Verify a matched-input scalar completion for the PG29 code

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
+}

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"
+  }
+}

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."
+}

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."
+    ]
+  }
+]

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."
+}

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]]}

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.