Independent audit: correct QQ16 shear native-frame claim

research/qq16-shear-native-frame-audit/README.md

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+# Native frame audit of the QQ16 identity shear
+
+Status: independent verification and a scoped correction; no new kappa.
+This package audits the native implementation claim in [PR2216](https://github.com/CrocSwap/integer-mult-bounds/pull/2216).
+The payload-constant rank certificate remains outside the correction.
+
+## Precise claim and inherited boundary
+
+Fix the retained QQ16 interface and the coordinate pairing below.
+Keep the F0 output boundary and B1 input boundary unchanged.
+The proposed insertion uses only the sixteen bare scalar updates shown here.
+
+```text
+A = [0, 7, 20, 27, 36, 46, 57, 111]
+T = [21, 37, 47, 76, 81, 87, 92, 110]
+X_T[j] += X_A[j]
+Y_T[j] -= X_A[j]       (j = 0,...,7)
+```
+
+For every listed pair, its Y update fails to implement the stated logical subtraction on arbitrary payloads.
+Its X update has equal source and target frames.
+The claim concerns this insertion at the retained boundary, with no intervening conversion or changed boundary convention.
+
+Let F=completed(0). The inherited boundary encodes logical values x and y as follows:
+
+```text
+physical X_p = F x_p
+physical Y_p = F C_(q_p)^-1 y_p
+C_q = ((1+i) I + (1-i) T_q)/2,    (T_q f)(z) = f(z XOR q)
+```
+
+This boundary is explicit in [CONSERVED-QQ16](../joint-query/evidence/CONSERVED-QQ16.md#cover-action-and-native-phases).
+The [native review](../joint-query/evidence/NATIVE-REVIEW.md) states that B1 first converts X_T to the Y type.
+The `boundary(stage)` function in [verify_native.py](../joint-query/verify_native.py) gives the same types.
+We inherit the retained core's output contract; we do not replay or prove that complete core here.
+The packet check confirms that F0's wrappers preserve the selected X types and never write Y_T.
+It also checks B1's first eight normalizations against the corresponding Y types.
+
+## Complete counterexample argument
+
+Start with logical Y_T[j]=0 and X_A[j]=x.
+A bare physical subtraction writes -F x.
+The desired logical subtraction requires -F C_q^-1 x.
+Since F is invertible, these outputs agree exactly when C_q x=x.
+All translation lines commute here, so interpretation in the Y frame gives -C_q x instead of -x.
+The two bare updates change the logical T sum by (I-C_q)x.
+
+Each selected label q is nonzero in the first nine binary coordinates.
+Choose w with q dot w=1 over F2, and set chi_w(z)=(-1)^(w dot z).
+Then T_q chi_w=-chi_w, hence C_q chi_w=i chi_w and C_q^-1 chi_w=-i chi_w.
+Thus the two outputs differ for every selected pair.
+The logical sum changes by (1-i)chi_w instead of zero.
+
+The witness sits at the identity-owner fiber with one nonconstant payload layer.
+Keep the other payload layers and spectator coordinates constant.
+This also gives a counterexample for every positive tensor length under the inherited tensor convention.
+We retain the full owner cover.
+
+For port 21, q=289 and w=1. Then F chi_w=i chi_w.
+At address zero, the bare and desired outputs are -i and -1, respectively.
+[RESULT.json](RESULT.json) records all eight exact witnesses.
+
+PR2216's [cost paragraph](https://github.com/CrocSwap/integer-mult-bounds/blob/b80e9ba43367fb8b20877a97da1cb677c34f9264/research/qq16-f0-b1-shear-seedccce426/PROOF.md#cost-and-remaining-obligations) describes all data frames as common.
+Its preceding experiment keeps each payload block constant.
+On that restricted subspace every C_q acts as identity, so its test cannot detect the frame mismatch.
+Sixteen bare additions do realize the shear on that subspace.
+This audit does not replay or refute the reported rank-eight minor on that subspace.
+
+## Independent checks and limits
+
+The verifier authenticates four retained inputs and checks the relevant literal wrapper events.
+It evaluates stored Z4 coefficient polynomials on all 512 active characters for each target.
+A separate physical implementation applies Gaussian-integer C-line convolutions to eight 512-entry character arrays.
+That implementation does not evaluate or generate phase polynomials and imports no predecessor executable.
+Its outputs match the polynomial prediction and reject each bare subtraction.
+
+Inverse-line adaptation passes; the positive-line sign fails.
+Physical decoding also checks the nonzero logical sum change.
+Constant payloads pass both paths and expose the restricted test's blind spot.
+
+The complete argument above proves failure of the unrestricted scalar identity.
+The finite checks bind its eight labels and witnesses to the pinned source.
+They do not independently validate the full retained traversal, its native core, hosting, or the multiplication theorem.
+The X count records eight equal-frame updates, rather than eight separate full-circuit tests.
+
+## Cost boundary and contribution
+
+A native implementation for arbitrary payloads needs an explicit typed adaptation or a fusion proof.
+The semantic inverse-line control is not a free primitive or a hosted construction.
+This audit proves no lower bound on additional children for a redesigned word.
+It does not rule out reusing B1's existing operations.
+The correction prevents an unrestricted controller from inheriting the sixteen-addition invoice without a typed implementation.
+It changes no selected frontier or supplier certificate.
+
+## Reproduce
+
+From the repository root, run:
+
+```sh
+python3 -I -O -B research/qq16-shear-native-frame-audit/verify.py
+```
+
+Expected: `PASS_QQ16_SHEAR_NATIVE_FRAME_AUDIT rejected_Y_adds=8 same_frame_X_updates=8 character_phases=4096 physical_vectors=8`.
+Research verification uses CPython 3.15.0 through the Math research-python wrapper.
+The generic package replay also passes in its required environment, CPython 3.12.12.
+That second run is an explicit compatibility exception, not independent mathematical verification.
+
+## Open next questions
+
+Can a typed rewrite fuse the missing conversion into B1's existing native operations?
+First emit that complete word and compare every arbitrary input and helper output.
+Then price its children, maps, storage, restoration, precision, and hosting.
+The current audit does not supply that construction.
+
+## Credit and provenance
+
+Ali Romman and the retained QQ16 lineage supply the maps, native words, and reviews.
+Cinna Davis supplies the shear in PR2216, head b80e9ba43367fb8b20877a97da1cb677c34f9264.
+The audit uses base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.
+See [SOURCES.json](SOURCES.json) for exact input hashes and Git blobs.
+PR2093's separate surviving A-defect concerns full-controller information, not this frame correction.
+
+Prepared for Charles Bethin with substantial OpenAI Codex assistance. Apache-2.0.
+No independent human review or formal-kernel proof occurs here.

research/qq16-shear-native-frame-audit/RESULT.json

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+{
+  "literal_shear_scalar_additions": 16,
+  "owner": "identity",
+  "phase_characters_checked": 4096,
+  "physical_character_vectors": 8,
+  "receipts": [
+    {
+      "A_port": 0,
+      "T_port": 21,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f23",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 1,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 289,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 7,
+      "T_port": 37,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f39",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 2,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 274,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 20,
+      "T_port": 47,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f49",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 4,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 268,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 27,
+      "T_port": 76,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f78",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 64,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 448,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 36,
+      "T_port": 81,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f83",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 2,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 478,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 46,
+      "T_port": 87,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f89",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 1,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 493,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 57,
+      "T_port": 92,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f94",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 1,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 499,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    },
+    {
+      "A_port": 111,
+      "T_port": 110,
+      "X_T_add_legal": true,
+      "X_frame": "f1",
+      "Y_T_add_legal": false,
+      "Y_frame": "f112",
+      "bare_target": [
+        0,
+        -1
+      ],
+      "desired_target": [
+        -1,
+        0
+      ],
+      "frequency_mask": 1,
+      "inverse_line_semantic_control": "PASS",
+      "logical_sum_change_at_witness": [
+        1,
+        -1
+      ],
+      "physical_counterexample_index": 0,
+      "positive_line_control": "REJECTED",
+      "q": 319,
+      "source_phase_Z4": 1,
+      "target_phase_Z4": 0
+    }
+  ],
+  "same_frame_X_additions": 8,
+  "scope": "Counterexamples to the literal sixteen-scalar native implementation on arbitrary payloads. PR2216 logical payload-constant rank result is not refuted. Fused or redesigned implementations remain open; no child-count lower bound or new kappa.",
+  "status": "PASS_QQ16_SHEAR_NATIVE_FRAME_AUDIT",
+  "tensor_payload_layers": 1,
+  "unadapted_Y_additions_rejected": 8
+}

research/qq16-shear-native-frame-audit/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "e8870e5917057d59b730eb14721a778639eca050",
+      "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7"
+    },
+    {
+      "path": "research/joint-query/certificate.json.gz",
+      "usage": "input",
+      "git_blob": "c6e876d8b48d768214deee265ade428f8983b566",
+      "sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7"
+    },
+    {
+      "path": "research/joint-query/evidence/CONSERVED-QQ16.md",
+      "usage": "input",
+      "git_blob": "4639583c1be02c2fb60ed8a8072c9969ef1569ce",
+      "sha256": "60f0de3a7205ba5046b5ae7ffa8bf2b1ea42ea46b498face0a77966b59e7f3fb"
+    },
+    {
+      "path": "research/joint-query/evidence/NATIVE-REVIEW.md",
+      "usage": "input",
+      "git_blob": "525b38dbdefed0e8192a9c5165e802136cc05034",
+      "sha256": "2247e3cbe73f3f0da55c647ffae15f98dd9445b2366ba9e255b9bebc9f742b70"
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+    }
+  ]
+}