diff --git a/research/pg29-matched-dirty-completion/COMPLETION-RESULT.json b/research/pg29-matched-dirty-completion/COMPLETION-RESULT.json
new file mode 100644
index 0000000000..e3e06e6eac
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/COMPLETION-RESULT.json
@@ -0,0 +1,21 @@
+{
+  "status": "PASS_PG29_MATCHED_DIRTY_COMPLETION",
+  "source_word_sha256": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f",
+  "field": "F3[t]/(t^2+1), encoded by a+3b",
+  "independent_field_operations": true,
+  "local_maps": 182,
+  "physical_transmissions": 735,
+  "independent_input_stubs": 175,
+  "matched_input_pairs": 9,
+  "matched_output_pairs": 9,
+  "quotient_dimension": 166,
+  "correction_rank": 9,
+  "all_formal_columns_restored": true,
+  "generic_schur_dimension": 18,
+  "generic_schur_invertible": true,
+  "D9_nonzeros": 74,
+  "correction_nonzeros": 1243,
+  "physical_frames": false,
+  "paid_supplier": false,
+  "new_kappa": false
+}
diff --git a/research/pg29-matched-dirty-completion/HISTORICAL-DIRTY-RESULT.json b/research/pg29-matched-dirty-completion/HISTORICAL-DIRTY-RESULT.json
new file mode 100644
index 0000000000..acca5e29e5
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/HISTORICAL-DIRTY-RESULT.json
@@ -0,0 +1,30 @@
+{
+  "primary_source_commit": "3436359a85d13a1bf6e87c3a3dbdaa64788277f4",
+  "field": "F3[t]/(t^2+1)",
+  "independent_input_stubs": 175,
+  "physical_transmissions": 735,
+  "all_local_5_by_5_maps_invertible": true,
+  "whole_transfer_invertible": true,
+  "B_to_B_identity": true,
+  "block_ranks": {
+    "B_from_B": 157,
+    "B_from_C": 9,
+    "J_from_B": 9,
+    "J_from_C": 18
+  },
+  "block_nonzero_entries": {
+    "B_from_B": 157,
+    "B_from_C": 2486,
+    "J_from_B": 2434,
+    "J_from_C": 263
+  },
+  "whole_transfer_is_permutation": false,
+  "schur_H_minus_GF_rank": 18,
+  "equal_paired_C_values_do_not_contaminate_B": true,
+  "paired_J_outputs_have_equal_B_contributions": true,
+  "scope": "A dirty GF9 completion. This is not a finite bit or complex supplier.",
+  "input_hashes": {
+    "upstream_verify.py": "3be25d94a25e8ea8b484a1fb614a697e0a24e4519b647febc64b2d314f44d758",
+    "182-vertex-code.json": "f47b7f8af378fe7f86c7da32f04533b419711e468997c30ddef30a3a791dba01"
+  }
+}
diff --git a/research/pg29-matched-dirty-completion/INDEPENDENT-DIRTY.json b/research/pg29-matched-dirty-completion/INDEPENDENT-DIRTY.json
new file mode 100644
index 0000000000..267fea627d
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/INDEPENDENT-DIRTY.json
@@ -0,0 +1,17 @@
+{
+  "status": "PASS",
+  "all_saved_local_maps_invertible": true,
+  "replayed_physical_transmissions": 735,
+  "independent_field_implementation": true,
+  "whole_dirty_word_rank": 175,
+  "block_ranks": {
+    "F": 9,
+    "G": 9,
+    "H": 18
+  },
+  "paired_C_quotient_rank": 166,
+  "paired_C_does_not_contaminate_B": true,
+  "paired_J_outputs_agree": true,
+  "dirty_quotient_junk_block_rank": 9,
+  "scope": "A separate replay of the saved finite GF9 word. No rational frame realization or recursive paid cost is checked."
+}
diff --git a/research/pg29-matched-dirty-completion/ORIGINS.json b/research/pg29-matched-dirty-completion/ORIGINS.json
new file mode 100644
index 0000000000..a963f0ec81
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/ORIGINS.json
@@ -0,0 +1,46 @@
+[
+  {
+    "file": "dirty-word.json",
+    "original_workspace_path": "work/p518-next/architecture/small-motif/dirty-word.json",
+    "original_sha256": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f",
+    "adaptations": []
+  },
+  {
+    "file": "independent_dirty.py",
+    "original_workspace_path": "work/p518-next/architecture/small-motif/independent_dirty.py",
+    "original_sha256": "686ddfa0443b1081eba1516121a2b1978ab9f38b076d9ad37cc8693e426fe168",
+    "adaptations": []
+  },
+  {
+    "file": "INDEPENDENT-DIRTY.json",
+    "original_workspace_path": "work/p518-next/architecture/small-motif/INDEPENDENT-DIRTY.json",
+    "original_sha256": "e53be4b542cb39b239742ac4db4db03edf3ce94887f403538a3c1e6043bed307",
+    "adaptations": []
+  },
+  {
+    "file": "HISTORICAL-DIRTY-RESULT.json",
+    "original_workspace_path": "work/p518-next/architecture/small-motif/dirty-result.json",
+    "original_sha256": "c0f73c6983a4aec4edb2c9a4d63a68336e93e6c24d75e2b7bcae6d33df800d84",
+    "adaptations": []
+  },
+  {
+    "file": "PG29-FACTORS.json",
+    "original_workspace_path": "work/p518-next/bit/PG29-FACTORS.json",
+    "original_sha256": "fcf9cd3c6a5d36972c351ece5ab8c0495349e385be224ebb26490adb30c009fb",
+    "adaptations": []
+  },
+  {
+    "file": "PG29-COMPLETION.json",
+    "original_workspace_path": "work/p518-next/bit/PG29-COMPLETION.json",
+    "original_sha256": "df3aeba706075dd89bafd114542a1f06f0ac8c709064916d7fe96c51f2c1b96a",
+    "adaptations": []
+  },
+  {
+    "file": "completion.py",
+    "original_workspace_path": "work/p518-next/bit/independent/pg29_verify.py",
+    "original_sha256": "1180797215f151cae485f99db46fadc2320ec5e22a502a9d58f71feb70aa5780",
+    "adaptations": [
+      "Use package-local paths. Remove the conditional profile-price section and its engine. Keep the complete field, transcript and scalar completion checks. Add a scope-specific receipt."
+    ]
+  }
+]
diff --git a/research/pg29-matched-dirty-completion/PG29-COMPLETION.json b/research/pg29-matched-dirty-completion/PG29-COMPLETION.json
new file mode 100644
index 0000000000..36a4c558d6
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/PG29-COMPLETION.json
@@ -0,0 +1,38 @@
+{
+  "status": "PASS_EXACT_MATCHED_STUB_DIRTY_COMPLETION",
+  "source_word_sha256": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f",
+  "field": "F3[t]/(t^2+1)",
+  "signal_count": 157,
+  "returned_junk_count": 9,
+  "matched_C_edges": [
+    102,
+    163,
+    164,
+    341,
+    386,
+    406,
+    476,
+    513,
+    862
+  ],
+  "matched_J_edges": [
+    103,
+    349,
+    470,
+    517,
+    603,
+    606,
+    674,
+    716,
+    861
+  ],
+  "signal_reads_independent_of_matched_junk": true,
+  "all_J_stub_pairs_equal": true,
+  "normalized_junk_restored_on_all_166_formal_columns": true,
+  "correction_rank": 9,
+  "generic_independent_stub_schur_size": 18,
+  "generic_independent_stub_schur_invertible": true,
+  "D9_nonzeros": 74,
+  "correction_nonzeros": 1243,
+  "scope": "This is a scalar GF9 completion. Matching C inputs, physical frames, calls, and the all-size compiler remain unproved."
+}
diff --git a/research/pg29-matched-dirty-completion/PG29-FACTORS.json b/research/pg29-matched-dirty-completion/PG29-FACTORS.json
new file mode 100644
index 0000000000..37127bde88
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/PG29-FACTORS.json
@@ -0,0 +1 @@
+{"B9":[[5,8,3,7,5,2,1,1,8,6,3,4,6,7,0,2,3,2,1,0,8,0,3,6,4,8,6,7,2,6,4,3,7,5,7,0,1,7,1,7,1,2,6,5,2,6,6,5,5,2,3,7,3,1,6,0,5,3,8,6,6,1,0,2,7,8,0,2,3,7,1,7,7,2,7,2,2,5,3,2,3,8,4,0,0,2,1,2,6,8,5,7,6,4,2,4,6,4,2,8,2,4,4,4,7,3,6,2,4,4,8,5,4,3,1,8,4,2,4,7,4,0,2,8,1,8,3,8,4,5,2,7,4,3,6,7,2,5,8,7,4,6,6,1,3,4,2,1,0,3,4,6,7,8,7,6,4],[6,6,6,1,7,1,0,3,1,7,2,1,3,7,3,1,8,8,5,8,8,6,8,1,0,8,5,1,0,7,5,6,8,1,5,0,1,5,8,3,6,4,0,7,0,1,7,2,0,0,6,1,3,8,8,1,4,0,0,3,2,7,1,3,0,3,3,1,2,0,2,8,2,5,0,5,2,3,3,7,6,5,7,2,1,5,1,1,5,7,0,8,7,2,1,2,8,5,4,7,4,6,4,0,4,2,1,2,8,4,0,0,2,0,5,2,1,4,2,7,4,0,1,1,5,4,6,7,3,1,0,8,1,8,3,1,8,0,8,8,2,0,4,5,0,2,4,0,4,4,3,1,5,6,4,2,1],[8,3,7,4,6,4,5,2,3,4,2,6,4,3,0,0,4,5,0,1,0,6,3,5,4,2,5,1,1,2,2,0,0,7,1,1,5,1,2,3,3,4,1,7,0,3,8,6,4,3,4,6,2,3,0,1,3,4,7,0,0,1,4,7,3,4,2,3,5,3,5,7,2,4,8,0,1,8,5,7,1,7,7,5,2,3,6,7,0,1,8,5,8,7,1,6,4,1,2,0,8,8,0,6,0,2,4,5,5,7,5,5,7,2,1,7,2,0,6,8,0,6,8,3,7,4,6,4,8,2,0,1,2,7,7,8,4,5,0,8,2,1,0,3,8,0,3,6,6,2,6,8,1,4,8,4,4],[1,5,6,8,3,3,0,8,6,3,4,6,4,6,4,7,8,2,7,2,8,6,0,2,0,0,0,7,8,5,7,7,3,7,2,4,5,8,2,6,0,7,4,0,0,4,1,1,4,3,3,8,6,6,0,6,8,8,7,6,2,7,4,6,6,1,4,8,6,7,7,2,4,8,8,0,0,0,7,0,6,4,4,3,7,7,6,5,2,2,2,2,5,6,4,2,0,2,2,8,6,6,2,8,1,4,3,1,3,3,3,7,5,4,5,0,4,7,8,7,7,8,4,3,2,4,2,7,2,2,7,8,6,6,4,8,3,0,3,6,4,6,5,1,6,3,6,3,2,4,8,1,6,0,8,0,0],[7,1,8,7,2,8,5,5,5,0,0,0,3,3,2,6,6,4,3,6,1,0,5,8,3,4,1,6,1,6,0,6,2,0,2,4,8,6,1,6,5,8,0,2,1,0,8,5,6,7,8,6,2,6,7,6,0,5,8,3,3,3,5,2,7,3,4,6,2,3,7,8,8,8,4,1,3,2,8,7,8,5,5,2,5,8,0,3,0,1,8,0,4,1,5,5,4,0,7,4,4,7,5,7,4,2,3,3,4,8,8,7,5,1,8,6,3,8,4,0,3,2,8,8,3,0,5,4,4,0,5,0,5,3,2,6,2,0,3,4,2,6,6,1,0,8,7,0,5,5,2,4,0,5,0,7,1],[5,8,8,5,2,3,8,0,1,7,0,1,8,6,2,0,8,8,6,3,4,0,3,0,4,5,4,7,0,0,2,7,7,6,0,8,6,0,8,3,6,3,5,1,7,2,5,8,6,4,1,8,4,8,1,0,1,4,7,3,2,2,7,0,2,4,0,3,5,3,5,8,7,3,7,4,5,5,1,2,5,3,2,8,6,7,5,5,2,2,1,0,5,0,4,1,2,3,8,2,5,7,0,3,2,4,0,0,3,7,0,0,0,8,2,2,1,3,3,2,3,4,3,8,3,5,0,1,3,5,6,6,1,6,1,0,5,8,0,3,8,7,7,1,4,4,2,0,5,2,2,6,4,7,1,0,3],[4,8,1,3,6,2,3,5,8,1,1,5,5,2,5,7,7,6,7,3,8,5,0,5,6,7,8,4,7,4,2,2,3,0,8,7,8,5,4,7,0,5,8,2,5,1,6,4,5,4,6,2,3,4,7,3,5,0,6,8,1,7,1,5,8,8,4,4,1,8,5,2,0,2,7,1,8,0,6,1,4,8,8,2,3,5,7,0,7,3,6,2,3,1,8,0,1,2,4,2,5,1,2,1,1,3,1,8,7,5,2,2,1,5,8,7,0,1,2,2,5,4,3,4,8,5,2,6,6,1,1,6,5,0,5,5,2,6,4,4,3,4,7,1,2,1,6,1,8,0,8,4,6,7,6,0,5],[6,5,8,1,0,2,0,2,6,4,6,0,0,6,6,0,5,3,8,4,0,0,0,0,0,8,8,2,3,2,7,3,6,5,8,1,0,7,5,7,6,2,0,1,5,6,3,6,3,5,0,8,0,0,0,7,8,7,2,7,6,4,8,4,2,7,6,8,7,2,2,3,0,0,0,0,0,8,5,8,6,2,0,1,5,0,0,0,2,6,8,7,1,4,0,6,4,7,0,0,0,0,6,8,6,0,6,0,8,0,0,7,6,2,7,8,7,5,0,0,0,0,6,5,4,8,0,0,3,7,0,6,1,3,3,0,2,0,2,7,3,4,0,3,7,0,0,5,8,3,1,1,6,8,1,3,2],[0,3,8,4,0,6,6,7,0,4,2,6,3,0,6,3,6,5,3,3,8,6,5,7,8,1,6,8,6,8,4,5,3,5,4,7,5,4,4,2,0,7,0,5,1,7,6,3,0,7,4,7,0,8,2,3,8,1,8,8,1,1,1,3,1,7,5,8,0,4,1,2,7,0,1,1,0,2,5,1,1,0,3,3,1,8,4,5,6,3,7,4,6,3,1,1,3,2,6,4,0,5,5,2,2,0,0,4,8,2,5,3,8,4,8,5,5,5,3,2,7,2,1,7,1,6,7,8,1,6,8,1,1,0,2,3,1,6,2,2,3,5,2,5,8,4,7,1,4,3,4,7,2,3,1,1,8]],"D9":[[2,5,4,6,6,5,2,8,8],[6,5,8,4,2,5,8,3,4],[7,8,1,7,5,5,3,0,1],[0,3,6,0,4,8,8,2,4],[5,1,6,8,0,1,8,0,6],[0,7,6,3,5,5,7,5,2],[1,3,2,7,0,6,8,6,7],[8,4,1,1,8,7,4,2,2],[8,4,8,2,8,8,7,7,2]],"inverse_D9":[[8,2,1,0,3,7,5,1,5],[4,5,3,1,8,7,8,4,3],[1,5,0,6,4,1,0,3,7],[4,7,4,6,5,4,0,7,6],[8,5,5,8,4,6,6,0,0],[0,8,1,7,5,2,0,1,7],[1,7,7,4,6,1,5,7,2],[3,1,4,3,6,1,2,3,8],[3,3,6,1,8,3,6,8,2]],"correction":[[6,7,4,0,4,7,7,2,1,0,4,4,5,8,0,6,8,5,2,3,4,7,8,4,2,6,6,4,0,6,8,6,3,0,2,8,8,6,7,5,3,5,2,5,2,8,6,6,6,1,0,8,7,5,0,0,6,6,7,1,2,6,8,8,4,2,2,7,4,6,7,4,8,0,4,2,1,1,2,4,3,0,2,5,8,8,8,0,5,6,6,1,3,7,3,3,1,3,6,5,1,8,5,4,1,2,6,6,1,8,7,6,8,4,0,4,2,0,1,6,5,1,8,7,0,6,7,6,5,1,0,5,4,7,5,8,5,1,7,1,8,3,6,6,6,4,1,5,3,5,6,6,4,4,7,7,8],[6,5,2,4,1,8,8,3,5,1,1,4,6,6,4,1,8,0,2,4,0,2,5,7,8,6,5,7,7,5,5,5,3,7,4,8,5,0,5,6,0,6,8,5,1,3,2,7,0,6,4,3,5,3,0,3,4,6,1,5,1,0,6,4,6,2,6,6,1,5,1,5,2,5,3,8,7,5,7,5,4,1,2,6,3,5,4,7,0,7,2,4,4,5,6,2,2,6,8,1,0,1,3,4,6,2,6,6,4,1,2,7,1,0,8,0,0,7,2,4,7,0,6,4,6,1,4,1,7,4,4,2,8,1,2,1,7,1,2,2,6,2,4,7,6,4,5,8,2,0,2,6,1,8,1,4,6],[8,4,4,2,7,4,3,0,0,3,2,5,5,3,7,2,5,5,1,0,6,2,3,2,2,2,2,8,3,0,8,4,3,5,6,6,4,4,1,0,1,5,6,8,4,0,3,8,3,5,2,6,1,3,1,7,5,0,0,5,7,7,1,2,2,5,7,3,5,7,0,3,4,4,2,8,4,2,4,2,1,7,0,7,2,0,6,0,7,4,1,3,8,2,2,0,1,1,6,5,1,1,4,2,4,8,3,7,0,6,6,8,3,6,3,4,8,7,8,4,0,7,4,0,3,0,5,6,0,3,3,4,8,5,1,4,4,6,0,5,4,0,6,2,2,6,3,5,4,5,5,8,7,7,0,0,2],[0,2,7,8,3,6,1,1,8,4,0,4,3,8,0,4,8,1,2,5,1,4,8,4,1,6,4,7,1,0,4,8,4,2,6,6,5,7,4,1,2,5,7,4,3,5,4,1,8,7,6,1,8,6,0,6,5,4,6,7,0,7,2,8,7,5,8,1,6,1,0,5,4,8,4,1,2,8,7,1,6,7,6,1,3,6,4,7,7,2,7,5,4,5,2,0,2,0,8,3,2,7,5,0,3,5,4,2,3,0,8,8,6,4,0,0,5,8,3,3,1,7,1,2,0,7,1,6,2,1,7,6,1,2,5,7,2,4,6,5,8,7,7,5,0,3,0,3,0,2,6,4,7,0,5,4,3],[2,7,3,5,8,0,3,1,0,0,0,3,4,3,5,1,0,2,0,5,6,5,4,0,3,0,3,7,3,1,2,6,0,1,2,3,1,5,1,2,8,0,7,1,8,6,3,7,4,2,6,7,7,3,8,8,3,1,5,2,6,0,0,2,6,4,1,5,7,3,5,0,8,0,7,3,3,6,6,6,2,4,6,0,2,7,7,2,2,8,4,1,2,1,3,4,2,7,3,3,2,3,0,1,4,7,5,8,6,2,4,8,4,6,5,7,8,4,0,4,0,2,4,8,8,7,2,7,2,4,2,0,7,0,7,1,5,6,3,6,1,1,4,1,0,3,7,4,4,1,4,8,8,4,3,0,3],[6,8,8,5,7,7,8,3,6,5,4,8,5,8,7,7,8,6,4,6,6,3,6,8,6,7,6,6,3,1,2,5,2,2,7,6,6,2,2,7,2,2,7,0,7,2,0,4,4,8,1,1,8,5,7,8,3,6,5,4,7,1,1,4,3,2,0,7,5,0,1,8,0,0,7,7,8,6,3,6,0,7,3,5,7,1,7,0,0,8,1,1,8,8,5,0,8,2,4,0,3,5,5,2,2,8,6,2,7,2,5,4,6,8,5,6,8,4,1,3,5,3,3,5,3,8,1,6,4,1,1,3,4,5,6,1,4,5,1,8,2,4,2,4,8,5,3,1,1,3,1,7,3,5,7,3,2],[1,4,8,7,3,0,6,3,5,2,6,0,3,1,8,1,1,2,8,1,4,8,1,7,4,8,4,3,1,0,1,4,0,3,6,4,2,6,8,4,7,8,5,3,5,7,2,1,4,8,6,0,1,1,2,7,8,6,2,6,7,8,7,6,7,3,5,0,4,5,7,8,4,4,0,1,4,5,5,8,7,4,6,5,4,6,6,2,3,2,0,7,8,5,7,1,4,6,7,5,0,2,4,6,6,1,7,1,4,3,5,4,7,2,4,7,1,5,1,8,5,8,3,1,1,3,7,4,1,5,8,5,4,4,1,8,2,5,4,7,4,3,1,5,8,6,4,0,8,8,5,2,2,6,0,0,1],[6,5,0,1,8,2,3,6,6,6,3,0,5,2,2,1,0,7,5,8,0,5,6,7,4,7,6,6,2,1,5,8,5,4,3,6,3,0,4,4,4,0,4,0,0,6,7,0,0,3,4,2,3,5,0,1,0,2,7,2,5,0,4,1,2,0,7,0,2,6,8,1,5,0,8,7,7,0,2,3,1,0,6,0,0,0,1,7,3,4,1,3,0,0,0,7,2,8,8,1,0,7,8,7,0,3,8,8,8,6,0,6,0,0,5,8,6,7,3,1,1,0,5,3,1,1,3,2,7,0,7,8,2,4,1,7,0,1,0,6,7,0,4,2,6,5,3,3,7,4,4,0,2,7,0,0,1],[6,3,4,0,5,7,8,4,8,3,3,5,5,7,4,5,1,0,4,8,8,4,3,1,3,2,4,2,4,6,8,0,1,0,7,8,1,8,2,0,7,1,0,0,2,7,1,8,0,3,8,7,8,7,6,7,3,6,6,1,2,4,1,6,5,1,7,6,4,2,3,0,2,7,7,2,8,7,8,6,7,1,4,2,3,7,5,2,8,0,1,5,2,6,6,6,0,1,1,6,4,2,2,4,7,1,2,4,6,0,0,6,5,4,2,2,0,8,2,6,8,0,7,8,1,2,8,4,6,1,5,8,0,5,7,2,2,0,3,0,1,6,2,2,2,6,8,3,8,2,6,7,1,8,7,0,1]],"S18":[[7,1,1,1,6,3,8,5,0,4,8,8,3,4,3,2,3,0],[7,0,2,5,4,7,2,5,3,2,2,1,1,5,6,7,6,7],[0,2,1,4,5,3,6,6,8,7,3,5,3,6,0,2,6,0],[5,1,3,3,1,5,8,8,2,7,6,5,3,5,3,3,0,3],[0,4,6,8,7,1,4,0,5,5,0,4,0,6,0,0,4,5],[5,3,0,7,7,0,3,6,1,7,8,1,8,4,6,5,4,7],[3,3,5,4,6,4,5,7,3,7,3,4,2,0,6,5,3,3],[3,4,2,6,4,4,2,5,2,5,4,0,6,0,2,3,5,4],[2,2,5,3,8,1,7,5,7,6,8,4,5,5,3,7,0,0],[3,5,2,5,5,3,6,8,3,8,4,5,0,0,5,2,5,4],[1,5,1,8,7,4,4,1,5,6,2,8,2,3,0,1,2,7],[4,5,0,0,8,8,6,1,6,4,2,5,6,2,8,0,1,0],[3,0,1,1,2,3,1,6,1,2,7,8,3,1,8,7,7,1],[8,2,5,4,3,4,7,6,0,5,3,7,0,4,6,5,1,6],[4,8,5,4,4,5,6,8,7,4,6,4,3,8,8,5,7,4],[0,1,1,2,4,2,4,7,4,0,4,7,7,6,8,3,3,1],[5,2,0,0,6,0,0,2,0,7,0,4,0,4,6,8,8,7],[6,5,4,0,6,3,6,3,6,0,4,7,0,0,4,2,2,5]],"inverse_S18":[[4,8,0,6,7,5,1,1,1,4,1,4,8,4,0,5,3,3],[7,3,4,7,3,5,2,0,5,6,2,1,5,6,4,5,3,2],[8,4,2,8,7,4,2,5,4,5,1,3,6,1,1,6,1,1],[0,4,0,1,5,5,5,7,0,4,4,6,0,7,0,2,8,3],[3,1,7,8,4,1,6,4,4,5,7,8,0,0,8,8,0,4],[8,6,8,0,4,0,4,1,8,4,5,2,1,8,0,2,7,2],[7,7,3,6,1,4,3,7,0,3,4,2,8,2,0,6,7,0],[0,0,0,7,6,1,2,3,0,3,4,8,0,0,0,0,8,1],[0,7,0,7,8,4,7,8,7,3,6,4,0,2,0,2,3,8],[3,5,7,6,0,5,2,6,6,5,3,8,3,3,4,5,3,6],[6,8,7,1,1,8,0,8,2,7,6,7,4,0,2,8,8,2],[8,2,1,2,5,3,5,7,6,7,8,5,3,4,1,0,2,4],[8,3,0,6,6,3,8,5,7,7,4,1,0,3,1,7,6,7],[0,8,0,1,4,0,5,4,6,4,3,6,4,3,0,7,0,6],[0,0,0,5,4,1,1,3,0,1,0,7,0,2,0,0,4,5],[1,2,1,8,5,5,1,8,4,2,0,3,0,2,5,6,2,6],[6,3,6,5,6,2,2,2,7,4,1,4,0,3,8,2,2,4],[0,0,0,0,4,3,6,0,0,8,5,0,0,0,0,3,8,5]]}
diff --git a/research/pg29-matched-dirty-completion/PROOF.md b/research/pg29-matched-dirty-completion/PROOF.md
new file mode 100644
index 0000000000..7d4f078221
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/PROOF.md
@@ -0,0 +1,86 @@
+# Matched-stub scalar completion over GF9
+
+Let `F=F3[t]/(t^2+1)`. The transcript in `dirty-word.json` specifies 182
+invertible local maps of size five. It orders their inputs and outputs on
+175 boundary stubs. The first 157 boundary inputs are message variables.
+The other 18 inputs are the two ends of each of nine C edges. The last
+18 outputs are the two ends of each of nine J edges. Every boundary input
+is a separate formal variable in the first replay.
+
+The transcript is a finite matrix over F, not a physical recursive supplier.
+It uses the projective-plane code of Braverman and He, with each former zero
+C stub made an independent input. Its field operations and local program are
+checked separately from the original verifier.
+
+## Independent-stub map
+
+The complete boundary transfer is
+
+```text
+M = [ I157  F ]
+    [  G    H ].
+```
+
+The exact replay gives `rank(F)=9`, `rank(G)=9`, and `rank(H)=18`.
+It gives `rank(M)=175` and an invertible 18 by 18 Schur matrix `H-GF`.
+These ranks do not make M a permutation of its input roles. In particular,
+F and G are nonzero. Arbitrary independent C inputs can affect message
+outputs, and messages can affect J outputs.
+
+The separate replay checks every local five by five matrix, follows every
+one of the 735 physical edge transmissions, and compares all 175 output
+coefficient rows with the saved transfer. It then checks rank(M) by exact
+elimination over F. This is coverage of every input, not random testing.
+
+## Matched inputs and the quotient
+
+Let P be the 18 by 9 matrix that gives the same value to both input stubs
+of each C edge. Its nine columns are indicators of the nine disjoint pairs.
+Let Q choose one output from each J pair. The exact checks establish:
+
+1. `FP=0`.
+2. The two rows of G in each J pair agree.
+3. The two rows of HP in each J pair agree.
+4. `D=QHP` is invertible.
+
+Put `B=QG`. On the 166-dimensional input space `(x,z)`, the matched transfer
+therefore has the exact form
+
+```text
+(x,z) -> (x, Bx + Dz).
+```
+
+The two copies of every J output agree before the quotient is taken. Thus
+choosing one row per pair loses no information on this specified input
+subspace. The result does not assert equality for arbitrary independent
+values on the 18 C stubs.
+
+Apply D inverse to the nine returned values, then subtract `D^-1 B x`.
+The composite is
+
+```text
+(x, Bx + Dz) -> (x, D^-1 Bx + z) -> (x,z).
+```
+
+The matrices in `PG29-FACTORS.json` give this complete scalar correction.
+`completion.py` computes them with separate field arithmetic and checks all
+166 formal columns of the identity. It also checks both products with each
+inverse and compares every saved factor entry. The correction `D^-1 B`
+has rank nine and 1,243 nonzero coefficients. D has 74 nonzero coefficients.
+These are matrix counts, not recursive call costs.
+
+## Interface and cost boundary
+
+This is a complete finite scalar identity on the matched input subspace.
+The correction uses unrestricted linear combinations of the message and
+junk values. It does not supply legal rational common frames for these
+combinations. It does not price preparation of matched inputs, the physical
+return of pairs, frame transitions, controller access, or recursive children.
+The 735 transmissions are the original network's physical edge count;
+they are not an admitted paid profile for integer multiplication.
+
+A physical implementation must first realize the matched-input injection,
+all local maps, the quotient, and the complete inverse correction at legal
+frames. It must then charge them and restore every borrowed value. A matrix
+inverse at the boundary does not meet those obligations. No complex companion,
+complete supplier, or kappa improvement follows from this scalar identity.
diff --git a/research/pg29-matched-dirty-completion/README.md b/research/pg29-matched-dirty-completion/README.md
new file mode 100644
index 0000000000..21015f3cbd
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/README.md
@@ -0,0 +1,85 @@
+# A finite dirty completion of the PG(2,9) scalar code
+
+This package gives an exact boundary transfer and a scalar completion for
+the Braverman-He 182-vertex code. It replaces the former zero-valued C stubs
+by independent formal inputs, obtains an invertible 175-input transfer, and
+identifies a 166-input matched-stub subspace on which all 157 message outputs
+remain correct. An explicit nine-value inverse correction restores the junk.
+
+This is a new finite interface calculation, not a physical supplier or a
+kappa improvement. It identifies exactly which arbitrary-input coupling a
+future physical construction must handle. [PROOF.md](PROOF.md) states the
+identity and its boundary. The local transcript and all correction matrices
+are included, so the result can be checked without a network fetch.
+
+## Result
+
+The 175 by 175 transfer is `M=[[I157,F],[G,H]]`, with F and G of rank nine,
+H of rank 18, and `H-GF` invertible. M is invertible but is not a permutation.
+If the two inputs of each C pair are equal, the 157 message outputs are
+independent of that junk. Both outputs in every J pair then agree. Taking
+one output per pair gives `(x,z)->(x,Bx+Dz)` with D invertible, of size nine.
+The included inverse correction gives the identity on all 166 formal inputs.
+
+The correction matrix `D^-1 B` has rank nine and 1,243 nonzero coefficients.
+The original transcript has 735 physical edge transmissions. Neither count
+is a recursive paid bill. Matched-input preparation, legal rational frames,
+physical return, correction cost, hosting, and the complete compiler remain
+unproved. There is no complex companion or verified kappa improvement.
+
+## Reproduce
+
+From the repository root, Python 3.10 or later and its standard library:
+
+```sh
+python3 -B research/pg29-matched-dirty-completion/verify.py
+```
+
+Expected final line:
+
+```text
+PASS_PG29_DIRTY_PACKAGE independent_stubs=175 matched_inputs=166 no_new_kappa
+```
+
+The wrapper checks source hashes, runs both separate-field replays in a
+temporary copy, and compares their complete receipts. The first replay
+checks local invertibility, every boundary coefficient, full rank, and
+matched-pair identities. The second computes and compares the inverse
+factors and checks all 166 identity columns. The supplied scripts remain
+active when the wrapper is run with `-O`, because it starts ordinary Python
+child processes. These are exact finite checks, not a Lean theorem, a
+complete supplier replay, independent human review, or hosted CI success.
+
+## Sources and credit
+
+Publication base: `cef4b52f2a59009865bf8eabde1be3f159063703`.
+Braverman and He supplied the code in
+[arXiv:2610.10108v1](https://arxiv.org/abs/2610.10108v1), section 4, and its
+[companion source](https://github.com/zhongtianhe/multiple-unicast-counterexample/tree/3436359a85d13a1bf6e87c3a3dbdaa64788277f4).
+The transcript was derived from that exact source and checked against its
+original verifier. Its source and input hashes are recorded in `SOURCES.json`.
+The original companion implementation is not redistributed here. The
+mathematical transcript and separate replay code are sufficient to verify
+the stated boundary map. The source derivation is provenance, not a claim
+that the present verifier independently derives the published code from
+the projective geometry.
+
+The known common-target sign-gauge obstruction in
+[PR #288](https://github.com/CrocSwap/integer-mult-bounds/pull/288) concerns a
+physical frame embedding. It is not supplied or resolved by this scalar
+completion. Its compiler and network-coding lineage retain their credit.
+
+Ali Romman directed this work with substantial OpenAI Codex assistance,
+including separate research agents for field replay and completion review.
+New work is Apache-2.0. `ORIGINS.json` records each local source and the
+limited publication changes. The original conditional price experiment was
+omitted because its proposed physical profiles remain unbuilt. Attribution
+does not imply review or endorsement by Braverman, He, or any predecessor.
+
+## Open next questions
+
+Can the matched-input injection and nine-value correction be realized at
+legal rational frames? First give a concrete physical implementation of
+one correction map with arbitrary dirt restored, then count its complete
+recursive children. The absence of a frame embedding and a paid invoice
+is the present blocker; the scalar inverse does not remove it.
diff --git a/research/pg29-matched-dirty-completion/SOURCE-HASHES.json b/research/pg29-matched-dirty-completion/SOURCE-HASHES.json
new file mode 100644
index 0000000000..453c0bce1a
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/SOURCE-HASHES.json
@@ -0,0 +1,15 @@
+{
+  "COMPLETION-RESULT.json": "e144d0745aeeaea08da0d7f9b2dcd9556dcc57e617ac8acbdef36cc0b0ceed3c",
+  "HISTORICAL-DIRTY-RESULT.json": "c0f73c6983a4aec4edb2c9a4d63a68336e93e6c24d75e2b7bcae6d33df800d84",
+  "INDEPENDENT-DIRTY.json": "e53be4b542cb39b239742ac4db4db03edf3ce94887f403538a3c1e6043bed307",
+  "ORIGINS.json": "40f8707e58aa14e21ad15d50cc74b35afd6bb5056fd583a1ccce15e427fddbcb",
+  "PG29-COMPLETION.json": "df3aeba706075dd89bafd114542a1f06f0ac8c709064916d7fe96c51f2c1b96a",
+  "PG29-FACTORS.json": "fcf9cd3c6a5d36972c351ece5ab8c0495349e385be224ebb26490adb30c009fb",
+  "PROOF.md": "464d0a3e7825d702b515af904e9058fd6ce8ff1220d8ea41bf54b86a0dd16112",
+  "README.md": "2de699a5c7a52b3c8559f11039fcf685bed126a540a06500ddee46e2131bb952",
+  "SOURCES.json": "fbc6c616f7bccb063054b0a0f530bf54f9ce0caeb4b728214215ee38f4922791",
+  "completion.py": "00fe61fc09e65c07e9d05e6e7e719fd10c1f04883009d6ca25d06bc52ecf56ba",
+  "dirty-word.json": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f",
+  "independent_dirty.py": "686ddfa0443b1081eba1516121a2b1978ab9f38b076d9ad37cc8693e426fe168",
+  "verify.py": "ae69c9ca45140c6407340b563d278f14306a85f4ca33b8cb66d5887edd5eb9a7"
+}
diff --git a/research/pg29-matched-dirty-completion/SOURCES.json b/research/pg29-matched-dirty-completion/SOURCES.json
new file mode 100644
index 0000000000..9dba0e1760
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/SOURCES.json
@@ -0,0 +1,19 @@
+{
+  "base_commit": "cef4b52f2a59009865bf8eabde1be3f159063703",
+  "primary_paper": "https://arxiv.org/abs/2610.10108v1",
+  "primary_repository": "https://github.com/zhongtianhe/multiple-unicast-counterexample",
+  "primary_commit": "3436359a85d13a1bf6e87c3a3dbdaa64788277f4",
+  "primary_code_provenance": {
+    "url": "https://github.com/zhongtianhe/multiple-unicast-counterexample/blob/3436359a85d13a1bf6e87c3a3dbdaa64788277f4/verify.py",
+    "sha256": "3be25d94a25e8ea8b484a1fb614a697e0a24e4519b647febc64b2d314f44d758",
+    "redistributed": false
+  },
+  "primary_parameter_sha256": "f47b7f8af378fe7f86c7da32f04533b419711e468997c30ddef30a3a791dba01",
+  "local_transcript": {
+    "path": "dirty-word.json",
+    "sha256": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f",
+    "role": "All local matrices and complete 175-input transfer; newly generated finite mathematical data."
+  },
+  "new_kappa": false,
+  "primary_parameter_url": "https://github.com/zhongtianhe/multiple-unicast-counterexample/blob/3436359a85d13a1bf6e87c3a3dbdaa64788277f4/data/182-vertex-code.json"
+}
diff --git a/research/pg29-matched-dirty-completion/completion.py b/research/pg29-matched-dirty-completion/completion.py
new file mode 100644
index 0000000000..252350b532
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/completion.py
@@ -0,0 +1,189 @@
+"""Check the finite scalar completion with separate field arithmetic."""
+
+import hashlib
+import json
+from collections import defaultdict
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+SOURCE = HERE / "dirty-word.json"
+
+
+def add(left, right):
+    lb, la = divmod(left, 3)
+    rb, ra = divmod(right, 3)
+    return (la + ra) % 3 + 3 * ((lb + rb) % 3)
+
+
+def product(left, right):
+    lb, la = divmod(left, 3)
+    rb, ra = divmod(right, 3)
+    polynomial = [la * ra, la * rb + lb * ra, lb * rb]
+    return (polynomial[0] - polynomial[2]) % 3 + 3 * (polynomial[1] % 3)
+
+
+def negative(value):
+    return product(2, value)
+
+
+def power(value, exponent):
+    result = 1
+    while exponent:
+        if exponent & 1:
+            result = product(result, value)
+        value = product(value, value)
+        exponent >>= 1
+    return result
+
+
+def inverse_element(value):
+    assert value != 0
+    result = power(value, 7)
+    assert product(value, result) == 1
+    return result
+
+
+def combination(coefficients, vectors):
+    assert len(coefficients) == len(vectors)
+    result = [0] * len(vectors[0])
+    for coefficient, vector in zip(coefficients, vectors):
+        if coefficient:
+            result = [add(current, product(coefficient, entry))
+                      for current, entry in zip(result, vector)]
+    return result
+
+
+def matrix_product(left, right):
+    assert len(left[0]) == len(right)
+    return [combination(row, right) for row in left]
+
+
+def identity(size):
+    return [[int(i == j) for j in range(size)] for i in range(size)]
+
+
+def reduced(matrix):
+    rows = [list(row) for row in matrix]
+    pivots = []
+    for j in range(len(rows[0])):
+        pivot = next((i for i in range(len(pivots), len(rows)) if rows[i][j]), None)
+        if pivot is None:
+            continue
+        r = len(pivots)
+        rows[r], rows[pivot] = rows[pivot], rows[r]
+        scale = inverse_element(rows[r][j])
+        rows[r] = [product(scale, entry) for entry in rows[r]]
+        for i in range(len(rows)):
+            if i != r and rows[i][j]:
+                coefficient = negative(rows[i][j])
+                rows[i] = [add(entry, product(coefficient, base))
+                           for entry, base in zip(rows[i], rows[r])]
+        pivots.append(j)
+    return rows, pivots
+
+
+def matrix_inverse(matrix):
+    n = len(matrix)
+    assert all(len(row) == n for row in matrix)
+    rows, pivots = reduced([row + unit for row, unit in zip(matrix, identity(n))])
+    assert pivots[:n] == list(range(n))
+    assert [row[:n] for row in rows] == identity(n)
+    result = [row[n:] for row in rows]
+    assert matrix_product(matrix, result) == matrix_product(result, matrix) == identity(n)
+    return result
+
+
+for a in range(1, 9):
+    assert power(a, 8) == 1
+assert product(3, 3) == 2
+raw = SOURCE.read_bytes()
+assert hashlib.sha256(raw).hexdigest() == "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f"
+word = json.loads(raw)
+assert len(word["inputs"]) == len(word["outputs"]) == 175
+assert len(word["local_words"]) == 182
+units = identity(175)
+inputs = {tuple(stub): units[i] for i, stub in enumerate(word["inputs"])}
+outputs = {}
+output_keys = {tuple(stub) for stub in word["outputs"]}
+packets = {}
+physical = 0
+for local in word["local_words"]:
+    vertex = local["vertex"]
+    assert len(local["known_edges"]) == len(local["unknown_edges"]) == 5
+    assert len(local["matrix"]) == 5
+    matrix_inverse(local["matrix"])
+    known = [inputs[vertex, edge] if (vertex, edge) in inputs else packets[edge]
+             for edge in local["known_edges"]]
+    unknown = matrix_product(local["matrix"], known)
+    for edge, vector in zip(local["unknown_edges"], unknown):
+        if (vertex, edge) in output_keys:
+            assert (vertex, edge) not in outputs
+            outputs[vertex, edge] = vector
+        else:
+            assert edge not in packets
+            packets[edge] = vector
+            physical += 1
+transfer = [outputs[tuple(stub)] for stub in word["outputs"]]
+assert transfer == word["transfer"]
+assert physical == 735
+assert [row[:157] for row in transfer[:157]] == identity(157)
+
+input_edges = defaultdict(list)
+output_edges = defaultdict(list)
+for i, (_, edge) in enumerate(word["inputs"][157:]):
+    input_edges[edge].append(i)
+for i, (_, edge) in enumerate(word["outputs"][157:]):
+    output_edges[edge].append(i)
+assert len(input_edges) == len(output_edges) == 9
+assert all(len(indices) == 2 for indices in (*input_edges.values(), *output_edges.values()))
+input_pairs = list(input_edges.values())
+output_pairs = list(output_edges.values())
+quotient_rows = [row[:157] + [add(row[157 + a], row[157 + b]) for a, b in input_pairs]
+                 for row in transfer]
+assert quotient_rows[:157] == [row + [0] * 9 for row in identity(157)]
+assert all(quotient_rows[157 + a] == quotient_rows[157 + b] for a, b in output_pairs)
+junk_rows = [quotient_rows[157 + a] for a, b in output_pairs]
+b9 = [row[:157] for row in junk_rows]
+d9 = [row[157:] for row in junk_rows]
+inverse_d9 = matrix_inverse(d9)
+correction = matrix_product(inverse_d9, b9)
+normalized = matrix_product(inverse_d9, junk_rows)
+completed = [[add(entry, negative(error)) for entry, error in zip(row, corr + [0] * 9)]
+             for row, corr in zip(normalized, correction)]
+assert completed == [[0] * 157 + row for row in identity(9)]
+full_completion = quotient_rows[:157] + completed
+assert full_completion == identity(166)
+correction_rank = len(reduced(correction)[1])
+assert correction_rank == 9
+
+a18 = [row[157:] for row in transfer[:157]]
+b18 = [row[:157] for row in transfer[157:]]
+d18 = [row[157:] for row in transfer[157:]]
+ba = matrix_product(b18, a18)
+s18 = [[add(entry, negative(error)) for entry, error in zip(row, other)]
+       for row, other in zip(d18, ba)]
+inverse_s18 = matrix_inverse(s18)
+factors_path = HERE / "PG29-FACTORS.json"
+factors = json.loads(factors_path.read_text())
+independent_factors = dict(B9=b9, D9=d9, inverse_D9=inverse_d9,
+                           correction=correction, S18=s18, inverse_S18=inverse_s18)
+assert factors == independent_factors
+producer = json.loads((HERE / "PG29-COMPLETION.json").read_text())
+assert producer["source_word_sha256"] == hashlib.sha256(raw).hexdigest()
+assert producer["matched_C_edges"] == list(input_edges)
+assert producer["matched_J_edges"] == list(output_edges)
+assert producer["D9_nonzeros"] == sum(bool(value) for row in d9 for value in row) == 74
+assert producer["correction_nonzeros"] == sum(bool(value) for row in correction for value in row) == 1243
+
+
+receipt = dict(status="PASS_PG29_MATCHED_DIRTY_COMPLETION", source_word_sha256=hashlib.sha256(raw).hexdigest(),
+    field="F3[t]/(t^2+1), encoded by a+3b", independent_field_operations=True,
+    local_maps=182, physical_transmissions=physical, independent_input_stubs=175,
+    matched_input_pairs=9, matched_output_pairs=9, quotient_dimension=166,
+    correction_rank=correction_rank, all_formal_columns_restored=True,
+    generic_schur_dimension=18, generic_schur_invertible=True,
+    D9_nonzeros=74, correction_nonzeros=1243,
+    physical_frames=False, paid_supplier=False, new_kappa=False)
+(HERE/"COMPLETION-RESULT.json").write_text(json.dumps(receipt,indent=2)+"\n")
+print(json.dumps(receipt,indent=2))
diff --git a/research/pg29-matched-dirty-completion/dirty-word.json b/research/pg29-matched-dirty-completion/dirty-word.json
new file mode 100644
index 0000000000..331d27c9f2
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/dirty-word.json
@@ -0,0 +1 @@
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0,0,0,2,6,8,7,1,4,0,6,4,7,0,0,0,0,6,8,6,0,6,0,8,0,0,7,6,2,7,8,7,5,0,0,0,0,6,5,4,8,0,0,3,7,0,6,1,3,3,0,2,0,2,7,3,4,0,3,7,0,0,5,8,3,1,1,6,8,1,3,2,2,0,7,5,8,2,5,6,4,6,8,7,5,4,3,8,2,0],[0,3,8,4,0,6,6,7,0,4,2,6,3,0,6,3,6,5,3,3,8,6,5,7,8,1,6,8,6,8,4,5,3,5,4,7,5,4,4,2,0,7,0,5,1,7,6,3,0,7,4,7,0,8,2,3,8,1,8,8,1,1,1,3,1,7,5,8,0,4,1,2,7,0,1,1,0,2,5,1,1,0,3,3,1,8,4,5,6,3,7,4,6,3,1,1,3,2,6,4,0,5,5,2,2,0,0,4,8,2,5,3,8,4,8,5,5,5,3,2,7,2,1,7,1,6,7,8,1,6,8,1,1,0,2,3,1,6,2,2,3,5,2,5,8,4,7,1,4,3,4,7,2,3,1,1,8,2,7,8,0,8,4,0,0,5,6,2,6,7,6,0,4,7,0],[5,8,3,7,5,2,1,1,8,6,3,4,6,7,0,2,3,2,1,0,8,0,3,6,4,8,6,7,2,6,4,3,7,5,7,0,1,7,1,7,1,2,6,5,2,6,6,5,5,2,3,7,3,1,6,0,5,3,8,6,6,1,0,2,7,8,0,2,3,7,1,7,7,2,7,2,2,5,3,2,3,8,4,0,0,2,1,2,6,8,5,7,6,4,2,4,6,4,2,8,2,4,4,4,7,3,6,2,4,4,8,5,4,3,1,8,4,2,4,7,4,0,2,8,1,8,3,8,4,5,2,7,4,3,6,7,2,5,8,7,4,6,6,1,3,4,2,1,0,3,4,6,7,8,7,6,4,4,6,5,4,5,4,3,3,3,7,5,5,5,8,2,1,8,4],[8,3,7,4,6,4,5,2,3,4,2,6,4,3,0,0,4,5,0,1,0,6,3,5,4,2,5,1,1,2,2,0,0,7,1,1,5,1,2,3,3,4,1,7,0,3,8,6,4,3,4,6,2,3,0,1,3,4,7,0,0,1,4,7,3,4,2,3,5,3,5,7,2,4,8,0,1,8,5,7,1,7,7,5,2,3,6,7,0,1,8,5,8,7,1,6,4,1,2,0,8,8,0,6,0,2,4,5,5,7,5,5,7,2,1,7,2,0,6,8,0,6,8,3,7,4,6,4,8,2,0,1,2,7,7,8,4,5,0,8,2,1,0,3,8,0,3,6,6,2,6,8,1,4,8,4,4,1,2,1,4,7,5,4,4,6,6,3,4,8,6,0,0,2,7],[0,3,8,4,0,6,6,7,0,4,2,6,3,0,6,3,6,5,3,3,8,6,5,7,8,1,6,8,6,8,4,5,3,5,4,7,5,4,4,2,0,7,0,5,1,7,6,3,0,7,4,7,0,8,2,3,8,1,8,8,1,1,1,3,1,7,5,8,0,4,1,2,7,0,1,1,0,2,5,1,1,0,3,3,1,8,4,5,6,3,7,4,6,3,1,1,3,2,6,4,0,5,5,2,2,0,0,4,8,2,5,3,8,4,8,5,5,5,3,2,7,2,1,7,1,6,7,8,1,6,8,1,1,0,2,3,1,6,2,2,3,5,2,5,8,4,7,1,4,3,4,7,2,3,1,1,8,4,1,3,6,8,2,2,8,4,4,5,7,2,3,5,6,8,0],[7,1,8,7,2,8,5,5,5,0,0,0,3,3,2,6,6,4,3,6,1,0,5,8,3,4,1,6,1,6,0,6,2,0,2,4,8,6,1,6,5,8,0,2,1,0,8,5,6,7,8,6,2,6,7,6,0,5,8,3,3,3,5,2,7,3,4,6,2,3,7,8,8,8,4,1,3,2,8,7,8,5,5,2,5,8,0,3,0,1,8,0,4,1,5,5,4,0,7,4,4,7,5,7,4,2,3,3,4,8,8,7,5,1,8,6,3,8,4,0,3,2,8,8,3,0,5,4,4,0,5,0,5,3,2,6,2,0,3,4,2,6,6,1,0,8,7,0,5,5,2,4,0,5,0,7,1,8,5,6,0,0,1,8,0,0,6,8,6,0,8,0,0,0,0],[4,8,1,3,6,2,3,5,8,1,1,5,5,2,5,7,7,6,7,3,8,5,0,5,6,7,8,4,7,4,2,2,3,0,8,7,8,5,4,7,0,5,8,2,5,1,6,4,5,4,6,2,3,4,7,3,5,0,6,8,1,7,1,5,8,8,4,4,1,8,5,2,0,2,7,1,8,0,6,1,4,8,8,2,3,5,7,0,7,3,6,2,3,1,8,0,1,2,4,2,5,1,2,1,1,3,1,8,7,5,2,2,1,5,8,7,0,1,2,2,5,4,3,4,8,5,2,6,6,1,1,6,5,0,5,5,2,6,4,4,3,4,7,1,2,1,6,1,8,0,8,4,6,7,6,0,5,4,6,1,7,0,8,2,0,2,6,0,8,6,6,1,1,6,0],[6,5,8,1,0,2,0,2,6,4,6,0,0,6,6,0,5,3,8,4,0,0,0,0,0,8,8,2,3,2,7,3,6,5,8,1,0,7,5,7,6,2,0,1,5,6,3,6,3,5,0,8,0,0,0,7,8,7,2,7,6,4,8,4,2,7,6,8,7,2,2,3,0,0,0,0,0,8,5,8,6,2,0,1,5,0,0,0,2,6,8,7,1,4,0,6,4,7,0,0,0,0,6,8,6,0,6,0,8,0,0,7,6,2,7,8,7,5,0,0,0,0,6,5,4,8,0,0,3,7,0,6,1,3,3,0,2,0,2,7,3,4,0,3,7,0,0,5,8,3,1,1,6,8,1,3,2,0,4,1,0,8,0,0,0,0,8,1,2,2,0,0,7,4,0],[5,8,8,5,2,3,8,0,1,7,0,1,8,6,2,0,8,8,6,3,4,0,3,0,4,5,4,7,0,0,2,7,7,6,0,8,6,0,8,3,6,3,5,1,7,2,5,8,6,4,1,8,4,8,1,0,1,4,7,3,2,2,7,0,2,4,0,3,5,3,5,8,7,3,7,4,5,5,1,2,5,3,2,8,6,7,5,5,2,2,1,0,5,0,4,1,2,3,8,2,5,7,0,3,2,4,0,0,3,7,0,0,0,8,2,2,1,3,3,2,3,4,3,8,3,5,0,1,3,5,6,6,1,6,1,0,5,8,0,3,8,7,7,1,4,4,2,0,5,2,2,6,4,7,1,0,3,5,5,6,2,8,2,6,0,2,7,4,0,5,5,0,3,1,6],[1,5,6,8,3,3,0,8,6,3,4,6,4,6,4,7,8,2,7,2,8,6,0,2,0,0,0,7,8,5,7,7,3,7,2,4,5,8,2,6,0,7,4,0,0,4,1,1,4,3,3,8,6,6,0,6,8,8,7,6,2,7,4,6,6,1,4,8,6,7,7,2,4,8,8,0,0,0,7,0,6,4,4,3,7,7,6,5,2,2,2,2,5,6,4,2,0,2,2,8,6,6,2,8,1,4,3,1,3,3,3,7,5,4,5,0,4,7,8,7,7,8,4,3,2,4,2,7,2,2,7,8,6,6,4,8,3,0,3,6,4,6,5,1,6,3,6,3,2,4,8,1,6,0,8,0,0,3,3,1,8,0,7,7,8,3,6,4,1,3,0,8,1,1,4],[6,6,6,1,7,1,0,3,1,7,2,1,3,7,3,1,8,8,5,8,8,6,8,1,0,8,5,1,0,7,5,6,8,1,5,0,1,5,8,3,6,4,0,7,0,1,7,2,0,0,6,1,3,8,8,1,4,0,0,3,2,7,1,3,0,3,3,1,2,0,2,8,2,5,0,5,2,3,3,7,6,5,7,2,1,5,1,1,5,7,0,8,7,2,1,2,8,5,4,7,4,6,4,0,4,2,1,2,8,4,0,0,2,0,5,2,1,4,2,7,4,0,1,1,5,4,6,7,3,1,0,8,1,8,3,1,8,0,8,8,2,0,4,5,0,2,4,0,4,4,3,1,5,6,4,2,1,3,2,1,3,4,2,0,1,8,3,1,8,5,3,7,3,8,7]]}
diff --git a/research/pg29-matched-dirty-completion/independent_dirty.py b/research/pg29-matched-dirty-completion/independent_dirty.py
new file mode 100644
index 0000000000..49dc1df238
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/independent_dirty.py
@@ -0,0 +1,78 @@
+"""Check the saved dirty GF9 word with separate field operations."""
+from pathlib import Path
+import json
+
+HERE=Path(__file__).resolve().parent
+word=json.loads((HERE/'dirty-word.json').read_text())
+def add(a,b):
+    return (a%3+b%3)%3+3*((a//3+b//3)%3)
+def neg(a):
+    return (-a%3)%3+3*((-(a//3))%3)
+def mul(a,b):
+    return ((a%3)*(b%3)-(a//3)*(b//3))%3+3*(((a%3)*(b//3)+(a//3)*(b%3))%3)
+def inv(a):
+    assert a
+    return next(b for b in range(1,9) if mul(a,b)==1)
+def rowcomb(coeff,rows):
+    out=[0]*len(rows[0])
+    for a,row in zip(coeff,rows):
+        for j,b in enumerate(row):
+            out[j]=add(out[j],mul(a,b))
+    return out
+def rank(matrix):
+    a=[row[:] for row in matrix]
+    out=0
+    for col in range(len(a[0])):
+        p=next((p for p in range(out,len(a)) if a[p][col]),None)
+        if p is None:
+            continue
+        a[out],a[p]=a[p],a[out]
+        scale=inv(a[out][col])
+        a[out]=[mul(scale,v) for v in a[out]]
+        for j in range(len(a)):
+            if j!=out and a[j][col]:
+                factor=neg(a[j][col])
+                a[j]=[add(u,mul(factor,v)) for u,v in zip(a[j],a[out])]
+        out+=1
+        if out==len(a):
+            break
+    return out
+n=len(word['inputs'])
+inputs={tuple(stub):[int(j==i) for j in range(n)] for i,stub in enumerate(word['inputs'])}
+packets={}
+outputs={}
+for local in word['local_words']:
+    assert rank(local['matrix'])==5
+    v=local['vertex']
+    rows=[inputs[v,e] if (v,e) in inputs else packets[e] for e in local['known_edges']]
+    for e,coeff in zip(local['unknown_edges'],local['matrix']):
+        value=rowcomb(coeff,rows)
+        if [v,e] in word['outputs']:
+            outputs[v,e]=value
+        else:
+            assert e not in packets
+            packets[e]=value
+matrix=[outputs[tuple(stub)] for stub in word['outputs']]
+assert matrix==word['transfer']
+assert len(packets)==735 and rank(matrix)==175
+assert [r[:157] for r in matrix[:157]]==[[int(i==j) for j in range(157)] for i in range(157)]
+inpairs={e:[] for v,e in word['inputs'][157:]}
+for j,(v,e) in enumerate(word['inputs'][157:],157):
+    inpairs[e].append(j)
+outpairs={e:[] for v,e in word['outputs'][157:]}
+for j,(v,e) in enumerate(word['outputs'][157:],157):
+    outpairs[e].append(j)
+assert all(len(p)==2 for p in inpairs.values())
+assert all(len(p)==2 for p in outpairs.values())
+Q=[row[:157]+[add(row[a],row[b]) for a,b in inpairs.values()] for row in matrix]
+assert all(not any(row[157:]) for row in Q[:157])
+for a,b in outpairs.values():
+    assert Q[a]==Q[b]
+quotient=Q[:157]+[Q[p[0]] for p in outpairs.values()]
+assert rank(quotient)==166
+assert rank([row[157:] for row in quotient[157:]])==9
+ranks={'F':rank([r[157:] for r in matrix[:157]]),'G':rank([r[:157] for r in matrix[157:]]),'H':rank([r[157:] for r in matrix[157:]])}
+assert ranks=={'F':9,'G':9,'H':18}
+result=dict(status='PASS',all_saved_local_maps_invertible=True,replayed_physical_transmissions=735,independent_field_implementation=True,whole_dirty_word_rank=175,block_ranks=ranks,paired_C_quotient_rank=166,paired_C_does_not_contaminate_B=True,paired_J_outputs_agree=True,dirty_quotient_junk_block_rank=9,scope='A separate replay of the saved finite GF9 word. No rational frame realization or recursive paid cost is checked.')
+(HERE/'INDEPENDENT-DIRTY.json').write_text(json.dumps(result,indent=2)+'\n')
+print(json.dumps(result,indent=2))
diff --git a/research/pg29-matched-dirty-completion/review/CHECKED-FILES.json b/research/pg29-matched-dirty-completion/review/CHECKED-FILES.json
new file mode 100644
index 0000000000..0e9d8e8290
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/CHECKED-FILES.json
@@ -0,0 +1,75 @@
+{
+  "package": "work/project-final-cleanup-20261022/early-remainder-audit/packages/pg29-matched-dirty-completion",
+  "files": [
+    {
+      "path": "COMPLETION-RESULT.json",
+      "bytes": 664,
+      "sha256": "e144d0745aeeaea08da0d7f9b2dcd9556dcc57e617ac8acbdef36cc0b0ceed3c"
+    },
+    {
+      "path": "HISTORICAL-DIRTY-RESULT.json",
+      "bytes": 978,
+      "sha256": "c0f73c6983a4aec4edb2c9a4d63a68336e93e6c24d75e2b7bcae6d33df800d84"
+    },
+    {
+      "path": "INDEPENDENT-DIRTY.json",
+      "bytes": 520,
+      "sha256": "e53be4b542cb39b239742ac4db4db03edf3ce94887f403538a3c1e6043bed307"
+    },
+    {
+      "path": "ORIGINS.json",
+      "bytes": 1898,
+      "sha256": "40f8707e58aa14e21ad15d50cc74b35afd6bb5056fd583a1ccce15e427fddbcb"
+    },
+    {
+      "path": "PG29-COMPLETION.json",
+      "bytes": 901,
+      "sha256": "df3aeba706075dd89bafd114542a1f06f0ac8c709064916d7fe96c51f2c1b96a"
+    },
+    {
+      "path": "PG29-FACTORS.json",
+      "bytes": 7486,
+      "sha256": "fcf9cd3c6a5d36972c351ece5ab8c0495349e385be224ebb26490adb30c009fb"
+    },
+    {
+      "path": "PROOF.md",
+      "bytes": 3725,
+      "sha256": "464d0a3e7825d702b515af904e9058fd6ce8ff1220d8ea41bf54b86a0dd16112"
+    },
+    {
+      "path": "README.md",
+      "bytes": 4395,
+      "sha256": "2de699a5c7a52b3c8559f11039fcf685bed126a540a06500ddee46e2131bb952"
+    },
+    {
+      "path": "SOURCE-HASHES.json",
+      "bytes": 1172,
+      "sha256": "d9572b2f14517dbd3d88e1b1277e5227b2a8c17eb92ebfa2ffdb3e13028be942"
+    },
+    {
+      "path": "SOURCES.json",
+      "bytes": 1088,
+      "sha256": "fbc6c616f7bccb063054b0a0f530bf54f9ce0caeb4b728214215ee38f4922791"
+    },
+    {
+      "path": "completion.py",
+      "bytes": 7243,
+      "sha256": "00fe61fc09e65c07e9d05e6e7e719fd10c1f04883009d6ca25d06bc52ecf56ba"
+    },
+    {
+      "path": "dirty-word.json",
+      "bytes": 93702,
+      "sha256": "112532d00d991979ce21b2f74b48cd5bffdb1420abea44f2571f667a628a261f"
+    },
+    {
+      "path": "independent_dirty.py",
+      "bytes": 3372,
+      "sha256": "686ddfa0443b1081eba1516121a2b1978ab9f38b076d9ad37cc8693e426fe168"
+    },
+    {
+      "path": "verify.py",
+      "bytes": 1260,
+      "sha256": "ae69c9ca45140c6407340b563d278f14306a85f4ca33b8cb66d5887edd5eb9a7"
+    }
+  ]
+}
diff --git a/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP-MATCHES.txt b/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP-MATCHES.txt
new file mode 100644
index 0000000000..182a40f625
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP-MATCHES.txt
@@ -0,0 +1,8 @@
+cef4b52f2a59009865bf8eabde1be3f159063703:research/abelian-cayley-metric-scope/sources/pr288-README.md:261:(Braverman–He, arXiv:2610.10108; Zhang–Li–Li, arXiv:2610.09367) are the natural seeds.
+cef4b52f2a59009865bf8eabde1be3f159063703:research/abelian-cayley-metric-scope/sources/pr288-README.md:275:the session distance, which is the opposite of the Tanner seeds: Braverman–He has degree 10 at distance 5.
+cef4b52f2a59009865bf8eabde1be3f159063703:research/abelian-cayley-metric-scope/sources/pr288-README.md:283:**(d) Braverman–He's PG(2,9) code with per-session sign gauges. [cert]**
+cef4b52f2a59009865bf8eabde1be3f159063703:research/abelian-cayley-metric-scope/sources/pr288-README.md:300:- Zhang–Li–Li and Braverman–He have no follow-ups.
+cef4b52f2a59009865bf8eabde1be3f159063703:research/abelian-cayley-metric-scope/sources/pr288-README.md:377:- The PG(2,9) instance and gap: Braverman and He. Amplification framework: Zhang, Li and Li.
+cef4b52f2a59009865bf8eabde1be3f159063703:research/kappa-0023-productive-jobs/LITERATURE.md:178:19. **Mark Braverman and Zhongtian He** (2026). “The Multiple Unicast
+cef4b52f2a59009865bf8eabde1be3f159063703:research/kappa-0023-productive-jobs/PR-BODY.md:467:19. **Mark Braverman and Zhongtian He** (2026). “The Multiple Unicast
+cef4b52f2a59009865bf8eabde1be3f159063703:research/kappa-rebuild/architecture/LITERATURE.md:132:**Mark Braverman and Zhongtian He (2026), _The Multiple Unicast Conjecture
diff --git a/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP.json b/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP.json
new file mode 100644
index 0000000000..aa25bfa04b
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/MAIN-OVERLAP.json
@@ -0,0 +1,6 @@
+{
+  "pin": "cef4b52f2a59009865bf8eabde1be3f159063703",
+  "pattern": "PG\\(2,[[:space:]]*9\\)|Braverman|pg29|182.vertex|matched.stub|matched.dirty|175.input|166.input",
+  "scope": "All tracked Markdown, TeX and text files in the pinned main tree; compressed sources and Discussions are not included",
+  "matching_lines": 8
+}
diff --git a/research/pg29-matched-dirty-completion/review/OPEN-PR-OVERLAP.json b/research/pg29-matched-dirty-completion/review/OPEN-PR-OVERLAP.json
new file mode 100644
index 0000000000..5d33746de5
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/OPEN-PR-OVERLAP.json
@@ -0,0 +1,15 @@
+{
+  "scope": "Parent-fetched 315 open PR titles and bodies",
+  "count": 315,
+  "matches": [
+    {
+      "number": 349,
+      "title": "Certify PR288's restricted sign-gauge obstruction with four constraints (no new \u03ba)",
+      "matches": [
+        "PG\\(?2[,; ]+9",
+        "Braverman"
+      ],
+      "head": "4b0e84065c2902808e33f14f423de43ed12b92a0"
+    }
+  ]
+}
diff --git a/research/pg29-matched-dirty-completion/review/ORIGIN-CHECK.json b/research/pg29-matched-dirty-completion/review/ORIGIN-CHECK.json
new file mode 100644
index 0000000000..7587aed248
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/ORIGIN-CHECK.json
@@ -0,0 +1,43 @@
+{
+  "status": "PASS",
+  "origins": [
+    {
+      "file": "dirty-word.json",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "independent_dirty.py",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "INDEPENDENT-DIRTY.json",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "HISTORICAL-DIRTY-RESULT.json",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "PG29-FACTORS.json",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "PG29-COMPLETION.json",
+      "original_hash_matches": true,
+      "unchanged": true
+    },
+    {
+      "file": "completion.py",
+      "original_hash_matches": true,
+      "unchanged": false
+    }
+  ],
+  "all_mathematical_function_ASTs_unchanged_in_completion_adaptation": true,
+  "source_and_receipt_paths_changed": true,
+  "conditional_price_section_removed": true
+}
diff --git a/research/pg29-matched-dirty-completion/review/PRIMARY-SOURCE-PINS.json b/research/pg29-matched-dirty-completion/review/PRIMARY-SOURCE-PINS.json
new file mode 100644
index 0000000000..ac4fd86ecc
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/PRIMARY-SOURCE-PINS.json
@@ -0,0 +1,17 @@
+{
+  "commit": "3436359a85d13a1bf6e87c3a3dbdaa64788277f4",
+  "live_github_tree_matched": true,
+  "license_file_present_at_pin": false,
+  "files": {
+    "upstream_verify.py": {
+      "bytes": 15293,
+      "sha256": "3be25d94a25e8ea8b484a1fb614a697e0a24e4519b647febc64b2d314f44d758",
+      "git_blob": "ebe576839f95d97d0a25c2f7b8f07422c31cb1ca"
+    },
+    "182-vertex-code.json": {
+      "bytes": 3312,
+      "sha256": "f47b7f8af378fe7f86c7da32f04533b419711e468997c30ddef30a3a791dba01",
+      "git_blob": "d84f5b3996d5e3b8bf886dfde4fde6bfc02981ca"
+    }
+  }
+}
diff --git a/research/pg29-matched-dirty-completion/review/REVIEW.json b/research/pg29-matched-dirty-completion/review/REVIEW.json
new file mode 100644
index 0000000000..46edcc75e2
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/REVIEW.json
@@ -0,0 +1,31 @@
+{
+  "status": "PASS_INDEPENDENT_AGENT_REVIEW",
+  "file_count": 14,
+  "source_hashes_sha256": "d9572b2f14517dbd3d88e1b1277e5227b2a8c17eb92ebfa2ffdb3e13028be942",
+  "checked_files_sha256": "be179aebae5506c89e1e100cd8723e2dfcbe5c664ec3ed639b0587350572ade1",
+  "review_sha256": "6eaeaa8d605d3290e589d8281fd61f4c64ae3acc16d66105c200a33329b01582",
+  "review_checker_sha256": "21b6f4e80dc5a36590466460e294785fba07891697fbaf38b01e3d72dbfdc0ee",
+  "python": "3.14.7",
+  "claims_approved": [
+    "The fixed 175-input GF9 transcript has the stated invertible boundary transfer",
+    "On the specified 166-input matched subspace, both J stubs agree and the explicit nine-value scalar correction restores the identity",
+    "Both field implementations and all 166 GF9 completion columns pass; an independent 2 by 2 F3 representation verifies all 332 F3 columns"
+  ],
+  "fixed_findings": [
+    {
+      "issue": "Inherited PYTHONOPTIMIZE could disable child assertions",
+      "fix": "The new wrapper adds -I to child Python invocations",
+      "validation": "The wrapper passed with PYTHONOPTIMIZE=1 and -O and rejected a semantically corrupted factor with its hash entry updated"
+    }
+  ],
+  "open_material_findings": [],
+  "limits": [
+    "Not arbitrary independent 18-stub borrowed state",
+    "No physical matched-input preparation or return",
+    "No legal frame or inverse-correction cost construction",
+    "No recursive paid profile or hosting proof",
+    "No verified complete kappa improvement",
+    "No human or formal-kernel review"
+  ],
+  "checks": "fresh/REVIEW-CHECKS.json"
+}
diff --git a/research/pg29-matched-dirty-completion/review/REVIEW.md b/research/pg29-matched-dirty-completion/review/REVIEW.md
new file mode 100644
index 0000000000..e3146d8842
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/REVIEW.md
@@ -0,0 +1,135 @@
+# Independent agent review: PG(2,9) matched-stub completion
+
+Result: PASS for the stated finite scalar identity and its exact input
+promise. One verifier robustness issue was fixed and checked. No material
+mathematical finding remains open. This review used a separate OpenAI
+Codex agent. It is not independent human review or a formal-kernel proof.
+
+The contribution supplies a checked scalar boundary contract and explicit
+correction matrices for the historical PG(2,9) transcript. It gives a new
+local capability: nine independent matched junk values can pass through
+the transcript with the 157 message values intact, and the stated scalar
+correction restores those nine values. It does not construct the physical
+matched-input preparation, physical return, or complete supplier. There
+is no verified complete kappa improvement.
+
+The reviewed files and their exact hashes are in `CHECKED-FILES.json`.
+The PR description standard at
+`/Users/aliromman/Projects/IntegerMultiplicationBounds/PR-DESCRIPTION-STANDARD.md`
+was read. The coordinator must check the final description, public source
+targets, and GitHub rendering before publication.
+
+## Mathematical contract
+
+The saved transcript defines a 175 by 175 transfer over
+`F3[t]/(t^2+1)`. Both replay implementations check all 182 local invertible
+five by five maps, follow the 735 transmitted edge values, and reconstruct
+every boundary coefficient. The first 157 by 157 block is the identity.
+The off-diagonal block ranks are nine and nine; the final 18 by 18 block
+has rank 18. The full transfer and the Schur matrix `H-GF` are invertible.
+The saved transfer is not a role permutation.
+
+The matched-input map duplicates each of nine independent values on the
+two stubs of one C edge. The resulting message block has no junk term.
+The two outputs of each J edge then agree, so one output per pair gives
+the map `(x,z) -> (x,Bx+Dz)`. The checked nine by nine D is invertible.
+Applying `D^-1` and then subtracting `D^-1 Bx` gives `(x,z)`.
+The original completion replay checks all 166 formal GF9 input columns,
+both inverse products, and every entry of all saved factor matrices.
+
+This review also used a third arithmetic representation. It maps
+`a+bt` to the matrix `[[a,-b],[b,a]]` over F3. It checked all 81 addition
+and multiplication table entries in both implementations, all eight
+nonzero inverses, and irreducibility of `t^2+1` over F3. With these
+two by two blocks, the final identity holds on all 332 formal F3 columns.
+The 74 nonzero D entries and 1,243 nonzero correction entries agree with
+the saved counts. These are matrix entries, not native call prices.
+
+The matched-input promise is necessary. For example, the transfer entry
+from boundary input column 157 to message output row 0 is the nonzero
+GF9 element encoded by 3. With all other inputs zero, this independent
+stub contaminates that message. Adding its matched partner cancels the
+message contribution. Thus arbitrary values on all 18 C stubs do not
+satisfy the nine-value contract. The proof states this restriction.
+
+Selecting one J output is an injective quotient only on the stated
+matched subspace. It is not a free physical erasure of a second arbitrary
+register. The theorem does not restore an additional nine independent
+borrowed values. Preparation of the input equality, handling of duplicate
+outputs, legal common rational frames, inverse-correction access and
+operations, physical return, recursive children, hosting, and the complete
+compiler bill remain open. The 735 edge transmissions are network-code
+transmissions, not an admitted multiplication-supplier profile.
+
+## Checks and the fixed finding
+
+The package wrapper passed normally. This review then ran the fixed
+wrapper with both `PYTHONOPTIMIZE=1` and `-O`. It passed both child replays
+and compared their complete receipts. The wrapper now starts the children
+with `-I`, which prevents the inherited environment from disabling their
+assertions. It does not pass `-O` to them.
+
+The issue was specific: the original wrapper removed its own `-O` flag
+from child arguments but still inherited `PYTHONOPTIMIZE`. That variable
+could disable the child checks. The packaging worker added `-I`; no
+mathematical source or saved transcript was changed.
+
+To check the fix, this review changed one saved correction factor in a
+scratch copy and updated only its source-hash entry. The wrapper rejected
+the changed factor at `factors == independent_factors`, even under the
+optimized environment. A separate scratch mutation made one local map
+singular; the first independent replay rejected its rank. The lifted
+matrix check also shows that omitting the message correction or D
+normalization fails. Original package files were unchanged by the tests.
+
+Commands run from the workspace root include:
+
+```sh
+python3 -I -B work/project-final-cleanup-20261022/early-remainder-audit/packages/pg29-matched-dirty-completion/verify.py
+env PYTHONOPTIMIZE=1 python3 -O -B work/project-final-cleanup-20261022/early-remainder-audit/packages/pg29-matched-dirty-completion/verify.py
+python3 -I -B work/project-final-cleanup-20261022/reviews/pg29-completion/check_review.py --package work/project-final-cleanup-20261022/early-remainder-audit/packages/pg29-matched-dirty-completion --out work/project-final-cleanup-20261022/reviews/pg29-completion/fresh --primary-dir work/p518-next/architecture/small-motif
+```
+
+The last command printed `PASS_PG29_INDEPENDENT_REVIEW_CHECKS`. Its
+reports and logs are under `fresh/`. It needs a new output directory.
+The review script accepts explicit paths; `--primary-dir` is optional.
+Without that option, it runs all scalar checks and rejection controls
+without the historical source folder. The runtime was Python 3.14.7.
+No Lean, full supplier, frame realization, outer kappa calculation, or
+hosted CI check was run.
+
+## Provenance, credit, and overlap
+
+The live pinned GitHub tree at
+`3436359a85d13a1bf6e87c3a3dbdaa64788277f4` confirms the local verifier and
+parameter file blob hashes. Their SHA-256 values agree with SOURCES.
+The tree has no license file. The package does not redistribute that
+companion implementation. Its Apache-2.0 statement applies to the new
+work; the mathematical transcript and newly written separate replay
+implementations are the submitted material.
+
+The credited primary authors are Mark Braverman and Zhongtian He, as
+listed on [the pinned paper](https://arxiv.org/abs/2610.10108v1). This
+review reran their pinned original verifier and the historical transcript
+generator in a temporary directory. The transcript regenerated byte for
+byte. This is a provenance replay that uses primary-source utilities,
+not a second independent derivation of the projective geometry. No
+primary source code is copied into the review output.
+
+All seven ORIGINS entries match their old source hashes. The six entries
+marked unchanged are byte-identical. The adapted completion script has
+unchanged mathematical function syntax trees. Its source paths were made
+local, its unsupported conditional-price section was removed, and its
+receipt was limited to the scalar result.
+
+A bounded search of all tracked Markdown, TeX, and text files at main
+`cef4b52f2a59009865bf8eabde1be3f159063703` found eight related literature
+or sign-gauge mentions, but no submitted scalar completion. The related
+PR #288 text concerns a rational common-target frame obstruction.
+The parent-fetched 315 open PR titles and bodies found
+[PR #349](https://github.com/CrocSwap/integer-mult-bounds/pull/349), which
+gives an explicit witness for that obstruction. It does not supply the
+matched-stub scalar completion and is not resolved by it. The README
+correctly retains the physical-frame limitation and predecessor credit.
+These checks do not establish novelty against all closed diffs,
+compressed archives, Discussions, unpublished work, or outside literature.
diff --git a/research/pg29-matched-dirty-completion/review/check_review.py b/research/pg29-matched-dirty-completion/review/check_review.py
new file mode 100644
index 0000000000..447d7a387e
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/check_review.py
@@ -0,0 +1,165 @@
+"""Check the scalar contract and rejection controls with explicit paths."""
+
+import argparse
+import ast
+from collections import defaultdict
+from hashlib import sha256
+import json
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import sys
+import tempfile
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def function_namespace(path):
+    source = ast.parse(path.read_text())
+    functions = [item for item in source.body if isinstance(item, ast.FunctionDef)]
+    namespace = {}
+    exec(compile(ast.Module(body=functions, type_ignores=[]), str(path), "exec", optimize=0), namespace)
+    return namespace
+
+
+def matrix(value):
+    a, b = value % 3, value // 3
+    return [[a, -b % 3], [b, a]]
+
+
+def product(left, right):
+    columns = list(zip(*right))
+    return [[sum(a * b for a, b in zip(row, column)) % 3 for column in columns]
+            for row in left]
+
+
+def identity(size):
+    return [[int(i == j) for j in range(size)] for i in range(size)]
+
+
+def lift(rows):
+    result = []
+    for row in rows:
+        blocks = [matrix(value) for value in row]
+        result.extend([[entry for block in blocks for entry in block[i]] for i in range(2)])
+    return result
+
+
+def field_sum(a, b):
+    return (a % 3 + b % 3) % 3 + 3 * ((a // 3 + b // 3) % 3)
+
+
+def run(command, env, prefix, out):
+    result = subprocess.run(command, capture_output=True, text=True, env=env, timeout=180)
+    (out / (prefix + "-stdout.txt")).write_text(result.stdout)
+    (out / (prefix + "-stderr.txt")).write_text(result.stderr)
+    return result
+
+
+def main(args):
+    package = args.package.resolve()
+    out = args.out.resolve()
+    out.mkdir(parents=True, exist_ok=False)
+    first = function_namespace(package / "independent_dirty.py")
+    second = function_namespace(package / "completion.py")
+    require(all((x * x + 1) % 3 for x in range(3)), "The quadratic is irreducible over F3")
+    for a in range(9):
+        for b in range(9):
+            total = [[(x + y) % 3 for x, y in zip(r, s)] for r, s in zip(matrix(a), matrix(b))]
+            require(matrix(first["add"](a, b)) == matrix(second["add"](a, b)) == total, "Both addition tables")
+            require(matrix(first["mul"](a, b)) == matrix(second["product"](a, b)) == product(matrix(a), matrix(b)), "Both multiplication tables")
+        if a:
+            inverse = first["inv"](a)
+            require(inverse == second["inverse_element"](a), "Both inverse tables")
+            require(product(matrix(a), matrix(inverse)) == identity(2), "Independent inverse check")
+
+    word = json.loads((package / "dirty-word.json").read_text())
+    factors = json.loads((package / "PG29-FACTORS.json").read_text())
+    inputs, outputs = defaultdict(list), defaultdict(list)
+    for i, (_, edge) in enumerate(word["inputs"][157:], 157):
+        inputs[edge].append(i)
+    for i, (_, edge) in enumerate(word["outputs"][157:], 157):
+        outputs[edge].append(i)
+    require(len(inputs) == len(outputs) == 9, "Nine pairs at each boundary")
+    require(all(len(v) == 2 for v in list(inputs.values()) + list(outputs.values())), "Each pair has two stubs")
+    quotient = [row[:157] + [field_sum(row[a], row[b]) for a, b in inputs.values()]
+                for row in word["transfer"]]
+    require(quotient[:157] == [row + [0] * 9 for row in identity(157)], "Matched inputs preserve messages")
+    require(all(quotient[a] == quotient[b] for a, b in outputs.values()), "Matched outputs agree")
+    junk = [quotient[a] for a, b in outputs.values()]
+    inverse = lift(factors["inverse_D9"])
+    require(product(inverse, lift(factors["D9"])) == identity(18), "Inverse over F3")
+    require(product(lift(factors["D9"]), inverse) == identity(18), "Other inverse order over F3")
+    normalized = product(inverse, lift(junk))
+    correction = lift(factors["correction"])
+    restored = [[(entry - error) % 3 for entry, error in zip(row, corr + [0] * 18)]
+                for row, corr in zip(normalized, correction)]
+    require(restored == [[0] * 314 + row for row in identity(18)], "All 332 F3 columns are restored")
+    require(any(row[:314] != [0] * 314 for row in normalized), "Omitting the message correction fails")
+    require(lift(factors["D9"]) != identity(18), "Omitting D normalization fails")
+    witness = next((i, j, row[j]) for i, row in enumerate(word["transfer"][:157])
+                   for j in range(157, 175) if row[j])
+    pair = next(pair for pair in inputs.values() if witness[1] in pair)
+    require(all(field_sum(row[pair[0]], row[pair[1]]) == 0 for row in word["transfer"][:157]), "The matched partner cancels contamination")
+
+    env = dict(os.environ, PYTHONOPTIMIZE="1")
+    result = run([sys.executable, "-O", "-B", str(package / "verify.py")], env, "optimized-environment", out)
+    require(result.returncode == 0 and "PASS_PG29_DIRTY_PACKAGE" in result.stdout, "Wrapper works in the optimized environment")
+    with tempfile.TemporaryDirectory(prefix="pg29-review-control-") as temp:
+        copied = Path(temp) / "package"
+        shutil.copytree(package, copied)
+        corrupted = json.loads((copied / "PG29-FACTORS.json").read_text())
+        corrupted["correction"][0][0] = (corrupted["correction"][0][0] + 1) % 9
+        (copied / "PG29-FACTORS.json").write_text(json.dumps(corrupted))
+        hashes = json.loads((copied / "SOURCE-HASHES.json").read_text())
+        hashes["PG29-FACTORS.json"] = sha256((copied / "PG29-FACTORS.json").read_bytes()).hexdigest()
+        (copied / "SOURCE-HASHES.json").write_text(json.dumps(hashes))
+        result = run([sys.executable, "-O", "-B", str(copied / "verify.py")], env, "wrong-factor-control", out)
+        require(result.returncode != 0 and "factors == independent_factors" in result.stderr,
+                "The semantic factor check remains active with PYTHONOPTIMIZE")
+        bad_word = json.loads((copied / "dirty-word.json").read_text())
+        bad_word["local_words"][0]["matrix"][0] = [0] * 5
+        (copied / "dirty-word.json").write_text(json.dumps(bad_word))
+        result = run([sys.executable, "-I", "-B", str(copied / "independent_dirty.py")], env, "singular-local-control", out)
+        require(result.returncode != 0 and "rank(local['matrix'])==5" in result.stderr, "Singular local map is rejected")
+
+    provenance = None
+    if args.primary_dir:
+        source = args.primary_dir.resolve()
+        pins = {"upstream_verify.py": "3be25d94a25e8ea8b484a1fb614a697e0a24e4519b647febc64b2d314f44d758",
+                "182-vertex-code.json": "f47b7f8af378fe7f86c7da32f04533b419711e468997c30ddef30a3a791dba01"}
+        for name, digest in pins.items():
+            require(sha256((source / name).read_bytes()).hexdigest() == digest, "Primary source pin")
+        with tempfile.TemporaryDirectory(prefix="pg29-review-provenance-") as temp:
+            temporary = Path(temp)
+            for name in ["upstream_verify.py", "182-vertex-code.json", "dirty_completion.py"]:
+                shutil.copy2(source / name, temporary / name)
+            result = run([sys.executable, "-B", str(temporary / "upstream_verify.py"), str(temporary / "182-vertex-code.json")], {}, "primary-verifier", out)
+            require(result.returncode == 0, "Primary verifier passes")
+            result = run([sys.executable, "-B", str(temporary / "dirty_completion.py")], {}, "transcript-regeneration", out)
+            require(result.returncode == 0, "Historical transcript generator passes")
+            require((temporary / "dirty-word.json").read_bytes() == (package / "dirty-word.json").read_bytes(), "Exact transcript regeneration")
+        provenance = {"primary_pins": pins, "generator_sha256": sha256((source / "dirty_completion.py").read_bytes()).hexdigest(),
+                      "original_verifier_passed": True, "transcript_regenerated_byte_exactly": True,
+                      "note": "The geometry generator uses primary-source utilities. This is a provenance replay, not an independent geometry implementation. No primary code is copied into this review output."}
+    report = {"status": "PASS_PG29_INDEPENDENT_REVIEW_CHECKS", "field_table_pairs_checked": 81,
+              "two_field_implementations_match_F3_matrix_representation": True,
+              "matched_GF9_columns": 166, "independent_lifted_F3_columns": 332,
+              "unmatched_input_contamination_witness": {"message_output_row": witness[0], "boundary_input_column": witness[1], "GF9_coefficient": witness[2]},
+              "missing_correction_fails": True, "missing_normalization_fails": True,
+              "wrong_factor_rejected_under_PYTHONOPTIMIZE": True, "singular_local_map_rejected": True,
+              "provenance": provenance, "new_kappa": False}
+    (out / "REVIEW-CHECKS.json").write_text(json.dumps(report, indent=2) + "\n")
+    print(report["status"])
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--package", type=Path, required=True)
+    parser.add_argument("--out", type=Path, required=True)
+    parser.add_argument("--primary-dir", type=Path)
+    main(parser.parse_args())
diff --git a/research/pg29-matched-dirty-completion/review/fresh/REVIEW-CHECKS.json b/research/pg29-matched-dirty-completion/review/fresh/REVIEW-CHECKS.json
new file mode 100644
index 0000000000..e8ce213433
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/review/fresh/REVIEW-CHECKS.json
@@ -0,0 +1,27 @@
+{
+  "status": "PASS_PG29_INDEPENDENT_REVIEW_CHECKS",
+  "field_table_pairs_checked": 81,
+  "two_field_implementations_match_F3_matrix_representation": true,
+  "matched_GF9_columns": 166,
+  "independent_lifted_F3_columns": 332,
+  "unmatched_input_contamination_witness": {
+    "message_output_row": 0,
+    "boundary_input_column": 157,
+    "GF9_coefficient": 3
+  },
+  "missing_correction_fails": true,
+  "missing_normalization_fails": true,
+  "wrong_factor_rejected_under_PYTHONOPTIMIZE": true,
+  "singular_local_map_rejected": true,
+  "provenance": {
+    "primary_pins": {
+      "upstream_verify.py": "3be25d94a25e8ea8b484a1fb614a697e0a24e4519b647febc64b2d314f44d758",
+      "182-vertex-code.json": "f47b7f8af378fe7f86c7da32f04533b419711e468997c30ddef30a3a791dba01"
+    },
+    "generator_sha256": "41d265375a67e24c3d57db2d77bb3459a6827b777641f7c4ed7d7637684361c4",
+    "original_verifier_passed": true,
+    "transcript_regenerated_byte_exactly": true,
+    "note": "The geometry generator uses primary-source utilities. This is a provenance replay, not an independent geometry implementation. No primary code is copied into this review output."
+  },
+  "new_kappa": false
+}
diff --git a/research/pg29-matched-dirty-completion/verify.py b/research/pg29-matched-dirty-completion/verify.py
new file mode 100644
index 0000000000..6ac15379b0
--- /dev/null
+++ b/research/pg29-matched-dirty-completion/verify.py
@@ -0,0 +1,25 @@
+"""Check both finite scalar replays in a temporary directory."""
+import hashlib
+import json
+import shutil
+import subprocess
+import sys
+import tempfile
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+for name, expected in json.loads((HERE/'SOURCE-HASHES.json').read_text()).items():
+    if hashlib.sha256((HERE/name).read_bytes()).hexdigest() != expected:
+        raise ValueError('Source hash mismatch: '+name)
+with tempfile.TemporaryDirectory(prefix='pg29-matched-dirty-') as temp:
+    work = Path(temp)/'package'
+    shutil.copytree(HERE, work, ignore=shutil.ignore_patterns('__pycache__'))
+    for script, result in [('independent_dirty.py','INDEPENDENT-DIRTY.json'),
+                           ('completion.py','COMPLETION-RESULT.json')]:
+        run = subprocess.run([sys.executable,'-I','-B',str(work/script)],cwd=work,
+                             capture_output=True,text=True,timeout=180)
+        if run.returncode:
+            raise ValueError(script+'\n'+run.stderr)
+        if json.loads((work/result).read_text()) != json.loads((HERE/result).read_text()):
+            raise ValueError('Receipt mismatch: '+result)
+        print('PASS '+script)
+print('PASS_PG29_DIRTY_PACKAGE independent_stubs=175 matched_inputs=166 no_new_kappa')