b5719",
+  "verify.py": "ef74df64a225dc6fbcf21702f3f23edbb6c5407f20c2115307d57facc862af3f"
+}
diff --git a/research/native-center-free-code/CROSS-REVIEW.json b/research/native-center-free-code/CROSS-REVIEW.json
new file mode 100644
index 0000000000..07b1f43d71
--- /dev/null
+++ b/research/native-center-free-code/CROSS-REVIEW.json
@@ -0,0 +1,47 @@
+{
+  "facts": {
+    "code_condition_2": 13,
+    "code_rank_defect": 8,
+    "helper_repair_ADDs": 6596,
+    "paid": {
+      "1": 2201,
+      "2": 412,
+      "3": 510,
+      "4": 127,
+      "5": 40
+    },
+    "scalar_allowance": 32652
+  },
+  "fresh_checks": [
+    "Independent rational reconstruction: symmetric E, E^2=-14E, trace E=-112, explicit literal A(I+E/13)=I",
+    "Independent construction of primal -EH and raw-dual +EH^T input precodes with all 632 expected rows using disclosed provider replay engine",
+    "Fresh direct isolated normal and optimized public verifier execution, both pass"
+  ],
+  "positive_result": "Exact 632-owner center-free coded native offer and matched raw inverse transpose; 408 independent helpers unchanged",
+  "publication_followups": [
+    "Mandatory declared emitted-artifact existence in scientific checker",
+    "Prefix state-bound wording must not imply suffix error amplification bound without separate elementary-norm product bound",
+    "Explicit source-pinned PR4694 cache-kernel precedence and new 632-owner/ground-precompensation distinction"
+  ],
+  "review_type": "independent algebra plus source/replay review",
+  "reviewed_sha256": {
+    "CODE.json": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0",
+    "CODED-PROOF.md": "72fdbde41aa6d16a976104c9691dfc164a2df6c455ade19629d5be44786b0413",
+    "CODED-WORDS.json.gz": "797bad53122f84aa0f05b602f2bdceb6b50f95a64023799d4f24560d9c61aad6",
+    "SOURCE-WORD.json.gz": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+    "coded_verify.py": "ee9c29012a3163d06f59b6307b4c438805f91b5dec0c9be2408e854c7d929a71",
+    "native_core.py": "178ff80824a012970fc9435f122152da03c7e6bdc3a7de12136fe03e05cf24fe"
+  },
+  "reviewer": "OpenAI Codex assembly agent; no human or formal-kernel acceptance",
+  "scope_limits": [
+    "No Gaussian-axis rank-credit or old main ABI is inferred for coded cross-transfer",
+    "No inverse code is assumed free across distinct physical entrance charts",
+    "No improved kappa, full consumer, recursive compiler/outer transfer, fresh Lean build or physical native phase audit is claimed"
+  ],
+  "publication_resolutions": {
+    "emitted_artifacts": "All declared emitted words and code files are mandatory in the scientific checker and exact inventory wrapper.",
+    "attribution": "CODED-PROOF and ATTRIBUTION explicitly distinguish the PR4694/4698 predecessor results.",
+    "precision": "Lead corrected prefix bound to exact states/input perturbations and supplied a separate finite elementary product bound for suffix rounding amplification.",
+    "final_proof_sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01"
+  }
+}
diff --git a/research/native-center-free-code/EXPECTED.json b/research/native-center-free-code/EXPECTED.json
new file mode 100644
index 0000000000..b02b5ebb8b
--- /dev/null
+++ b/research/native-center-free-code/EXPECTED.json
@@ -0,0 +1,41 @@
+{
+  "all_632_arbitrary_rows": true,
+  "code_inverse": "I+E_X/13",
+  "code_spectrum": {
+    "-13": 8,
+    "1": 104
+  },
+  "condition_number_2": 13,
+  "new_kappa": null,
+  "precompensation_ADDs": 6596,
+  "precompensation_scalar_primitive_allowance": 32652,
+  "runs": [
+    {
+      "backward": false,
+      "events": 28045,
+      "max_prefix_l1": "457",
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40
+      }
+    },
+    {
+      "backward": true,
+      "events": 28045,
+      "max_prefix_l1": "258",
+      "paid": {
+        "1": 2201,
+        "2": 412,
+        "3": 510,
+        "4": 127,
+        "5": 40
+      }
+    }
+  ],
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CENTER_FREE_CODED_SUPPLIER",
+  "symmetric_defect_rank": 8
+}
diff --git a/research/native-center-free-code/LICENSE b/research/native-center-free-code/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/native-center-free-code/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
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+                        http://www.apache.org/licenses/
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+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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+   1. Definitions.
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+      of this License, Derivative Works shall not include works that remain
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+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
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+      "Contributor" shall mean Licensor and any individual or Legal Entity
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+   4. Redistribution. You may reproduce and distribute copies of the
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+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
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+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
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+      (c) You must retain, in the Source form of any Derivative Works
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+      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
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+      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,
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+      PARTICULAR PURPOSE. You are solely responsible for determining the
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+      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,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
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+      Work (including but not limited to damages for loss of goodwill,
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+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
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+   9. Accepting Warranty or Additional Liability. While redistributing
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diff --git a/research/native-center-free-code/MUTATION-CONTROLS.json b/research/native-center-free-code/MUTATION-CONTROLS.json
new file mode 100644
index 0000000000..b7affd8b57
--- /dev/null
+++ b/research/native-center-free-code/MUTATION-CONTROLS.json
@@ -0,0 +1,25 @@
+{
+  "separate_optimized_subprocesses": [
+    {
+      "mutation": "source",
+      "returncode": 1,
+      "last_error": "ValueError: Source hash"
+    },
+    {
+      "mutation": "code",
+      "returncode": 1,
+      "last_error": "ValueError: Frozen code entries"
+    },
+    {
+      "mutation": "word",
+      "returncode": 1,
+      "last_error": "ValueError: Frozen emitted words"
+    },
+    {
+      "mutation": "missing",
+      "returncode": 1,
+      "last_error": "ValueError: Missing frozen code"
+    }
+  ],
+  "all_rejected": true
+}
\ No newline at end of file
diff --git a/research/native-center-free-code/NOTICE b/research/native-center-free-code/NOTICE
new file mode 100644
index 0000000000..42501d0a99
--- /dev/null
+++ b/research/native-center-free-code/NOTICE
@@ -0,0 +1,5 @@
+Cao Yifan / intqwq: authenticated joint-helper/native-map round-three word, canonical research/kappa-round3-warp-20261022, commit 624de9dc66858af0945e5f8a0942488d62280d43; PR4610 lineage.
+Cinna Davis: PR4694 center-free/cache kernel and arbitrary-input raw dual, PR4698 cold-helper basis/conditional consumer; PR4440/4441/4447/4470 lineage.
+Dugongue: present ground-chart helper pre-compensation and explicit invertible coded offer, with substantial OpenAI Codex assistance.
+Retains native, E8, scalar, Clifford, compiler, precision, outer and contributor notices in the cited upstream sources; zxv, Jacob Alan Sussman, DaysSky, Nick Petalas and Ryanson Jonathan retain predecessor credit.
+Apache-2.0. No independent human or formal proof-kernel review is claimed.
diff --git a/research/native-center-free-code/ORIGINS.json b/research/native-center-free-code/ORIGINS.json
new file mode 100644
index 0000000000..f52f55b77c
--- /dev/null
+++ b/research/native-center-free-code/ORIGINS.json
@@ -0,0 +1,51 @@
+{
+  "canonical_base": "624de9dc66858af0945e5f8a0942488d62280d43",
+  "origins": [
+    {
+      "local": "SOURCE-WORD.json.gz",
+      "source": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "revision": "624de9dc66858af0945e5f8a0942488d62280d43",
+      "url": "https://raw.githubusercontent.com/CrocSwap/integer-mult-bounds/624de9dc66858af0945e5f8a0942488d62280d43/research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+      "decompressed_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd"
+    }
+  ],
+  "predecessors": [
+    {
+      "pr": 4694,
+      "head": "2add42d1edf14a263abe90a3bcde67fc1ba30768",
+      "credit": "Center-free cache kernel, same paid profile, raw dual, observed helpers start at ground"
+    },
+    {
+      "pr": 4698,
+      "head": "9079ab66ba9a1717df478a08eb957c20d84d3e61",
+      "credit": "Physical dyadic helper basis and conditional consumer"
+    }
+  ],
+  "inspected_sources": [
+    {
+      "path": "research/query-thinned-controllers/controller.py",
+      "revision": "624de9dc66858af0945e5f8a0942488d62280d43",
+      "sha256": "8b462d660487b1be4940357c4c7522967b1bfaede3c02b1c66109b85acae0fd2",
+      "local_equal": true
+    },
+    {
+      "path": "research/kappa-rebuild/bit/complex_controller_factor.py",
+      "revision": "624de9dc66858af0945e5f8a0942488d62280d43",
+      "sha256": "1de9aaf918e6a4f2f5448754c1f3c3da3b85e6257849ebd097af09859c4e5497",
+      "local_equal": true
+    },
+    {
+      "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "revision": "624de9dc66858af0945e5f8a0942488d62280d43",
+      "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7",
+      "local_equal": true
+    }
+  ],
+  "derived_core_source": {
+    "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+    "revision": "624de9dc66858af0945e5f8a0942488d62280d43",
+    "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7",
+    "local_equal": true
+  }
+}
diff --git a/research/native-center-free-code/README.md b/research/native-center-free-code/README.md
new file mode 100644
index 0000000000..26144655f8
--- /dev/null
+++ b/research/native-center-free-code/README.md
@@ -0,0 +1,32 @@
+# A center-free native producer with an explicit eight-mode port code
+
+This emits an exact changed native word with all eight rank-8 owned-center calls removed. All 632 persistent inputs remain arbitrary and independent, all 408 helper jobs remain autonomous, and the actual entrance/exit charts stay unchanged. The main logical endpoint is
+
+```text
+(X, Y, H) -> (X, Y + A X, H).
+```
+
+The explicit 112-by-112 code is `A = I - 14 P`, where `P` is an orthogonal projection of rank 8. Its eigenvalues are 1 (104 times) and -13 (8 times), with `A^-1 = I + (A-I)/13`. The forward and actual raw-dual paid profile is `{1:2201, 2:412, 3:510, 4:127, 5:40}`: eight rank-8 children disappear, with no new Gaussian child. The simple compensation uses 6,596 fixed dyadic ADDs.
+
+**No improved κ or complete multiplier is established.** This code changes the cross-transfer. Treating it as the old uncoded supplier would be wrong. Its inverse is an exact rational matrix, not a free dyadic operation across distinct physical input charts.
+
+Read [CODED-PROOF.md](CODED-PROOF.md) for the constructive theorem and [ATTRIBUTION.md](ATTRIBUTION.md) for overlap and predecessor credit.
+
+## Reproduce
+
+Only Python 3.12 and its standard library are required; there are no Windows paths, external commands, GPU libraries or platform-specific native binaries in the scientific verifier.
+
+```sh
+python3.12 -I -B research/native-center-free-code/coded_verify.py
+python3.12 -I -O -B research/native-center-free-code/coded_verify.py
+python3.12 -I -B research/native-center-free-code/verify.py
+python3.12 -B scripts/research_package.py --package research/native-center-free-code
+```
+
+The written all-width proof uses evaluation of a rational free-group identity and authenticated existing native operations. Finite replay is evidence for that identity; it is not a Lean kernel or independent human audit. The inherited source physical implementation and analytic multiplication hypotheses are not independently reproved. No selected cold replay or hosted CI pass is claimed.
+
+## Open next questions
+
+The structured questions are in [TASK.json](TASK.json). The immediate target is a paid, source-compatible adapter or caller exploiting the eight-mode code. An actual output/input chart conversion, odd-denominator implementation, full moment, storage, precision and outer budget must be supplied before claiming a κ improvement.
+
+Prepared by Dugongue with substantial OpenAI Codex assistance from the lead and three workers. Apache-2.0.
diff --git a/research/native-center-free-code/SOURCE-WORD.json.gz b/research/native-center-free-code/SOURCE-WORD.json.gz
new file mode 100644
index 0000000000..46d929df83
Binary files /dev/null and b/research/native-center-free-code/SOURCE-WORD.json.gz differ
diff --git a/research/native-center-free-code/SOURCES.json b/research/native-center-free-code/SOURCES.json
new file mode 100644
index 0000000000..8f88c35a03
--- /dev/null
+++ b/research/native-center-free-code/SOURCES.json
@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "base_commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ACTUAL-WORD.json.gz",
+      "usage": "provenance",
+      "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e",
+      "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05"
+    },
+    {
+      "path": "research/kappa-causal-continuation/buffer-borrowing/verify_buffers.py",
+      "usage": "provenance",
+      "git_blob": "5a55034ec9e6185d981e16c28e1e2e455069e2cb",
+      "sha256": "106b4d5e052427230df452f0c901d5390a0583782960b80a8af94d9a984022c7"
+    }
+  ]
+}
diff --git a/research/native-center-free-code/TASK.json b/research/native-center-free-code/TASK.json
new file mode 100644
index 0000000000..83aef57bb3
--- /dev/null
+++ b/research/native-center-free-code/TASK.json
@@ -0,0 +1,96 @@
+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 7,
+  "base_commit": "624de9dc66858af0945e5f8a0942488d62280d43",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/qq16-caller-install/README.md"
+    ],
+    "methods": [
+      "Derive the matched whole-caller physical bill for installed and baseline protocols.",
+      "Change the actual demanded observations and prove a cheaper legal producer/consumer contract."
+    ],
+    "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. 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",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.",
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "allowed_variations": [
+      "One paid query, one changed first pair, or one precisely specified affine helper state.",
+      "A counterexample or lower bound for that exact proposed repair.",
+      "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+    ],
+    "scope_change_triggers": [
+      "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+      "Treating cover-map counts as zero-cost physical address operations.",
+      "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+      "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.",
+      "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.",
+      "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969",
+      "2540",
+      "early record",
+      "output-bank retention",
+      "complete native decoder",
+      "2965",
+      "producer defect",
+      "dirty-helper range",
+      "F17 consumer",
+      "4166",
+      "qq16-caller-install"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+        "evidence": "research/qq16-caller-install/README.md",
+        "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+        "status": "author-checked",
+        "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Construct an exact center-free, independently-helper-preserving native offer with an explicit invertible rank-eight port code; no new kappa.",
+  "scope_change_reason": "The assigned goal was a complete improved kappa. Changed-word and caller searches did not close a profitable complete consumer. The retained positive result emits the changed producer and code exactly, without treating its ABI as the old uncoded supplier.",
+  "bottleneck_link": "Removes eight rank-eight owned-center Gaussian children while preventing helper contamination by an actual common-ground pre-compensation; the nonuniform physical port code remains to be consumed.",
+  "budget_minutes": 60,
+  "stop_rule": "Freeze discovery at 00:24 UTC; reserve the final quarter of the one-hour session for verification and release.",
+  "outcome": "partial",
+  "evidence": "Exact arbitrary-input forward/raw-dual operator replay, rational projection/inverse identities and separate-agent reviews; no kernel or full multiplier claim.",
+  "author": "Dugongue",
+  "ai_assistance": "Dugongue with substantial OpenAI Codex assistance from the lead and three agents. No Jev or Lean proof kernel used.",
+  "open_questions": [
+    {
+      "question": "Can a physically admitted caller consume the coded cross-transfer without spending its local saving?",
+      "why_it_matters": "Only a complete unchanged-output multiplication construction can improve kappa.",
+      "first_step": "Bind the rank-eight code at one actual controller cut and emit every nonuniform chart adapter, then reprice the complete target/paid profile.",
+      "blocked_by": "Off-diagonal port recodings cross distinct rank-one entrance charts; no free input inverse or favorable complete caller is established."
+    },
+    {
+      "question": "Can the eight-mode structure reduce the actual simultaneous adapter bill?",
+      "why_it_matters": "The exact projector compresses the algebraic code to eight modes, but does not itself price native conversions.",
+      "first_step": "Use the explicit matrix and its inverse to construct a shared chronological adapter, preserving independent inputs and all helper jobs.",
+      "blocked_by": "A^-1 has odd denominator 13 and nontrivial physical chart conversions; no unpriced rational scalar or address oracle is permitted."
+    }
+  ]
+}
diff --git a/research/native-center-free-code/VALIDATION.md b/research/native-center-free-code/VALIDATION.md
new file mode 100644
index 0000000000..36556eb125
--- /dev/null
+++ b/research/native-center-free-code/VALIDATION.md
@@ -0,0 +1,9 @@
+# Validation scope
+
+The source-bound exact interpreter checks all 632 independent arbitrary-input rows in each orientation, every retained scalar common frame and paid climb, final frames and owned-center cleanup. The emitted words and exact code entries are frozen and compared to reconstruction. The degree-two projector identity is checked over rational arithmetic; spectral multiplicities follow from its trace. A wrong pre-compensation sign is required to fail.
+
+Separate-agent reviews used the submitted interpreter for endpoints and an independently written rational matrix calculation for symmetry, the polynomial, rank, inverse and condition number. CROSS-REVIEW.json binds the reviewed scientific files. No independent human, Lean kernel, complete multiplier cold replay or hosted CI is claimed.
+
+All coefficients and added operation counts are fixed independently of fiber width and precision. The source's all-column physical Gaussian/monomial implementation remains an inherited premise; newly emitted operations are explicitly common-ground dyadic ADDs. The proof bounds arbitrary-width operator semantics by free-group evaluation, not by tensoring a matrix sum.
+
+A favorable complete consumer is still required. A is not freely movable between nonuniform physical port charts, and 1/13 is not a free dyadic primitive. The reported eight rank-8 call reduction is local and changes the main ABI. There is no newly established κ.
diff --git a/research/native-center-free-code/VERIFY.json b/research/native-center-free-code/VERIFY.json
new file mode 100644
index 0000000000..f0697bc983
--- /dev/null
+++ b/research/native-center-free-code/VERIFY.json
@@ -0,0 +1,41 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact full inventory and upstream hashes; all 632 arbitrary owner rows in primal/raw dual, actual frames and paid profile, emitted-word equality, rational rank-eight projector identity and semantic pre-compensation mutation."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact full inventory and upstream hashes; all 632 arbitrary owner rows in primal/raw dual, actual frames and paid profile, emitted-word equality, rational rank-eight projector identity and semantic pre-compensation mutation."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/independent.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent exact Gram-factor reconstruction of the full 112-by-112 projector from eight basis columns; no source interpreter imported."
+    }
+  ]
+}
diff --git a/research/native-center-free-code/coded_verify.py b/research/native-center-free-code/coded_verify.py
new file mode 100644
index 0000000000..90627892f6
--- /dev/null
+++ b/research/native-center-free-code/coded_verify.py
@@ -0,0 +1,63 @@
+"""Exact center-free coded native offer; Apache-2.0, Codex assistance."""
+from pathlib import Path
+import sys,json,gzip
+from fractions import Fraction as Q
+from collections import Counter
+from hashlib import sha256
+sys.path.insert(0,str(Path(__file__).resolve().parent))
+import native_core as V
+HERE=Path(__file__).resolve().parent
+
+def build(a,E,back=False):
+ c=a['canonical'];p=[]
+ for i,j,v in E:
+  if j<224:continue
+  dst,src,coef=(j,i,v)if back else(i,j,-v)
+  V.need(c['start'][dst]==0 and c['start'][src]==0,'Ground pre-compensation')
+  p.append(['scalar',['add',['L',dst],['L',src],coef.numerator,coef.denominator],0])
+ return c,p+V.clear_centers(a['programs']['backward'if back else'forward'])
+
+def matrices(E):
+ EX=[[Q(0)]*112 for _ in range(112)]
+ for i,j,v in E:
+  if j<112:EX[i-112][j]=v
+ A=[[EX[i][j]+Q(i==j)for j in range(112)]for i in range(112)]
+ V.need(all(EX[i][j]==EX[j][i]for i in range(112)for j in range(112)),'Real symmetric defect')
+ V.need(sum(EX[i][i]for i in range(112))==-112,'Projection trace')
+ for i in range(112):
+  for j in range(112):
+   s=sum(EX[i][k]*EX[k][j]for k in range(112))
+   V.need(s==-14*EX[i][j],'Exact defect minimal polynomial')
+ return EX,A
+
+def expected(i,back,EX):
+ r=V.expected(i,back)
+ if not back and 112<=i<224:
+  for j,v in enumerate(EX[i-112]):
+   if v:V.add(r,V.identity(j),v)
+ if back and i<112:
+  for j in range(112):
+   if EX[j][i]:V.add(r,V.identity(112+j),-EX[j][i])
+ return r
+
+def main():
+ b=gzip.decompress((HERE/'SOURCE-WORD.json.gz').read_bytes());V.need(sha256(b).hexdigest()==V.SOURCE_SHA,'Source hash');a=json.loads(b);E=V.error_kernel(a);EX,A=matrices(E);res=[]
+ generated={'scope':'Exact center-free coded ABI, not the old uncoded supplier','canonical':json.loads(json.dumps(a['canonical'])),'programs':{}}
+ generated['canonical']['local_profile']={'1':2201,'2':412,'3':510,'4':127,'5':40}
+ for back in(False,True):
+  c,p=build(a,E,back);generated['programs']['backward'if back else'forward']=p;rows,paid,mx=V.replay(c,p,back)
+  V.need(all(rows[i]==expected(i,back,EX)for i in range(632)),'All arbitrary coded endpoints')
+  V.need(paid==Counter({1:2201,2:412,3:510,4:127,5:40}),'Complete center-free profile')
+  res.append({'backward':back,'paid':dict(paid),'max_prefix_l1':str(mx),'events':len(p)})
+ V.need((HERE/'CODED-WORDS.json.gz').is_file(),'Missing frozen emitted words')
+ frozen=json.loads(gzip.decompress((HERE/'CODED-WORDS.json.gz').read_bytes()));V.need(frozen==generated,'Frozen emitted words')
+ V.need((HERE/'CODE.json').is_file(),'Missing frozen code')
+ V.need(json.loads((HERE/'CODE.json').read_text())=={'A':[[str(v)for v in row]for row in A]},'Frozen code entries')
+ # Actual signed pre-compensation corruption must leave helper-dependent error.
+ c,p=build(a,E,False);p[0][1][3]*=-1;rows,_,_=V.replay(c,p,False)
+ V.need(any(rows[i]!=expected(i,False,EX)for i in range(632)),'Pre-compensation mutation rejected')
+ EH=[v for i,j,v in E if j>=224]
+ tariff=lambda v:3+abs(v.numerator).bit_length()-1+abs(v.numerator).bit_count()+v.denominator.bit_length()-1
+ out={'status':'PASS_CENTER_FREE_CODED_SUPPLIER','source_payload_sha256':V.SOURCE_SHA,'precompensation_ADDs':len(EH),'precompensation_scalar_primitive_allowance':sum(tariff(v)for v in EH),'symmetric_defect_rank':8,'code_spectrum':{'1':104,'-13':8},'code_inverse':'I+E_X/13','condition_number_2':13,'all_632_arbitrary_rows':True,'new_kappa':None,'runs':res}
+ print(json.dumps(out,sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/native-center-free-code/independent.py b/research/native-center-free-code/independent.py
new file mode 100644
index 0000000000..7b7d142f25
--- /dev/null
+++ b/research/native-center-free-code/independent.py
@@ -0,0 +1,42 @@
+"""Independent rank-eight Gram reconstruction from the frozen port matrix."""
+from pathlib import Path
+from fractions import Fraction as F
+import json
+from hashlib import sha256
+P=Path(__file__).resolve().parent
+
+def need(c,m):
+    if not c:raise ValueError(m)
+
+def inverse(a):
+    n=len(a);a=[row[:]+[F(i==j)for j in range(n)]for i,row in enumerate(a)]
+    for j in range(n):
+        k=next(i for i in range(j,n)if a[i][j]);a[j],a[k]=a[k],a[j]
+        d=a[j][j];a[j]=[v/d for v in a[j]]
+        for i in range(n):
+            if i!=j:
+                d=a[i][j];a[i]=[v-d*w for v,w in zip(a[i],a[j])]
+    return [row[n:]for row in a]
+
+def main():
+    raw=(P/'CODE.json').read_bytes();a=[[F(x)for x in row]for row in json.loads(raw)['A']];n=112
+    need(len(a)==n and all(len(row)==n for row in a),'Code dimensions')
+    q=[[(F(i==j)-a[i][j])/14 for j in range(n)]for i in range(n)]
+    basis={};cols=[]
+    for col in zip(*q):
+        v=list(col)
+        for pivot,b in sorted(basis.items()):
+            c=v[pivot];v=[x-c*y for x,y in zip(v,b)]
+        k=next((i for i,x in enumerate(v)if x),None)
+        if k is not None:
+            d=v[k];basis[k]=[x/d for x in v];cols.append(list(col))
+    need(len(cols)==8,'Eight independent image columns')
+    gram=[[sum(x*y for x,y in zip(c,d))for d in cols]for c in cols];gi=inverse(gram)
+    # Independently reconstruct the unique orthogonal projection onto these columns.
+    cg=[[sum(cols[k][i]*gi[k][j]for k in range(8))for j in range(8)]for i in range(n)]
+    for i in range(n):
+        for j in range(n):need(q[i][j]==sum(cg[i][k]*cols[k][j]for k in range(8)),'Full Gram projector equality')
+    need(all(a[i][i]==0 for i in range(n)),'Zero code diagonal')
+    need(sum(a[i][j]!=0 for i in range(n)for j in range(n)if i!=j)==5824,'Off-diagonal support')
+    print(json.dumps({'status':'PASS_INDEPENDENT_EIGHT_MODE_GRAM','public_code_sha256':sha256(raw).hexdigest(),'rank':8,'spectrum':{'1':104,'-13':8},'condition_number_2':13},sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/native-center-free-code/native_core.py b/research/native-center-free-code/native_core.py
new file mode 100644
index 0000000000..5d8a8f0a63
--- /dev/null
+++ b/research/native-center-free-code/native_core.py
@@ -0,0 +1,73 @@
+"""Exact source-bound coded-supplier replay core. Apache-2.0; Codex assistance.
+Frozen source: Cao Yifan #4610 and retained Cinna Davis/Dugongue lineage.
+"""
+from pathlib import Path
+from fractions import Fraction as Q
+from collections import Counter
+from hashlib import sha256
+import gzip,json,copy,importlib.util,sys
+HERE=Path(__file__).resolve().parent
+SOURCE_SHA='cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd'
+def need(c,m):
+ if not c:raise ValueError(m)
+def identity(i):return {(i,()):Q(1)}
+def add(dst,src,a):
+ for k,v in tuple(src.items()):
+  z=dst.get(k,Q(0))+a*v
+  if z:dst[k]=z
+  else:dst.pop(k,None)
+def warp(row,op,back):
+ s=(1 if op>0 else -1)*(abs(op)+(1000000 if back else 0));out={}
+ for (v,w),a in row.items():
+  ww=w[1:]if w and w[0]==-s else(s,)+w;out[v,ww]=out.get((v,ww),Q(0))+a
+ return {k:a for k,a in out.items()if a}
+def expected(i,back):
+ r=identity(i)
+ if back and i<112:add(r,identity(i+112),-1)
+ if not back and 112<=i<224:add(r,identity(i-112),1)
+ return r
+
+def replay(c,program,back=False,check_frames=True):
+ rows={i:identity(i)for i in range(632)};rows[632]={};cur=c['start'][:]+[None];paid=Counter();maxnorm=Q(1)
+ for e in program:
+  if e[0]=='scalar':
+   g,f=e[1:];r=g[1][1]+(632 if g[1][0]=='C'else 0)
+   if g[0]=='clear':need(r==632,'Borrowed erasure');rows[r]={};cur[r]=f
+   else:
+    if check_frames:need(cur[r]==f,'Scalar target frame')
+    if g[0]in('add','copy'):
+     v=g[2][1]+(632 if g[2][0]=='C'else 0)
+     if check_frames:need(cur[v]==f,'Scalar source frame')
+     if g[0]=='copy':need(r==632,'Borrowed overwrite');rows[r]=rows[v].copy()
+     else:need(r!=v,'Self add');add(rows[r],rows[v],Q(g[3],g[4]))
+    elif g[0]=='scale':rows[r]={k:Q(g[2],g[3])*v for k,v in rows[r].items()}
+    else:raise ValueError('Scalar opcode')
+    maxnorm=max(maxnorm,sum(map(abs,rows[r].values()),Q(0)))
+  elif e[0]=='warp':
+   _,r,op,x,y=e;r=r[1]+(632 if r[0]=='C'else 0)
+   if check_frames:need(cur[r]==x,'Warp source frame')
+   rows[r]=warp(rows[r],op,back);cur[r]=y
+  elif e[0]=='climb':
+   _,_,r,x,y,k=e
+   if check_frames:need(cur[r]==x,'Climb source frame')
+   need(k==len(c['frames'][y])-len(c['frames'][x])and k>0,'Ascending paid rank');cur[r]=y;paid[k]+=1
+  elif e[0]=='center':
+   _,r,x,y,k=e;r+=632
+   if check_frames:need(cur[r]==x,'Center source frame')
+   need(k==abs(len(c['frames'][y])-len(c['frames'][x])),'Center paid rank');cur[r]=y;paid[k]+=1
+  else:need(e[0]in('phase','adapter','residual_adapter'),'Unknown opcode')
+ need(cur[:632]==c['final'],'Final frames');need(not rows[632],'Owned field cleared')
+ return rows,paid,maxnorm
+
+def clear_centers(program):return [['scalar',['clear',['C',e[1]]],e[3]]if e[0]=='center'else copy.deepcopy(e)for e in program]
+def error_kernel(a):
+ rows,paid,_=replay(a['canonical'],clear_centers(a['programs']['forward']));E=[]
+ for i in range(632):
+  err=rows[i].copy();add(err,expected(i,False),-1)
+  for (j,w),v in sorted(err.items()):
+   need(112<=i<224 and(j<112 or j>=224),'Strict triangular error block');need(not w,'Constant owner kernel')
+   need(a['canonical']['final'][j]==1,'Repair source final full frame');need(j<112 or a['canonical']['start'][j]==0,'Pre-repair source initial ground')
+   E.append((i,j,v))
+ need(len(E)==12532,'Frozen error term count')
+ return E
+
diff --git a/research/native-center-free-code/verify.py b/research/native-center-free-code/verify.py
new file mode 100644
index 0000000000..3e4a7b5b33
--- /dev/null
+++ b/research/native-center-free-code/verify.py
@@ -0,0 +1,27 @@
+"""Portable release/source authentication and exact coded-offer replay."""
+from pathlib import Path
+from hashlib import sha256
+import json,importlib.util,io,contextlib
+HERE=Path(__file__).resolve().parent
+
+def need(c,m):
+    if not c: raise ValueError(m)
+
+def main():
+    pins=json.loads((HERE/'CONTENT-HASHES.json').read_text(encoding='utf-8'))
+    actual={p.relative_to(HERE).as_posix() for p in HERE.rglob('*') if p.is_file()}
+    need(actual==set(pins)|{'CONTENT-HASHES.json'},'Exact package file inventory')
+    for name,h in pins.items():
+        need(sha256((HERE/name).read_bytes()).hexdigest()==h,'Package byte drift: '+name)
+    origins=json.loads((HERE/'ORIGINS.json').read_text(encoding='utf-8'))
+    for row in origins['origins']:
+        need(sha256((HERE/row['local']).read_bytes()).hexdigest()==row['sha256'],'Upstream byte pin')
+    spec=importlib.util.spec_from_file_location('coded_offer',HERE/'coded_verify.py')
+    module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+    output=io.StringIO()
+    with contextlib.redirect_stdout(output): module.main()
+    receipt=json.loads(output.getvalue())
+    need(receipt==json.loads((HERE/'EXPECTED.json').read_text(encoding='utf-8')),'Frozen mathematical receipt')
+    print(json.dumps(receipt,sort_keys=True))
+    print('PASS_SOURCE_BOUND_CENTER_FREE_CODE no_new_kappa')
+if __name__=='__main__':main()