diff --git a/certificates/research/fanout-optimality-package-validation-v1.json b/certificates/research/fanout-optimality-package-validation-v1.json
new file mode 100644
index 0000000000..cbf2432405
--- /dev/null
+++ b/certificates/research/fanout-optimality-package-validation-v1.json
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diff --git a/certificates/research/fanout-optimality-replay-evidence-v1.json b/certificates/research/fanout-optimality-replay-evidence-v1.json
new file mode 100644
index 0000000000..3c7dc8d29f
--- /dev/null
+++ b/certificates/research/fanout-optimality-replay-evidence-v1.json
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+      "raw_stdout_utf8": "CHECK Authenticate byte-exact upper/lower proofs, source closure and restricted model; replay unchanged upper checker once in fresh original-path sandbox; full raw-byte and typedJSON equality for result/program, zero exclusions; preserve lossless complete fresh artifacts;10meaningful source/model/type controls. No extra engine, native/Powers/global caller or lower-kernel run.\nFRESH_FANOUT_EVIDENCE {\"command\": [\"/usr/bin/python3\", \"-I\", \"-Werror\", \"-B\", \"-X\", \"pycache_prefix=/tmp/fanout-unchanged-source-ahl8y5vh/cache\", \"/tmp/fanout-unchanged-source-ahl8y5vh/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py\", \"--input\", \"/tmp/fanout-unchanged-source-ahl8y5vh/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json\", \"--program\", \"/tmp/fanout-unchanged-source-ahl8y5vh/FANOUT-PROGRAM-v1.json\", \"--result\", \"/tmp/fanout-unchanged-source-ahl8y5vh/FANOUT-RESULT-v1.json\"], \"exit_code\": 0, \"program_raw_bytes\": 1282103, \"program_raw_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"program_zlib_base64\": 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\"result_utf8\": \"{\\n  \\\"schema\\\": \\\"exact-fanout-component-result/v1\\\",\\n  \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\",\\n  \\\"source_rows\\\": 112,\\n  \\\"common_modes\\\": 8,\\n  \\\"leftcoset_count\\\": 112,\\n  \\\"rationalrank_sum_Qqueries\\\": 112,\\n  \\\"query_savings_vs112\\\": 0,\\n  \\\"owned_arbitrary\\\": 17,\\n  \\\"owned_zero_return\\\": 17,\\n  \\\"all512_alias_columns_checked\\\": 57344,\\n  \\\"group_sizes\\\": [\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    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\\\"GAUSSIAN\\\": 112\\n  },\\n  \\\"ADD_census\\\": {\\n    \\\"1\\\": 392,\\n    \\\"1/2\\\": 88,\\n    \\\"-1\\\": 168,\\n    \\\"-1/2\\\": 24\\n  },\\n  \\\"monomial_primitive_census\\\": {\\n    \\\"D\\\": 232,\\n    \\\"P\\\": 232,\\n    \\\"X\\\": 232,\\n    \\\"phase\\\": 120\\n  },\\n  \\\"scalar_tariff\\\": 6114,\\n  \\\"controls\\\": [\\n    {\\n      \\\"name\\\": \\\"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"reversedalias multiplicationorder\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"oneimpulse-only grouping merges differentcompleteLEFTclasses\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"alias absolute phase flipped\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"positiveQ substituted for inverseQ or omittedcentralX\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"droppedactualnonzero M coefficient\\\",\\n      \\\"row\\\": 0,\\n      \\\"mode\\\": 0,\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"tensor exterioronehalf into twocolumns\\\",\\n      \\\"legal\\\": \\\"1/2\\\",\\n      \\\"illegal\\\": \\\"1/4\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"phase2columnlift replacedby exteriornegativeone\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"legal\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"illegal\\\": [\\n        -1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"illegal two-termwhole-fieldQshortcut\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"mixed_output\\\": [\\n        0,\\n        1\\n      ],\\n      \\\"actual_numerator\\\": [\\n        2,\\n        0\\n      ],\\n      \\\"actual_denominator_power2\\\": 2,\\n      \\\"shortcut_numerator\\\": [\\n        0,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"integer reconstruction coefficient changed\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"uncleared arbitraryb0 owned entry\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"write originalh instead ofownedcopy\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"premature queriedbasis CLEAR beforelastread\\\",\\n      \\\"rejected\\\": true\\n    }\\n  ],\\n  \\\"input_sha256\\\": \\\"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\\\",\\n  \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\",\\n  \\\"checker_sha256\\\": \\\"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\\\",\\n  \\\"oracle_sha256\\\": \\\"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\\\",\\n  \\\"scope\\\": \\\"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\\\"\\n}\\n\", \"stderr\": \"\", \"stdout\": \"{\\\"leftcoset_count\\\": 112, \\\"program_counts\\\": {\\\"ADD\\\": 672, \\\"CLEAR\\\": 249, \\\"COPY\\\": 8, \\\"GAUSSIAN\\\": 112, \\\"MONOMIAL\\\": 344, \\\"ZERO_RETAG\\\": 249}, \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\", \\\"query_savings_vs112\\\": 0, \\\"rationalrank_sum_Qqueries\\\": 112, \\\"scalar_tariff\\\": 6114, \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\"}\\n\"}\n{\"canonical_base\": \"1a3ced60b2f7a46bc70280a04f2eeb8ca027c700\", \"comparison_exclusions\": [], \"fresh_program_transport\": \"losslesszlibbase64; compare uncompressedrawbytes, notcontaineridentity\", \"fresh_upper_checker\": true, \"full_137_field_physical_endpoint_replay\": false, \"full_rawdual_or_compiler_admission\": false, \"immutable_files\": 32, \"incremental_global_bound\": false, \"inputs_and_modes_unchanged\": true, \"lower_proof_execution\": \"hash/scope authentication only; retained independent static review, no formal kernel\", \"minimum_total_calls_in_fixed_grammar\": 112, \"new_kappa\": null, \"optimized\": false, \"original_upper_controls\": 13, \"post_custody_sha256\": \"1cc0d26c589ab010e1d81fe16a6e7c43b74df2f3d2e7c34f42255b1e0c9718ad\", \"pre_custody_sha256\": \"1cc0d26c589ab010e1d81fe16a6e7c43b74df2f3d2e7c34f42255b1e0c9718ad\", \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings\": 0, \"result_sha256\": \"bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7\", \"status\": \"PASS_SCOPED_FANOUT_OPTIMALITY_SUPPORT_PACKAGE\", \"upper_H1_calls\": 112, \"wrapper_controls\": [\"changed_lower_proof_bytes_rejected\", \"forged_canonical_origin_rejected\", \"cached_initial_observation_rejected\", \"width_subsequence_rejected\", \"changed_field_capacity_rejected\", \"incremental_bound_rejected\", \"physical137_replay_claim_rejected\", \"width_dependent_coefficients_rejected\", \"bool_for_zero_result_rejected\", \"float_for_integer_program_rejected\"]}\nCHECK Authenticate byte-exact upper/lower proofs, source closure and restricted model; replay unchanged upper checker once in fresh original-path sandbox; full raw-byte and typedJSON equality for result/program, zero exclusions; preserve lossless complete fresh artifacts;10meaningful source/model/type controls. No extra engine, native/Powers/global caller or lower-kernel run.\nFRESH_FANOUT_EVIDENCE {\"command\": [\"/usr/bin/python3\", \"-I\", \"-Werror\", \"-B\", \"-X\", \"pycache_prefix=/tmp/fanout-unchanged-source-orkfbqc5/cache\", \"-O\", \"/tmp/fanout-unchanged-source-orkfbqc5/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py\", \"--input\", \"/tmp/fanout-unchanged-source-orkfbqc5/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json\", \"--program\", \"/tmp/fanout-unchanged-source-orkfbqc5/FANOUT-PROGRAM-v1.json\", \"--result\", \"/tmp/fanout-unchanged-source-orkfbqc5/FANOUT-RESULT-v1.json\"], \"exit_code\": 0, \"program_raw_bytes\": 1282103, \"program_raw_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"program_zlib_base64\": 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\"result_utf8\": \"{\\n  \\\"schema\\\": \\\"exact-fanout-component-result/v1\\\",\\n  \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\",\\n  \\\"source_rows\\\": 112,\\n  \\\"common_modes\\\": 8,\\n  \\\"leftcoset_count\\\": 112,\\n  \\\"rationalrank_sum_Qqueries\\\": 112,\\n  \\\"query_savings_vs112\\\": 0,\\n  \\\"owned_arbitrary\\\": 17,\\n  \\\"owned_zero_return\\\": 17,\\n  \\\"all512_alias_columns_checked\\\": 57344,\\n  \\\"group_sizes\\\": [\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    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\\\"GAUSSIAN\\\": 112\\n  },\\n  \\\"ADD_census\\\": {\\n    \\\"1\\\": 392,\\n    \\\"1/2\\\": 88,\\n    \\\"-1\\\": 168,\\n    \\\"-1/2\\\": 24\\n  },\\n  \\\"monomial_primitive_census\\\": {\\n    \\\"D\\\": 232,\\n    \\\"P\\\": 232,\\n    \\\"X\\\": 232,\\n    \\\"phase\\\": 120\\n  },\\n  \\\"scalar_tariff\\\": 6114,\\n  \\\"controls\\\": [\\n    {\\n      \\\"name\\\": \\\"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"reversedalias multiplicationorder\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"oneimpulse-only grouping merges differentcompleteLEFTclasses\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"alias absolute phase flipped\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"positiveQ substituted for inverseQ or omittedcentralX\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"droppedactualnonzero M coefficient\\\",\\n      \\\"row\\\": 0,\\n      \\\"mode\\\": 0,\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"tensor exterioronehalf into twocolumns\\\",\\n      \\\"legal\\\": \\\"1/2\\\",\\n      \\\"illegal\\\": \\\"1/4\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"phase2columnlift replacedby exteriornegativeone\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"legal\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"illegal\\\": [\\n        -1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"illegal two-termwhole-fieldQshortcut\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"mixed_output\\\": [\\n        0,\\n        1\\n      ],\\n      \\\"actual_numerator\\\": [\\n        2,\\n        0\\n      ],\\n      \\\"actual_denominator_power2\\\": 2,\\n      \\\"shortcut_numerator\\\": [\\n        0,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"integer reconstruction coefficient changed\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"uncleared arbitraryb0 owned entry\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"write originalh instead ofownedcopy\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"premature queriedbasis CLEAR beforelastread\\\",\\n      \\\"rejected\\\": true\\n    }\\n  ],\\n  \\\"input_sha256\\\": \\\"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\\\",\\n  \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\",\\n  \\\"checker_sha256\\\": \\\"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\\\",\\n  \\\"oracle_sha256\\\": \\\"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\\\",\\n  \\\"scope\\\": \\\"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\\\"\\n}\\n\", \"stderr\": \"\", \"stdout\": \"{\\\"leftcoset_count\\\": 112, \\\"program_counts\\\": {\\\"ADD\\\": 672, \\\"CLEAR\\\": 249, \\\"COPY\\\": 8, \\\"GAUSSIAN\\\": 112, \\\"MONOMIAL\\\": 344, \\\"ZERO_RETAG\\\": 249}, \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\", \\\"query_savings_vs112\\\": 0, \\\"rationalrank_sum_Qqueries\\\": 112, \\\"scalar_tariff\\\": 6114, \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\"}\\n\"}\n{\"canonical_base\": \"1a3ced60b2f7a46bc70280a04f2eeb8ca027c700\", \"comparison_exclusions\": [], \"fresh_program_transport\": \"losslesszlibbase64; compare uncompressedrawbytes, notcontaineridentity\", \"fresh_upper_checker\": true, \"full_137_field_physical_endpoint_replay\": false, \"full_rawdual_or_compiler_admission\": false, \"immutable_files\": 32, \"incremental_global_bound\": false, \"inputs_and_modes_unchanged\": true, \"lower_proof_execution\": \"hash/scope authentication only; retained independent static review, no formal kernel\", \"minimum_total_calls_in_fixed_grammar\": 112, \"new_kappa\": null, \"optimized\": true, \"original_upper_controls\": 13, \"post_custody_sha256\": \"1cc0d26c589ab010e1d81fe16a6e7c43b74df2f3d2e7c34f42255b1e0c9718ad\", \"pre_custody_sha256\": \"1cc0d26c589ab010e1d81fe16a6e7c43b74df2f3d2e7c34f42255b1e0c9718ad\", \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings\": 0, \"result_sha256\": \"bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7\", \"status\": \"PASS_SCOPED_FANOUT_OPTIMALITY_SUPPORT_PACKAGE\", \"upper_H1_calls\": 112, \"wrapper_controls\": [\"changed_lower_proof_bytes_rejected\", \"forged_canonical_origin_rejected\", \"cached_initial_observation_rejected\", \"width_subsequence_rejected\", \"changed_field_capacity_rejected\", \"incremental_bound_rejected\", \"physical137_replay_claim_rejected\", \"width_dependent_coefficients_rejected\", \"bool_for_zero_result_rejected\", \"float_for_integer_program_rejected\"]}\nPASS_REGISTERED_RESEARCH_PACKAGE research/fanout-optimality-support outcome=completed\n",
+      "raw_stdout_sha256": "e4605e04f0b21f6185fbb206f7bf3f9c43db7d589efe2cd1bdfc9d271d97022c"
+    },
+    {
+      "name": "fanout-optimality-readonly-normal-v1",
+      "guard_receipt_utf8": "{\n  \"schema\": \"serial-research-run/v1\",\n  \"command\": [\n    \"/usr/bin/env\",\n    \"-u\",\n    \"GIT_DIR\",\n    \"-u\",\n    \"GIT_WORK_TREE\",\n    \"-u\",\n    \"GIT_COMMON_DIR\",\n    \"PATH=\",\n    \"GIT_CEILING_DIRECTORIES=/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1\",\n    \"/usr/bin/python3\",\n    \"-I\",\n    \"-Werror\",\n    \"-B\",\n    \"verify.py\"\n  ],\n  \"cwd\": \"/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1\",\n  \"exit_code\": 0,\n  \"termination\": null,\n  \"elapsed_seconds\": 4.230012246989645,\n  \"sampled_peak_descendant_rss_bytes\": 57831424,\n  \"rss_samples\": 42,\n  \"memory_limit_mib\": 256,\n  \"timeout_seconds\": 30.0,\n  \"python\": \"3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]\",\n  \"log_sha256\": \"5bccc91a8147d71c08a46c7e49d3f8dbcde3a75b5623eaba4494650c6d9e9f6c\",\n  \"scope\": \"Fresh command execution only; scientific claim determined by reviewed output.\"\n}\n",
+      "guard_receipt_sha256": "77b72312ea67333c1a5f4cdaa07f13286d4ea3a06aa03ce2cad42498d43501c7",
+      "raw_stdout_utf8": "FRESH_FANOUT_EVIDENCE {\"command\": [\"/usr/bin/python3\", \"-I\", \"-Werror\", \"-B\", \"-X\", \"pycache_prefix=/tmp/fanout-unchanged-source-svslgf6h/cache\", \"/tmp/fanout-unchanged-source-svslgf6h/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py\", \"--input\", \"/tmp/fanout-unchanged-source-svslgf6h/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json\", \"--program\", \"/tmp/fanout-unchanged-source-svslgf6h/FANOUT-PROGRAM-v1.json\", \"--result\", \"/tmp/fanout-unchanged-source-svslgf6h/FANOUT-RESULT-v1.json\"], \"exit_code\": 0, \"program_raw_bytes\": 1282103, \"program_raw_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"program_zlib_base64\": 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\"result_utf8\": \"{\\n  \\\"schema\\\": \\\"exact-fanout-component-result/v1\\\",\\n  \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\",\\n  \\\"source_rows\\\": 112,\\n  \\\"common_modes\\\": 8,\\n  \\\"leftcoset_count\\\": 112,\\n  \\\"rationalrank_sum_Qqueries\\\": 112,\\n  \\\"query_savings_vs112\\\": 0,\\n  \\\"owned_arbitrary\\\": 17,\\n  \\\"owned_zero_return\\\": 17,\\n  \\\"all512_alias_columns_checked\\\": 57344,\\n  \\\"group_sizes\\\": [\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    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\\\"GAUSSIAN\\\": 112\\n  },\\n  \\\"ADD_census\\\": {\\n    \\\"1\\\": 392,\\n    \\\"1/2\\\": 88,\\n    \\\"-1\\\": 168,\\n    \\\"-1/2\\\": 24\\n  },\\n  \\\"monomial_primitive_census\\\": {\\n    \\\"D\\\": 232,\\n    \\\"P\\\": 232,\\n    \\\"X\\\": 232,\\n    \\\"phase\\\": 120\\n  },\\n  \\\"scalar_tariff\\\": 6114,\\n  \\\"controls\\\": [\\n    {\\n      \\\"name\\\": \\\"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"reversedalias multiplicationorder\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"oneimpulse-only grouping merges differentcompleteLEFTclasses\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"alias absolute phase flipped\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"positiveQ substituted for inverseQ or omittedcentralX\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"droppedactualnonzero M coefficient\\\",\\n      \\\"row\\\": 0,\\n      \\\"mode\\\": 0,\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"tensor exterioronehalf into twocolumns\\\",\\n      \\\"legal\\\": \\\"1/2\\\",\\n      \\\"illegal\\\": \\\"1/4\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"phase2columnlift replacedby exteriornegativeone\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"legal\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"illegal\\\": [\\n        -1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"illegal two-termwhole-fieldQshortcut\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"mixed_output\\\": [\\n        0,\\n        1\\n      ],\\n      \\\"actual_numerator\\\": [\\n        2,\\n        0\\n      ],\\n      \\\"actual_denominator_power2\\\": 2,\\n      \\\"shortcut_numerator\\\": [\\n        0,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"integer reconstruction coefficient changed\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"uncleared arbitraryb0 owned entry\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"write originalh instead ofownedcopy\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"premature queriedbasis CLEAR beforelastread\\\",\\n      \\\"rejected\\\": true\\n    }\\n  ],\\n  \\\"input_sha256\\\": \\\"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\\\",\\n  \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\",\\n  \\\"checker_sha256\\\": \\\"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\\\",\\n  \\\"oracle_sha256\\\": \\\"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\\\",\\n  \\\"scope\\\": \\\"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\\\"\\n}\\n\", \"stderr\": \"\", \"stdout\": \"{\\\"leftcoset_count\\\": 112, \\\"program_counts\\\": {\\\"ADD\\\": 672, \\\"CLEAR\\\": 249, \\\"COPY\\\": 8, \\\"GAUSSIAN\\\": 112, \\\"MONOMIAL\\\": 344, \\\"ZERO_RETAG\\\": 249}, \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\", \\\"query_savings_vs112\\\": 0, \\\"rationalrank_sum_Qqueries\\\": 112, \\\"scalar_tariff\\\": 6114, \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\"}\\n\"}\n{\"canonical_base\": \"1a3ced60b2f7a46bc70280a04f2eeb8ca027c700\", \"comparison_exclusions\": [], \"fresh_program_transport\": \"losslesszlibbase64; compare uncompressedrawbytes, notcontaineridentity\", \"fresh_upper_checker\": true, \"full_137_field_physical_endpoint_replay\": false, \"full_rawdual_or_compiler_admission\": false, \"immutable_files\": 32, \"incremental_global_bound\": false, \"inputs_and_modes_unchanged\": true, \"lower_proof_execution\": \"hash/scope authentication only; retained independent static review, no formal kernel\", \"minimum_total_calls_in_fixed_grammar\": 112, \"new_kappa\": null, \"optimized\": false, \"original_upper_controls\": 13, \"post_custody_sha256\": \"7027a456774c6fc9de39e2e290bc099a9d16ccd36d7c5463c6a91c831b148930\", \"pre_custody_sha256\": \"7027a456774c6fc9de39e2e290bc099a9d16ccd36d7c5463c6a91c831b148930\", \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings\": 0, \"result_sha256\": \"bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7\", \"status\": \"PASS_SCOPED_FANOUT_OPTIMALITY_SUPPORT_PACKAGE\", \"upper_H1_calls\": 112, \"wrapper_controls\": [\"changed_lower_proof_bytes_rejected\", \"forged_canonical_origin_rejected\", \"cached_initial_observation_rejected\", \"width_subsequence_rejected\", \"changed_field_capacity_rejected\", \"incremental_bound_rejected\", \"physical137_replay_claim_rejected\", \"width_dependent_coefficients_rejected\", \"bool_for_zero_result_rejected\", \"float_for_integer_program_rejected\"]}\n",
+      "raw_stdout_sha256": "5bccc91a8147d71c08a46c7e49d3f8dbcde3a75b5623eaba4494650c6d9e9f6c"
+    },
+    {
+      "name": "fanout-optimality-readonly-optimized-v1",
+      "guard_receipt_utf8": "{\n  \"schema\": \"serial-research-run/v1\",\n  \"command\": [\n    \"/usr/bin/env\",\n    \"-u\",\n    \"GIT_DIR\",\n    \"-u\",\n    \"GIT_WORK_TREE\",\n    \"-u\",\n    \"GIT_COMMON_DIR\",\n    \"PATH=\",\n    \"GIT_CEILING_DIRECTORIES=/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1\",\n    \"/usr/bin/python3\",\n    \"-I\",\n    \"-O\",\n    \"-Werror\",\n    \"-B\",\n    \"verify.py\"\n  ],\n  \"cwd\": \"/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1\",\n  \"exit_code\": 0,\n  \"termination\": null,\n  \"elapsed_seconds\": 4.637755592993926,\n  \"sampled_peak_descendant_rss_bytes\": 62660608,\n  \"rss_samples\": 46,\n  \"memory_limit_mib\": 256,\n  \"timeout_seconds\": 30.0,\n  \"python\": \"3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]\",\n  \"log_sha256\": \"63fa9f527e479d852c8b48e95c7962809947ff0d1f380d4f2c55a876a63a2854\",\n  \"scope\": \"Fresh command execution only; scientific claim determined by reviewed output.\"\n}\n",
+      "guard_receipt_sha256": "2b7c241711f5f0de098de36dc78e30cb1434372070e76dd4e931d9e475fb24b4",
+      "raw_stdout_utf8": "FRESH_FANOUT_EVIDENCE {\"command\": [\"/usr/bin/python3\", \"-I\", \"-Werror\", \"-B\", \"-X\", \"pycache_prefix=/tmp/fanout-unchanged-source-zjux0w2e/cache\", \"-O\", \"/tmp/fanout-unchanged-source-zjux0w2e/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py\", \"--input\", \"/tmp/fanout-unchanged-source-zjux0w2e/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json\", \"--program\", \"/tmp/fanout-unchanged-source-zjux0w2e/FANOUT-PROGRAM-v1.json\", \"--result\", \"/tmp/fanout-unchanged-source-zjux0w2e/FANOUT-RESULT-v1.json\"], \"exit_code\": 0, \"program_raw_bytes\": 1282103, \"program_raw_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"program_zlib_base64\": 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\"result_utf8\": \"{\\n  \\\"schema\\\": \\\"exact-fanout-component-result/v1\\\",\\n  \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\",\\n  \\\"source_rows\\\": 112,\\n  \\\"common_modes\\\": 8,\\n  \\\"leftcoset_count\\\": 112,\\n  \\\"rationalrank_sum_Qqueries\\\": 112,\\n  \\\"query_savings_vs112\\\": 0,\\n  \\\"owned_arbitrary\\\": 17,\\n  \\\"owned_zero_return\\\": 17,\\n  \\\"all512_alias_columns_checked\\\": 57344,\\n  \\\"group_sizes\\\": [\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    1,\\n    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\\\"GAUSSIAN\\\": 112\\n  },\\n  \\\"ADD_census\\\": {\\n    \\\"1\\\": 392,\\n    \\\"1/2\\\": 88,\\n    \\\"-1\\\": 168,\\n    \\\"-1/2\\\": 24\\n  },\\n  \\\"monomial_primitive_census\\\": {\\n    \\\"D\\\": 232,\\n    \\\"P\\\": 232,\\n    \\\"X\\\": 232,\\n    \\\"phase\\\": 120\\n  },\\n  \\\"scalar_tariff\\\": 6114,\\n  \\\"controls\\\": [\\n    {\\n      \\\"name\\\": \\\"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"reversedalias multiplicationorder\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"oneimpulse-only grouping merges differentcompleteLEFTclasses\\\",\\n      \\\"rows\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"alias absolute phase flipped\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"positiveQ substituted for inverseQ or omittedcentralX\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"droppedactualnonzero M coefficient\\\",\\n      \\\"row\\\": 0,\\n      \\\"mode\\\": 0,\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"tensor exterioronehalf into twocolumns\\\",\\n      \\\"legal\\\": \\\"1/2\\\",\\n      \\\"illegal\\\": \\\"1/4\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"phase2columnlift replacedby exteriornegativeone\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"legal\\\": [\\n        1,\\n        0\\n      ],\\n      \\\"illegal\\\": [\\n        -1,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"illegal two-termwhole-fieldQshortcut\\\",\\n      \\\"fiberwidth\\\": 2,\\n      \\\"mixed_output\\\": [\\n        0,\\n        1\\n      ],\\n      \\\"actual_numerator\\\": [\\n        2,\\n        0\\n      ],\\n      \\\"actual_denominator_power2\\\": 2,\\n      \\\"shortcut_numerator\\\": [\\n        0,\\n        0\\n      ],\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"integer reconstruction coefficient changed\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"uncleared arbitraryb0 owned entry\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"write originalh instead ofownedcopy\\\",\\n      \\\"rejected\\\": true\\n    },\\n    {\\n      \\\"name\\\": \\\"premature queriedbasis CLEAR beforelastread\\\",\\n      \\\"rejected\\\": true\\n    }\\n  ],\\n  \\\"input_sha256\\\": \\\"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\\\",\\n  \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\",\\n  \\\"checker_sha256\\\": \\\"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\\\",\\n  \\\"oracle_sha256\\\": \\\"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\\\",\\n  \\\"scope\\\": \\\"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\\\"\\n}\\n\", \"stderr\": \"\", \"stdout\": \"{\\\"leftcoset_count\\\": 112, \\\"program_counts\\\": {\\\"ADD\\\": 672, \\\"CLEAR\\\": 249, \\\"COPY\\\": 8, \\\"GAUSSIAN\\\": 112, \\\"MONOMIAL\\\": 344, \\\"ZERO_RETAG\\\": 249}, \\\"program_sha256\\\": \\\"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\\\", \\\"query_savings_vs112\\\": 0, \\\"rationalrank_sum_Qqueries\\\": 112, \\\"scalar_tariff\\\": 6114, \\\"status\\\": \\\"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\\\"}\\n\"}\n{\"canonical_base\": \"1a3ced60b2f7a46bc70280a04f2eeb8ca027c700\", \"comparison_exclusions\": [], \"fresh_program_transport\": \"losslesszlibbase64; compare uncompressedrawbytes, notcontaineridentity\", \"fresh_upper_checker\": true, \"full_137_field_physical_endpoint_replay\": false, \"full_rawdual_or_compiler_admission\": false, \"immutable_files\": 32, \"incremental_global_bound\": false, \"inputs_and_modes_unchanged\": true, \"lower_proof_execution\": \"hash/scope authentication only; retained independent static review, no formal kernel\", \"minimum_total_calls_in_fixed_grammar\": 112, \"new_kappa\": null, \"optimized\": true, \"original_upper_controls\": 13, \"post_custody_sha256\": \"7027a456774c6fc9de39e2e290bc099a9d16ccd36d7c5463c6a91c831b148930\", \"pre_custody_sha256\": \"7027a456774c6fc9de39e2e290bc099a9d16ccd36d7c5463c6a91c831b148930\", \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings\": 0, \"result_sha256\": \"bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7\", \"status\": \"PASS_SCOPED_FANOUT_OPTIMALITY_SUPPORT_PACKAGE\", \"upper_H1_calls\": 112, \"wrapper_controls\": [\"changed_lower_proof_bytes_rejected\", \"forged_canonical_origin_rejected\", \"cached_initial_observation_rejected\", \"width_subsequence_rejected\", \"changed_field_capacity_rejected\", \"incremental_bound_rejected\", \"physical137_replay_claim_rejected\", \"width_dependent_coefficients_rejected\", \"bool_for_zero_result_rejected\", \"float_for_integer_program_rejected\"]}\n",
+      "raw_stdout_sha256": "63fa9f527e479d852c8b48e95c7962809947ff0d1f380d4f2c55a876a63a2854"
+    }
+  ],
+  "fresh_transports": [
+    {
+      "run": "fanout-optimality-registered-normal-optimized-v1",
+      "event_number": 1,
+      "exact_log_event": {
+        "command": [
+          "/usr/bin/python3",
+          "-I",
+          "-Werror",
+          "-B",
+          "-X",
+          "pycache_prefix=/tmp/fanout-unchanged-source-ahl8y5vh/cache",
+          "/tmp/fanout-unchanged-source-ahl8y5vh/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+          "--input",
+          "/tmp/fanout-unchanged-source-ahl8y5vh/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+          "--program",
+          "/tmp/fanout-unchanged-source-ahl8y5vh/FANOUT-PROGRAM-v1.json",
+          "--result",
+          "/tmp/fanout-unchanged-source-ahl8y5vh/FANOUT-RESULT-v1.json"
+        ],
+        "exit_code": 0,
+        "program_raw_bytes": 1282103,
+        "program_raw_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+        "program_zlib_base64": 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+        "result_utf8": "{\n  \"schema\": \"exact-fanout-component-result/v1\",\n  \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\",\n  \"source_rows\": 112,\n  \"common_modes\": 8,\n  \"leftcoset_count\": 112,\n  \"rationalrank_sum_Qqueries\": 112,\n  \"query_savings_vs112\": 0,\n  \"owned_arbitrary\": 17,\n  \"owned_zero_return\": 17,\n  \"all512_alias_columns_checked\": 57344,\n  \"group_sizes\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"group_ranks\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"nonzero_rows\": 112,\n  \"H_abs\": 448,\n  \"T_abs\": 112,\n  \"maximum_integer_coefficient_bitlength\": 1,\n  \"maximum_certificate_integer_bitlength\": 1,\n  \"runtime_coefficients\": \"integersandhalvesonly\",\n  \"runtime_odd_divisions\": 0,\n  \"program_counts\": {\n    \"CLEAR\": 249,\n    \"ZERO_RETAG\": 249,\n    \"COPY\": 8,\n    \"MONOMIAL\": 344,\n    \"ADD\": 672,\n    \"GAUSSIAN\": 112\n  },\n  \"ADD_census\": {\n    \"1\": 392,\n    \"1/2\": 88,\n    \"-1\": 168,\n    \"-1/2\": 24\n  },\n  \"monomial_primitive_census\": {\n    \"D\": 232,\n    \"P\": 232,\n    \"X\": 232,\n    \"phase\": 120\n  },\n  \"scalar_tariff\": 6114,\n  \"controls\": [\n    {\n      \"name\": \"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"reversedalias multiplicationorder\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"oneimpulse-only grouping merges differentcompleteLEFTclasses\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"alias absolute phase flipped\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"positiveQ substituted for inverseQ or omittedcentralX\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"droppedactualnonzero M coefficient\",\n      \"row\": 0,\n      \"mode\": 0,\n      \"rejected\": true\n    },\n    {\n      \"name\": \"tensor exterioronehalf into twocolumns\",\n      \"legal\": \"1/2\",\n      \"illegal\": \"1/4\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"phase2columnlift replacedby exteriornegativeone\",\n      \"fiberwidth\": 2,\n      \"legal\": [\n        1,\n        0\n      ],\n      \"illegal\": [\n        -1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"illegal two-termwhole-fieldQshortcut\",\n      \"fiberwidth\": 2,\n      \"mixed_output\": [\n        0,\n        1\n      ],\n      \"actual_numerator\": [\n        2,\n        0\n      ],\n      \"actual_denominator_power2\": 2,\n      \"shortcut_numerator\": [\n        0,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"integer reconstruction coefficient changed\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"uncleared arbitraryb0 owned entry\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"write originalh instead ofownedcopy\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"premature queriedbasis CLEAR beforelastread\",\n      \"rejected\": true\n    }\n  ],\n  \"input_sha256\": \"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\",\n  \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\",\n  \"checker_sha256\": \"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\",\n  \"oracle_sha256\": \"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\",\n  \"scope\": \"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\"\n}\n",
+        "stderr": "",
+        "stdout": "{\"leftcoset_count\": 112, \"program_counts\": {\"ADD\": 672, \"CLEAR\": 249, \"COPY\": 8, \"GAUSSIAN\": 112, \"MONOMIAL\": 344, \"ZERO_RETAG\": 249}, \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings_vs112\": 0, \"rationalrank_sum_Qqueries\": 112, \"scalar_tariff\": 6114, \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\"}\n"
+      },
+      "program_uncompressed_bytes": 1282103,
+      "program_uncompressed_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_utf8_bytes": 4909,
+      "result_raw_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "comparison_exclusions": []
+    },
+    {
+      "run": "fanout-optimality-registered-normal-optimized-v1",
+      "event_number": 2,
+      "exact_log_event": {
+        "command": [
+          "/usr/bin/python3",
+          "-I",
+          "-Werror",
+          "-B",
+          "-X",
+          "pycache_prefix=/tmp/fanout-unchanged-source-orkfbqc5/cache",
+          "-O",
+          "/tmp/fanout-unchanged-source-orkfbqc5/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+          "--input",
+          "/tmp/fanout-unchanged-source-orkfbqc5/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+          "--program",
+          "/tmp/fanout-unchanged-source-orkfbqc5/FANOUT-PROGRAM-v1.json",
+          "--result",
+          "/tmp/fanout-unchanged-source-orkfbqc5/FANOUT-RESULT-v1.json"
+        ],
+        "exit_code": 0,
+        "program_raw_bytes": 1282103,
+        "program_raw_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+        "program_zlib_base64": 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+        "result_utf8": "{\n  \"schema\": \"exact-fanout-component-result/v1\",\n  \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\",\n  \"source_rows\": 112,\n  \"common_modes\": 8,\n  \"leftcoset_count\": 112,\n  \"rationalrank_sum_Qqueries\": 112,\n  \"query_savings_vs112\": 0,\n  \"owned_arbitrary\": 17,\n  \"owned_zero_return\": 17,\n  \"all512_alias_columns_checked\": 57344,\n  \"group_sizes\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"group_ranks\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"nonzero_rows\": 112,\n  \"H_abs\": 448,\n  \"T_abs\": 112,\n  \"maximum_integer_coefficient_bitlength\": 1,\n  \"maximum_certificate_integer_bitlength\": 1,\n  \"runtime_coefficients\": \"integersandhalvesonly\",\n  \"runtime_odd_divisions\": 0,\n  \"program_counts\": {\n    \"CLEAR\": 249,\n    \"ZERO_RETAG\": 249,\n    \"COPY\": 8,\n    \"MONOMIAL\": 344,\n    \"ADD\": 672,\n    \"GAUSSIAN\": 112\n  },\n  \"ADD_census\": {\n    \"1\": 392,\n    \"1/2\": 88,\n    \"-1\": 168,\n    \"-1/2\": 24\n  },\n  \"monomial_primitive_census\": {\n    \"D\": 232,\n    \"P\": 232,\n    \"X\": 232,\n    \"phase\": 120\n  },\n  \"scalar_tariff\": 6114,\n  \"controls\": [\n    {\n      \"name\": \"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"reversedalias multiplicationorder\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"oneimpulse-only grouping merges differentcompleteLEFTclasses\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"alias absolute phase flipped\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"positiveQ substituted for inverseQ or omittedcentralX\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"droppedactualnonzero M coefficient\",\n      \"row\": 0,\n      \"mode\": 0,\n      \"rejected\": true\n    },\n    {\n      \"name\": \"tensor exterioronehalf into twocolumns\",\n      \"legal\": \"1/2\",\n      \"illegal\": \"1/4\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"phase2columnlift replacedby exteriornegativeone\",\n      \"fiberwidth\": 2,\n      \"legal\": [\n        1,\n        0\n      ],\n      \"illegal\": [\n        -1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"illegal two-termwhole-fieldQshortcut\",\n      \"fiberwidth\": 2,\n      \"mixed_output\": [\n        0,\n        1\n      ],\n      \"actual_numerator\": [\n        2,\n        0\n      ],\n      \"actual_denominator_power2\": 2,\n      \"shortcut_numerator\": [\n        0,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"integer reconstruction coefficient changed\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"uncleared arbitraryb0 owned entry\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"write originalh instead ofownedcopy\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"premature queriedbasis CLEAR beforelastread\",\n      \"rejected\": true\n    }\n  ],\n  \"input_sha256\": \"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\",\n  \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\",\n  \"checker_sha256\": \"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\",\n  \"oracle_sha256\": \"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\",\n  \"scope\": \"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\"\n}\n",
+        "stderr": "",
+        "stdout": "{\"leftcoset_count\": 112, \"program_counts\": {\"ADD\": 672, \"CLEAR\": 249, \"COPY\": 8, \"GAUSSIAN\": 112, \"MONOMIAL\": 344, \"ZERO_RETAG\": 249}, \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings_vs112\": 0, \"rationalrank_sum_Qqueries\": 112, \"scalar_tariff\": 6114, \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\"}\n"
+      },
+      "program_uncompressed_bytes": 1282103,
+      "program_uncompressed_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_utf8_bytes": 4909,
+      "result_raw_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "comparison_exclusions": []
+    },
+    {
+      "run": "fanout-optimality-readonly-normal-v1",
+      "event_number": 1,
+      "exact_log_event": {
+        "command": [
+          "/usr/bin/python3",
+          "-I",
+          "-Werror",
+          "-B",
+          "-X",
+          "pycache_prefix=/tmp/fanout-unchanged-source-svslgf6h/cache",
+          "/tmp/fanout-unchanged-source-svslgf6h/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+          "--input",
+          "/tmp/fanout-unchanged-source-svslgf6h/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+          "--program",
+          "/tmp/fanout-unchanged-source-svslgf6h/FANOUT-PROGRAM-v1.json",
+          "--result",
+          "/tmp/fanout-unchanged-source-svslgf6h/FANOUT-RESULT-v1.json"
+        ],
+        "exit_code": 0,
+        "program_raw_bytes": 1282103,
+        "program_raw_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+        "program_zlib_base64": 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+        "result_utf8": "{\n  \"schema\": \"exact-fanout-component-result/v1\",\n  \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\",\n  \"source_rows\": 112,\n  \"common_modes\": 8,\n  \"leftcoset_count\": 112,\n  \"rationalrank_sum_Qqueries\": 112,\n  \"query_savings_vs112\": 0,\n  \"owned_arbitrary\": 17,\n  \"owned_zero_return\": 17,\n  \"all512_alias_columns_checked\": 57344,\n  \"group_sizes\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"group_ranks\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"nonzero_rows\": 112,\n  \"H_abs\": 448,\n  \"T_abs\": 112,\n  \"maximum_integer_coefficient_bitlength\": 1,\n  \"maximum_certificate_integer_bitlength\": 1,\n  \"runtime_coefficients\": \"integersandhalvesonly\",\n  \"runtime_odd_divisions\": 0,\n  \"program_counts\": {\n    \"CLEAR\": 249,\n    \"ZERO_RETAG\": 249,\n    \"COPY\": 8,\n    \"MONOMIAL\": 344,\n    \"ADD\": 672,\n    \"GAUSSIAN\": 112\n  },\n  \"ADD_census\": {\n    \"1\": 392,\n    \"1/2\": 88,\n    \"-1\": 168,\n    \"-1/2\": 24\n  },\n  \"monomial_primitive_census\": {\n    \"D\": 232,\n    \"P\": 232,\n    \"X\": 232,\n    \"phase\": 120\n  },\n  \"scalar_tariff\": 6114,\n  \"controls\": [\n    {\n      \"name\": \"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"reversedalias multiplicationorder\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"oneimpulse-only grouping merges differentcompleteLEFTclasses\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"alias absolute phase flipped\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"positiveQ substituted for inverseQ or omittedcentralX\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"droppedactualnonzero M coefficient\",\n      \"row\": 0,\n      \"mode\": 0,\n      \"rejected\": true\n    },\n    {\n      \"name\": \"tensor exterioronehalf into twocolumns\",\n      \"legal\": \"1/2\",\n      \"illegal\": \"1/4\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"phase2columnlift replacedby exteriornegativeone\",\n      \"fiberwidth\": 2,\n      \"legal\": [\n        1,\n        0\n      ],\n      \"illegal\": [\n        -1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"illegal two-termwhole-fieldQshortcut\",\n      \"fiberwidth\": 2,\n      \"mixed_output\": [\n        0,\n        1\n      ],\n      \"actual_numerator\": [\n        2,\n        0\n      ],\n      \"actual_denominator_power2\": 2,\n      \"shortcut_numerator\": [\n        0,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"integer reconstruction coefficient changed\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"uncleared arbitraryb0 owned entry\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"write originalh instead ofownedcopy\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"premature queriedbasis CLEAR beforelastread\",\n      \"rejected\": true\n    }\n  ],\n  \"input_sha256\": \"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\",\n  \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\",\n  \"checker_sha256\": \"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\",\n  \"oracle_sha256\": \"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\",\n  \"scope\": \"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\"\n}\n",
+        "stderr": "",
+        "stdout": "{\"leftcoset_count\": 112, \"program_counts\": {\"ADD\": 672, \"CLEAR\": 249, \"COPY\": 8, \"GAUSSIAN\": 112, \"MONOMIAL\": 344, \"ZERO_RETAG\": 249}, \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings_vs112\": 0, \"rationalrank_sum_Qqueries\": 112, \"scalar_tariff\": 6114, \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\"}\n"
+      },
+      "program_uncompressed_bytes": 1282103,
+      "program_uncompressed_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_utf8_bytes": 4909,
+      "result_raw_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "comparison_exclusions": []
+    },
+    {
+      "run": "fanout-optimality-readonly-optimized-v1",
+      "event_number": 1,
+      "exact_log_event": {
+        "command": [
+          "/usr/bin/python3",
+          "-I",
+          "-Werror",
+          "-B",
+          "-X",
+          "pycache_prefix=/tmp/fanout-unchanged-source-zjux0w2e/cache",
+          "-O",
+          "/tmp/fanout-unchanged-source-zjux0w2e/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+          "--input",
+          "/tmp/fanout-unchanged-source-zjux0w2e/work/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+          "--program",
+          "/tmp/fanout-unchanged-source-zjux0w2e/FANOUT-PROGRAM-v1.json",
+          "--result",
+          "/tmp/fanout-unchanged-source-zjux0w2e/FANOUT-RESULT-v1.json"
+        ],
+        "exit_code": 0,
+        "program_raw_bytes": 1282103,
+        "program_raw_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+        "program_zlib_base64": 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+        "result_utf8": "{\n  \"schema\": \"exact-fanout-component-result/v1\",\n  \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\",\n  \"source_rows\": 112,\n  \"common_modes\": 8,\n  \"leftcoset_count\": 112,\n  \"rationalrank_sum_Qqueries\": 112,\n  \"query_savings_vs112\": 0,\n  \"owned_arbitrary\": 17,\n  \"owned_zero_return\": 17,\n  \"all512_alias_columns_checked\": 57344,\n  \"group_sizes\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"group_ranks\": [\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1,\n    1\n  ],\n  \"nonzero_rows\": 112,\n  \"H_abs\": 448,\n  \"T_abs\": 112,\n  \"maximum_integer_coefficient_bitlength\": 1,\n  \"maximum_certificate_integer_bitlength\": 1,\n  \"runtime_coefficients\": \"integersandhalvesonly\",\n  \"runtime_odd_divisions\": 0,\n  \"program_counts\": {\n    \"CLEAR\": 249,\n    \"ZERO_RETAG\": 249,\n    \"COPY\": 8,\n    \"MONOMIAL\": 344,\n    \"ADD\": 672,\n    \"GAUSSIAN\": 112\n  },\n  \"ADD_census\": {\n    \"1\": 392,\n    \"1/2\": 88,\n    \"-1\": 168,\n    \"-1/2\": 24\n  },\n  \"monomial_primitive_census\": {\n    \"D\": 232,\n    \"P\": 232,\n    \"X\": 232,\n    \"phase\": 120\n  },\n  \"scalar_tariff\": 6114,\n  \"controls\": [\n    {\n      \"name\": \"wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"reversedalias multiplicationorder\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"oneimpulse-only grouping merges differentcompleteLEFTclasses\",\n      \"rows\": [\n        1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"alias absolute phase flipped\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"positiveQ substituted for inverseQ or omittedcentralX\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"droppedactualnonzero M coefficient\",\n      \"row\": 0,\n      \"mode\": 0,\n      \"rejected\": true\n    },\n    {\n      \"name\": \"tensor exterioronehalf into twocolumns\",\n      \"legal\": \"1/2\",\n      \"illegal\": \"1/4\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"phase2columnlift replacedby exteriornegativeone\",\n      \"fiberwidth\": 2,\n      \"legal\": [\n        1,\n        0\n      ],\n      \"illegal\": [\n        -1,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"illegal two-termwhole-fieldQshortcut\",\n      \"fiberwidth\": 2,\n      \"mixed_output\": [\n        0,\n        1\n      ],\n      \"actual_numerator\": [\n        2,\n        0\n      ],\n      \"actual_denominator_power2\": 2,\n      \"shortcut_numerator\": [\n        0,\n        0\n      ],\n      \"rejected\": true\n    },\n    {\n      \"name\": \"integer reconstruction coefficient changed\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"uncleared arbitraryb0 owned entry\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"write originalh instead ofownedcopy\",\n      \"rejected\": true\n    },\n    {\n      \"name\": \"premature queriedbasis CLEAR beforelastread\",\n      \"rejected\": true\n    }\n  ],\n  \"input_sha256\": \"f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb\",\n  \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\",\n  \"checker_sha256\": \"b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3\",\n  \"oracle_sha256\": \"15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba\",\n  \"scope\": \"ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.\"\n}\n",
+        "stderr": "",
+        "stdout": "{\"leftcoset_count\": 112, \"program_counts\": {\"ADD\": 672, \"CLEAR\": 249, \"COPY\": 8, \"GAUSSIAN\": 112, \"MONOMIAL\": 344, \"ZERO_RETAG\": 249}, \"program_sha256\": \"5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7\", \"query_savings_vs112\": 0, \"rationalrank_sum_Qqueries\": 112, \"scalar_tariff\": 6114, \"status\": \"PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION\"}\n"
+      },
+      "program_uncompressed_bytes": 1282103,
+      "program_uncompressed_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_utf8_bytes": 4909,
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+      "path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1/retained/swarm-provider-audit-sol-high-20261024/agents/algebra",
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+      "path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout",
+      "mode": "0o555"
+    },
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+      "path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1/retained/swarm-coupled-caller-sol-high-20261024/agents/caller",
+      "mode": "0o555"
+    },
+    {
+      "path": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1/canonical/docs/research",
+      "mode": "0o555"
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+  ],
+  "current_readback_provenance": {
+    "reader": "Packageworker static filesystem/hash read; no scientific code",
+    "started_at_UTC": "2026-10-24T08:34:04.310113+00:00",
+    "completed_at_UTC": "2026-10-24T08:34:04.327473+00:00",
+    "against": "Exact peer preinventory10bc0f...; separately retained peer post-summary7a2f... attests unchanged historical pre/post state.",
+    "independently_captured_historical_postrun_snapshot": false,
+    "source_record_breakdown": {
+      "working_source": 32,
+      "readonly_source": 32,
+      "runner": 1,
+      "guard": 1,
+      "source_freeze": 1
+    },
+    "interpretation": "These are new current after-execution static readback rows, not a reconstructed claim of an independent historical postrun capture. Wrapper digests and peer historical summary are separate retained evidence."
+  }
+}
diff --git a/docs/ci-verification.md b/docs/ci-verification.md
index 494b7ca1d4..3bf623230e 100644
--- a/docs/ci-verification.md
+++ b/docs/ci-verification.md
@@ -1,8 +1,40 @@
 # CI verification
 
-## Current selected-family replay: #4610 with #5241
+## Current selected-family replay: #5413 with #5407 and #5414
 
 The [selected record](../certificates/selected-result.json) binds conditional
+κ = 0.003027288235, the [promotion and scope](research/pr-intake-evidence/pr5413-promotion/PROMOTION.md),
+[explicit source closure](../certificates/frontier5413-source.json),
+[review validation](research/pr-intake-evidence/pr5413-promotion/VALIDATION.json), and
+[integration receipt](research/pr-intake-evidence/pr5413-promotion/INTEGRATION.json).
+
+`make frontier5413-verify` authenticates the selected source manifest, derives
+the certificate from frozen numerical evidence, and exports the complete
+three-package execution closure. It replays #5407's five-stage provider audit,
+#5413's eight-stage admission, and #5414's independent companion screen serially.
+The exported inputs are checked again afterward. Source-bound #4610/#5241 and
+earlier BIT/native/compiler/tape/analytic foundation coverage is explicitly
+reused; its historical suites are not rerun.
+
+Each package runs under an external sampled 1 GiB aggregate descendant-memory
+guard, with timeouts of 660 seconds for the provider and primary packages and
+120 seconds for the companion. On macOS the replay uses the reviewed RLIMIT_AS
+adapter; on Linux it invokes the unmodified package wrappers. The recorded
+successful local macOS replay does not establish a hosted Linux pass.
+
+The [frontier5413 workflow](../.github/workflows/frontier5413.yml) is manual-only,
+uses Python 3.12 on Ubuntu, materializes the declared source closure, and uploads
+receipts and logs. Its status is separate from local validation and recorded in
+the integration receipt. Routine donor PRs do not launch this selected replay.
+
+`make selected-record-check` verifies metadata and source/proof hashes. It does
+not execute the operators or prove the five inherited framework assumptions.
+The finite checks do not establish the full integer multiplication theorem,
+and the uniform word remains unmaterialized.
+
+## Historical selected-family replay: #4610 with #5241
+
+The historical [selected record](../certificates/checkpoints/frontier4610.json) binds conditional
 κ = 0.0030217758, the [review](research/pr-intake-evidence/pr4610/PROOF-REVIEW.md),
 [explicit source closure](../certificates/frontier4610-source.json),
 [review validation](research/pr-intake-evidence/pr4610/VALIDATION.json), and
diff --git a/research/fanout-optimality-support/.gitattributes b/research/fanout-optimality-support/.gitattributes
new file mode 100644
index 0000000000..fa1385d99a
--- /dev/null
+++ b/research/fanout-optimality-support/.gitattributes
@@ -0,0 +1 @@
+* -text
diff --git a/research/fanout-optimality-support/CLAIMS.json b/research/fanout-optimality-support/CLAIMS.json
new file mode 100644
index 0000000000..3540615034
--- /dev/null
+++ b/research/fanout-optimality-support/CLAIMS.json
@@ -0,0 +1,58 @@
+{
+  "schema": "fanout-scoped-optimality-claims/v1",
+  "status": "MATCHING_STANDALONE_UPPER_AND_STATICALLY_REVIEWED_SCOPED_LOWER",
+  "interface": "y112 += q^-1 W_s h8; h strictly read-only;17arbitrary-owned returned zero",
+  "upper": {
+    "paid_H1": 112,
+    "query_savings": 0,
+    "ordinary_counts": {
+      "CLEAR": 249,
+      "ZERO_RETAG": 249,
+      "COPY": 8,
+      "MONOMIAL": 344,
+      "ADD": 672,
+      "GAUSSIAN": 112
+    },
+    "source_rows": 112,
+    "singleton_classes": 112,
+    "class_rank_sum": 112,
+    "alias_column_comparisons": 57344,
+    "alias_coverage": "112 singleton SELF-alias identities,512columns each",
+    "full_137_field_physical_endpoint_replay": false,
+    "endpoint_basis": "COMPOSITIONAL_SOURCE_FACTORIZATION_LITERAL_COEFFICIENTS_AND_LIFETIMES",
+    "runtime_odd_divisions": 0,
+    "owned_arbitrary_entry_zero_exit": 17
+  },
+  "lower": {
+    "minimum_total_gaussian_field_calls": 112,
+    "bound_interpretation": "TOTAL_STANDALONE_NOT_INCREMENTAL",
+    "fixed_finite_program": true,
+    "fixed_exterior_coefficients": true,
+    "finite_columnwise_ordinary_group": true,
+    "width_quantifier": "ALL_POSITIVE_WIDTHS_OR_ONE_CONSECUTIVE_TAIL",
+    "ordinary_initial_span_only": true,
+    "fixed_common_field_capacity": true,
+    "paid_output_rows_per_call": 1,
+    "central_scalar_M_shared_right_Km": true,
+    "arbitrary_independent_originals": true,
+    "exact_per_column_phases": true,
+    "finite_feedback_allowed": true,
+    "ordinary_zero_divisors_allowed": true,
+    "weighted_recursive_invoice_claimed": false,
+    "proof_kind": "WRITTEN_PROOF_WITH_INDEPENDENT_STATIC_REVIEW_NOT_FORMAL_KERNEL"
+  },
+  "exclusions": [
+    "nonordinary Gaussian/native/cached initial observations",
+    "incremental112per global cut or additive sharing bound",
+    "width-dependent or width-growing programs/coefficients",
+    "restricted subsequences of widths",
+    "inter-column ordinary operations",
+    "packing/splitting/changed field capacity or multiple outputs per chargedcall",
+    "dependent originals or changed source/right-factor structure",
+    "approximate/nonlinear/antilinear or projective-phase computations"
+  ],
+  "full_physical_raw_dual": false,
+  "complete_caller": false,
+  "compiler_precision_stock_admitted": false,
+  "new_kappa": null
+}
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diff --git a/research/fanout-optimality-support/LICENSE b/research/fanout-optimality-support/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/fanout-optimality-support/LICENSE
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+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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+          of the NOTICE file are for informational purposes only and
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+      the terms of any separate license agreement you may have executed
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+   6. Trademarks. This License does not grant permission to use the trade
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+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json",
+      "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da",
+      "bytes": 281582,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md",
+      "sha256": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5",
+      "bytes": 12418,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json",
+      "sha256": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65",
+      "bytes": 145658,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "evidence/RECEIPT.json",
+      "source_path": "swarm-price-plane-20261023T112711Z/runs/race0033-exact-source-fanout-v1/RECEIPT.json",
+      "sha256": "5fa7b4eabd0b6b9a3675ffbcb6b12003091093eee5094171388caf8f3fdc5035",
+      "bytes": 1046,
+      "availability": "LOCAL actual one-time original guard evidence; package replay is separate"
+    },
+    {
+      "path": "evidence/stdout.log",
+      "source_path": "swarm-price-plane-20261023T112711Z/runs/race0033-exact-source-fanout-v1/stdout.log",
+      "sha256": "8b8bd05d6e5557fac33e8a5a3d077ca99f21172c35785e0b2a09df5a82db386e",
+      "bytes": 357,
+      "availability": "LOCAL actual one-time original guard evidence; package replay is separate"
+    }
+  ],
+  "unmodified_originals": true,
+  "canonical_history_claim": "Only selected record/catalogue canonical1a3 provenance is declared in SOURCES. Generated upper program and lower note are retained LOCAL sources, not forged canonical ancestors."
+}
diff --git a/research/fanout-optimality-support/NOTICE b/research/fanout-optimality-support/NOTICE
new file mode 100644
index 0000000000..59d8e0cf31
--- /dev/null
+++ b/research/fanout-optimality-support/NOTICE
@@ -0,0 +1,415 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
+
+Partial-gauge extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The pair-first cube assembly, compatible backward frame enlargement,
+partial source-gauge schedule and stopped whole-projector composition are
+contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834.
+
+The physical deferred bit word, reflected event accounting, fan-order
+clarification and signed two-stage endpoint are adopted from Zhihao Chen
+(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with
+Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen
+witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38,
+with the original Claude disclosure retained. Cyclic interval and core-aware
+pair primitives build on Avi Eisenberg (ikeboy), PR #62,
+ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance.
+Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and
+precision credits remain in force. Imported source notices and licenses
+are preserved under references/partial-gauge/; see SOURCES.json.
+
+Three-stage cover extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry,
+weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring
+fallback, uniform batching, internal row borrowing and exact composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This
+repository integration uses Codex assistance and extends
+PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86.
+
+The selected local complex DAG and support/label replay are adopted from
+Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf,
+with its original Apache-2.0 terms and Claude assistance disclosure.
+The unchanged bit physical word retains Zhihao Chen (jacklightChen),
+PR #97, and Swapnil Jain's underlying witness and assistance notices.
+The prior opposite-bank, stopped ordinary-leaf, copied-center, topology,
+semantic/bulk, precision and analytic credits remain applicable.
+Original source notices and license bytes are preserved in
+references/three-stage-cover/pr117/ and references/partial-gauge/.
+
+Paired-cube and shared-core extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The paired-coordinate triple-cube identity, signed overlap channels,
+original-source involution, coordinate-star centers, concrete frame/carrier
+compiler, chronological source gauges, PR97 gauge-subset selection,
+orthogonal cross-stage routing and exact supplier/assembly integration
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance.
+Repository integration uses Codex assistance and extends PR #130 at
+6a9970a530119174507904e23592fd59ede19a5d.
+
+The substantial completed-core workspace-sharing principle is credited to
+an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported
+OpenAI Codex assistance. No source code, partition or serialized witness
+from that PR is imported. The new routing and paired-motif integration
+are described separately and claim no exclusive priority for broad sharing,
+paired-coordinate, Fourier or carrier-matching ideas.
+
+Selected coarse queries restrict the retained eumemic PR #117 positive DAG;
+its original Apache-2.0 and Claude assistance notices remain unchanged.
+The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil
+Jain's frozen witness, notices and historical assistance disclosures.
+Earlier generalized Clifford, three-stage, uniform weighted recursion,
+ordinary-leaf, semantic/bulk, precision and analytic credits remain in force.
+Source-specific license bytes are preserved under references/.
+
+October 9 recycled-bit integration:
+DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146),
+Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122).
+The original notices and assistance disclosures are retained under research/,
+including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat
+(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's
+scoped finite and formal-transfer packages are included separately; they do
+not establish the full multiplication theorem. Earlier and parallel credits
+remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance.
+
+SovereignSteak PR151 independently supplies the matching gauge/recycling
+composition and the selected 473/10^6 atom refinement; its original package
+and assistance disclosure are retained under research/gauge-recycling/.
+
+October 9 coordinated-frame and completed-entrance-bank integration:
+Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on
+Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad,
+and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17.
+The frozen package and prerequisite archive preserve all author, source-license
+and assistance notices, including PR175's compiler optimization. DaysSky's
+carrier closure, James Chang's terminal substitution and balanced assembly,
+geckods' stopping refinements and all preceding framework credits remain.
+Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed
+parallel contributions; their gains are not added to the selected witness.
+Douglas Colkitt integrated the package and supplied the bank scheduling
+supplement with OpenAI Codex assistance, under Apache-2.0. The all-size
+interfaces remain conditional; finite verification is not full formalization.
diff --git a/research/fanout-optimality-support/ORIGINS.json b/research/fanout-optimality-support/ORIGINS.json
new file mode 100644
index 0000000000..2d48072110
--- /dev/null
+++ b/research/fanout-optimality-support/ORIGINS.json
@@ -0,0 +1,55 @@
+[
+  {
+    "authority": "canonical",
+    "retained": "canonical/docs/research/agent-task-catalog.json",
+    "proof": {
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+      "path": "docs/research/agent-task-catalog.json",
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+      "trees": [
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fi0fxobRidi4aRc0b1Wcgw8haMTAwNjQ0IGNvbW11bml0eS1mcm9udGllcjc5OS1pbnRlZ3JhdGlvbi5qc29uACpumsAGbgpa5LMqH3FOkUQqSI8kMTAwNjQ0IGNvbW11bml0eS1mcm9udGllcjc5OS1yZXZpZXcubWQAeizQpkGZ4Kr5NFE3esvtPox65rcxMDA2NDQgY29tbXVuaXR5LWZyb250aWVyODkwLWludGVncmF0aW9uLmpzb24AaqEVrc5Jix63gxrtiGgQHJywaPwxMDA2NDQgY29tbXVuaXR5LWZyb250aWVyODkwLXJldmlldy5tZABrZUYXJLqZo2MzyzqPRDz19kjKZzEwMDY0NCBjb21tdW5pdHktaGlzdG9yaWNhbC1maXZlLXJldmlldy5tZABZTqqGNLN6U8i2Wqo/2zLw1OzlejEwMDY0NCBjb21tdW5pdHktaHlwZXJwbGFuZTU5OS1pbnRlZ3JhdGlvbi5qc29uANg4O6jSC6EeP+X+nv198cKACr7mMTAwNjQ0IGNvbW11bml0eS1oeXBlcnBsYW5lNTk5LXJldmlldy5tZADMJZMqk6oWxX99AlVBS6/hbrcapTEwMDY0NCBjb21tdW5pdHktaW50ZWdyYXRpb24tdmFsaWRhdGlvbi5qc29uAED9Vod7EvXuqzeEMfitGHbsq3QNMTAwNjQ0IGNvbW11bml0eS1pbnRlZ3JhdGlvbi5tZAA/jLy877SWhSb4SbUkQYrsnwQwrDEwMDY0NCBjb21tdW5pdHktam9pbnQ0NDcwLWNvbnRyaWJ1dG9ycy5tZAB4W91cYRHVFwAyjRvfG84fGe+6FDEwMDY0NCBjb21tdW5pdHktazQ5Mi1pbnRlZ3JhdGlvbi5qc29uAFo8GLVKQzqtldccvFUiTiEghZONMTAwNjQ0IGNvbW11bml0eS1rNDkyLXJldmlldy5tZAAR780Hriudk9NVxq2vdz3KcNvOkTEwMDY0NCBjb21tdW5pdHktbmF0aXZlNDYxMC1jb250cmlidXRvcnMubWQAl36rUIwYPv1fclYX4w7XzNGaH/IxMDA2NDQgY29tbXVuaXR5LW5ldXRyYWw1NDEzLWNvbnRyaWJ1dG9ycy5tZABxAvBXYjeMU9F+cGdJbBB0MOo7oTEwMDY0NCBjb21tdW5pdHktcGFpci1hcml0aG1ldGljLmpzb24A24i45eBp1/BFHuvZzjRnp+XQDG8xMDA2NDQgY29tbXVuaXR5LXBpbG90MjAtcmV2aWV3Lm1kAMET/Ha6Hvvuceew4BR2XZD23OxLMTAwNjQ0IGNvbW11bml0eS1wcjIxMC1pbnRlZ3JhdGlvbi5qc29uAN8V/UxT95KIF0QDoGlXSZdXDOTYMTAwNjQ0IGNvbW11bml0eS1wcjIxMC1yZXZpZXcubWQA7Nazs5sbDoj8JV0fr1yMHV1P6MUxMDA2NDQgY29tbXVuaXR5LXByMjc5LWFubm91bmNlbWVudC5tZAD5HmGCSkQN5sgECPbLNPjV2JD6OTEwMDY0NCBjb21tdW5pdHktcHIyNzktaW50ZWdyYXRpb24uanNvbgDs1uzYCWSrT3FcGdGA7cMZb2Fl4jEwMDY0NCBjb21tdW5pdHktcHIyNzktcmV2aWV3Lm1kAL7BM7lEVW2f3l0q+XAb59yb1IobMTAwNjQ0IGNvbW11bml0eS1wcjUzMS1pbnRlZ3JhdGlvbi5qc29uAHpNPbbk3kXsR4RPyucU/uLJFG7CMTAwNjQ0IGNvbW11bml0eS1wcjUzMS1yZXZpZXcubWQAj8cOikLKTft5rEJlq52rgmirF/cxMDA2NDQgY29tbXVuaXR5LXByb2R1Y3RpdmU0MzU5LWNvbnRyaWJ1dG9ycy5tZAB3Q5ZCNJp9dOQJT+/T3t4xomVj5TEwMDY0NCBjb21tdW5pdHktcHJvZHVjdGl2ZTQzNTktdHdpdHRlci5tZADM7zEl42UNPSTo0Nd6nldcFP1Z0TEwMDY0NCBjb21tdW5pdHktcmVjb25jaWxpYXRpb24tZm91cnRoMTAwLXJldmlldy5tZABbvWWiJfFqG8Uhj+Vgji+K48ofCTEwMDY0NCBjb21tdW5pdHktcmVjb25jaWxpYXRpb24tbmV4dDEwMC1yZXZpZXcubWQAYj1PrFxDyhDwqKS9O25X5CnMDLQxMDA2NDQgY29tbXVuaXR5LXJlY29uY2lsaWF0aW9uLXRoaXJkMTAwLXJldmlldy5tZADuZkiofnkKlAEv7CIT85B2MMcc6TEwMDY0NCBjb21tdW5pdHktcmVjb25jaWxpYXRpb24xMDAtcmV2aWV3Lm1kADvsb8CA3t6jc4b/mcchx+gy1w1mMTAwNjQ0IGNvbW11bml0eS1yZWNvbmNpbGlhdGlvbjkyLXJldmlldy5tZAD1jmbmlFXCabTd1AYzIUcobT4R6jEwMDY0NCBjb21tdW5pdHktcm91bmQyLWFyaXRobWV0aWMuanNvbgBjeqAZnxZ8xsgxnPxzJ1sIAadAyTEwMDY0NCBjb21tdW5pdHktcm91bmQyLXJldmlldy5tZAAi9AFUVadaf2NOSWFe44/E4U54lTEwMDY0NCBjb21tdW5pdHktcm91bmQyLXR3aXR0ZXIubWQAjsd/1UNxirmqrJnFMmFAERw+OG4xMDA2NDQgY29tbXVuaXR5LXJvdW5kMi12YWxpZGF0aW9uLmpzb24ATqwww33xCXyox7x+MEULRC6GUFExMDA2NDQgY29tbXVuaXR5LXJvdW5kMy1sZWFuLWF1ZGl0Lmpzb24A/PPzs2XeUAdIoUdjoVWl75+uhC0xMDA2NDQgY29tbXVuaXR5LXJvdW5kMy1yZXZpZXcubWQACIg3i1H4yaul4lVj2nKbOeIuMv8xMDA2NDQgY29tbXVuaXR5LXJvdW5kMy12YWxpZGF0aW9uLmpzb24A3J8j+wAyplI3asLgq9wIs5SVcA8xMDA2NDQgY29tbXVuaXR5LXJvdW5kNC1yZXZpZXcubWQAQ+X+fzHzhsw8kcxx66uPV+k3MjIxMDA2NDQgY29tbXVuaXR5LXJvdW5kNC12YWxpZGF0aW9uLmpzb24AZjLjTt5K+RHChXoiEV7JaADueJoxMDA2NDQgY29tbXVuaXR5LXJvdW5kNS1xdWV1ZS5qc29uAI/mO0MH7PxXtgMD6eHnspYqlQjNMTAwNjQ0IGNvbW11bml0eS1yb3VuZDUtcmV2aWV3Lm1kAAD2/x02IGnNniaw+H5CSbueabpiMTAwNjQ0IGNvbW11bml0eS1yb3VuZDUtdmFsaWRhdGlvbi5qc29uAEnJMhV5+vkbkar7GQtwY5AsHs1sMTAwNjQ0IGNvbW11bml0eS1yb3VuZDYtaW50ZWdyYXRpb24tdmFsaWRhdGlvbi5qc29uAHJS9QMeQ/kagxUQ8pZxk4+qc64VMTAwNjQ0IGNvbW11bml0eS1yb3VuZDYtaW50ZWdyYXRpb24ubWQAQIVqkdaSdM1uaFAtfqDqOyIIDsoxMDA2NDQgY29tbXVuaXR5LXJvdW5kNi1yZXZpZXcubWQAtd1I6N++tTHuHaWxOrmgOgCxZl8xMDA2NDQgY29tbXVuaXR5LXJvdW5kNi12YWxpZGF0aW9uLmpzb24Av4u3tE9mnwx+CJatJFGmVqT8/gUxMDA2NDQgY29tbXVuaXR5LXJvdW5kNy1tb3JuaW5nLm1kAChGzYSvPGPxcFAgxR8Ci3ghFmz9MTAwNjQ0IGNvbW11bml0eS1yb3VuZDctcmV2aWV3Lm1kAB7U/SwCqDweqWEndcNQOrdzbID2MTAwNjQ0IGNvbW11bml0eS1yb3VuZDctdmFsaWRhdGlvbi5qc29uACOKuAoQa0aLxgllflAzmEYhurTHMTAwNjQ0IGNvbW11bml0eS1yb3VuZDgtaW50ZWdyYXRpb24uanNvbgA3x6y9tEbavg4E8MZN9ELqDvRTjDEwMDY0NCBjb21tdW5pdHktcm91bmQ4LXJldmlldy5tZAAqF3W9GE37SkpBE3OfjQnRFQDcczEwMDY0NCBjb21tdW5pdHktdHJhbnNmZXItcmV2aWV3Lm1kAHFeQRVDQCcS2b5of9PJX/jL9OdvMTAwNjQ0IGNvbXBhY3QtY29udHJvbC1hdWRpdC5tZAAF7D5gMY8NgTVPHSWa/6LBuni2YDEwMDY0NCBjb21wYWN0LWNvbnRyb2wtcmV2aWV3Lm1kAPYadGWrlyj/oxRJERzPEOvt/scJMTAwNjQ0IGNvbXBsZXgtY29tcHJlc3Npb24tcmV2aWV3Lm1kACch1TlOTVM/lp253Bdg4NszkwF/MTAwNjQ0IGNvbXBsZXgtY29tcHJlc3Npb24ubWQAUd1uGilghBMk1FMLjj+cwSmJ6QgxMDA2NDQgY29tcGxleC1kZWNvZGVyLXNjb3BlLW1hcC5tZAByeo4L2J2kfkhCsCZIyTRm9C/yfzEwMDY0NCBjb25zdHJ1Y3Rpb24tcHJvZmlsZXMuanNvbgA9loOHVZMsqb14UbFPOYZn+7tTsDEwMDY0NCBjb250cmlidXRpb24tcmV2aWV3Lm1kAG1lNzf+uJQuDKrVjkbEu96BJQzUMTAwNjQ0IGNvbnRyaWJ1dGlvbi1zbmFwc2hvdC5qc29uAAtRY8e0/QM9NQN86WBPkObd1lOeMTAwNjQ0IGNvbnRyaWJ1dG9yLWFubm91bmNlbWVudHMubWQA/d4ctzw0tCnillhZU8UE1eDmKiwxMDA2NDQgY29udHJpYnV0b3Itc29jaWFsLXNvdXJjZXMuanNvbgBtDt8hM34mn8ZoSRx1OIVpzgQwQTEwMDY0NCBjb29yZGluYXRpb24ubWQAlttZvjGBgZOdHgK1TrumJrmX14cxMDA2NDQgY29yZS1saW1pdHMubWQABbrgUrXCr1h2auXCQaFeDU5ijMMxMDA2NDQgY3Jvc3MtcG9pbnQtc2hhcmluZy5tZAAtl/apjoNhzM7eqSvwlm0kfhUTdjEwMDY0NCBjdWJlLWNvcmUtZmFtaWx5Lm1kAPlaoa9RoGAmG24rcsZdfsu3Pv96MTAwNjQ0IGN1cnJlbnQtcHJpb3JpdGllcy5tZAC07Ol6YNzDozsE2D6fEJPmAyasSjEwMDY0NCBjdXJyZW50LXN0YXR1cy5tZADkr9UseTBWH9NcuaHlyX8Zf3jnEjEwMDY0NCBjeWNsaWMtdG9wb2xvZ3ktYXVkaXQubWQAI0QQ8ZIutODBRINqZHgX73yOiMAxMDA2NDQgZGlzam9pbnQtdGVuc29yLWNvbXByZXNzaW9uLm1kAFxvj1L3nkxW9H1enNJtVUnwK2D8MTAwNjQ0IGR5YWRpYy1jZW50cmFsLWZhY3Rvci5tZAADNTfwHT/O2FFfrJ4sELcEjTUd8zEwMDY0NCBlYXJseS1zaGFyaW5nLWFuZC1jZW50ZXJzLm1kAJRWYfmVQVWs+H3Z1tvKR9GFCbvdMTAwNjQ0IGZhbm8tY29tcGxldGlvbi1hdWRpdC5tZACCDwcMVaFXS1txR1MUlQYkNOyRVzEwMDY0NCBmYW5vLXBlcm11dGF0aW9uLWF1ZGl0Lm1kAMgMxh4QoGoLVhHk4HBW+TJVDkxRMTAwNjQ0IGZpdmUtc291cmNlLWNvbm5lY3Rvci1zY29wZS1tYXAuanNvbgAO65vQTI7Oyk4uLEnvCbDGHk27FjEwMDY0NCBmaXZlLXNvdXJjZS1jb25uZWN0b3Itc2NvcGUtbWFwLm1kAMS1YlDjXrUvB5h/fpbH26GPrHXRMTAwNjQ0IGZyb250aWVyLXJlcGxheS1jb3ZlcmFnZS5tZADHyC9mTqKBmVHXjeAZnpVtCNhLKDEwMDY0NCBmcm9udGllcjc0MS1jb25jdXJyZW50LXJlcGxheS5tZACoseEKTUNtHVcGoWtZZhGFxQtyaDEwMDY0NCBmdXNlZC1ibG9jay1hdWRpdC5tZACmAgwnKDWgDUQapxGy3FZkAt6qsDEwMDY0NCBnYXRoZXItc2NoZWR1bGUtYXVkaXQubWQACSrycoyEOAxS3M3J1e147/8JSKMxMDA2NDQgZ2VuZXJhbC1uZXR3b3JrLWd1YXJkLm1kADrnpYMwg1VTXU8y20Eq9NdQGQI0MTAwNjQ0IGdpdC1ibG9iLWRlc2NlbmRhbnQtb3duZXJzaGlwLm1kACBjL3YNksv41WGcDGXYVmpykJiuMTAwNjQ0IGdpdC1ibG9iLXJlc3BvbnNlLWRlYWRsaW5lcy5tZADgbSvE10YpSW04jXFGQVYzlLaYmTEwMDY0NCBnaXQtcmVwb3NpdG9yeS1yb290LWJpbmRpbmcubWQANgvrbnQbNcXKmFHM28ZimgmRlFoxMDA2NDQgaW5jaWRlbmNlLW5ldHdvcmsubWQA6NNHBMxRoXqNUchzpkZAP2cUKiMxMDA2NDQgaW5wbGFjZS1zaWRlLm1kAKC7V8rNJ9fCkh9gYPWbQq6xNVMRMTAwNjQ0IGlzb2xhdGVkLXRlc3QtY2FuY2VsbGF0aW9uLm1kAFdcS63X8skMYMyUA0rYvhODtYQ0MTAwNjQ0IGlzb2xhdGVkLXRlc3QtY29tcGxldGlvbi5tZABw0x/vvBr3Qu03J2CNQaD8umUyAzEwMDY0NCBpc29sYXRlZC10ZXN0LWV4aXQtY2xlYW51cC5tZAAHXCKP484K2QSPIl5N4Qcz0VQVYjEwMDY0NCBpc29sYXRlZC10ZXN0LXBvc2l4LXBpcGVzLm1kAHbLT2fiVPEvjvL40vKwtoQdRwSeMTAwNjQ0IGlzb2xhdGVkLXRlc3Qtd2luZG93cy1leGl0Lm1kAJDHc/jyE10YQwD4vvXMIF/b2ivgMTAwNjQ0IGlzb2xhdGVkLXRlc3Qtd29ya2VyLXdpZHRoLTIwMjYtMTAtMTcubWQARaDgVNRkGIRWnZsOt0o5+Gr7s80xMDA2NDQgaXNvbGF0ZWQtd29ya2VyLWNhcHR1cmUtZmluYWxpemF0aW9uLm1kAEkCVzCkH57Gfl/KE73nnFrj83X8MTAwNjQ0IGlzb2xhdGVkLXdvcmtlci1mYWlsZmFzdC5tZABrGr+9zLWCrQNTGpsYSBNgIhJ8STEwMDY0NCBqb2ludC1mcmFtZS1hdWRpdC5tZAClsA0Ww+gdI1mBxXIAkzn3fI8fWzEwMDY0NCBqb2ludC1yZXR1cm4tYXVkaXQubWQAkfoMBZM2oOA1a0wcY/44AbaYIzMxMDA2NDQgbGF5ZXItcHJlcGFyYXRpb24ubWQAPUFuNhrQW34j/lm3KD6XHp7zu7AxMDA2NDQgbWl4ZWQtcG9pbnQtYXVkaXQubWQAMfcSuPeM7ooFuMtJDIyXnHkmXuIxMDA2NDQgbmF0aXZlLXRlbnNvci1jdXRvZmYubWQAwEyusPlbD8skwzv3+u3TnSkejjMxMDA2NDQgbmV0d29yay1zY3JlZW5zLm1kALxphw98+jB1LuiYcZBV22qLaQP3MTAwNjQ0IG5ldHdvcmstc2VhcmNoLWxvZy5tZADan8PdcARX3D07iLKLN6iZ93LjBjEwMDY0NCBuZXh0LXN0ZXBzLm1kAH+7hjmTWhlvmF0cQYc3mPzMKv+gMTAwNjQ0IG92ZXJsYXAtdGFzay1yZWZlcmVuY2UtbWF0Y2hpbmcubWQAyL+nfIvRcAlGtUb3PR1PzqmJyeoxMDA2NDQgb3Zlcm5pZ2h0LTI1LXByb2dyZXNzLm1kAE9AYmL8VkoWyeNgaWqoBfsjYuSdMTAwNjQ0IHAxMDQtaGVscGVyLWxpZmV0aW1lLXNjb3BlLW1hcC5tZADYfUhRitoiniAZGJU5f3GeoUewIjEwMDY0NCBwMTA0LWxpdmUtc3VwcG9ydC1tYXAubWQADSJkSbsvjpRGYGGB8DJOH8Ih0mMxMDA2NDQgcDEwNC1wcmVjaXNpb24tY29udHJhY3QtbWFwLm1kAEt/hyWu87Y2USG884mHlhvepr7lMTAwNjQ0IHAxMDQtc2lkZS1jb3JyZWN0aW9uLXNjb3BlLW1hcC5tZAAu6szray+Zw73IH36oEKzB4L7qSDEwMDY0NCBwYWNrYWdlLWV4cG9ydC5tZADPzNsamkuA9Sc4QtgqhQx2wnLTQTEwMDY0NCBwYWlyLXJhbmtlZC1zY3JlZW4uanNvbgA0IIYc1yUwejCxisCwrPR+VPWTejEwMDY0NCBwYWlyZWQtbmV0d29yay5tZABeL7KF9oOs8hkwtwRVUCxl2KfIDTEwMDY0NCBwYWlyZWQtcGxhbmUtY29udHJhY3QtbWFwLm1kAA93LI+GGO+Df2hOdpYBddm9xlbOMTAwNjQ0IHBhcml0eS1zaWRlLm1kALNsQEggs+nA8ovmS6TqKo6SRwSzMTAwNjQ0IHBhcnRpYWwtc3dhcC1yZXRhaW5lZC10b3RhbC1maXgubWQAQQDzYaJJUM/IqdutENf1qNn1f34xMDA2NDQgcG9zaXRpdmUtc2lkZS1jb3JlLm1kAK4WiE7NPYNkqn1oxIdWsIcvMGANMTAwNjQ0IHBvc2l4LXNpZ3Rlcm0tY2xlYW51cC5tZACne2pXFud772TEx74LEEW9t6FkhTEwMDY0NCBwci1iYXRjaC1yZXZpZXctcG9saWN5Lm1kAEOn8Y5E+iQ8LjW5JolGUSiu0C4jMTAwNjQ0IHByLWludGFrZS1jaGVja3BvaW50Lmpzb24ATMXkkTk+JYBDEKLJ7sR4hXfp6pMxMDA2NDQgcHItaW50YWtlLWRlY2lzaW9ucy5qc29uABKtGRdfL8jVnLU3hgUgxlHYFOUUNDAwMDAgcHItaW50YWtlLWV2aWRlbmNlAHcRg6L9iXCniUBK+pmGoacp4OWdMTAwNjQ0IHByLWludGFrZS1zdGF0ZS5qc29uAPviFzqralM6iqUj8Ejkmp3BA7TXMTAwNjQ0IHByLWludGFrZS5tZADkEtTkmr7RZbKMXcvkR64Df1HAAzEwMDY0NCBwci1sZWRnZXIuanNvbgDMM8z/Wr+tfupqtSoV+Mo7QSkB9DEwMDY0NCBwci1sZWRnZXIubWQAwQz4xBjwi31tPLN7WBil61n4f9MxMDA2NDQgcHItcXVldWUtMjAyNjEwMTEuanNvbgA+t1vBE3fZqkxQ7KDRKbR1ePGgHDEwMDY0NCBwci1xdWV1ZS1uZXh0LWFjdGlvbnMubWQA4sduPotgG316YPXkdkbnZd5WVicxMDA2NDQgcHItcmV2aWV3LXF1ZXVlLTIwMjYxMDEyLmpzb24AQCBF/68EG0U3HyXme0rUuvZ3MJoxMDA2NDQgcHIxMDQ4LWNvcnJlY3Rpb24tbWFwLmpzb24ANEllY85vjXxSjGDnY5bRaKYAXEIxMDA2NDQgcHIxMDQ4LWNvcnJlY3Rpb24tbWFwLm1kAAIbvG5lbyeBzBSp/pKHzcFyqa+oMTAwNjQ0IHByNDEwMC1hdWRpdC1jb3ZlcmFnZS1tYXAubWQAi8+HgELBX59FZSZkmZBYs4yUQDAxMDA2NDQgcHJlLWNvbW11bml0eS1yZXNlYXJjaC1oaXN0b3J5Lm1kAFWj7nh+NRLRtT0bc6HenlaIOBg7MTAwNjQ0IHByZS1jb21tdW5pdHktcmVzZWFyY2gtc3RhdHVzLm1kAJ7d50nUpdG4kaQ3toAyZUzghVRFMTAwNjQ0IHByZXNlcnZlZC1sb2NhbC1oaXN0b3J5LTIwMjYxMDA5Lmpzb24AvmvKvs2D7/fWD3Zzc+Z+0FEWGBsxMDA2NDQgcHJlc2VydmVkLWxvY2FsLWhpc3RvcnktMjAyNjEwMDkubWQAX9oNHI7u/zPGqWOnUSdLGyDgzJ4xMDA2NDQgcHJlc2VydmVkLXJlc2VhcmNoLW1hbmlmZXN0Lmpzb24Amf6Z6JFkp+fwlm70qgYcAcVAgQUxMDA2NDQgcHJlc2VydmVkLXJlc2VhcmNoLXZhbGlkYXRpb24uanNvbgAeI6IVgBvM7kiIO+MLEnH1TPTRqzEwMDY0NCBwcmVzZXJ2ZWQtcmVzZWFyY2gubWQA5I2vAG5lLcDTkTu6feTGHj2NK58xMDA2NDQgcHJpbWUtc3Vic2V0LWxpbWl0cy5tZABYYTWjwnUuYlu6/kINFM12KCtaYDEwMDY0NCBxcTE2LWNvbnRyb2xsZXItc2NvcGUtbWFwLm1kADiK4ugid/U6Ay61Vf+1P/OH8XwpMTAwNjQ0IHFxMTYtbnVtZXJpY2FsLWNvbnRyYWN0LW1hcC5tZAClLMawRBXfaD12+HIw0dC0qtLF/zEwMDY0NCBxdWFkcmF0aWMtYWZmaW5lLXZlY3RvcnMubWQAdeI0Q/BNyk+25GmhdOhUgfqc0sgxMDA2NDQgcXVpY2stNjctc2NyZWVuLm1kAOpwxPkt10X326ipZO89sZChhxWmMTAwNjQ0IHJhbmstcHJvZHVjdC1jb3JlLm1kAJtoOGQjPXm02dmCpIve/RobyHXQMTAwNjQ0IHJlY3Vyc2l2ZS1pbnZvaWNlLXByZWZsaWdodC5tZADVX2wTbMjpbhRnnU7VLAL8fZiiZzEwMDY0NCByZXBsYXktY29uc29sZS1wb3J0YWJpbGl0eS5tZADudBYJPMRc41uqBOEXWK5z5HSF8DEwMDY0NCByZXBsYXktaW5wdXQtanVuY3Rpb25zLm1kAIjmbLtss2udw15nDXKMFtE4a5FzMTAwNjQ0IHJlcGxheS1pbnNwZWN0LWZhbHNlLWFjY2VwdGFuY2UubWQAgvQC8CkVd5ax9K+2Bv08+gH1dS8xMDA2NDQgcmVwbGF5LXBhdGgtaW5kZXgtYmVuY2htYXJrLmpzb24A+TMmB6yYUr/aY8b95XK5QWTNsPQxMDA2NDQgcmVwbGF5LXBhdGgtaW5kZXgubWQABGpbfir3tg584YxXRnupmBiPWh8xMDA2NDQgcmVwbGF5LXBsYW5uZXItaW52ZW50b3J5Lm1kADEwEzo8E8l+EuZAe4Ww4hglDq1SMTAwNjQ0IHJlc2VhcmNoLWFyY2hpdmUtaW50YWtlLm1kAIqJNOITbOacaGHqoHSWVGOrtPh9MTAwNjQ0IHJlc2VhcmNoLWZhbWlseS1zdGF0dXMubWQAdDoa/LxGxxXSA1A3eX4vgbMuWKUxMDA2NDQgcmVzZWFyY2gtZ2xvc3NhcnkubWQA7ZzHTOMJg3ACVUFqauv+upQoiQAxMDA2NDQgcmVzZWFyY2gtbm90ZXMtMjAyNjEwMTEuanNvbgDP6mpqxUt8ON2dCjW2CKbd+nyoajEwMDY0NCByZXNlYXJjaC1ub3Rlcy0yMDI2MTAxMS5tZAAsN3XKHRLS/4kHXYgnfGjzd8olCzEwMDY0NCByZXNlYXJjaC1wYWNrYWdlLWd1aWRlLm1kALKFbWlAcGROJd9b9WgK64DRRYwlMTAwNjQ0IHJlc2VhcmNoLXByaW9yaXR5LWxvZy5tZAAuS5sFEGqFe8NgVbyEvZsblHOcTDEwMDY0NCByZXNlYXJjaC1zY2FmZm9sZC1iYXRjaGluZy5tZAASr3IrDWm40EZ0yiJnFeJ8YRP/MDEwMDY0NCByZXN1bHQtaGlzdG9yeS5tZABY+PMxTuNALgQtEixqNFcPm9LMUjEwMDY0NCBzY3JpcHQtcnVubmVyLWNhbmNlbGxhdGlvbi5tZABfO2wNaHOJJJOcw54kZCrekiH14zEwMDY0NCBzY3JpcHQtcnVubmVyLWV4aXQtY2xlYW51cC5tZABwXuoXQnDFqnAFG23IUjMSXSTGxDEwMDY0NCBzZWxlY3RlZC1iYXNlbGluZS5tZADubJkr8rprsYJdy3a0g+5kBqG8JjEwMDY0NCBzZWxlY3RlZC1iaXQtY2FsbGVyLXN0b3JhZ2UtbWFwLm1kAKYpBTNB2ZhUzBvx5sqaUcu/qcMWMTAwNjQ0IHNlbGVjdGVkLWJpdC1waHlzaWNhbC1jb250cmFjdC1tYXAubWQAvCgQ76kLqNWiXMlieun/1P+lxaAxMDA2NDQgc2VsZWN0ZWQtYm9vdHN0cmFwLXNjb3BlLW1hcC5tZACvjyMs0jhfiKIQld+79zzrwgtt8TEwMDY0NCBzZWxlY3RlZC1zb3VyY2UtbG9hZGluZy5tZADPd4CedOazJwydeYjkbqyJvNPoGjEwMDY0NCBzaGFyZWQtY29tcHV0YXRpb24ubWQAOgBWu5bDRxtotC4IvxAKzIZy0bExMDA2NDQgc2hhcmVkLWNvcmUubWQAPGweAjB4LlDJ/VQMZ0NqfWxqtHMxMDA2NDQgc2hvcnQtZ3VhcmQtYXVkaXQubWQAWsAD3Cf52rB9ZTZxBlNgoctOwaAxMDA2NDQgc2lnbmVkLXNwYXJzZS1jb3JlLm1kAGDLBBlEJoDhJ0ZYHIcVGy7TDbVsMTAwNjQ0IHNpbmdsZS1pbnRlcnNlY3Rpb24tcGFja2luZy5tZADLVVG7Ju5GEr++mthjhP+yWfPFPjEwMDY0NCBzaW5nbGUtaW50ZXJzZWN0aW9uLm1kAHzfRVXp+eBD3rv+HjpJ+iASNNcQMTAwNjQ0IHNtYWxsLWJsb2NrLWNvbnRyb2wubWQA4dDpeu4kYq46ITouzv4/1d+wxgAxMDA2NDQgc3BhcnNlLWJhc2VsaW5lLXdpbmRvd3MtYXJndi5tZAAHqLz1Huwdcdqz+ak0oy9Vgke2ujEwMDY0NCBzcGFyc2UtZnVzaW9uLWF1ZGl0Lm1kADKjVTqeilBy8bZpEw5ijZLKhotcMTAwNjQ0IHN0YWdlLXBhaXItYXVkaXQubWQANXF2zGbEINjEqIajil88Zw+dgOExMDA2NDQgc3Ryb25nZXItcmFuay1zY3JlZW5zLm1kAF5CUs7eCxknsfobF/1tbZyJcnL4MTAwNjQ0IHN1YnNldC1jb3JlLWZhbWlseS5tZADabY11aX4nHbHg7vFMqiT/RCm5jzEwMDY0NCBzdXBwbGllci1jaXJjdWl0LWNvbnNvbGlkYXRpb24ubWQAbUO4qHTlrBNJroSCq+1YJrvDznUxMDA2NDQgdGFzay1zdGFydHVwLWNvbXBhdGliaWxpdHkubWQAzruhiyr37iGM5kUJy0mRCgA8oNUxMDA2NDQgdGVybmFyeS1yZWxlYXNlLm1kAEfOhKs5fCJHcgdN/bs+jt94QnSoMTAwNjQ0IHRlcm5hcnktcmV2aWV3Lm1kACyjzInJpy+4OjZF9gp1gzOGzvAiMTAwNjQ0IHRlcm5hcnktc2lkZS1jYW5kaWRhdGUubWQAURSR3q2ETG8Mxv6mD2OrLfuOqJ0xMDA2NDQgdHdvLWZ1bGwtY29udHJvbGxlci1jb250cmFjdC1tYXAuanNvbgAn5YtbrjUjosN5qsXUyxQfLH80jjEwMDY0NCB0d28tZnVsbC1jb250cm9sbGVyLWNvbnRyYWN0LW1hcC5tZABH5Y4qT0299/MZAdG/F6jB6TVR5TEwMDY0NCB1bml2ZXJzYWwtZGlydHktY2lyY3VpdC1ndWlkZS5tZADM/SyluOyxjQTLs0ZxlKl1VGujPjEwMDY0NCB3aW5kb3dzLWdpdC1iYXRjaC1waXBlLWVycm9ycy5tZADG7KroH5ovI9lTcGOUmfNTBiMHiTEwMDY0NCB3aW5kb3dzLWluc3RhbGxlZC1naXQubWQAMftZtr6kbm23Njb/jrqKEFGcyqMxMDA2NDQgd2luZG93cy1yZXBsYXktbGlmZXRpbWUubWQAEleuYsMCQeQ+R2B9zxDkBZub9esxMDA2NDQgd2luZG93cy1yZXBsYXktdGltZW91dC1hdWRpdC5tZAAeDmgDAs3ykHzC9PLMzpFBih3XGzEwMDY0NCB3aW5kb3dzLXVuaWNvZGUtcmVwbGF5LWFyZ3YubWQAMyBPr1NtNDxVxZ7d1Wu24bZROf40MDAwMCB3aW5kb3dzLXdvcmtlci1mYWlsdXJlLWF1ZGl0AHLAKBVdVbeaPhcXeaa1hh7urSFbNDAwMDAgd2luZG93czMxNC1saWZldGltZS1yZXBsYXkAFlK+kpuw/l2YvKD8UCqOzpqRmHY=",
+          "component": "agent-task-catalog.json"
+        }
+      ],
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+    }
+  },
+  {
+    "authority": "canonical",
+    "retained": "canonical/certificates/selected-result.json",
+    "proof": {
+      "commit": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+      "path": "certificates/selected-result.json",
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+      "trees": [
+        {
+          "oid": "e6a590f1fd9b3167fa4e49e46ceb56ec01476bc2",
+          "bytes_base64": "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",
+          "component": "certificates"
+        },
+        {
+          "oid": "e2eb3bf5ebde0de18dd5be7a763b31f15adfd40c",
+          "bytes_base64": "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",
+          "component": "selected-result.json"
+        }
+      ],
+      "blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "bytes": 6427,
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    }
+  }
+]
diff --git a/research/fanout-optimality-support/PROOF.md b/research/fanout-optimality-support/PROOF.md
new file mode 100644
index 0000000000..7e2404f931
--- /dev/null
+++ b/research/fanout-optimality-support/PROOF.md
@@ -0,0 +1,147 @@
+# Exact standalone fanout: composition and total-call lower bound
+
+This is an explanatory synthesis of the unchanged construction contract and
+module note retained below `retained/`. The peer owns those results; root's
+independent static reviews accept their stated scope. The registered checker
+regenerates only the original upper certificate. It does not formally verify
+the written lower proof or replay a global physical endpoint.
+
+## Constructive upper bound
+
+For eight arbitrary independent h inputs, the source has
+
+```
+W_i h = Kp_i^-1 sum_j M_ij Km_j h_j / 2,
+A_i = q^-1 Kp_i^-1,
+(q^-1 W h)_i = A_i sum_j M_ij b_j / 2,  b_j=Km_j h_j.
+```
+
+The boundary scalar2 in the native provider is excluded from Km. The mode index,
+M orientation, exact source words, phases, stage axes and spectators are pinned.
+The desired shear adds this row to independent original y_i and preserves h
+at every instruction. Its 17 owned fields are disjoint, arbitrary on entry and
+zero on exit; they are not productive originals.
+
+For each orbit under ordinary left multiplication choose representative a,
+and write `A_i=L_i A_a`. The code's full pullback-Z Lagrangian key decides
+monomial equivalence; a complete signed tableau and absolute anchor fix the
+alias phase. Sparse 512-column checks independently compare each accepted alias.
+For the observed 112 singleton classes these are all self-alias comparisons,
+not a physical 137-field endpoint replay.
+
+For each class, integer certificates give `H=S M`, `M=T H`, with exact integer
+unimodular inverse checks and rational rank agreement. Form each H row from the
+read-only copies b, apply representative Kp^-1 and one positive central Q followed
+by its charged central X to implement q^-1, then reconstruct using exterior T/2.
+Apply L_i and add once to y_i. The identity
+
+```
+L_i sum_l (T_il/2) A_a (sum_j H_lj b_j)
+  = A_i sum_j M_ij b_j / 2
+```
+
+proves the intended added row. Exterior coefficients are applied once; they are
+not tensor-powered. Exact one-column word equalities lift columnwise with
+per-column phase `i^(f gamma)` and identity spectators. The program's literal
+unit/half coefficients and lifetime checks establish read-only h, untouched
+initial y backgrounds and zero-owned returns compositionally. No width-one
+two-term expansion of Q is used as a whole-field implementation.
+
+The retained outcome is 112 singleton nonzero scalar rows, so C=112. It uses
+112 H1 calls, 672 ADDs, 344 maps, eight COPYs and 249 CLEAR/zero-retag episodes
+each, with no odd runtime division. This is an upper bound, not a saving or an
+ordinary/precision/compiler optimum.
+
+## Lower bound in the fixed grammar
+
+The25 source coordinates are binary address axes: the one-column amplitude
+space V has dimension2^25, not25, with the nine active axes embedded among
+identity spectators. No such dense matrix is constructed.
+
+Let K=Q(i). Fix a finite-dimensional one-column space V, a finite ordinary
+monomial group G and one fixed finite program with exterior K coefficients
+independent of width f. Each physical gate lifts columnwise; a paid call acts
+on one whole field of fixed capacity and supplies one new output row. Paid
+queries may use earlier outputs through arbitrary finite feedback. Initial
+genuine fields and dirty owned fields are independent, and their free initial
+observations have only ordinary span. Known-zero scratch contributes no new
+input direction.
+
+Let H be the subgroup of GL(V,K) generated by G and paid operators/inverses.
+The formal group algebra K[H] distinguishes group elements from exterior
+coefficients. In particular `[iI]` evaluates as `i^f I`, whereas `i[I]`
+evaluates as `i I`.
+
+For finitely many distinct nonzero matrices h_1,...,h_t, choose a K-linear
+functional ell with pairwise distinct nonzero values lambda_j=ell(h_j). Such a
+functional exists because K is infinite and finitely many proper hyperplanes
+are excluded. If `sum_j c_j h_j^(tensor f)=0` for every positive f, applying
+`ell^(tensor f)` at f=1,...,t gives the invertible Vandermonde system
+`sum_j c_j lambda_j^f=0`. Thus all c_j vanish. The combined tensor family is
+faithful on the formal group algebra.
+
+The same argument works on **one consecutive tail** f>=F: use F,...,F+t-1;
+the determinant is a nonzero Vandermonde determinant multiplied by
+`product_j lambda_j^F`. This is a direct corollary of the retained proof, not
+permission for a width-dependent program or an arbitrary subsequence. For
+example `[iI]-[I]` vanishes on every width divisible by4 despite being nonzero
+formally, so that subsequence does not justify faithfulness.
+
+Put R=K[G], with finite positive K-dimension |G|. With N independent initial
+directions, retain conceptually all initial rows and every paid output row,
+even after overwrite or CLEAR. After m calls the history module satisfies
+
+```
+M_m = R^N + R t_1 + ... + R t_m,
+dim_K M_m <= (N+m)|G|.
+```
+
+Ordinary operations preserve that span. Each actual paid output adjoins one
+generator regardless of its input's feedback history. This does not assume
+that a paid operator commutes with R or acts on all stored rows for free.
+
+Subtracting the ordinary initial y backgrounds shows that all required fanout
+rows lie in M_m. Right-multiply each h_j coordinate by its common Km_j^-1.
+This is an invertible left-R-linear change of coordinates and preserves R^N;
+it does not commute a Gaussian with Km. Targets become `[A_i] M_i/2`.
+
+For one class G a, remove ordinary units and exterior factor1/2. Independent
+scalar rows v_1,...,v_r have a right inverse over K. If
+`sum_l r_l [a] v_l=0`, multiply by that scalar right inverse to obtain
+`r_l[a]=0` separately; [a] is a unit in K[H], so r_l=0. The target class is
+therefore a free R-module of rank r. No ordinary nonunit is cancelled and R
+need not be a domain.
+
+Distinct sets G a have disjoint formal group-basis supports. They are disjoint
+from the initial ordinary support G because each A_i is nonmonomial. Thus the
+required target modules and initial span give
+
+```
+(N+C)|G| <= dim_K M_m <= (N+m)|G|,
+m >= C.
+```
+
+Dirty owned inputs increase N on both sides and cancel; known-zero scratch,
+COPY/CLEAR, projectors and zero divisors do not create a free extra paid row.
+The source receipt supplies C=112, so 112 total Gaussian field calls are
+necessary and the 112-H1 upper program attains that call count in this grammar.
+
+## Exact boundaries
+
+The fixed finite word and exterior coefficients, finite columnwise ordinary
+group, all-positive-width or consecutive-tail quantifier, shared right Km
+factors, independent inputs and one-output-row fixed capacity are essential.
+Changed field capacity, packing/splitting, inter-column gates, width-dependent
+programs or coefficients, restricted width subsequences, nonordinary initial
+backgrounds, approximate/nonlinear/antilinear operations or different source
+factorizations require new proofs.
+
+In particular, Gaussian/native/cached observations already held at a caller cut
+enlarge its initial module. This proof supplies no automatic additional 112
+calls there and cannot be summed per cut over shared global history. A different
+consumer or constructor is not refuted by this standalone theorem.
+
+The count is not a weighted recursive invoice, machine-time bound, full raw
+dual, source/compiler admission or new κ. The original lower note remains
+byte-exact, including its historical proposed status; the later independent
+static verdict is scoped acceptance, not a formal kernel or human signoff.
diff --git a/research/fanout-optimality-support/README.md b/research/fanout-optimality-support/README.md
new file mode 100644
index 0000000000..153872a515
--- /dev/null
+++ b/research/fanout-optimality-support/README.md
@@ -0,0 +1,156 @@
+# 112-call optimality for a fixed columnwise all-width fanout
+
+This is a **scoped standalone field-call result**. For the exact source shear
+`y112 += q^-1 W_s h8`, a retained constructive program uses 112 H1 calls. A
+separately reviewed module argument proves at least 112 total Gaussian field
+calls under the fixed finite grammar stated below. Thus the call count is
+optimal in that grammar, with **no grouping saving over 112**.
+
+The lower bound requires one fixed finite exact program, fixed exterior scalar
+coefficients, a finite ordinary one-column group acting columnwise, a common
+fixed whole-field capacity, independent initial inputs with only ordinary
+initial span, and correctness at every positive width (or one consecutive tail
+of widths). A call supplies one transformed output row. These conditions are
+part of the theorem. A cut already holding Gaussian/native/cached responses,
+width-dependent programs, inter-column operations, larger-field packing or a
+restricted subsequence of widths requires a different argument. There is no
+automatic **additional** 112-call charge at a global caller cut.
+
+No full caller, full physical raw dual, compiler, precision/stock funding or new
+κ is established. This result does not settle a separately owned constructor or
+exclude changed input observations, targets or geometries.
+
+## Retained upper construction and coverage
+
+The original checker, input, program, result, construction contract and module
+proof are retained byte-for-byte at their original paths below `retained/`.
+Generated sources are honestly LOCAL; the attributed source head is PR5402
+`3348fccea855082786d5f0fc5558b73d4974e745`. Six runtime dependencies, including
+the independent signed-tableau/anchor oracle and exact source words, are bundled.
+
+The original result is SHA256
+`bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7`;
+the literal program is
+`5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7`.
+It reports 112 singleton classes, each with nonzero scalar row rank one, and
+112 paid H1 calls. There is no query reduction.
+
+| Literal operation or resource | Count |
+|---|---:|
+| Positive H1 calls | 112 |
+| ADD | 672 (560 unit, 112 half) |
+| Whole-field monomial maps | 344 |
+| COPY | 8 |
+| CLEAR and zero-retag episodes | 249 each |
+| Arbitrary-entry owned fields, all zero at exit | 17 |
+| Runtime odd divisions | 0 |
+
+The scalar tariff subtotal is 6114 under the retained contract. It excludes
+monomial primitive, routing, storage, precision and compiler costs. The schedule
+conservatively retains identity aliases; no ordinary-work or scratch optimum is
+claimed.
+
+The 57,344 sparse-column comparisons are 112 alias checks on 512 base columns
+each. **For this singleton outcome they are self-alias checks.** They are not a
+physical replay of all 137 field directions. The endpoint follows
+compositionally from the source/alias identity, exact integer factorization,
+literal coefficient checkpoints and typed lifetime/clear/retag argument.
+Independent original y backgrounds stay unchanged except for their prescribed
+update; h is read-only at every primitive. All 17 owned entry directions are
+cleared before use and returned zero.
+
+`PROOF.md` explains this composition and the module lower bound.
+`CLAIMS.json` makes the coverage and exclusions machine-readable.
+`REVIEW-SUMMARY.json` adapts the relevant verdicts from root's independent static
+upper and lower reviews with exact LOCAL origin hashes. It is not another
+scientific run, a fresh independent review by the packager or a formal-kernel
+proof. The original lower note's proposed/unreviewed status is historical;
+the later static review accepts only its stated restricted grammar.
+
+## Why the lower bound is restricted
+
+Write `A_i=q^-1 Kp_i^-1`. Ordinary left multiplication gives classes `G A_i`;
+these sets are right cosets in conventional group terminology. The physical
+alias is explicitly `A_i=L_i A_rep`, so the side of multiplication is fixed.
+For each class take the rational rank of its scalar M rows. Their sum C is 112
+for this retained source.
+
+Over `R=Q(i)[G]`, each paid output adds at most one history-module generator.
+The all-width tensor-family argument distinguishes formal group elements,
+including per-column phase, from exterior scalars. After the common right Km
+normalization, disjoint source classes require C free copies of R beyond the
+ordinary initial span. Finite dimension yields `m>=C`. This accommodates finite
+feedback, overwrite/CLEAR and zero divisors; it does not assume a division ring
+or cancel an ordinary nonunit.
+
+The conclusion is a count of total calls at the same capacity. Allowing higher-
+rank Gaussian calls does not turn it into a weighted recursive invoice. Width-
+one identities, projective phases, coefficients that depend on width, and
+arbitrary subsequences of widths do not meet the proof's hypotheses. Nor does
+the proof price a caller that begins with already paid nonordinary history.
+
+## Actual execution, source custody and replay
+
+The original sole-peer guard exited zero without termination in 4.130925 seconds,
+with 32,763,904 sampled peak descendant RSS bytes under a 30-second/256-MiB guard.
+Its raw receipt and stdout are retained under `evidence/`. Sampled RSS is an
+environment measurement, not a memory-optimality theorem. The upper result and
+program contain no runtime, RSS or path fields; **no comparison exclusions are
+needed**.
+
+The canonical metadata base is
+`1a3ced60b2f7a46bc70280a04f2eeb8ca027c700`, selected κ=.003027288235 under the
+same five assumptions. Selected-record/catalogue Git pins are provenance only;
+the new upper/lower sources and review notes remain LOCAL origins. Peer-owner
+permission covers unchanged source publication with credit after audit and
+granted portability. Local preparation itself is not publication.
+
+Prepared registered replay:
+
+```sh
+python3 -B scripts/research_package.py --package research/fanout-optimality-support
+```
+
+The wrapper authenticates the entire package, proofs, scope and source remap.
+It makes a fresh temporary mirror containing only the unchanged checker/input
+and six dependencies. Original relative paths preserve `HERE.parents[3]` without
+editing the checker. Fresh program/result destinations never overwrite retained
+artifacts. Both regenerated complete raw byte strings and typed JSON must equal
+the original program/result, with zero excluded fields. Full fresh artifacts and
+stdout are captured in replay evidence. The complete fresh program is carried
+losslessly as zlib/base64 in the log envelope, with its raw SHA256 and length;
+the small result is full UTF-8. Compression is transport only: comparison uses
+uncompressed raw program bytes, never a compressed-container hash.
+The written lower proof is authenticated
+and its scope checked; no lower-proof kernel or extra classifier is run.
+
+Direct standalone replay uses an absolute Python 3.12 interpreter with `-I -B
+verify.py` (add `-O`). The planned read-only transport test also uses an empty PATH
+and explicit Git discovery ceiling. Only root can grant the sole peer's bounded
+normal/optimized and portable runs. No checker, phase oracle, classifier or
+package hook has been executed by this preparation worker. Expected replay time
+is seconds; each requested guard is at most 30 seconds and 256 MiB.
+
+## Open next questions
+
+Can a particular caller apply this standalone component to its actual source
+version and 17 disjoint scratch fields? First bind the source/target owners,
+charts, phases, field capacity and lifetimes; that application is not supplied
+here. Can a lower bound be proved at a cut containing prior nonordinary
+observations? Start with its actual initial module and jointly required targets;
+the ordinary-initial proof gives no incremental charge there. Can ordinary work,
+scratch and full physical dual/precision/compiler costs improve? Those require
+their own constructive program and complete caller ledger.
+
+## Credit
+
+The peer owns the fanout construction/checker and source extraction; the peer
+Astra query-sharing adviser owns the module proof. Root's independent static
+review supplied the source/coverage and zero-divisor/finite-feedback audit.
+Retain Dillon Amburgey/dillona's PR5402 source, Ali Romman's HCODE/native lineage,
+Cao Yifan's Clifford/normalizer work, Cinna Davis, zxv, Jacob Alan Sussman,
+Dugongue and all native/helper/compiler/precision/analytic predecessors and
+notices. Wrapper and custody packaging: Chris R / Clear1nsight, with substantial
+OpenAI Codex assistance. Apache-2.0; retained LICENSE/NOTICE and source-specific
+attribution apply. Static proof review and finite certificates are not human
+approval or formal verification of the multiplication theorem.
diff --git a/research/fanout-optimality-support/REVIEW-SUMMARY.json b/research/fanout-optimality-support/REVIEW-SUMMARY.json
new file mode 100644
index 0000000000..2a4058c14d
--- /dev/null
+++ b/research/fanout-optimality-support/REVIEW-SUMMARY.json
@@ -0,0 +1,152 @@
+{
+  "schema": "adapted-public-static-review-summary/v1",
+  "status": "ROOT_INDEPENDENT_STATIC_UPPER_AND_SCOPED_LOWER_PASS",
+  "adaptation": "Selected relevant exact fields from unchanged LOCAL review JSON. Unrelated private candidate-status flags and review bookkeeping are omitted. This is a packaging adaptation, not another independent review or scientific run. Original review bytes remain unchanged at their local paths.",
+  "origins": [
+    {
+      "local_path": "outputs/global120-fanout-independent-static-20261024/RESULT.json",
+      "sha256": "cb115b597d90e938f687881c78ed53a5bf84d28b9f6a33367f6c8f35279cb1a8"
+    },
+    {
+      "local_path": "outputs/global120-fanout-independent-static-20261024/module-lower-v1-audit/RESULT.json",
+      "sha256": "01d3a2f5bc5336111cde977d69130e2a1ebd2a84884f8599537ca9cfccb35007"
+    }
+  ],
+  "forward_upper": {
+    "status": "STATIC_FORWARD_UPPER_PROGRAM_ACCEPTABLE_UNDER_PINNED_SOURCE",
+    "source_head": "3348fccea855082786d5f0fc5558b73d4974e745",
+    "retained_result_status": "PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION",
+    "retained_scientific_metadata": {
+      "source_rows": 112,
+      "common_modes": 8,
+      "leftcoset_count": 112,
+      "rationalrank_sum_Qqueries": 112,
+      "query_savings_vs112": 0,
+      "owned_arbitrary": 17,
+      "owned_zero_return": 17,
+      "all512_alias_columns_checked": 57344,
+      "H_abs": 448,
+      "T_abs": 112,
+      "maximum_integer_coefficient_bitlength": 1,
+      "runtime_odd_divisions": 0,
+      "program_counts": {
+        "CLEAR": 249,
+        "ZERO_RETAG": 249,
+        "COPY": 8,
+        "MONOMIAL": 344,
+        "ADD": 672,
+        "GAUSSIAN": 112
+      },
+      "ADD_census": {
+        "1": 392,
+        "1/2": 88,
+        "-1": 168,
+        "-1/2": 24
+      },
+      "monomial_primitive_census": {
+        "D": 232,
+        "P": 232,
+        "X": 232,
+        "phase": 120
+      },
+      "scalar_tariff": 6114
+    },
+    "accepted_static_derivations": [
+      "Actual source A_p=q^-1 Kp_p^-1, represented chronologically by Kp inverse then positiveQ then centralX",
+      "Mode-indexed Km excludes native scalar2 and N output normalizers",
+      "M=TH integer factorization plus one exterior1/2 gives the correct source fanout",
+      "All-width lift tensors individual physical identities, not owner sums or scalar1/2",
+      "Phase tokens use i^(f gamma); source axis0 stays central under the25-axis embedding",
+      "Strict h readonly and all17 private entry dirt removed before use and zero at exit",
+      "Forward y coefficientI and disjoint versioned source copies maintained",
+      "Reported scalar6114 excludes monomial/routing/stock/compiler costs"
+    ],
+    "coverage_limits": [
+      "57344 full-column comparisons are112 aliases, all self-aliases for the observed singleton classes; not a137-field physical endpoint replay",
+      "Stored112-class/rank outcome and13 control rejections are retained peer/root observations, not independently executed here",
+      "Typed lifetime and scalar checkpoints plus factorization prove endpoint compositionally",
+      "q^-1 W h does not supply qh for q^-1 W qh",
+      "No broad lower bound, raw-dual implementation, complete caller, target admission or funded kappa"
+    ],
+    "credit": "Peer Astra query-sharing/fanout construction and pinned native/helper/Clifford/normalizer sources; independent static review with substantial OpenAI Codex assistance"
+  },
+  "module_lower": {
+    "status": "PASS_SCOPED_STATIC_PROOF_REVIEW",
+    "proof_sha256": "cfa9f3df855f96a3e73bcb8042a750a3aa41d18ec098d6a34268370f3e84d782",
+    "proof_steps": [
+      {
+        "source_lines": [
+          59,
+          94
+        ],
+        "claim": "Injectivity of the combined all-positive-width tensor family on finitely supported K[H]",
+        "verdict": "PASS",
+        "reason": "A separating K-linear functional gives distinct nonzero values; Vandermonde equations force every coefficient to vanish; phases remain actual group elements."
+      },
+      {
+        "source_lines": [
+          98,
+          130
+        ],
+        "claim": "Finite-dimensional history upper bound with arbitrary finite paid feedback",
+        "verdict": "PASS",
+        "reason": "Each actual paid output adjoins one R-generator; no R-linearity or commutation of the paid operator is assumed. Overwritten forms are retained only conceptually."
+      },
+      {
+        "source_lines": [
+          134,
+          142
+        ],
+        "claim": "Shared right Km normalization preserves the dimension comparison",
+        "verdict": "PASS",
+        "reason": "Coordinatewise right multiplication by Km_j^-1 is invertible left-R-linear and maps I onto I."
+      },
+      {
+        "source_lines": [
+          144,
+          160
+        ],
+        "claim": "Each class target module is free of its scalar row rank",
+        "verdict": "PASS",
+        "reason": "Central scalar right inverse separates r_l[a], then the group element[a] is a unit; no ordinary nonunit is cancelled."
+      },
+      {
+        "source_lines": [
+          160,
+          181
+        ],
+        "claim": "Direct-sum lower dimension and m>=C despite zero divisors",
+        "verdict": "PASS",
+        "reason": "Distinct right cosets and G have disjoint formal group-basis supports, so dimensions add; dirty-original N cancels from the two bounds."
+      }
+    ],
+    "source_specialization": {
+      "retained_C": 112,
+      "source_head": "3348fccea855082786d5f0fc5558b73d4974e745",
+      "source_result_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "minimum_total_field_calls_in_stated_standalone_grammar": 112,
+      "matching_H1_upper_program": true,
+      "numerical_specialization_rerun": false
+    },
+    "essential_scope": [
+      "One fixed finite exact program and fixed exterior K coefficients for every positive width",
+      "Finite ordinary one-column group, lifted columnwise with exact phases",
+      "Arbitrary independent initial fields; initial ordinary module R^N without free nonordinary history",
+      "One output row per paid call at fixed common whole-field capacity",
+      "Central scalar source matrix and shared right Km factor per input column"
+    ],
+    "excluded_applications": [
+      "Incremental lower bound at a cut already containing Gaussian observations or qh",
+      "Adding112 per cut in a globally shared paid history without a new module argument",
+      "Width-dependent or inter-column ordinary operations, capacities or coefficients",
+      "Restricted residue classes of widths, projective phases or width-one matrix-span replacement",
+      "Approximate, nonlinear or antilinear computations",
+      "Weighted recursive invoice, physical compiler or arithmetic lower bound"
+    ],
+    "concrete_gap_in_stated_proof": null,
+    "repair_required_in_stated_grammar": false,
+    "boundary_example": "[iI]-[I] is nonzero formally but evaluates to zero for all widths divisible by4; the theorem requires all positive widths.",
+    "credit": "Peer Astra query-sharing proposed proof; peer source fanout certificate; pinned native/helper/Clifford/normalizer sources; root zero-divisor caveat; substantial OpenAI Codex assistance in this independent static review."
+  },
+  "scientific_execution_by_packager": false
+}
diff --git a/research/fanout-optimality-support/RUNTIME-INPUTS.json b/research/fanout-optimality-support/RUNTIME-INPUTS.json
new file mode 100644
index 0000000000..ba66e1e8f9
--- /dev/null
+++ b/research/fanout-optimality-support/RUNTIME-INPUTS.json
@@ -0,0 +1,66 @@
+{
+  "schema": "unchanged-source-path-sandbox/v1",
+  "path_policy": "Copy these byte-identical files below a fresh temporary root, preserving original relative paths so unchanged checker HERE.parents[3] resolves this root. Generate fresh result/program outside immutable package; never copy original output files into their fresh destination.",
+  "checker": "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+  "input": "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+  "files": [
+    {
+      "path": "retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md",
+      "source_path": "race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md",
+      "sha256": "ead89d4f96531d96f38ae7103b99eabef35768b2e57e7a173ce482048092e206",
+      "bytes": 16445,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+      "source_path": "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+      "sha256": "f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb",
+      "bytes": 71703,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+      "source_path": "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+      "sha256": "b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3",
+      "bytes": 22726,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json",
+      "source_path": "swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json",
+      "sha256": "d065d98d97fc772e567a0f2bf3e3f308e0d9372c6a8c0ffd6368c05a6ea1a90a",
+      "bytes": 244098,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py",
+      "source_path": "swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py",
+      "sha256": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba",
+      "bytes": 4011,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json",
+      "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da",
+      "bytes": 281582,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md",
+      "sha256": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5",
+      "bytes": 12418,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    },
+    {
+      "path": "retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json",
+      "source_path": "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json",
+      "sha256": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65",
+      "bytes": 145658,
+      "availability": "LOCAL retained source with explicit peer vendor permission; source_head is attribution, not an invented canonical Git ancestor"
+    }
+  ],
+  "expected_result": "retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json",
+  "expected_program": "retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json"
+}
diff --git a/research/fanout-optimality-support/SOURCES.json b/research/fanout-optimality-support/SOURCES.json
new file mode 100644
index 0000000000..b6c7f5181d
--- /dev/null
+++ b/research/fanout-optimality-support/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    }
+  ]
+}
diff --git a/research/fanout-optimality-support/TASK.json b/research/fanout-optimality-support/TASK.json
new file mode 100644
index 0000000000..afaea1a6da
--- /dev/null
+++ b/research/fanout-optimality-support/TASK.json
@@ -0,0 +1,112 @@
+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 7,
+  "base_commit": "1a3ced60b2f7a46bc70280a04f2eeb8ca027c700",
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/staged-fourth-mixture-ceiling/README.md",
+      "research/r437-two-window-carrier/README.md"
+    ],
+    "methods": [
+      "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+      "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification.",
+      "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure",
+      "2979",
+      "rank7 joint endframes",
+      "paired extraction",
+      "joint lowering",
+      "4088",
+      "4091",
+      "4067",
+      "staged544-mixed-fourth-entry",
+      "staged-fourth-mixture-ceiling",
+      "r437-two-window-carrier"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+        "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+        "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+        "status": "author-checked",
+        "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+        "evidence": "research/r437-two-window-carrier/README.md",
+        "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+        "status": "author-checked",
+        "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Package the peer-owner-requested matching112-call upper construction and scoped fixed-columnwise all-width module lower proof for one standalone fanout. Authenticate/replay only unchanged upper checker through root-granted sole-peer package gates.",
+  "scope_change_reason": "Explicit separate donor task; preserve existing GLOBAL120budget package and peer constructors. New source is LOCAL with peer permission, not canonical ancestry or new kappa.",
+  "bottleneck_link": "Clarify exactly where112totalcalls are optimal and where cached observations/changed geometry make that lower bound inapplicable.",
+  "budget_minutes": 60,
+  "stop_rule": "Freeze source/request for root static audit before any checker/oracle execution. Sole peer shared guard only; at most4 upper-checker calls for registered normal/O and read-only transport. No separate phase/classifier/native/price/Lean/global engines or commit/publication before root ready.",
+  "outcome": "completed",
+  "evidence": "Immutable upper input/checker/program/result/contract, original guard, written module proof and adapted independent static review summary. Package replay remains separate gate.",
+  "author": "Chris R / Clear1nsight",
+  "ai_assistance": "Substantial OpenAI Codex assistance. Peer owns fanout construction/checker and Astra query-sharing module proof; root independent static reviews supply forward coverage and finite-feedback/zero-divisor analysis. This contribution supplies wrapper/custody and scoped explanatory packaging.",
+  "open_questions": [
+    {
+      "question": "Can a given caller legally apply this standalone component?",
+      "why_it_matters": "Its source version, independent originals, capacity and17disjoint scratch fields are actual premises.",
+      "first_step": "Bind actual owners, charts, phases and lifetimes to the exact source shear.",
+      "blocked_by": "Caller-specific physical/source application."
+    },
+    {
+      "question": "What is the lower bound with a nonordinary initial observation module?",
+      "why_it_matters": "The112totalbound gives no automatic additional cost at a cached-response cut.",
+      "first_step": "Write the actual initial module and jointly required target rows before any dimension comparison.",
+      "blocked_by": "Different application-specific proof; not supplied here."
+    },
+    {
+      "question": "Can ordinary work, scratch and full dual/compiler costs improve?",
+      "why_it_matters": "Call-count optimality does not optimize other resources or fund a complete caller.",
+      "first_step": "Produce and audit a new fully charged ordinary/owned/dual schedule without changing retained sources.",
+      "blocked_by": "Separate constructive and compiler/precision/stock obligations."
+    }
+  ]
+}
diff --git a/research/fanout-optimality-support/VERIFY.json b/research/fanout-optimality-support/VERIFY.json
new file mode 100644
index 0000000000..b9b63e6336
--- /dev/null
+++ b/research/fanout-optimality-support/VERIFY.json
@@ -0,0 +1,32 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-Werror",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 30,
+      "checks": "Authenticate byte-exact upper/lower proofs, source closure and restricted model; replay unchanged upper checker once in fresh original-path sandbox; full raw-byte and typedJSON equality for result/program, zero exclusions; preserve lossless complete fresh artifacts;10meaningful source/model/type controls. No extra engine, native/Powers/global caller or lower-kernel run."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-Werror",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 30,
+      "checks": "Authenticate byte-exact upper/lower proofs, source closure and restricted model; replay unchanged upper checker once in fresh original-path sandbox; full raw-byte and typedJSON equality for result/program, zero exclusions; preserve lossless complete fresh artifacts;10meaningful source/model/type controls. No extra engine, native/Powers/global caller or lower-kernel run."
+    }
+  ]
+}
diff --git a/research/fanout-optimality-support/canonical/certificates/selected-result.json b/research/fanout-optimality-support/canonical/certificates/selected-result.json
new file mode 100644
index 0000000000..fc3d4ba105
--- /dev/null
+++ b/research/fanout-optimality-support/canonical/certificates/selected-result.json
@@ -0,0 +1,103 @@
+{
+  "status": "Selected maintainer-reviewed conditional PR5413 completion, with PR5407 provider and PR5414 companion audits and explicit inherited foundation reuse",
+  "kappa": "605457647/200000000000",
+  "decimal": "0.003027288235",
+  "source_prs": [
+    5413,
+    5414,
+    5402,
+    5407,
+    5398,
+    5400,
+    4610,
+    5241,
+    4470,
+    4447,
+    4441,
+    4440,
+    4416,
+    4433,
+    4359,
+    4268,
+    3945,
+    4085,
+    2979,
+    4076,
+    4088,
+    1673,
+    1758,
+    1786,
+    23,
+    555,
+    589
+  ],
+  "source_manifest": "certificates/frontier5413-source.json",
+  "certificate": "certificates/frontier5413/CLAIM.json",
+  "certificate_sha256": "344a955984f2daee912592d63810af9e7c8e61771b871c77a25b5b8c76809694",
+  "proof": "docs/research/pr-intake-evidence/pr5413-promotion/PROMOTION.md",
+  "proof_supplements": {
+    "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c",
+    "notes/batched-complex-rows.tex": "64c70926a8705874f1c9b42a2f703e42cad4e90f927f544458cfdf729540236c",
+    "notes/compact-control-movement.tex": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6",
+    "notes/general-clifford-frames.tex": "c9bb9655b594583c6b4bab8cb485233f1d1e588f83858cf1e4c3530cee8fed54",
+    "notes/stopped-product-complex.tex": "4738089103a4b263b3b0ef458f5ef35519c696f1ea871ae79e508d3720f5870a",
+    "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "references/semantic-bulk/pr23/semantic-bulk-17-note.tex": "652242b05174bb776ffc6165af170df9c8cf220dbd0fc26c24d778f320dbabc8",
+    "research/e8-bit-carrier-skeleton/code/bit/export_records.py": "8a5999601f917dbb492bb9ae9a344611f18cc7cedc53dc3c76496a369e530eb3",
+    "research/e8-bit-carrier-skeleton/code/nine/geometry.py": "36eeda3184bd009e89462b65c8725d10860c444f8da8f1f87e5f6e50120011ca",
+    "research/e8-bit-p111-tuned/code/gen_p3.py": "438b83f10d70ceca7cf78049420204b7de2dc61682f913c50a62596106ad84cd",
+    "research/e8-bit-p111-tuned/code/xcheck_p.py": "af3decc877e27c00001cf56f50c6c09566e8e101297ab34c7860aed96a06d80e",
+    "research/e8-bit-p111-tuned/tune/EXPECTED.json": "b9f0e5ca038abe837b0007c8fe006f366a6f02009244ac57705a8a200e2301f4",
+    "research/e8-bit-p111-tuned/tune/apply.py": "806ae4cb2648e4f05dcf56bd089891fd3ba33a6ee5fe76d3329e322c6770c1a1",
+    "research/e8-bit-p111-tuned/tune/wlib.py": "a37fdf3cdf5f62945c2a90193401c0e9edc9dd3cda8d8cb36a3b9c329ebe4dbc",
+    "research/t74-native-fast/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+    "docs/research/pr-intake-evidence/pr4359/PROOF-REVIEW.md": "7d67bb814285f7634029fbd378c6457156545f0b38858cc1c6ec34b68cd9d162",
+    "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md": "5c111dd56beb53dc44ab727d96e1af03aaf50f3023d4342e2b0a89ede6cf585b",
+    "docs/research/pr-intake-evidence/pr4416/PROOF-REVIEW.md": "2c2bbe6fe1bab44778192118f27e59a0d23dbe02c47aa8a42845093f1ce46f49",
+    "docs/research/pr-intake-evidence/pr4610/PROOF-REVIEW.md": "b84f833e3072cbab372fbda2ece98fbc031c15e590cf73003ddea35a5222e148",
+    "research/final4610-independent-admission/PROOF.md": "e573cbbe6fa5481c0533e773de404e10f4dc7907b5ebfe404bdcd02dcf9844d8",
+    "research/final4610-independent-admission/SPECIALIZATION.md": "70430114f744108223bc1d44b98bc25b696c4b408b7b044c2a8bbdfdb434ac5c",
+    "docs/research/pr-intake-evidence/pr5413-promotion/PROMOTION.md": "9419931de95e317f5e08ffa98c86e069836b53f6438c2f413b0722377819aa44",
+    "docs/research/pr-intake-evidence/pr5413/PROOF-REVIEW.md": "1edba0567d35b099e67d5503cf335d5d143782b5cf4c1e4f98fc2d620ed4c644",
+    "research/coupled-helper-neutral-completion/reports/proofs/NEUTRAL-PROOF-v16c.md": "dca94625cd0d49de6b81e4a7dd4108b8b6f711e90496d9116806242d30b35737",
+    "research/coupled-helper-neutral-completion/reports/proofs/WHOLECALLER-COMPLETION-THEOREM.md": "ecefd9b890ccaa46e9f00a6e43faf16aaaf8ec8c992ab48bf245af38aa3e3f23",
+    "research/coupled-helper-neutral-completion/reports/proofs/V16-APPLICATION-PROOF-v3.md": "cda8f596f7854f42a228f757d5f8e68f6b2256a19c5ae3771fb40753cedc5b39"
+  },
+  "review": "docs/research/pr-intake-evidence/pr5413-promotion/PROMOTION.md",
+  "validation": "docs/research/pr-intake-evidence/pr5413-promotion/VALIDATION.json",
+  "integration": "docs/research/pr-intake-evidence/pr5413-promotion/INTEGRATION.json",
+  "reproduce": "make frontier5413-verify",
+  "scope": "Maintainer-reviewed conditional PR5413 complete neutral caller, with PR5407 provider and PR5414 companion audits. The five selected framework assumptions are unchanged. Uniform words are not materialized.",
+  "previous_kappa": "15108879/5000000000",
+  "previous_record": "certificates/checkpoints/frontier4610.json",
+  "audited_source_head": "0c1fa2f47fb5ea17b93a4b67063d08e49cc38e51",
+  "source_certificate": "research/coupled-helper-neutral-completion/reports/expected/funding.json",
+  "source_certificate_sha256": "70ab7d13548962097ad83ad393b8482f52e827b8996869011ce6d071146bd3eb",
+  "replay_mode": "Fresh serial provider, primary eight-engine and companion replay in a closed export; source-bound PR4610 foundation reuse; explicit Darwin resource adapter where needed",
+  "contributors": "docs/research/community-neutral5413-contributors.md",
+  "assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ],
+  "audit_pr": 5414,
+  "audit_head": "bc37fb01c58d20e799d3299dec63e654f67d9d1b"
+}
diff --git a/research/fanout-optimality-support/canonical/docs/research/agent-task-catalog.json b/research/fanout-optimality-support/canonical/docs/research/agent-task-catalog.json
new file mode 100644
index 0000000000..f126dd2e2d
--- /dev/null
+++ b/research/fanout-optimality-support/canonical/docs/research/agent-task-catalog.json
@@ -0,0 +1,1242 @@
+{
+  "schema_version": 1,
+  "priority_revision": 7,
+  "priority_log": "docs/research/research-priority-log.md",
+  "assessed_on": "2026-10-20",
+  "status": "Research suggestions, not reservations or assertions that these questions are unclaimed. Check current main and live PRs.",
+  "tracks": [
+    {
+      "id": "bit-mechanisms",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "bit-helper-contract",
+          "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/r439-bsection-stars-seed01/README.md",
+            "research/r439-copy-path-sharing-barrier/README.md"
+          ],
+          "methods": [
+            "Derive a replacement interface lemma and price its implementation.",
+            "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement."
+          ],
+          "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/r439-bsection-stars-seed01/verify.py"
+            ],
+            "expected": "PASS_R439_BSECTION_STARS",
+            "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.",
+          "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.",
+          "allowed_variations": [
+            "Choose one helper-star or quartet instance; narrow to one boundary implication."
+          ],
+          "scope_change_triggers": [
+            "Changing only source count or scalar addition count without an interface argument."
+          ],
+          "overlap_terms": [
+            "H2_D_frame0_targets_from_helpers",
+            "K_equals_D",
+            "helper-star"
+          ]
+        },
+        {
+          "id": "bit-new-register-model",
+          "question": "Can an explicitly larger or nonabelian register model escape the scoped three-register obstruction?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/bit-three-register-lower-bound/README.md",
+            "certificates/selected-result.json",
+            "research/bit-gl3-mixed-targets-length10/README.md",
+            "docs/research/community-efficient1000-review.md"
+          ],
+          "methods": [
+            "Construct the smallest exact identity in a newly specified legal operation alphabet.",
+            "Derive a target-specific relaxation bound for that same explicit alphabet."
+          ],
+          "acceptance_gate": "Name the changed hypothesis, all counted roles and a uniform identity; finite column tests alone do not certify it. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read Model section 1 of the three-register bound and identify the exact excluded free operations.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "First compare the alphabet, role count and length with the fully replayed #1974 census and #2027 mixed-root tariff. Identify a changed premise and a legal native implementation; then price one smallest completed instance before searching larger words.",
+          "bottleneck_link": "A small-width completed saving changes the bit primitive; a finite-address identity alone is insufficient.",
+          "allowed_variations": [
+            "Choose a fixed larger register count or a specified nonabelian operation family."
+          ],
+          "scope_change_triggers": [
+            "Remaining inside the already-excluded three-register abelian model.",
+            "Repeating the two-register GL3 census or a covered three-register length without changing a hypothesis; a formal group-algebra word without native conversion is a partial result."
+          ],
+          "overlap_terms": [
+            "three-register",
+            "nonabelian",
+            "group algebra"
+          ]
+        },
+        {
+          "id": "r437-carrier-integration",
+          "question": "Can the paid R437 two-window carrier improvement be admitted by the actual pooled compiler and physical caller?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/r437-two-window-carrier/README.md",
+            "research/r437-reverse-row-coefficient/README.md"
+          ],
+          "methods": [
+            "Close one compiler/request, caller or precision/stock implication for the pinned paid exchange.",
+            "Falsify that exact interface with an arbitrary-dirty-state or chronology counterexample."
+          ],
+          "acceptance_gate": "Pin the complete source and destination contracts, exact paid and scalar deltas, and all remaining assumptions. A local moment gain is not a physical or all-size supplier admission.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4067 paid profile and open integration obligations; #4147 covers the reverse row coefficient. Three additional ADDs per call and all helpers remain charged. This is not a selected supplier.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Choose one unclaimed obligation: pooled compiler codebook/request alignment, actual physical caller, or precision/stock envelope using the already reported reverse coefficient. Pin the input and receiver, preserve dirty/source windows, and test one binding with a rejection control. Stop at unresolved dependencies; do not rederive the coefficient or quote the local moment as a completed bound.",
+          "bottleneck_link": "The exchange changes the paid profile; integration must establish that its gain survives the complete caller.",
+          "allowed_variations": [
+            "One compiler rebind, one actual caller boundary, or one precision/stock implication."
+          ],
+          "scope_change_triggers": [
+            "Ignoring added ADDs, retaining an obsolete reverse coefficient, or declaring global admission from the local histogram."
+          ],
+          "overlap_terms": [
+            "R437",
+            "two-window carrier",
+            "4067",
+            "4147",
+            "pooled compiler",
+            "request alignment",
+            "reverse row coefficient"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4067: source-bound two-window carrier with (2,2) to (1,3) paid exchange and fixed OQ4 host.",
+              "evidence": "research/r437-two-window-carrier/README.md",
+              "remaining": "Pooled compiler/request rebind, physical caller and precision/stock admission.",
+              "status": "author-checked",
+              "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4147: reverse row coefficient follow-up.",
+              "evidence": "research/r437-reverse-row-coefficient/README.md",
+              "remaining": "Use the exact coefficient in a caller-bound precision/stock proof rather than repeat the arithmetic.",
+              "status": "author-checked",
+              "source_commit": "72e7bb797adf82aeb525a399f56ab8adbab8e93c",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    },
+    {
+      "id": "complex-mechanisms",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "p104-side-correction",
+          "question": "Can a changed P104 producer/consumer contract escape the scoped slot, chart and completion obstructions with a favorable full bill?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/p104-literal-slot-defect/README.md",
+            "research/p104-uniform-commutation-gap/README.md",
+            "research/p104-uniform-encoding-gap/README.md",
+            "research/p104-source-chart-shortcut/README.md",
+            "research/p104-fiber-tag-seam/README.md"
+          ],
+          "methods": [
+            "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+            "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+          ],
+          "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the named successor obstructions before extending #2981 static flags. Distinguish literal-slot action, commutation, uniform encoding, source-chart shortcut and fiber-tag seam scopes; none excludes all P104 mechanisms.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Name one hypothesis changed from these exact interfaces. Write a literal producer-to-consumer timeline and an arbitrary-dirty-input positive/control pair, then charge acquisition, coefficients, completion, hosting and restoration. Stop if the same slot/fiber mismatch persists or the favorable full budget already fails. A scoped independent audit remains useful; another static count is not a new completion.",
+          "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+          "allowed_variations": [
+            "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+            "A changed correction schedule with an updated full bill and native frame contract."
+          ],
+          "scope_change_triggers": [
+            "Recompiling the already certified low-rank channel without closing a new obligation.",
+            "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.",
+            "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.",
+            "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful.",
+            "Repeating a static cover, source-chart shortcut or fiber-tag seam without changing the hypothesis responsible for its obstruction."
+          ],
+          "overlap_terms": [
+            "P104",
+            "I-G/2",
+            "side correction",
+            "native channel",
+            "1972",
+            "1991",
+            "2586",
+            "endpoint transport",
+            "physical dual",
+            "relay composition",
+            "2981",
+            "joint unit flags",
+            "acquisition delivery",
+            "static nesting",
+            "4133",
+            "4136",
+            "4140",
+            "4153",
+            "4154",
+            "p104-literal-slot-defect",
+            "p104-uniform-commutation-gap",
+            "p104-uniform-encoding-gap",
+            "p104-source-chart-shortcut",
+            "p104-fiber-tag-seam"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4133: literal-slot defect",
+              "evidence": "research/p104-literal-slot-defect/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4136: uniform commutation gap",
+              "evidence": "research/p104-uniform-commutation-gap/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4140: uniform encoding gap",
+              "evidence": "research/p104-uniform-encoding-gap/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+              "evidence": "research/p104-source-chart-shortcut/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4154: fiber-tag seam mismatch",
+              "evidence": "research/p104-fiber-tag-seam/README.md",
+              "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+              "status": "author-checked",
+              "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "complex-rank-shape-decoder",
+          "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/complex-decoder-field-extension-seed44/README.md",
+            "research/complex-frame-pair-decoders/README.md",
+            "research/selected-k8-unrestricted-ends/README.md",
+            "research/eisenstein-reduction-copy-floor/README.md"
+          ],
+          "methods": [
+            "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.",
+            "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration."
+          ],
+          "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).",
+          "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.",
+          "allowed_variations": [
+            "One masked, overcomplete or block decoder family with exact labels and supports.",
+            "A scoped lower bound on effective rank for one alphabet.",
+            "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+          ],
+          "scope_change_triggers": [
+            "Repacking idle remainders of an unchanged word (covered by the packing ceiling).",
+            "Repeating the eight-term all-pairs search inside its proved scope.",
+            "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+            "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "rank shape",
+            "block climb",
+            "masked decoder",
+            "overcomplete",
+            "effective rank"
+          ]
+        },
+        {
+          "id": "complex-new-helper-inventory",
+          "question": "Can a new local cost interface change the deficit-to-recursive-cost ratio beyond current packing?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/heterogeneous-owner-assembly/README.md",
+            "certificates/selected-result.json",
+            "research/selected-k8-unrestricted-ends/README.md"
+          ],
+          "methods": [
+            "Propose a changed helper inventory and derive an optimistic exact moment.",
+            "Design a small completed instance and independently verify its endpoint and rank bill."
+          ],
+          "acceptance_gate": "A new physically realizable contract outside the frozen catalogue whose per-call profile, screened with ceiling.ceiling(), beats the selected word's packing ceiling; a lower cap does not establish identical circuitry or order attainable optima, and is insufficient to pass the stronger-budget target under this model. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin.",
+          "bottleneck_link": "Packing of the selected word is capped at +0.87% (ceiling model); only a lower local excess spend or a changed coverage law raises the cap.",
+          "allowed_variations": [
+            "Narrow to one changed boundary or helper type with explicit counts.",
+            "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+          ],
+          "scope_change_triggers": [
+            "Mixing only providers already inside the pinned catalogue.",
+            "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "helper inventory",
+            "heterogeneous-owner",
+            "mutable leaver"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "recursive-interfaces",
+      "weight": 20,
+      "tasks": [
+        {
+          "id": "joint-query-controller",
+          "question": "Can the installed QQ16 caller win a complete matched protocol bill, or can a changed demand eliminate actual paid work?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/qq16-caller-install/README.md"
+          ],
+          "methods": [
+            "Derive the matched whole-caller physical bill for installed and baseline protocols.",
+            "Change the actual demanded observations and prove a cheaper legal producer/consumer contract."
+          ],
+          "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4166 COST.md and ADMISSION.json. An actual caller connection is now proposed. Its native-component profile loses; parent park/restore versus external-call costs remain unresolved. Retain the producer and recovery lineage rather than rebuild it.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "At the actual installed cut, compare matched complete parent park/restore and external input/return protocols at the same bank/packet geometry, including every later root call and service cost. Alternatively pin both bridge observations and derive a genuinely smaller source-compatible demand. Stop if the complete necessary inequality fails or an essential cost is unknown; no larger decoder scan from a local tape-action saving.",
+          "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+          "allowed_variations": [
+            "One paid query, one changed first pair, or one precisely specified affine helper state.",
+            "A counterexample or lower bound for that exact proposed repair.",
+            "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+          ],
+          "scope_change_triggers": [
+            "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+            "Treating cover-map counts as zero-cost physical address operations.",
+            "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+            "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate.",
+            "Recreating completed-output recovery or caller wiring already supplied by #4166 without new independent coverage.",
+            "Dropping retained later root calls or claiming native-profile dominance from the isolated publication saving."
+          ],
+          "overlap_terms": [
+            "QQ16",
+            "joint-query",
+            "changing-chart controller",
+            "selected observation",
+            "1969",
+            "2540",
+            "early record",
+            "output-bank retention",
+            "complete native decoder",
+            "2965",
+            "producer defect",
+            "dirty-helper range",
+            "F17 consumer",
+            "4166",
+            "qq16-caller-install"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+              "evidence": "research/qq16-caller-install/README.md",
+              "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+              "status": "author-checked",
+              "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "centre-path-sharing",
+          "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.",
+            "Prove a lower bound on copied information per call for the selected decoder contract."
+          ],
+          "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).",
+          "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.",
+          "allowed_variations": [
+            "One sharing pattern across a fixed number of calls.",
+            "One reduced copied-total contract for the existing decoder.",
+            "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+          ],
+          "scope_change_triggers": [
+            "Removing copies without a replacement contract for the decoder's copied totals.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "centre path",
+            "copied totals",
+            "private temporary",
+            "shared centre",
+            "batching"
+          ]
+        },
+        {
+          "id": "coverage-law-change",
+          "question": "Can a template or call contract leave two or more unpaid coordinates per live family?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/complex-local-word-ceiling/README.md",
+            "research/idle-axis-hosting/PROOF.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "State a replacement for the coverage identity (mass = 72W + 64N) and the contract change that realizes it, with its implementation cost.",
+            "Find an obstruction: show which data-endpoint obligation forces exactly one unpaid coordinate in the current template."
+          ],
+          "acceptance_gate": "An explicit replacement identity, verified on a small complete instance with dirty inputs, priced with ceiling.ceiling(unpaid=...). A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/complex-local-word-ceiling/verify.py"
+            ],
+            "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING",
+            "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.",
+            "scope": "Positive control and planning budget only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Explain where the single unpaid coordinate per family comes from in the hosted template; propose one change and price it. Ideal budget: two unpaid coordinates per family is 3.77x (levers.py).",
+          "bottleneck_link": "The deficit is one coordinate per family minus the centre charge; doubling unpaid coordinates per family scales it directly.",
+          "allowed_variations": [
+            "One template change or one endpoint-contract change.",
+            "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+          ],
+          "scope_change_triggers": [
+            "Counting a coordinate as unpaid while leaving it unadvanced in the data endpoint.",
+            "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts."
+          ],
+          "overlap_terms": [
+            "coverage identity",
+            "unpaid coordinate",
+            "deficit law",
+            "W - 64N"
+          ]
+        },
+        {
+          "id": "connector-alphabet-change",
+          "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "research/universal-connector-boundary/README.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Construct and charge a legal extra operation on a minimal instance.",
+            "Prove a target-specific bound after adding one specified operation family."
+          ],
+          "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "research/universal-connector-boundary/verify.py"
+            ],
+            "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY",
+            "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.",
+          "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.",
+          "allowed_variations": [
+            "Choose one additional operation and a small source count for its first counterexample."
+          ],
+          "scope_change_triggers": [
+            "Keeping the alphabet and only increasing the source count; record this as a changed assignment.",
+            "Extending a source-count census without naming a supplier/interface decision it could change; audit #2973 pruning concerns before relying on the affected predecessor exclusions."
+          ],
+          "overlap_terms": [
+            "universal connector",
+            "source-toggle",
+            "connector alphabet"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "adversarial-audit",
+      "weight": 15,
+      "tasks": [
+        {
+          "id": "selected-stock-envelope",
+          "question": "What explicit uniform stock envelope does the actual selected stopped producer supply at one bootstrap stage?",
+          "starting_points": [
+            "research/selected-bootstrap-stock-audit/README.md",
+            "research/bootstrap-cutoff-time-space-split/README.md",
+            "certificates/selected-result.json",
+            "docs/research/community-efficient1000-review.md",
+            "research/stock-margin-chain/README.md"
+          ],
+          "methods": [
+            "Derive a source-bound reserve recurrence at the actual selected atom widths, separating parent stock from completed inner borrowing.",
+            "Find an exact missing implication or counterexample to a proposed selected-stage stock envelope."
+          ],
+          "acceptance_gate": "Bind every coefficient and depth factor to the selected producer and state the width domain. Compare a proved envelope with the sufficient cutoff guard; a large numerical headroom or a historical m=120 coefficient is not a selected m=73 proof.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #2972 stock-margin chain and the selected stock audit. The new source archive reports the remaining cutoff comparisons, but leaves every actual stock coefficient unresolved; it is not an independently validated reserve envelope.",
+            "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+          },
+          "first_experiment": "Choose one actual selected producer/stage and derive its parent reserve and depth coefficient from source. Check whether newer handoffs already cover that exact obligation. Stop with the missing implementation lemma if it cannot be bounded; do not rerun #2972 cutoff/headroom arithmetic as a new contribution.",
+          "bottleneck_link": "This reduces a concrete inherited implementation obligation without confusing unchanged kappa arithmetic with a completed theorem.",
+          "allowed_variations": [
+            "One stage or one explicit reserve/depth implication.",
+            "An independently checked same-domain proof repair, retaining all remaining assumptions."
+          ],
+          "scope_change_triggers": [
+            "Importing the historical 57604 or 252 allowance without a selected-producer binding.",
+            "Calling a conditional fit lemma a full outer-proof adoption.",
+            "Replacing an actual selected stock coefficient with cutoff comparisons or a conditional fit inequality."
+          ],
+          "overlap_terms": [
+            "selected stock",
+            "stock envelope",
+            "bootstrap cutoff",
+            "1956",
+            "1965",
+            "1990",
+            "2972",
+            "stock-margin-chain",
+            "actual_stock_coefficient"
+          ],
+          "existing_checks": [
+            {
+              "scope": "Retained stock audit identifies missing actual selected-stage coefficients; later cutoff-chain arithmetic does not supply them.",
+              "evidence": "docs/research/research-family-status.md#revision-6-handoffs-source-archives-awaiting-independent-validation",
+              "remaining": "Derive one actual reserve/depth coefficient from the selected producer.",
+              "status": "reviewed",
+              "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "supplier-boundary-audit",
+          "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-mixed-fourth-entry/README.md",
+            "research/scatter-boundary-decision/README.md"
+          ],
+          "methods": [
+            "Trace one hypothesis through the source, checker and complete caller.",
+            "Construct one semantically invalid but superficially well-formed fixture and test rejection."
+          ],
+          "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.",
+          "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.",
+          "allowed_variations": [
+            "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage."
+          ],
+          "scope_change_triggers": [
+            "Reporting the historical timing-only diagnostic as a new current acceptance bug.",
+            "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.",
+            "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass."
+          ],
+          "overlap_terms": [
+            "owner boundary",
+            "bridge omission",
+            "hosting",
+            "2977",
+            "scatter export",
+            "duplicate index",
+            "parity semantics",
+            "4088",
+            "3801",
+            "staged544-mixed-fourth-entry",
+            "scatter-boundary-decision"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #3801: successor scatter-boundary decision package.",
+              "evidence": "research/scatter-boundary-decision/README.md",
+              "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.",
+              "status": "author-checked",
+              "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "uniform-transfer-audit",
+          "question": "Does one quantified step of the proposed #4100 all-size construction hold at its actual caller?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/unconditional-batched-crt/README.md"
+          ],
+          "methods": [
+            "Prove one missing implication with explicit quantified hypotheses.",
+            "Find an exact counterexample at the claimed interface boundary."
+          ],
+          "acceptance_gate": "Identify the proposition and what would change downstream; do not equate a finite replay with a universal proof.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read PROOF.md and AUDIT.md in #4100. Select one distinct obligation: CRT total repair, native/free-algebra lifting, precision/conditioning, or complete fixed-tape cost. This is an author-submitted proof, not an accepted unconditional theorem.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Check live handoffs; name one proposition, its caller, quantified domain and dependency closure. Independently prove the implication or exhibit a precise gap/counterexample. Prioritize CRT.md total repair or COMPLEX.md free-algebra lift only if unclaimed. Stop at the chosen obligation; do not substitute finite samples or root arithmetic for an all-size proof, or launch the complete package by default.",
+          "bottleneck_link": "Finite supplier improvements are useful only under the retained transfer obligations.",
+          "allowed_variations": [
+            "One CRT repair, native lift, precision/conditioning or tape-cost proposition, with its exact caller."
+          ],
+          "scope_change_triggers": [
+            "Replacing a quantified obligation with another finite smoke test.",
+            "Treating archive intake, an author PASS receipt or a finite composed fixture as discharge of the universal hypotheses."
+          ],
+          "overlap_terms": [
+            "uniform transfer",
+            "all-size",
+            "precision",
+            "4100",
+            "unconditional-batched-crt"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4100: proposed unconditional construction and finite checks, without independent acceptance.",
+              "evidence": "research/unconditional-batched-crt/README.md",
+              "remaining": "Independent proof audit of one caller-bound all-size implication; all other premises remain explicit.",
+              "status": "author-checked",
+              "source_commit": "337d04939571a637aeab54a0f58f54fde811663a",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "census-pruning-audit",
+          "question": "Does the reported word-census parity-pruning error invalidate a specific exclusion we still rely on, and what bounded repair is justified?",
+          "starting_points": [
+            "research/f7-weight-parity-census-correction/README.md",
+            "docs/research/research-family-status.md"
+          ],
+          "methods": [
+            "Independently reconstruct the tiny counterexample and trace one affected exclusion to its exact pruning code.",
+            "Compare corrected and unpruned enumeration on a small exhaustive domain, then audit the changed pruning implication."
+          ],
+          "acceptance_gate": "Pin the old and proposed corrected engines, distinguish a disproved pruning rule from a disproved final bound, and state exactly which downstream exclusions need revalidation. #2973 is an author-checked source archive; neither its new f(7) claim nor all old conclusions are automatically accepted or rejected.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #2973 error description and MATH.md; manually reconstruct the prefix states of 01021323 before running any large census.",
+            "scope": "Source-binding orientation only; no full enumeration or mathematical validation."
+          },
+          "first_experiment": "Reconstruct the eight prefix states of 01021323 and compare bit-0 versus Hamming-weight parity budgets independently. Trace the reported false prune to one pinned predecessor (#2542, #2634 or #2691), then test a small exhaustive domain. Stop after a source-impact handoff or corrected-prune proof; a full seven-label replay needs a separate resource budget and a named research decision it can change.",
+          "bottleneck_link": "An unsound exclusion can wrongly close a mechanism; correcting its dependency boundary is more useful than extending the same census.",
+          "allowed_variations": [
+            "One predecessor pruning rule, one independently exhaustive small domain, or one downstream dependency audit."
+          ],
+          "scope_change_triggers": [
+            "Launching a larger census before validating the prune and explaining which active decision it changes.",
+            "Treating a small-domain counterexample to the old rule as a counterexample to every reported seven-label bound."
+          ],
+          "overlap_terms": [
+            "2973",
+            "2542",
+            "2634",
+            "2691",
+            "weight parity",
+            "bit-0",
+            "01021323",
+            "census pruning"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "independent-verification",
+      "weight": 10,
+      "tasks": [
+        {
+          "id": "independent-moment",
+          "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-mixed-fourth-entry/README.md",
+            "research/staged-fourth-mixture-ceiling/README.md",
+            "research/r437-two-window-carrier/README.md"
+          ],
+          "methods": [
+            "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+            "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+          ],
+          "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+          "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+          "allowed_variations": [
+            "Reconstruct either a source ledger or a numeric enclosure with a different method."
+          ],
+          "scope_change_triggers": [
+            "Importing the primary function and calling its output independent verification.",
+            "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+          ],
+          "overlap_terms": [
+            "independent moment",
+            "rank histogram",
+            "exact enclosure",
+            "2979",
+            "rank7 joint endframes",
+            "paired extraction",
+            "joint lowering",
+            "4088",
+            "4091",
+            "4067",
+            "staged544-mixed-fourth-entry",
+            "staged-fourth-mixture-ceiling",
+            "r437-two-window-carrier"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+              "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+              "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+              "status": "author-checked",
+              "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+              "evidence": "research/r437-two-window-carrier/README.md",
+              "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+              "status": "author-checked",
+              "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "formal-interface-lemma",
+          "question": "Can one uncovered interface implication be formalized with exact caller and certificate bindings?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/gate-operand-parity-lean/README.md",
+            "research/staged544-certified-endpoint/README.md",
+            "research/unconditional-batched-crt/README.md"
+          ],
+          "methods": [
+            "Formalize a missing boundary lemma identified by the selected review.",
+            "Audit a formal theorem-to-certificate binding independently."
+          ],
+          "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Inventory the gate-operand parity lemma (#3807) and certified endpoint arithmetic (#3857). Neither is a full multiplication proof. For #4100, audit the compact-switch statement and its hypotheses before formalizing it.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.",
+          "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.",
+          "allowed_variations": [
+            "Narrow to one formal lemma or one theorem-to-certificate binding."
+          ],
+          "scope_change_triggers": [
+            "Formalizing already-covered arithmetic and claiming the full multiplication theorem."
+          ],
+          "overlap_terms": [
+            "hyperplane end",
+            "formal interface",
+            "Lean binding",
+            "3807",
+            "3857",
+            "4100",
+            "gate-operand-parity-lean",
+            "staged544-certified-endpoint",
+            "unconditional-batched-crt"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #3807: scoped gate-operand parity formalization.",
+              "evidence": "research/gate-operand-parity-lean/README.md",
+              "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.",
+              "status": "author-checked",
+              "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #3857: certified real-power moment/endpoint arithmetic.",
+              "evidence": "research/staged544-certified-endpoint/README.md",
+              "remaining": "Uniform algorithmic implications, not another endpoint digit.",
+              "status": "author-checked",
+              "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4100: compact-switch formalization proposed as future validation.",
+              "evidence": "research/unconditional-batched-crt/README.md",
+              "remaining": "Audit the statement and assumptions before a formal proof campaign.",
+              "status": "author-checked",
+              "source_commit": "337d04939571a637aeab54a0f58f54fde811663a",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    },
+    {
+      "id": "verifier-engineering",
+      "weight": 8,
+      "tasks": [
+        {
+          "id": "replay-runtime",
+          "question": "Can one measured replay bottleneck be sped up without dropping coverage?",
+          "starting_points": [
+            "scripts/run_isolated_tests.py",
+            "scripts/verify_replay_coverage.py",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Profile one isolated replay and optimize the measured bottleneck.",
+            "Design source-bound reuse with explicit dependency invalidation and negative controls."
+          ],
+          "acceptance_gate": "Report before/after wall time on the same fixture, retained checks and invalidation behavior.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the selected reproduction command and choose a single replay stage for profiling.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Measure one unchanged fixture, preserve check coverage, and test one optimization with invalidation controls.",
+          "bottleneck_link": "Faster trustworthy replays increase review throughput and let mechanism candidates be checked sooner.",
+          "allowed_variations": [
+            "Profile one stage or design one source-bound cache boundary."
+          ],
+          "scope_change_triggers": [
+            "Skipping coverage or comparing different fixtures to claim speedup."
+          ],
+          "overlap_terms": [
+            "replay runtime",
+            "cache invalidation",
+            "isolated tests"
+          ]
+        },
+        {
+          "id": "portable-replay",
+          "question": "Can one reproducible environment or artifact-comparison failure be repaired?",
+          "starting_points": [
+            "research/gzip-container-reproducibility/README.md",
+            "docs/ci-verification.md"
+          ],
+          "methods": [
+            "Reproduce one portability failure and add a minimal cross-environment fix.",
+            "Audit one canonical-payload comparison for omitted proof-relevant fields."
+          ],
+          "acceptance_gate": "Preserve immutable source hashes and proof-relevant content; a different compressed byte stream alone is not a mathematical mismatch.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the gzip-container reproducibility examples and distinguish frozen source bytes from regenerated payloads.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Reproduce one specific mismatch or audit one canonical comparison for omitted proof-relevant fields.",
+          "bottleneck_link": "Portable exact checks prevent environment failures from blocking valid contributions.",
+          "allowed_variations": [
+            "One interpreter/version mismatch or one payload field comparison."
+          ],
+          "scope_change_triggers": [
+            "Removing immutable-source pins because generated compressed bytes differ."
+          ],
+          "overlap_terms": [
+            "gzip container",
+            "reproducibility",
+            "canonical payload"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "consolidation",
+      "weight": 5,
+      "tasks": [
+        {
+          "id": "overlap-receipt",
+          "question": "What exact content and credit of a small named PR set has already been retained?",
+          "starting_points": [
+            "docs/research/pr-ledger.md",
+            "CONTRIBUTORS.md"
+          ],
+          "methods": [
+            "Compare exact heads and retained artifacts to write a source-bound disposition receipt.",
+            "Audit an existing receipt for missing content or predecessor attribution."
+          ],
+          "acceptance_gate": "Separate complete integration, partial retention and changed heads; make no autonomous closures.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read one small PR set in the ledger and identify exact reviewed heads and unresolved content.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Compare that set to retained artifacts; produce a complete or explicitly partial disposition receipt.",
+          "bottleneck_link": "Reliable overlap evidence preserves credit and prevents repeated review of already-retained material.",
+          "allowed_variations": [
+            "One small related PR family or one existing integration receipt."
+          ],
+          "scope_change_triggers": [
+            "Treating matching titles or one shared blob as proof of full incorporation."
+          ],
+          "overlap_terms": [
+            "overlap receipt",
+            "partial integration",
+            "attribution"
+          ]
+        },
+        {
+          "id": "scope-navigation",
+          "question": "Can one misleading historical-current claim or missing research cross-reference be corrected?",
+          "starting_points": [
+            "docs/research/current-status.md",
+            "docs/research/pr-ledger.md",
+            "certificates/selected-result.json"
+          ],
+          "methods": [
+            "Trace one confusing path from onboarding to its authoritative source.",
+            "Index one tightly related family of obstructions with explicit excluded and open hypotheses."
+          ],
+          "acceptance_gate": "Produce evidence-backed navigation, preserve historical records and avoid a duplicate global survey.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Follow one link from the selected record to its review and compare a potentially stale historical claim.",
+            "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+          },
+          "first_experiment": "Repair one confusing path or produce a scoped map of one related obstruction family.",
+          "bottleneck_link": "Clear navigation lowers entry cost for central research; a global survey without a concrete fix is not required.",
+          "allowed_variations": [
+            "One historical-current ambiguity or one bounded family index."
+          ],
+          "scope_change_triggers": [
+            "Rewriting frozen scientific packages just to change their historical wording."
+          ],
+          "overlap_terms": [
+            "current status",
+            "historical checkpoint",
+            "scope navigation"
+          ]
+        }
+      ]
+    },
+    {
+      "id": "incumbent-optimization",
+      "weight": 2,
+      "tasks": [
+        {
+          "id": "selected-packing",
+          "question": "Does a named residual packing task have meaningful uncovered headroom after its exact fixed-inventory ceiling?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged-fourth-mixture-ceiling/README.md",
+            "research/staged544-mixed-fourth-entry/README.md"
+          ],
+          "methods": [
+            "Check a fixed-inventory ceiling and source equivalence before any explicitly bounded residual search.",
+            "Price a genuinely changed word/interface under a newly applicable model."
+          ],
+          "acceptance_gate": "Check live overlap and exact model/source binding first. Distinguish a chronological construction from a pooled optimum. State the applicable fixed-inventory ceiling and remaining headroom; changed words or interfaces require a new fully charged model. Do not launch a residual search without an explicit scope and time cap.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read #4091 fixed-word pooled ceiling and #4088 later 1090-call literal fill. Bind the unchanged local invoices/capacities/stock before transferring the ceiling; its earlier 1080-call residual-bin recipe is historical.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Default to a bounded headroom/source-equivalence check. Only start residual search with an explicit unclaimed domain, time cap and reason the tiny remaining gain matters. Otherwise hand off or select a changed-word mechanism. A changed word or interface needs a fresh cost model, not the old ceiling. Stop at the fixed-inventory cap; do not extend by new random seeds.",
+          "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+          "allowed_variations": [
+            "One bounded residual packing instance or exact relaxation.",
+            "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+          ],
+          "scope_change_triggers": [
+            "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+          ],
+          "overlap_terms": [
+            "T16",
+            "owner exchange",
+            "packing",
+            "4091",
+            "4088",
+            "staged-fourth-mixture-ceiling",
+            "staged544-mixed-fourth-entry"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #4091: pooled optimum at one-third staging for pinned fixed words; not a chronological fill.",
+              "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+              "remaining": "Independent scope/source check; any residual optimization is explicitly bounded and optional.",
+              "status": "author-checked",
+              "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4088: later 1090-call literal fill improves the earlier 1080-call witness.",
+              "evidence": "research/staged544-mixed-fourth-entry/README.md",
+              "remaining": "Complete admission remains separate; old residual-bin instructions must not be copied blindly.",
+              "status": "author-checked",
+              "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        },
+        {
+          "id": "scalar-to-moment",
+          "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?",
+          "starting_points": [
+            "docs/research/research-family-status.md",
+            "certificates/selected-result.json",
+            "research/staged544-a2-graph-rewrite/README.md",
+            "research/staged544-separated-a2/README.md",
+            "research/staged544-a2-composition-audit/README.md",
+            "research/staged544-a1858-contraction-audit/README.md"
+          ],
+          "methods": [
+            "Derive the changed legal frame itinerary and exact child histogram.",
+            "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+          ],
+          "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+          "first_step": {
+            "command": [
+              "python3",
+              "-B",
+              "scripts/research_baseline.py"
+            ],
+            "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+            "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.",
+            "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+          },
+          "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.",
+          "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+          "allowed_variations": [
+            "One existing scalar simplification and one proposed frame-path change."
+          ],
+          "scope_change_triggers": [
+            "Submitting only another scalar count as completion of a paid-profile task."
+          ],
+          "overlap_terms": [
+            "scalar simplification",
+            "paid profile",
+            "R439",
+            "3998",
+            "4019",
+            "4112",
+            "4152",
+            "staged544-a2-graph-rewrite",
+            "staged544-separated-a2",
+            "staged544-a2-composition-audit",
+            "staged544-a1858-contraction-audit"
+          ],
+          "existing_checks": [
+            {
+              "scope": "PR #3998: consecutive A2 scalar contraction",
+              "evidence": "research/staged544-a2-graph-rewrite/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+              "evidence": "research/staged544-separated-a2/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4112: composition audit",
+              "evidence": "research/staged544-a2-composition-audit/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            },
+            {
+              "scope": "PR #4152: A1858 contraction audit",
+              "evidence": "research/staged544-a1858-contraction-audit/README.md",
+              "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+              "status": "author-checked",
+              "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+              "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+            }
+          ]
+        }
+      ]
+    }
+  ],
+  "selection_context": {
+    "refreshed_on": "2026-10-22",
+    "kappa": "60403/20000000",
+    "source_pr": 4470,
+    "record": "certificates/selected-result.json",
+    "review": "docs/research/pr-intake-evidence/pr4470/PROOF-REVIEW.md",
+    "orientation_command": "python3 -B scripts/research_selected_baseline.py",
+    "scope": "Metadata refresh only. Revision-7 weights and cards remain historical suggestions pending separate strategic reassessment; check current contracts and overlap before adopting them."
+  }
+}
diff --git a/research/fanout-optimality-support/evidence/RECEIPT.json b/research/fanout-optimality-support/evidence/RECEIPT.json
new file mode 100644
index 0000000000..ef1355f657
--- /dev/null
+++ b/research/fanout-optimality-support/evidence/RECEIPT.json
@@ -0,0 +1,25 @@
+{
+  "schema": "serial-research-run/v1",
+  "command": [
+    "python3",
+    "-B",
+    "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+    "--input",
+    "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+    "--program",
+    "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json",
+    "--result",
+    "race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json"
+  ],
+  "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453",
+  "exit_code": 0,
+  "termination": null,
+  "elapsed_seconds": 4.130925373989157,
+  "sampled_peak_descendant_rss_bytes": 32763904,
+  "rss_samples": 41,
+  "memory_limit_mib": 256,
+  "timeout_seconds": 30.0,
+  "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]",
+  "log_sha256": "8b8bd05d6e5557fac33e8a5a3d077ca99f21172c35785e0b2a09df5a82db386e",
+  "scope": "Fresh command execution only; scientific claim determined by reviewed output."
+}
diff --git a/research/fanout-optimality-support/evidence/stdout.log b/research/fanout-optimality-support/evidence/stdout.log
new file mode 100644
index 0000000000..9173c2a056
--- /dev/null
+++ b/research/fanout-optimality-support/evidence/stdout.log
@@ -0,0 +1 @@
+{"leftcoset_count": 112, "program_counts": {"ADD": 672, "CLEAR": 249, "COPY": 8, "GAUSSIAN": 112, "MONOMIAL": 344, "ZERO_RETAG": 249}, "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7", "query_savings_vs112": 0, "rationalrank_sum_Qqueries": 112, "scalar_tariff": 6114, "status": "PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION"}
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md
new file mode 100644
index 0000000000..3bb835718f
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md
@@ -0,0 +1,201 @@
+# Exact q-inverse W fanout: construction and cost contract
+
+Status: **STATIC_METHOD_READY; ACTUAL_GROUP_COST_AWAITS_ROOT_RUN**.
+
+This contract specifies one executable upper-bound construction for all 112 rows of one source map `q^-1 W_s` on eight arbitrary whole-field sources. It is not another 35-class lower-bound test. The required result is an emitted literal program, its exact paid/ordinary/owned bill, and certificates for every source row. The actual cost is the sum of the rational row ranks within the complete exact left-monomial classes. It is not merely the number of classes.
+
+The construction builder owns `lanes/construction/coset-fanout/`. Root alone executes the bounded checker. This adviser has performed no classifier, matrix-rank census, scientific execution, pricing, feed lookup or new delegation. No numerical grouped-query count is claimed here. A direct per-row construction already supplies the conservative upper bound of at most112 H1 calls; the grouped program must demonstrate any improvement over it.
+
+## One frozen source and interface
+
+Use the #5402 source at `3348fccea855082786d5f0fc5558b73d4974e745` and these files, relative to the shared project root:
+
+| Source | SHA256 |
+|---|---|
+| `swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json` | `ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da` |
+| `swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json` | `676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65` |
+| `swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md` | `2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5` |
+
+Extract the complete `Kp_p` word from `NORMALIZERS.ports[p].K_word`, for p=0..111. Set `M[p,j]=NORMALIZERS.mode_columns[j][p]`, for j=0..7; the stored matrix is transposed relative to the displayed W formula. Extract the eight exact Km words from the provider's `mode_boundaries[j].input_K`, binding each mode index explicitly. The source's boundary factor2 must NOT be included in Km here. The exact map being implemented is
+
+```text
+W_p h = Kp_p^-1 sum_j M[p,j] Km_j h_j / 2,
+(q^-1 W h)_p = A_p sum_j M[p,j] b_j / 2,
+A_p = q^-1 Kp_p^-1,
+b_j = Km_j h_j.
+```
+
+The single emitted interface is the shear
+
+```text
+y_p <- y_p + (q^-1 W_s h)_p,    p=0..111,
+h_j unchanged at EVERY instruction, j=0..7.
+```
+
+All y and h fields are arbitrary independent original fields. They are disjoint from each other and from17 declared owned fields. The owned fields have arbitrary entry dirt and must all return zero. This creates no productive input or target from scratch. A caller asking for `q^-1 W_s q h` must separately supply and charge the actual qh version; this contract does not grant eight input queries for free.
+
+The one-column classification dimension is9. Its stage embedding into the common25-axis ABI maps the central coordinate to axis0 and the other eight coordinates to the chosen stage's eight fresh axes, with identity action on all other axes. The exact embedding must be emitted and bound. No 2^25 dense matrix is required.
+
+## Exact left-monomial classes
+
+Use
+
+```text
+p ~ r  iff  L_p,r := A_p A_r^-1
+                 = q^-1 Kp_p^-1 Kp_r q
+                 is a computational-basis monomial operator.
+```
+
+This is LEFT equivalence: a valid alias satisfies `A_p = L_p,r A_r`. A right alias would require a different input-program factorization and is not licensed here.
+
+Represent a Pauli as `i^phase X^x Z^z`, including its phase modulo4. Obtain each A_p's signed Clifford tableau from the literal source words. Let Z0 denote the nine-dimensional diagonal Pauli subspace `{(0,z)}`. With S_A the binary symplectic action of conjugation by A, the deterministic class key is
+
+```text
+canonical binary RREF basis of S_Ap^-1 Z0.
+```
+
+The key is a nine-plane in18 binary coordinates. Equal keys are equivalent to `S_Ap S_Ar^-1` preserving Z0, hence to `A_p A_r^-1` being monomial. Indeed a unitary preserving the diagonal Pauli algebra sends its simultaneous one-dimensional eigenspaces to each other, so it permutes computational basis vectors up to phases. Conversely every computational-basis monomial preserves that algebra. Signs do not affect class membership, but they do affect the required emitted alias.
+
+This proves a complete classifier, not merely a necessary central-image test. The earlier 35 distinct central images may be retained as an optional sanity witness; they must not replace the full112-row classification or the rank calculation. Every source port must occur in exactly one class. Use a deterministic representative, such as the smallest port index in each class.
+
+For each p in the class of representative r, compile L_p,r into a literal source-compatible monomial word. One canonical chronological form is
+
+```text
+D(Q,alpha); P(G); X(b); phase(gamma).
+```
+
+The displayed chronological word represents `i^gamma X_b P_G D(Q,alpha)`. Emit G, b, the symmetric quadratic data Q, linear Z4 coefficients alpha, and the exact global phase gamma. Validate all source parity/invertibility constraints and the full signed tableau. Equality merely up to global phase is a rejection.
+
+The monomial predicate is equivalent to every image of Z_j having zero X part; its Hermitian phase must then be even. That predicate alone does not provide the alias's absolute phase. A matching complete signed tableau plus one exact nonzero state-column anchor proves full operator equality, since two operators with identical Pauli conjugation differ by a scalar. Prefer the additional direct audit of ALL512 base computational columns for every accepted alias. The source-specific word `q^-1 Kp_p^-1 Kp_r q` has at most four terms per column, so this audit need not store a512-by512 dense matrix.
+
+The required literal identities are `L_p,r = A_p A_r^-1` and therefore `L_p,r A_r = A_p`. Do not classify from `A_p|0>` alone. Here the inherited Kp words fix the zero address with phase0; many distinct A_p have exactly the same zero column, making that shortcut particularly unsafe.
+
+## Scalar basis: integer certificates avoid new odd divisions
+
+For one class C, let M_C be its m-by8 integer row matrix, retaining the original port ordering. Its rational rank is r_C<=min(m,8). The factor1/2 is kept outside this matrix and does not change its rank.
+
+The preferred basis is an integer basis of the row lattice generated by M_C. An extended-gcd row-Hermite procedure can emit integer unimodular matrices U,V with
+
+```text
+U V = V U = I_m,
+U M_C = [ H_C ; 0 ],
+H_C = S_C M_C,       S_C = first r_C rows of U,
+M_C = T_C H_C,       T_C = first r_C columns of V.
+```
+
+Require H_C to have r_C independent rows and verify r_C against exact rational rank. Verify all displayed integer equalities independently of the basis-generation procedure. This guarantees both that the queries span precisely the required row space and that all recovery coefficients T_C are integers. No runtime Hermite algorithm or division by a pivot is part of the emitted field program.
+
+For each basis row l, form the whole-field input
+
+```text
+u_l = sum_j H_C[l,j] b_j.
+```
+
+Apply A_r once to each u_l. Then reconstruct port p in C using
+
+```text
+(q^-1 W h)_p
+ = L_p,r sum_l (T_C[p,l]/2) A_r u_l.
+```
+
+This is a constructive program with exactly r_C H1 calls for that class. It does not pack several independent fields into one query: r_C independent scalar forms receive r_C separate calls.
+
+An original-row basis with rational recovery weights would also give a formal algebraic factorization, but any odd denominators would require a newly implemented and charged arithmetic contract. The frozen construction should use the integer certificate above, whose runtime coefficients are integers for input preparation and integer halves for recovery. Do not silently introduce DIV3, DIV7, DIV13 or an expanded source grid. Exact Fraction arithmetic used by the checker is not a runtime field operation.
+
+Coefficient growth matters. Emit the complete H and T matrices, maximum integer bit lengths, and a cap on the fully lowered instruction count. Exceeding the cap is a reported construction/resource failure, not permission to truncate, omit large coefficients, widen a search or claim a completed program. The source permits a fixed finite ordinary program; it does not make large coefficients or precision growth free.
+
+## One explicit owned-field schedule
+
+The agreed copy variant uses17 reusable owned fields:
+
+```text
+b0..b7       eight common normalized-input copies,
+t0..t7       up to eight queried basis fields for one class,
+z            one port-reconstruction field.
+```
+
+All17 receive entry CLEAR and zero-retag before use. They are disjoint from originals and every live caller cache or helper bank. At entry COPY h_j into zero b_j and apply the exact Km_j word. h is never normalized in place.
+
+Process classes sequentially. For a class of rank r_C:
+
+1. Form each u_l in zero t_l using repeated unit ADDs with sign from H_C[l,j], reading the unchanged b_j. This is an explicit lowering of integer coefficients, not an uncharged arbitrary-scalar operation.
+2. Apply the literal inverse Kp_r word to t_l, then one positive central Q child, then the phase-zero central X word implementing q². The resulting array is exactly `q^-1 Kp_r^-1 u_l`. The last X is ordinary but charged. No second paid child is used for the inverse.
+3. For each nonzero row p in the class, form `z=sum_l (T_C[p,l]/2)t_l` using repeated signed half-ADDs. Apply the exact phase-bearing L_p,r word to z. Execute the unit ADD `y_p += z`. CLEAR and zero-retag z after this read.
+4. After every port in that class has read the queried basis, CLEAR and zero-retag t0..t(r_C-1). Their next class use starts from actual zero. The unused t fields stay zero.
+
+After the last class, CLEAR and zero-retag all eight b fields. Every original h is unchanged, each original y has received its prescribed row once, and all17 arbitrary owned directions are zero at exit. Zero source rows require no target update. No live nonzero field receives a zero-retag.
+
+The program is a pure source fanout, so y updates cannot change later queries: all query inputs depend only on the read-only h copies. An actual caller must bind the physical h version, y destination version, source/owned IDs and lifetime placement before using this component. This note does not borrow the17 fields from occupied source scratch.
+
+## Exact bill to emit
+
+Let
+
+```text
+C = sum_C r_C,
+N = number of nonzero source rows M[p,:],
+H_abs = sum_C sum_l,j |H_C[l,j]|,
+T_abs = sum_C sum_p,l |T_C[p,l]|.
+```
+
+For the fixed schedule above, using one record per whole-field monomial word and retaining identity aliases as explicit records if present:
+
+| Item | Exact count |
+|---|---:|
+| Paid positive H1 | C |
+| Ordinary inverse-Q central-X maps | C |
+| Km input monomial maps | 8 |
+| Kp representative inverse monomial maps | C |
+| Left alias monomial maps | N |
+| Owned COPY | 8 |
+| Unit ADDs for query preparation | H_abs |
+| Half-ADDs for recovery | T_abs |
+| Unit ADDs into original targets | N |
+| CLEAR | 25+C+N |
+| Zero-retag | 25+C+N |
+| Peak additional owned fields | 17 |
+
+The CLEAR count is17 at entry, C queried-field returns, N reconstruction-field returns, and8 normalized-input returns. Emit primitive monomial gate counts separately from whole-field map counts, and retain every phase word. If the emitter omits proven identity maps, report the actual reduced bill with that exact omission policy; do not mix its count with the conservative table.
+
+At a fixed whole-field capacity, the emitted Gaussian upper bound is C. Since r_C is at most the number of nonzero rows in its class, C<=N<=112. Singleton classes with H=M[p,:] and recovery1 supply the conservative direct program independently of any sharing claim. The actual root result must print the full class sizes/ranks, C, H_abs, T_abs, maximum coefficient size, and the literal program's independently recounted bill. A class count by itself is insufficient.
+
+This is an upper construction and the exact bill of this program. It is not a lower bound for layered query circuits, operator-valued cross-class cancellation, changed source versions, cached paid values or a different complete caller. The old three-call34/42.5 moment allowances are not applied here. Any global120 termination budget and actual occurrence multipliers belong to a later complete invoice.
+
+## All-width proof, including absolute phases
+
+At one source column, the positive Q gate is
+
+```text
+q|x> = ((1+i)/2)|x> + ((1-i)/2)|x xor e0>,
+q^-1|x> = ((1-i)/2)|x> + ((1+i)/2)|x xor e0>.
+```
+
+These formulas are permitted for the finite one-column classifier and its sparse exact column checks. They are NOT a whole-field two-term implementation for arbitrary fiber width f. The physical `q_f^-1` is the columnwise tensor product of the one-column gate and has2^f support per central row. One positive paid Q_f followed by the columnwise X_f implements it because `q_f²=X_f`.
+
+The source proof §5 fixes the lift: P and X act columnwise, D sums its Z4 polynomial over columns, and a phase gate gamma contributes `i^(f gamma)`. Consequently an alias identity `A_p=L_p,r A_r` checked as an exact9-axis one-column operator lifts, after the declared stage embedding and spectator identities, to
+
+```text
+A_p,f = L_p,r,f A_r,f
+```
+
+for every positive f. Its absolute phase is part of L_p,r,f. It must not be replaced by an exterior scalar `i^gamma`, nor folded into a rational recovery coefficient. In particular a source phase2 is `(-1)^f`, whereas an ordinary negative ADD coefficient is the exterior scalar -1 applied once.
+
+The finite owner matrices H_C, T_C and M_C and the scalar1/2 remain OUTSIDE the tensor product. For arbitrary whole-field inputs,
+
+```text
+L_p,r,f sum_l (T_C[p,l]/2) A_r,f (sum_j H_C[l,j] b_j)
+ = sum_j ((T_C H_C)[p,j]/2) L_p,r,f A_r,f b_j
+ = A_p,f sum_j (M[p,j]/2) Km_j,f h_j.
+```
+
+This is the uniform lift proof. It uses linearity of the whole-field operators after each individual operator identity has been lifted; it does not tensor a scalar sum, raise a source coefficient to f, or expand q into two whole-field monomials. Inactive axes are identity factors, so the same proof holds on arbitrary25-axis fields without a dense25-axis evaluation.
+
+## Required bounded checker output and controls
+
+The builder should freeze the checker, input manifest and deterministic emission policy before root's one run, with the agreed30-second/256-MiB cap. It must not import or run the source author evaluator. Static source parsing, a fresh exact signed-tableau/column implementation, integer/Fraction matrix certificates and a literal owner-lifetime counter suffice.
+
+The output must contain all112 source row IDs; every class key and representative; each member's exact L word, signed tableau and absolute phase/full-column receipt; M_C,H_C,S_C,T_C and U,V certificates; all basis preparation and per-port recovery records; the source/stage hashes; the complete literal shear program; exact paid/ordinary/owned counts; and the all-width scope above. It must retain arbitrary original y/h columns and arbitrary owned entry directions, with strict source read-only and complete owned zero return. No result may depend on dropping a source row with an inconvenient phase or coefficient.
+
+Required negative controls include: grouping from one impulse only; a nonmonomial pair incorrectly merged; reversed left/right alias order; altered alias absolute phase despite unchanged tableau; wrong Kp inverse or Q sign; omitted inverse-Q X; a dropped or transposed M coefficient; altered basis/recovery coefficient; tensoring an exterior1/2; treating a per-column phase as an exterior scalar; omitted dirty-entry CLEAR; writing an original h; and premature query-field CLEAR. A small f=2 witness distinguishes the illegal two-term whole-field Q shortcut and exterior/columnwise scalar confusion without constructing a2^25 matrix.
+
+Only a root-executed complete PASS can establish the actual grouped upper count and program component. It will still not establish source precision/tape realization, caller storage compatibility, a full decoder, funding or a new kappa. Source notices and predecessor credit remain inherited; this contract adds only the explicit grouping, integer-basis realization and resource certificate requirements.
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-MODULE-LOWER-v1.md b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-MODULE-LOWER-v1.md
new file mode 100644
index 0000000000..9deb79ed06
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-MODULE-LOWER-v1.md
@@ -0,0 +1,207 @@
+# Proposed module lower bound for the fixed all-width fanout grammar
+
+Status: **PROPOSED_STATIC_PROOF_PENDING_INDEPENDENT_REVIEW**.
+
+The proposed argument is valid under the precise grammar below. It extends the class-rank bound beyond a single query layer to arbitrary finite feedback among Gaussian field calls. The essential device is the formal group algebra represented faithfully by the ENTIRE all-width tensor family, not the algebra spanned by width-one matrices. Zero divisors in the ordinary group algebra do not invalidate the argument.
+
+No classifier, rank calculation, mathematical evaluator, census, pricing, new agent or scientific run was executed by this adviser. Root has now executed the separately prepared upper-program checker. This note reads and binds that receipt but does not reinterpret its PASS as validation of the new lower-bound proof.
+
+## Source-bound numerical specialization, kept separate from this proof
+
+The previous static construction contract remains unchanged at SHA256 `ead89d4f96531d96f38ae7103b99eabef35768b2e57e7a173ce482048092e206`, in `EXACT-FANOUT-COST-CONTRACT-v1.md`.
+
+The root-executed artifacts are under `lanes/construction/coset-fanout/`, relative to `race-kappa0033-sol-high-20261024`:
+
+| Artifact | SHA256 |
+|---|---|
+| `FANOUT-RESULT-v1.json` | `bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7` |
+| `FANOUT-PROGRAM-v1.json` | `5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7` |
+| `FANOUT-INPUT-v1.json` | `f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb` |
+| `check_emit_fanout_v1.py` | `b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3` |
+
+The result reports `PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION`, 112 source rows, 112 distinct monomial-equivalence classes, and rational-rank sum C=112. Each class is a singleton with a nonzero coefficient row. The emitted upper program uses112 H1 calls. Its stated scope is an upper program and cost, with no universal-minimum claim.
+
+The following theorem uses a symbolic C. If its independent review accepts the grammar and lemma chain, this receipt specializes the lower bound to112 Gaussian field calls for this standalone fanout. It would match the emitted112-H1 upper bound in that grammar. The receipt alone does not prove the theorem, and neither result transfers automatically to a global caller or an incremental termination budget.
+
+## 1. Exact grammar and target
+
+Fix a finite one-column coordinate space V over K=Q(i), with one-column address dimension n fixed independently of fiber width f. For the supplied program n=25, with the nine source coordinates embedded in the declared stage axes. Up to the fixed address-layout permutation, every whole field at width f belongs to V tensor-powered f times.
+
+The ordinary address gates are the fixed source columnwise unit monomials: binary P maps, X translations, Z4 diagonal-polynomial D gates, and per-column fourth-root phases. They generate a finite group G. One may conservatively enlarge G to all computational-basis monomial matrices on V with fourth-root entries; that group is still finite and contains every allowed source ordinary address gate. This enlargement does not turn a nonmonomial operator into a monomial operator.
+
+All other ordinary operations are K-linear whole-field ADDs, COPYs, uniform exterior scalar multiplications, and CLEARs. Coefficients and the finite straight-line program are fixed independently of f. The program may use arbitrary fixed numbers of known-zero or arbitrary-dirty owned fields; may overwrite, copy, clear, reuse or preserve intermediates; and may feed earlier paid outputs into later paid inputs. Arbitrary positive-rank Gaussian field calls are permitted, each applying one invertible fixed one-column operator lifted columnwise to ONE whole field of the declared capacity. Ordinary pre/post maps and an unchanged copy of the input do not create an additional paid output row.
+
+Let H be the subgroup of GL(V,K) generated by G and every allowed paid one-column operator and its inverse. H need not be finite. Including inverses in this ambient group is algebraic bookkeeping, not a free implementation of them.
+
+All genuine original input fields are arbitrary and jointly independent. The target contains the112 rows
+
+```text
+y_i' = y_i + f_i(h),
+f_i(h) = A_i sum_j M[i,j] Km_j h_j / 2,
+A_i = q^-1 Kp_i^-1,
+```
+
+where M is the pinned rational112-by8 matrix, the eight Km_j and all Kp_i belong to G, and the same Km_j is used for that input column in EVERY row. Arbitrary ordinary signed or monomial backgrounds in place of y_i are also covered, provided each background lies in the ordinary span of the initial input rows. Other final outputs do not weaken the required equations above.
+
+Define classes by
+
+```text
+i ~ r  iff  A_i A_r^-1 is in G,
+equivalently A_i belongs to G A_r.
+```
+
+These are orbits under LEFT multiplication by ordinary monomials. In standard group terminology, sets G A_r are RIGHT cosets of the subgroup G. This note uses the explicit notation G A_r to avoid reversing the module orientation. For each class C_alpha, let r_alpha be the rational rank of its scalar row matrix M_alpha, and put `C=sum_alpha r_alpha`.
+
+For this source every A_i is outside G: if `q^-1 Kp_i^-1` were monomial, multiplying on the right by the monomial Kp_i would make q^-1 monomial. Its actual one-column Gaussian has two nonzero entries per column, so that is impossible. Classes with rank0 would contribute0.
+
+## 2. Faithfulness of the all-width tensor family
+
+For h in H, write [h] for a BASIS ELEMENT of the formal group algebra K[H]. Define
+
+```text
+Phi_f([h]) = h tensor-powered f times,
+Phi_f(sum_h c_h [h]) = sum_h c_h (h tensor-powered f times).
+```
+
+The scalar c_h is exterior and applied once. Each Phi_f is a K-algebra homomorphism, because tensor powers preserve operator products. The combined map over all positive f is injective on K[H].
+
+Proof: take distinct nonzero matrices h_1,...,h_t and suppose
+
+```text
+sum_j c_j h_j^(tensor f) = 0  for every f>=1.
+```
+
+Since K is infinite, choose a K-linear functional ell on End(V) such that the values `lambda_j=ell(h_j)` are nonzero and pairwise distinct. The excluded choices form only finitely many proper hyperplanes. Apply ell tensor-powered f times to the operator identity. For f=1,...,t this gives
+
+```text
+sum_j c_j lambda_j^f = 0.
+```
+
+The matrix of these equations has determinant, up to sign,
+
+```text
+(product_j lambda_j) (product_{a<b}(lambda_b-lambda_a)),
+```
+
+which is nonzero. Hence every c_j=0. This proves injectivity. No finiteness of H is required; each group-algebra element has finite support.
+
+The source address layout may conjugate every tensor-powered operator by the same fixed layout permutation at width f. That does not change the proof. The declared stage embedding adds identity spectator factors and likewise preserves it.
+
+This is the crucial distinction from the width-one matrix algebra. At width1, `q=aI+bX` is a valid matrix equality. It is NOT the group-algebra identity `[q]=a[I]+b[X]`: at width f the left side becomes q^(tensor f), whereas the right side remains `a I^(tensor f)+b X^(tensor f)`. A two-term width-one expansion cannot be substituted into a fixed all-width program.
+
+Likewise `[iI]` and `i[I]` are different group-algebra elements. Their evaluations are respectively `i^f I` and `i I`. The source phase prescription is exactly the first for a phase gate, while exterior scalar multiplication is exactly the second. Using the actual width-one matrix span instead of formal K[G] would collapse these distinctions and invalidate the proposed lower bound.
+
+Because the target equality holds on all independent original fields, it gives a separate operator equality for every input column at every f. The injectivity lemma therefore promotes each such equality to an equality in K[H], component by component.
+
+## 3. One paid field call adds at most one ordinary module generator
+
+Set `R=K[G]` as a formal group algebra. Its K-dimension is the finite positive integer |G|. Let N count all independent initial input coordinates, including arbitrary owned dirt if present. Known-zero owned fields have row0 and need no new input coordinate.
+
+Represent every field at every point of the fixed program by a row in `K[H]^N`. Initially the independent rows are the coordinate vectors e_1,...,e_N. Define the conceptual history module to retain ALL initial rows and ALL paid output rows, even after their physical fields have been overwritten or cleared.
+
+Before any paid call, ordinary operations keep each current row in the left R-module
+
+```text
+I = R e_1 + ... + R e_N = R^N.
+```
+
+After k paid calls, let t_1,...,t_k be their actual output rows and define
+
+```text
+M_k = I + R t_1 + ... + R t_k.
+```
+
+Every current field row belongs to M_k. This is an induction over the actual chronology:
+
+- an ordinary address gate left-multiplies a current row by an element of G;
+- ADD and exterior SCALE form R-linear combinations;
+- COPY repeats an existing row;
+- CLEAR replaces a row by0;
+- the next Gaussian applies its H element to its actual current input row and creates one new row t_(k+1), which is then adjoined.
+
+The input of a later Gaussian may contain any earlier paid outputs. No one-layer assumption is made. Keeping overwritten rows only enlarges the history module, making this a valid upper bound on what the physical program can access.
+
+There is a surjective K-linear map `R^(N+k) -> M_k`, sending the standard generators to the initial and paid-output rows. Thus
+
+```text
+dim_K M_k <= (N+k) |G|.
+```
+
+This inequality does not require R to be a division ring or an integral domain. In particular, zero divisors and ordinary projector combinations are allowed.
+
+## 4. The targets require C additional free copies of R
+
+At the final time m, each required target row and each initial background row lie in M_m. Subtracting the ordinary initial background conceptually shows that every f_i lies in M_m. This is a containment argument, not an extra physical operation or a promise that erased data can be recovered for free.
+
+First remove the shared right normalizers mathematically. Right-multiply the h_j coordinate of every row by Km_j^-1, and leave other coordinates unchanged. This is an invertible LEFT R-linear map on the ambient row space, since left multiplication commutes with this coordinatewise right multiplication. It sends I to I because Km_j is in G. It sends the required rows to
+
+```text
+f_i_tilde = [A_i] M[i,:] / 2
+```
+
+on their eight h columns. Thus the common right-diagonal Km factor cannot alter the dimension comparison. This step is not an assumption that a paid operator commutes with Km.
+
+For a class with representative a, write `A_i=g_i a`, with g_i in G. Multiplication by the unit [g_i]^-1 and the exterior factor2 shows that its required row module is generated by
+
+```text
+[a] M[i,:],  i in that class.
+```
+
+Let v_1,...,v_r be any rational basis of those scalar rows. They also have rank r over K, since extending scalars from Q to Q(i) does not change the rank of a rational matrix. The class module is generated by `[a]v_1,...,[a]v_r` and is FREE of rank r over R.
+
+To prove freeness without ignoring zero divisors, suppose
+
+```text
+sum_l r_l [a] v_l = 0,    r_l in R.
+```
+
+The r-by8 scalar matrix with rows v_l has a right inverse over K. Multiply the eight coordinate equations by that scalar right inverse. Scalar coefficients are central, so this gives `r_l [a]=0` for every l. Right multiplication by the group element [a] is invertible in K[H], hence every r_l=0. This proves injectivity of the map `R^r -> K[H]^N` and therefore K-dimension `r |G|` for this class contribution.
+
+For distinct classes, the possible group-basis supports of their coefficients are disjoint sets G a. Consequently their row submodules form a direct sum. Each is also disjoint from I, whose coefficients are supported in G itself, because every A_i is nonordinary. The common right normalization above is what makes this support separation simultaneous in all eight input coordinates.
+
+It follows that M_m contains an internal direct sum isomorphic, as a left R-module, to
+
+```text
+R^N  direct-sum  (direct-sum_alpha R^(r_alpha)),
+```
+
+and hence
+
+```text
+dim_K M_m >= (N+C) |G|.
+```
+
+Combining the lower and upper dimensions gives
+
+```text
+(N+C)|G| <= dim_K M_m <= (N+m)|G|,
+therefore m >= C.
+```
+
+Arbitrary dirty owned entries do not provide a loophole: including them increases N on BOTH sides, and N cancels. Arbitrarily many fixed known-zero scratch fields add no independent initial rows. COPY/CLEAR and noninvertible ordinary projectors likewise add no paid generator. Zero divisors cannot pack the required FREE class modules into fewer generators because the finite K-dimension comparison remains valid.
+
+## 5. Source-specific conclusion and exact limits
+
+Under Sections1–4, every fixed finite exact program implementing this full arbitrary-input `y += q^-1 W_s h` requires at least C paid Gaussian whole-field calls. These calls may form arbitrarily many layers and may use earlier outputs through ordinary feedback. If only central H1 queries are permitted, this is at least C H1 calls. If higher-rank Gaussian field calls are also permitted, it remains a bound on their total NUMBER at the same whole-field capacity; no weighted invoice is inferred here.
+
+The root receipt binds C=112 for the exact112-row source. Subject to independent acceptance of this proof,112 is therefore the optimal Gaussian FIELD-CALL count in this fixed standalone grammar, matched by the emitted112-H1 upper construction. This does not optimize its ordinary work, scratch, precision, transport or source/compiler constants.
+
+The following boundaries are essential:
+
+1. **Fixed columnwise ordinary gates.** G must be finite. The actual P/X/Z4-D/per-column-phase grammar has this property. A different ordinary model with unrestricted address operations coupling fiber columns, non-root per-column scalings, or an infinite ordinary group requires a different argument. Finite dimension is used explicitly.
+2. **Fixed finite program and exterior coefficients.** The same finite word and the same exterior K coefficients must establish the target for every positive f. A width-dependent or width-growing program is not covered by the tensor-family injection as used here. Nor are approximation schemes, nonlinear/data-dependent operations or anti-linear operations outside the stated K-linear grammar.
+3. **All original inputs independent.** Restricting h or y to a special image, imposing a relation between fields, changing the target background to a nonordinary one, or requesting only selected original columns changes the target module. The arbitrary whole-field interface is part of the theorem.
+4. **No free nonordinary initial observations.** If a caller starts this cut with a correctly versioned qh, a Gaussian cache, a native observation, or another correlated nonordinary row, the initial module is not merely R^N. The proof must then bound the new dimension gained beyond that actual initial module. It gives no automatic additional112-call lower bound at such a cut.
+5. **Fixed whole-field capacity.** A paid call returns one new transformed row on the declared common field space. Packing original fields into a larger address geometry, changing capacities, splitting field domains, or obtaining multiple independent transformed outputs from one charged call changes this model and its invoice.
+6. **Central scalar source matrix and common right factors.** The source factorization `A_i M[i,j] Km_j/2` is used essentially. Arbitrary operator-valued coefficients or row-dependent right factors do not receive this class-rank conclusion without a new proof.
+7. **Exact phases and lift.** A per-column phase is a group element, not an exterior scalar; rational M coefficients are exterior, not tensor-powered. Projective cosets or an impulse-only source test do not establish the required decomposition.
+
+In particular, this theorem must NOT be transferred directly to the global120 termination problem, a complete coupled caller, a noisy-helper construction, or a stream with previously paid observations. It also proves no unconditional arithmetic or multiplication lower bound. Those tasks may have different initial nonordinary modules, field geometries, targets or allowed operations.
+
+## 6. Independent review checklist
+
+The decisive checks are: the source's actual ordinary grammar embeds in a finite G on the fixed column geometry; every allowed paid operation adds only one row at the charged field capacity; all-width equalities have fixed exterior coefficients; the common Km diagonal is genuinely shared; the exact source equivalence classes are G A_i; and the desired endpoint supplies every f_i after subtraction of an ordinary initial background.
+
+The tensor-family injectivity lemma, the free-module proof using a scalar right inverse, and the two K-dimension inequalities are self-contained above. No appeal to division in R, a generic rank over a noncommutative ring, a width-one linear independence claim, or a one-layer restriction is needed. Independent review should reject or narrow the theorem if any listed source/interface condition fails, rather than extending it by analogy.
+
+Decision: the root hypothesis yields a coherent scoped proposed proof. Freeze this note for independent review. Keep the accepted upper-program receipt and this unaccepted lower-proof status separate until that review completes.
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json
new file mode 100644
index 0000000000..0582cf4e6e
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json
@@ -0,0 +1,6145 @@
+{
+  "schema": "one-sourcefanout-fixedinput/v1",
+  "source_head": "3348fccea855082786d5f0fc5558b73d4974e745",
+  "interface": "y112 += q^-1 W h8; h strictlyread-only;17arbitraryownedreturnzero",
+  "source_sha256": {
+    "swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da",
+    "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65",
+    "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md": "2d59282f3b5e9fb848d0099ce91729fa433162e6975f877a441e2ab4f57a29c5",
+    "swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json": "d065d98d97fc772e567a0f2bf3e3f308e0d9372c6a8c0ffd6368c05a6ea1a90a",
+    "swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba",
+    "race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-COST-CONTRACT-v1.md": "ead89d4f96531d96f38ae7103b99eabef35768b2e57e7a173ce482048092e206"
+  },
+  "normalizers_path": "swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json",
+  "provider_path": "swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json",
+  "hcode_path": "swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json",
+  "Kp_words": [
+    [
+      [
+        "P",
+        [
+          11,
+          13,
+          14,
+          7,
+          16,
+          32,
+          64,
+          128,
+          256
+        ]
+      ],
+      [
+        "D",
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          2,
+          2,
+          2,
+          2,
+          0,
+          0,
+          0,
+          0,
+          0
+        ]
+      ]
+    ],
+    [
+      [
+        "P",
+        [
+          19,
+          21,
+          22,
+          8,
+          7,
+          32,
+          64,
+          128,
+          256
+        ]
+      ],
+      [
+        "D",
+        [
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0,
+          0
+        ],
+        [
+          2,
+          2,
+          2,
+          0,
+          2,
+          0,
+          0,
+          0,
+          0
+        ]
+      ]
+    ],
+    [
+      [
+        "P",
+        [
+          35,
+          37,
+          38,
+          8,
+          16,
+          7,
+          64,
+          128,
+          256
+        ]
+      ],
+      [
+        "D",
+        [
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diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json
new file mode 100644
index 0000000000..5ca6ba0bcf
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json
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+    },
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+      "slot": 136,
+      "range": [
+        1373,
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+      "expected_T_over2": [
+        "-1/2"
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+    },
+    {
+      "kind": "basis_form",
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+        -1,
+        -1,
+        0
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+    },
+    {
+      "kind": "reconstruction",
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+      "slot": 136,
+      "range": [
+        1387,
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+      "expected_T_over2": [
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+    },
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+        0,
+        0,
+        -1
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+    },
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+      "kind": "reconstruction",
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+      "slot": 136,
+      "range": [
+        1401,
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+      "expected_T_over2": [
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+    },
+    {
+      "kind": "basis_form",
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+      "slot": 128,
+      "range": [
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+      "expected_H_row": [
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+        -1,
+        0,
+        0,
+        1
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+    },
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+      "slot": 136,
+      "range": [
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+      "expected_T_over2": [
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+      "expected_T_over2": [
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+    },
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+      "expected_T_over2": [
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+    },
+    {
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+      "slot": 136,
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+      "expected_T_over2": [
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+    {
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+    {
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+    {
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+    {
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+      "expected_T_over2": [
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+  "runtime_odd_divisions": 0,
+  "phase_policy": "Each phase token lifts i^gamma to i^(f*gamma). IntegerH and dyadicT/2 remain exterior scalar coefficients once. No f1Q linear decomposition is used as the field implementation.",
+  "proof_factorization": "H=S M, M=T H; A_i=L_i A_rep by allcolumnoperatoridentity. Therefore L_i sum_l(T_il/2)*A_rep(H_l b)=A_i(M_i b/2). b_k=Km_k h_k. All originaly coefficients stayI and owned dirt is CLEARed.",
+  "all_width": "Operatorwords equal onall512sourcecolumns, so their prescribed columnwise lifts agree for everyf; tensorwith spectatoridentityonother16axes. Ownerlinearcoefficients are exterior.",
+  "ordinary_counts": {
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+    "COPY": 8,
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+  "joint_norm_SUFFIX_log2_bound": 680,
+  "not_admitted": [
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+    "tape routing/storage/precision/compiler",
+    "any optimality outside this fixedcoset-latticegrammar"
+  ],
+  "controls": [
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+      "rows": [
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+      "rejected": true
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+    {
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+      "row": 0,
+      "mode": 0,
+      "rejected": true
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+    {
+      "name": "tensor exterioronehalf into twocolumns",
+      "legal": "1/2",
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+    {
+      "name": "illegal two-termwhole-fieldQshortcut",
+      "fiberwidth": 2,
+      "mixed_output": [
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+        1
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+      "actual_numerator": [
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+      "actual_denominator_power2": 2,
+      "shortcut_numerator": [
+        0,
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+      "rejected": true
+    },
+    {
+      "name": "integer reconstruction coefficient changed",
+      "rejected": true
+    },
+    {
+      "name": "uncleared arbitraryb0 owned entry",
+      "rejected": true
+    },
+    {
+      "name": "write originalh instead ofownedcopy",
+      "rejected": true
+    },
+    {
+      "name": "premature queriedbasis CLEAR beforelastread",
+      "rejected": true
+    }
+  ]
+}
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json
new file mode 100644
index 0000000000..f529514afb
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json
@@ -0,0 +1,366 @@
+{
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+  "leftcoset_count": 112,
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+      ],
+      "illegal": [
+        -1,
+        0
+      ],
+      "rejected": true
+    },
+    {
+      "name": "illegal two-termwhole-fieldQshortcut",
+      "fiberwidth": 2,
+      "mixed_output": [
+        0,
+        1
+      ],
+      "actual_numerator": [
+        2,
+        0
+      ],
+      "actual_denominator_power2": 2,
+      "shortcut_numerator": [
+        0,
+        0
+      ],
+      "rejected": true
+    },
+    {
+      "name": "integer reconstruction coefficient changed",
+      "rejected": true
+    },
+    {
+      "name": "uncleared arbitraryb0 owned entry",
+      "rejected": true
+    },
+    {
+      "name": "write originalh instead ofownedcopy",
+      "rejected": true
+    },
+    {
+      "name": "premature queriedbasis CLEAR beforelastread",
+      "rejected": true
+    }
+  ],
+  "input_sha256": "f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb",
+  "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+  "checker_sha256": "b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3",
+  "oracle_sha256": "15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba",
+  "scope": "ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim."
+}
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/README-v1.md b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/README-v1.md
new file mode 100644
index 0000000000..39c0410fe4
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/README-v1.md
@@ -0,0 +1,27 @@
+# One exact left-coset fanout upper program
+
+Prepared under `EXACT-FANOUT-COST-CONTRACT-v1.md`, SHA256 `ead89d4f96531d96f38ae7103b99eabef35768b2e57e7a173ce482048092e206`. Root alone executes the frozen request. The preparer has performed JSON/source extraction, AST parsing and hashing only; no phase, grouping, rank, native, price or global science was run here. All files outside this new folder remain unchanged.
+
+The fixed interface is `y112 += q^-1 W h8`, with arbitrary disjoint y/h originals, h read-only at every instruction, and17 additional arbitrary-owned fields returned zero. The source is pinned #5402 with its actual112 Kp words, eight Km words (without the native boundary factor2) and112-by8 M. Km is independently metadata-matched to the accepted HCODE and the provider's explicit mode index. This is one source fanout, not a parameter sweep, helper-class census or re-run of the old35-witness lower argument.
+
+For each row define A_p=q^-1 Kp_p^-1. The complete exact LEFT-class key is the binary RREF of A_p^-1's pullback of the computational Z Lagrangian. For each class choose its first port as representative r and certify `L_p=A_p A_r^-1` as a phase-bearing ordinary monomial. The checker compiles L from its complete signed tableau and absolute anchor, verifies source-compatible symmetric quadratic/linear parity and affine invertibility, then independently compares all512 sparse computational columns. Its sparse evaluator is separate from the pinned signed-tableau/anchor oracle. No2^25 dense matrix is constructed.
+
+Integer extended-gcd row-Hermite certificates give `H=S M_C`, `M_C=T H`, together with integer inverse matrices U,V. An independent exact Fraction rank is checked. Only integer H and integer-halves T/2 appear at runtime. There is no DIV3/7/13 or odd-grid expansion. A coefficient or instruction-cap failure stops the construction rather than changing a basis, dropping a row or widening a search.
+
+The emitted program copies all8 sources to owned b and applies Km there. Each group forms its H rows in up to8 reusable query slots, applies representative Kp^-1, one paid positiveQ and the ordinary centralX to implement inverseQ. One owned rowwork reconstructs T/2, applies the actual left alias including its native phase, and updates the original y once. Queried fields are cleared after their last group reads; rowwork after each target; b after allgroups. Every original h is untouched and every original y retains coefficientI. Seventeen entry CLEARs remove all private dirt. All nonzero retags are forbidden.
+
+Let C be the sum of actual group rational ranks, N the number of nonzero source rows, H_abs=sum|H| and T_abs=sum|T|. The deterministic conservative schedule retains identity aliases and uses repeated unit ADDs for H and half-ADDs for T/2. Its exact census is:
+
+- C paidH1; no other added Gaussian.
+- H_abs+N unit ADDs and T_abs half-ADDs.
+- 8 COPY and25+C+N CLEAR/zero-retag episodes each.
+- 8+2C+N whole-field monomial maps: Km8, representativeKp^-1 C, inverseQ centralX C and leftaliases N.
+-17 additional owned fields, all arbitrary-entry/zero-exit.
+
+Primitive monomial gates, actual lowered coefficients, H/T maxima/bit lengths, full U/V certificates, query count, all112 row memberships and full literal program are emitted separately. Scalar tariff is8 per unitADD,10 per halfADD,2 per COPY/CLEAR; monomial/tape/routing cost is not hidden in that subtotal. A max-field suffix bound2^(#ADD), or conservative joint bound2^(#ADD+#COPY), is a finite local bound, not wholecaller precision funding.
+
+The concrete25-axis lift uses central0 and freshstage1 axes9..16; every other axis is identity. Exact operator equality on all512 nine-axis columns lifts by the source prescription: P/X columnwise, D polynomial summed over columns, phasei^gamma lifted to i^(f gamma). M,H,T and1/2 remain exterior coefficients. Therefore A_p,f=L_p,f A_r,f and `M_C=T H` give the desired whole-field fanout for every positivewidth, with spectators unchanged. The finite sparse C-gate expansion is an oracle only. The field program uses an actual paid Q, never a two-term whole-field approximation.
+
+Controls include wrong RIGHT/LEFT grouping and reversed alias order, an impulse-only false merge, absolute phase, wrongQ/omittedX, a droppedM coefficient, changed integer recovery, tensoring exterior1/2, treating a per-column phase as exterior, a two-column counterexample to the two-term whole-Q shortcut, uncleared private dirt, originalh mutation and premature query CLEAR.
+
+The root result may report a smaller C or honestly report no reduction versus112. This is a constructive upper bound and its program cost, not optimality for broader query grammars, a complete decoder, source stock compatibility, a price admission or newkappa. The containing caller must bind its actual h version, y destinations,17 disjoint scratch slots, invocation multiplicity, movement, precision and compiler funding.
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/RUN-REQUEST-v1.json b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/RUN-REQUEST-v1.json
new file mode 100644
index 0000000000..91866eb0e6
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/RUN-REQUEST-v1.json
@@ -0,0 +1,30 @@
+{
+  "schema": "root-only-bounded-exactfanout-request/v1",
+  "purpose": "ONE actual112row sourcefanout LEFTcoset classification, exactintegerbasis program andcost; not a familysweep or lowerboundrepackaging",
+  "argv": [
+    "python3",
+    "-B",
+    "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py",
+    "--input",
+    "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-INPUT-v1.json",
+    "--program",
+    "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-PROGRAM-v1.json",
+    "--result",
+    "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/FANOUT-RESULT-v1.json"
+  ],
+  "script_sha256": "b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3",
+  "input_sha256": "f07e7fa96a6adc4242f77bcbf2a9aec17bc3e5d035127452281d8bf600688bbb",
+  "readme_sha256": "abd612e15a03531b00a6908a3b2de01d1c43ae54df316df3f34d438c1f0c87d1",
+  "time_limit_seconds": 30,
+  "memory_limit_mib": 256,
+  "root_shared_serial_guard_only": true,
+  "scientific_execution_by_preparer": false,
+  "sources": "Allpinnedsource hashes are insideFANOUT-INPUT-v1; no author/sourceevaluator imported, only retainedindependentphase_exact oracle.",
+  "expected_fresh_outputs": [
+    "FANOUT-PROGRAM-v1.json",
+    "FANOUT-RESULT-v1.json"
+  ],
+  "complete_scope": "All112 A_i, exactLEFTLagrangianclassification, fullsignedtableau+absolutephase+512sparsecolumns/member, integerU/V/H/S/T and rationalrank certificates, actualunit/halfADDlowered137fieldprogram,17dirtyownedlifetime, counts/controls. No2^25dense/native/provider/helper-classcensus/global/price replay.",
+  "failure_policy": "Anyphase/basis/lifetime/cap failure is a failedfixedconstruction; do nottruncate, switchbasis/searchfamily or admitpartialcost. Freezev1outputs andusea newversion foranyrepair.",
+  "gain_policy": "ActualC=sum group ranks; PASS withC>=112 ishonestNO_QUERY_REDUCTION; no\u03ba/fullcaller claim evenifC<112."
+}
diff --git a/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py
new file mode 100644
index 0000000000..43847ba649
--- /dev/null
+++ b/research/fanout-optimality-support/retained/race-kappa0033-sol-high-20261024/lanes/construction/coset-fanout/check_emit_fanout_v1.py
@@ -0,0 +1,275 @@
+#!/usr/bin/env python3
+"""ROOT ONLY. One exact q^-1 W fanout quotient/program, no search or native replay.
+Classification: pullback computational-Z Lagrangians (LEFT monomial cosets).
+Alias oracle: pinned signed tableau + absolute anchor AND all512 sparse columns.
+Integer row-lattice certificates avoid all runtime odd divisions.
+"""
+from pathlib import Path
+from collections import Counter,defaultdict
+from fractions import Fraction
+from functools import lru_cache
+import argparse,hashlib,importlib.util,json,math,sys
+HERE=Path(__file__).resolve().parent;BASE=HERE.parents[3]
+PH=BASE/'swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py'
+N=9;D=512
+
+def need(x,msg):
+ if not x:raise ValueError(msg)
+def sha(p):return hashlib.sha256(p.read_bytes()).hexdigest()
+def dump(path,value):
+ need(not path.exists(),'immutable output exists: '+str(path));path.write_text(json.dumps(value,indent=2)+'\n')
+def zmat(m,n):return [[0]*n for _ in range(m)]
+def eye(m):return [[int(i==j)for j in range(m)]for i in range(m)]
+def mul(A,B):
+ if not A:return []
+ return [[sum(a*b for a,b in zip(row,col))for col in zip(*B)]for row in A]
+def rational_rank(M):
+ a=[[Fraction(x)for x in row]for row in M];r=0
+ for c in range(8):
+  k=next((k for k in range(r,len(a))if a[k][c]),None)
+  if k is None:continue
+  a[r],a[k]=a[k],a[r];v=a[r][c];a[r]=[x/v for x in a[r]]
+  for k in range(len(a)):
+   if k!=r and a[k][c]:
+    v=a[k][c];a[k]=[x-v*y for x,y in zip(a[k],a[r])]
+  r+=1
+ return r
+
+def rref2(rows):
+ a=list(rows);r=0
+ for c in range(17,-1,-1):
+  k=next((k for k in range(r,len(a))if a[k]>>c&1),None)
+  if k is None:continue
+  a[r],a[k]=a[k],a[r]
+  for k in range(len(a)):
+   if k!=r and a[k]>>c&1:a[k]^=a[r]
+  r+=1
+ return tuple(a[:r])
+def egcd(a,b):
+ oldr,r=a,b;olds,s=1,0;oldt,t=0,1
+ while r:
+  q=oldr//r;oldr,r=r,oldr-q*r;olds,s=s,olds-q*s;oldt,t=t,oldt-q*t
+ if oldr<0:return -oldr,-olds,-oldt
+ return oldr,olds,oldt
+
+def integer_basis(M):
+ """Row-Hermite via unimodular operations, maintaining exact inverse V."""
+ m=len(M);A=[row[:]for row in M];U=eye(m);V=eye(m);rank=0;pivots=[]
+ def swap(i,j):
+  A[i],A[j]=A[j],A[i];U[i],U[j]=U[j],U[i]
+  for row in V:row[i],row[j]=row[j],row[i]
+ def plus(i,j,q):
+  A[i]=[x+q*y for x,y in zip(A[i],A[j])];U[i]=[x+q*y for x,y in zip(U[i],U[j])]
+  for row in V:row[j]-=q*row[i]
+ for col in range(8):
+  k=next((k for k in range(rank,m)if A[k][col]),None)
+  if k is None:continue
+  swap(rank,k)
+  for i in range(rank+1,m):
+   if not A[i][col]:continue
+   aa,bb=A[rank][col],A[i][col];g,x,y=egcd(aa,bb)
+   a0,a1=A[rank][:],A[i][:];u0,u1=U[rank][:],U[i][:]
+   A[rank]=[x*z+y*w for z,w in zip(a0,a1)];A[i]=[-(bb//g)*z+(aa//g)*w for z,w in zip(a0,a1)]
+   U[rank]=[x*z+y*w for z,w in zip(u0,u1)];U[i]=[-(bb//g)*z+(aa//g)*w for z,w in zip(u0,u1)]
+   for row in V:
+    v0,v1=row[rank],row[i];row[rank]=(aa//g)*v0+(bb//g)*v1;row[i]=-y*v0+x*v1
+  if A[rank][col]<0:
+   A[rank]=[-x for x in A[rank]];U[rank]=[-x for x in U[rank]]
+   for row in V:row[rank]=-row[rank]
+  pivot=A[rank][col]
+  for i in range(rank):
+   q=A[i][col]//pivot
+   if q:plus(i,rank,-q)
+  pivots.append(col);rank+=1
+  if rank==m:break
+ H=A[:rank];S=U[:rank];T=[row[:rank]for row in V]
+ need(rank==rational_rank(M),'independent exact rational rank agrees')
+ need(mul(U,V)==eye(m)and mul(V,U)==eye(m),'integer unimodular inverse certificate')
+ need(mul(U,M)==A and all(not any(row)for row in A[rank:]),'Hermite transformed matrix certificate')
+ need(mul(S,M)==H and (mul(T,H)if rank else zmat(m,8))==M,'M=TH and H=SM exact')
+ need(all(H[j][pivots[j]]>0 and all(not H[j][c]for c in range(pivots[j]))for j in range(rank)),'independent echelon basis')
+ return {'rank':rank,'H':H,'S':S,'T':T,'U':U,'V':V,'pivots':pivots}
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--input',type=Path,required=True);ap.add_argument('--program',type=Path,required=True);ap.add_argument('--result',type=Path,required=True);args=ap.parse_args()
+ for p in [args.program,args.result]:need(not p.exists(),'immutable output exists')
+ inp=json.loads(args.input.read_text())
+ for rel,h in inp['source_sha256'].items():need(sha(BASE/rel)==h,'source hash '+rel)
+ need(sha(PH)=='15e90b63c5659090f02902cb38951ec4ab252352fb0b967b411ed547c501e2ba','pinned independent phase oracle')
+ spec=importlib.util.spec_from_file_location('fanout_phase',PH);ph=importlib.util.module_from_spec(spec);sys.modules[spec.name]=ph;spec.loader.exec_module(ph)
+ Kp=[ph.freeze(w)for w in inp['Kp_words']];Km=[ph.freeze(w)for w in inp['Km_words']];M=inp['M_rows'];axes=inp['local_axes_25'];need(len(Kp)==112 and len(Km)==8 and len(M)==112 and all(len(row)==8 for row in M),'actual112x8 source')
+ norm=json.loads((BASE/inp['normalizers_path']).read_text());hc=json.loads((BASE/inp['hcode_path']).read_text());provider=json.loads((BASE/inp['provider_path']).read_text())
+ need([ph.freeze(z['K_word'])for z in norm['ports']]==Kp,'all112 actualKp words')
+ need([[norm['mode_columns'][k][i]for k in range(8)]for i in range(112)]==M,'actual M rows orientation')
+ need([ph.freeze(hc['operations'][112+k]['word'])for k in range(8)]==Km,'actual8 commonKm from acceptedHcode')
+ need([ph.freeze(next(z['input_K']['literal_word']for z in provider['mode_boundaries']if z['mode']==k))for k in range(8)]==Km,'actualproviderKm without boundaryfactor2')
+ A=[ph.adjoint(w)+(('C',1,-1),)for w in Kp]
+ keys=[];bykey={}
+ for i,word in enumerate(A):
+  inv=ph.adjoint(word);rows=[]
+  for j in range(9):
+   x,z,p=ph.pauli(inv,0,1<<j);rows.append(x|(z<<9))
+  key=rref2(rows);need(len(key)==9,'nine-dimensional pullbackZ Lagrangian');keys.append(key);bykey.setdefault(key,[]).append(i)
+ # Exact monomial compiler from the full signed tableau and absolute anchor.
+ def monomial_alias(word):
+  sig=ph.signature(word);tab,anchor,den=sig
+  need(all(tab[9+j][0]==0 and tab[9+j][2]%2==0 for j in range(9)),'left quotient preserves computationalZ')
+  support=[j for j,v in enumerate(anchor)if v!=(0,0)];need(len(support)==1 and den==0,'unit-modulus absolute monomial anchor')
+  b=support[0];gamma={(1,0):0,(0,1):1,(-1,0):2,(0,-1):3}[anchor[b]]
+  cols=tuple(tab[j][0]for j in range(9));need(ph.rank(cols)==9,'invertible monomial affine map');F=ph.transpose(cols)
+  alpha=tuple((tab[j][2]+2*ph.parity(tab[j][1]&b))%4 for j in range(9))
+  Q=tuple(sum(ph.parity(tab[j][1]&cols[k])<<k for k in range(9))for j in range(9))
+  need(all(((Q[j]>>k)&1)==((Q[k]>>j)&1)for j in range(9)for k in range(9))and all(alpha[j]%2==((Q[j]>>j)&1)for j in range(9)),'source-compatible symmetricQ/linear parity')
+  alias=(('D',Q,alpha),('P',F),('X',b),('phase',gamma))
+  need(ph.signature(alias)==sig,'full signed tableau and phase alias equality')
+  return alias,sig
+ def rot(z,p):
+  a,b=z;return ((a,b),(-b,a),(-a,-b),(b,-a))[p%4]
+ def column(word,index):
+  values={index:(1,0)};den=0
+  for e in word:
+   op=e[0]
+   if op=='P':values={ph.mv(e[1],x):v for x,v in values.items()}
+   elif op=='X':values={x^e[1]:v for x,v in values.items()}
+   elif op=='D':values={x:rot(v,ph.polynomial(e,x))for x,v in values.items()}
+   elif op=='phase':values={x:rot(v,e[1])for x,v in values.items()}
+   elif op=='C':
+    out=defaultdict(lambda:(0,0));s=e[2];need(s in(-1,1),'sparseGaussian signed primitive')
+    for x,(a,b)in values.items():
+     for y,v in [(x,(a-s*b,b+s*a)),(x^e[1],(a+s*b,b-s*a))]:
+      z=out[y];out[y]=(z[0]+v[0],z[1]+v[1])
+    values={x:v for x,v in out.items()if v!=(0,0)};den+=1
+   else:raise ValueError('alias primitive')
+   while den and all(a%2==0 and b%2==0 for a,b in values.values()):values={x:(a//2,b//2)for x,(a,b)in values.items()};den-=1
+  return tuple(sorted(values.items())),den
+ groups=[];allalias={};controls=[]
+ for gid,(key,rows)in enumerate(bykey.items()):
+  rep=rows[0];basis=integer_basis([M[i]for i in rows]);members=[]
+  for i in rows:
+   # L_i=A_i A_rep^-1; chronological inverse representative THEN A_i.
+   left=ph.adjoint(A[rep])+A[i];alias,sig=monomial_alias(left);digest=hashlib.sha256()
+   for x in range(512):
+    actual=column(left,x);need(actual==column(alias,x),'all512 alias columns');digest.update(json.dumps(actual,separators=(',',':')).encode())
+   members.append({'row':i,'L_native_word9':left,'left_monomial_alias_word9':alias,'signed_tableau':sig[0],'anchor_index':next(j for j,z in enumerate(sig[1])if z!=(0,0)),'anchor_gamma':alias[-1][1],'all512_columns_sha256':digest.hexdigest()});allalias[i]=(alias,left,gid)
+  groups.append({'group':gid,'representative_row':rep,'rows':rows,'pullbackZ_rref':key,'integer_row_lattice':basis,'members':members})
+ need(len(allalias)==112,'every actualrow once')
+ # Meaningful controls: right cosets all coincide but do not give left aliases.
+ pair=next(((i,j)for i in range(112)for j in range(i)if keys[i]!=keys[j]),None)
+ need(pair is not None,'source needs a nontrivial coset control');i,j=pair
+ # Name by chronological circuit, to prevent a verbal left/right reversal.
+ bad_left=ph.adjoint(A[j])+A[i]
+ need(any(ph.pauli(bad_left,0,1<<k)[0]for k in range(9)),'cross-left-class quotient is nonmonomial')
+ opposite=A[j]+ph.adjoint(A[i]) # A_i^-1 A_j, always ordinary here
+ need(all(not ph.pauli(opposite,0,1<<k)[0]for k in range(9)),'wrong RIGHT-coset grouping would merge these source rows')
+ controls.append({'name':'wrong RIGHT cosets collapse allrows and are rejected by actualLEFT alias test','rows':[i,j],'rejected':True})
+ need(ph.signature(A[i]+opposite)!=ph.signature(A[j]),'RIGHTalias incorrectlyusedonLEFT cannot reproduce sourceoperator');controls.append({'name':'reversedalias multiplicationorder','rows':[i,j],'rejected':True})
+ need(column(A[i],0)==column(A[j],0)and keys[i]!=keys[j],'actualsource impulse-only falsemerge witness');controls.append({'name':'oneimpulse-only grouping merges differentcompleteLEFTclasses','rows':[i,j],'rejected':True})
+ first=groups[0]['members'][0];alias=ph.freeze(first['left_monomial_alias_word9']);left=ph.freeze(first['L_native_word9'])
+ need(column(alias+(('phase',2),),0)!=column(left,0),'absolute phase alias mutant');controls.append({'name':'alias absolute phase flipped','rejected':True})
+ need(ph.signature(A[0])!=ph.signature(ph.adjoint(Kp[0])+(('C',1,1),)),'query orientation mutant');controls.append({'name':'positiveQ substituted for inverseQ or omittedcentralX','rejected':True})
+ badM=[row[:]for row in M];mi,mk=next((ii,kk)for ii,row in enumerate(M)for kk,x in enumerate(row)if x);badM[mi][mk]=0
+ need(badM!=[[norm['mode_columns'][kk][ii]for kk in range(8)]for ii in range(112)],'dropped M coefficient sourcebindingcontrol');controls.append({'name':'droppedactualnonzero M coefficient','row':mi,'mode':mk,'rejected':True})
+ need(Fraction(1,2)!=Fraction(1,2)**2,'exteriorhalf isnot tensoredownercoefficient');controls.append({'name':'tensor exterioronehalf into twocolumns','legal':'1/2','illegal':'1/4','rejected':True})
+ need(rot((1,0),4)!=rot((1,0),2),'percolumnphase cannotbe exteriorphase');controls.append({'name':'phase2columnlift replacedby exteriornegativeone','fiberwidth':2,'legal':[1,0],'illegal':[-1,0],'rejected':True})
+ one,den=column((('C',1,-1),),0);one=dict(one);aa,bb=one[0],one[1];cross=(aa[0]*bb[0]-aa[1]*bb[1],aa[0]*bb[1]+aa[1]*bb[0])
+ need(cross!=(0,0)and cross==(2,0)and den==1,'actualtwo-column inverseQtensor hasmixedoutput');controls.append({'name':'illegal two-termwhole-fieldQshortcut','fiberwidth':2,'mixed_output':[0,1],'actual_numerator':list(cross),'actual_denominator_power2':2,'shortcut_numerator':[0,0],'rejected':True})
+ # Each source row basis has exact integer certificates; a changed reconstruction cannot pass.
+ g=next(g for g in groups if g['integer_row_lattice']['rank']);bb=g['integer_row_lattice'];bad=[z[:]for z in bb['T']];bad[0][0]+=1
+ need(mul(bad,bb['H'])!=[M[i]for i in g['rows']],'reconstruction coefficient mutation');controls.append({'name':'integer reconstruction coefficient changed','rejected':True})
+ # Emit one concrete copy-preserving17-owned program.
+ ops=[];role={'h':list(range(8)),'y':list(range(8,120)),'b':list(range(120,128)),'query':list(range(128,136)),'rowwork':136};private=list(range(120,137));counts=Counter();addcoeff=Counter();primitive=Counter();unit=half=0
+ def lift(word):
+  out=[]
+  for e in word:
+   if e[0]=='P':
+    rows=[1<<j for j in range(25)]
+    for a0,aa in enumerate(axes):rows[aa]=sum(((e[1][a0]>>b0)&1)<<bb for b0,bb in enumerate(axes))
+    out.append(['P',rows])
+   elif e[0]=='D':
+    qr=[0]*25;lin=[0]*25
+    for a0,aa in enumerate(axes):qr[aa]=sum(((e[1][a0]>>b0)&1)<<bb for b0,bb in enumerate(axes));lin[aa]=e[2][a0]
+    out.append(['D',qr,lin])
+   elif e[0]=='X':out.append(['X',sum(((e[1]>>a0)&1)<<aa for a0,aa in enumerate(axes))])
+   elif e[0]=='phase':out.append(list(e))
+   else:raise ValueError('noGaussian inmonomiallift')
+  return out
+ def put(e):
+  need(len(ops)<inp['instruction_cap'],'literal instruction cap exceeded; no truncation');ops.append(e);counts[e['op']]+=1
+ def clear(dst):put({'op':'CLEAR','dst':dst});put({'op':'ZERO_RETAG','dst':dst,'new_chart':'ambient25_common','premise':'immediately preceding CLEAR'})
+ def mono(dst,word,why):
+  need(all(e[0]in('P','D','X','phase')for e in word),'monomial alphabet');put({'op':'MONOMIAL','dst':dst,'word9':word,'word25':lift(word),'purpose':why})
+  for e in word:primitive[e[0]]+=1
+ def add(dst,src,coefficient):
+  nonlocal unit,half
+  q=Fraction(coefficient);need(q in(Fraction(1),Fraction(-1),Fraction(1,2),Fraction(-1,2)),'literal unit/halfADD only');need(dst!=src,'no selfADD');put({'op':'ADD','dst':dst,'src':src,'coefficient':str(q)});addcoeff[str(q)]+=1
+  if abs(q)==1:unit+=1
+  else:half+=1
+ def scaledadd(dst,src,n,den=1):
+  need(den in(1,2),'no odd runtime division');need(abs(n)<=inp['coefficient_cap'],'coefficient cap failure, no alternatebasis/search');sign=1 if n>=0 else-1
+  if den==1:
+   for _ in range(abs(n)):add(dst,src,sign)
+  else:
+   for _ in range(abs(n)):add(dst,src,Fraction(sign,2))
+ for slot in private:clear(slot)
+ for k in range(8):put({'op':'COPY','dst':role['b'][k],'src':role['h'][k],'owned_zero_destination':True});mono(role['b'][k],Km[k],'sourcecommonKm input copy')
+ checkpoints=[];C=0
+ for g in groups:
+  gid,rep=g['group'],g['representative_row'];bb=g['integer_row_lattice'];rank=bb['rank'];H,T=bb['H'],bb['T']
+  for l,row in enumerate(H):
+   slot=role['query'][l];start=len(ops)
+   for k,n in enumerate(row):scaledadd(slot,role['b'][k],n)
+   checkpoints.append({'kind':'basis_form','group':gid,'basis':l,'slot':slot,'range':[start,len(ops)],'expected_H_row':row})
+   mono(slot,ph.adjoint(Kp[rep]),'representativeKp inverse');put({'op':'GAUSSIAN','dst':slot,'rank':1,'positive_operator':'C1','active_axis25':axes[0],'paid':True});mono(slot,(('X',1),),'positiveQ followedbycentralX givesinverseQ');C+=1
+  for rowindex,i in enumerate(g['rows']):
+   if not any(M[i]):continue
+   work=role['rowwork'];start=len(ops)
+   for l,n in enumerate(T[rowindex]):scaledadd(work,role['query'][l],n,2)
+   checkpoints.append({'kind':'reconstruction','group':gid,'source_row':i,'slot':work,'range':[start,len(ops)],'expected_T_over2':[str(Fraction(n,2))for n in T[rowindex]]})
+   mono(work,allalias[i][0],'phaseboundLEFTalias row'+str(i));add(role['y'][i],work,1);clear(work)
+  for l in range(rank):clear(role['query'][l])
+ for slot in role['b']:clear(slot)
+ need(C==sum(g['integer_row_lattice']['rank']for g in groups)and C<=112,'Gaussian charge is sum ofactual rationalranks')
+ # Static typed/lifetime and exact scalar-census replay of the emitted code.
+ def audit(program):
+  initialized={f:False for f in private};zero={f:False for f in private};seenq=0
+  for at,e in enumerate(program):
+   op=e['op'];dst=e['dst'];need(dst not in role['h'],'original modeinputs strictly read-only')
+   if op=='CLEAR':need(dst in private,'CLEAR only owned');initialized[dst]=True;zero[dst]=True
+   elif op=='ZERO_RETAG':need(dst in private and initialized[dst]and zero[dst]and at and program[at-1]['op']=='CLEAR'and program[at-1]['dst']==dst,'retag exactownedzero immediatelyafterCLEAR')
+   elif op=='COPY':need(dst in private and initialized[dst]and zero[dst],'COPY only initializedownedzero');need(e['src']in role['h'],'copyactualsource');zero[dst]=False
+   elif op=='ADD':
+    src=e['src'];need(src!=dst,'distinctADD fields');need(src not in private or initialized[src],'no dirtyownedsource');need(src not in role['query']or not zero[src],'no premature read ofcleared queriedbasis');need(dst not in private or initialized[dst],'no dirtyownedreceiver');need(dst in private or dst in role['y'],'onlydesty orprivatewrite')
+    if dst in private:zero[dst]=False
+   elif op=='MONOMIAL':need(dst in private and initialized[dst],'monomialonlyinitializedprivate');need(e['word25']==lift(ph.freeze(e['word9'])),'actual25axislift')
+   elif op=='GAUSSIAN':need(dst in role['query']and initialized[dst]and e['rank']==1 and e['active_axis25']==axes[0],'actual paidpositivecenterQ');seenq+=1
+   else:raise ValueError('literal program alphabet')
+  need(all(initialized[f]and zero[f]for f in private),'all17 arbitraryowned returnzero');return seenq
+ need(audit(ops)==C,'typedpaid charge')
+ target_updates=Counter(e['dst']for e in ops if e['op']=='ADD'and e['dst']in role['y']);need(all(target_updates[role['y'][i]]==int(any(M[i]))for i in range(112)),'all originaly targets updatedonce iff source rownonzero')
+ badops=ops[2:] # remove initialCLEAR/retag of b0; its actualCOPY must reject.
+ try:audit(badops)
+ except ValueError:controls.append({'name':'uncleared arbitraryb0 owned entry','rejected':True})
+ else:raise ValueError('dirty ownedcontrolaccepted')
+ badops=[dict(e)for e in ops];where=next(j for j,e in enumerate(badops)if e['op']=='MONOMIAL');badops[where]['dst']=role['h'][0]
+ try:audit(badops)
+ except ValueError:controls.append({'name':'write originalh instead ofownedcopy','rejected':True})
+ else:raise ValueError('originalhwritecontrolaccepted')
+ where=next(j for j,e in enumerate(ops)if e['op']=='ADD'and e['src']in role['query']);slot=ops[where]['src'];badops=ops[:where]+[{'op':'CLEAR','dst':slot},{'op':'ZERO_RETAG','dst':slot,'premise':'CLEAR'}]+ops[where:]
+ try:audit(badops)
+ except ValueError:controls.append({'name':'premature queriedbasis CLEAR beforelastread','rejected':True})
+ else:raise ValueError('prematureCLEARcontrolaccepted')
+ # Check each actual lowered ADD range against its emitted coefficient vector.
+ for z in checkpoints:
+  size=8 if z['kind']=='basis_form'else groups[z['group']]['integer_row_lattice']['rank'];got=[Fraction(0)]*size;sources=role['b']if z['kind']=='basis_form'else role['query'][:size]
+  for e in ops[z['range'][0]:z['range'][1]]:
+   need(e['op']=='ADD'and e['dst']==z['slot']and e['src']in sources,'loweredlinearcomb source/slot');got[sources.index(e['src'])]+=Fraction(e['coefficient'])
+  expected=[Fraction(x)for x in(z['expected_H_row']if z['kind']=='basis_form'else z['expected_T_over2'])];need(got==expected,'actual unit/half lowerings match certifiedbasis/reconstruction')
+ Nrows=sum(any(row)for row in M);Habs=sum(abs(x)for g in groups for row in g['integer_row_lattice']['H']for x in row);Tabs=sum(abs(x)for g in groups for row in g['integer_row_lattice']['T']for x in row)
+ need(counts['ADD']==Habs+Tabs+Nrows and unit==Habs+Nrows and half==Tabs,'exactcontractADD census')
+ need(counts['CLEAR']==25+C+Nrows and counts['ZERO_RETAG']==25+C+Nrows and counts['COPY']==8 and counts['MONOMIAL']==8+2*C+Nrows,'exactcontractowned/mapcensus')
+ scalar=8*unit+10*half+2*counts['COPY']+2*counts['CLEAR']
+ program={'schema':'exact-leftcoset-fanout-program/v1','status':'EXACT_COMPONENT_UPPER_PROGRAM','interface':'y112 += q^-1 W h8; h read-only; all137 directions include17arbitraryownedclearedtozero','roles':role,'private_ids':private,'local_axes_25':axes,'source_input_sha256':sha(args.input),'groups':groups,'queries':C,'nonzero_rows':Nrows,'H_abs':Habs,'T_abs':Tabs,'max_H_coefficient':max((abs(x)for g in groups for row in g['integer_row_lattice']['H']for x in row),default=0),'max_T_coefficient':max((abs(x)for g in groups for row in g['integer_row_lattice']['T']for x in row),default=0),'operations':ops,'linear_checkpoints':checkpoints,'runtime_odd_divisions':0,'phase_policy':'Each phase token lifts i^gamma to i^(f*gamma). IntegerH and dyadicT/2 remain exterior scalar coefficients once. No f1Q linear decomposition is used as the field implementation.','proof_factorization':'H=S M, M=T H; A_i=L_i A_rep by allcolumnoperatoridentity. Therefore L_i sum_l(T_il/2)*A_rep(H_l b)=A_i(M_i b/2). b_k=Km_k h_k. All originaly coefficients stayI and owned dirt is CLEARed.','all_width':'Operatorwords equal onall512sourcecolumns, so their prescribed columnwise lifts agree for everyf; tensorwith spectatoridentityonother16axes. Ownerlinearcoefficients are exterior.','ordinary_counts':dict(counts),'ADD_coefficient_census':dict(addcoeff),'monomial_primitive_census':dict(primitive),'scalar_tariff':scalar,'positiveQpaid_profile':{'1':C},'max_norm_SUFFIX_log2_bound':counts['ADD'],'joint_norm_SUFFIX_log2_bound':counts['ADD']+counts['COPY'],'not_admitted':['wholecaller target/price/funding','tape routing/storage/precision/compiler','any optimality outside this fixedcoset-latticegrammar'],'controls':controls}
+ dump(args.program,program)
+ result={'schema':'exact-fanout-component-result/v1','status':'PASS_EXACT_COMPONENT_QUERY_REDUCTION'if C<112 else'PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION','source_rows':112,'common_modes':8,'leftcoset_count':len(groups),'rationalrank_sum_Qqueries':C,'query_savings_vs112':112-C,'owned_arbitrary':17,'owned_zero_return':17,'all512_alias_columns_checked':112*512,'group_sizes':[len(g['rows'])for g in groups],'group_ranks':[g['integer_row_lattice']['rank']for g in groups],'nonzero_rows':Nrows,'H_abs':Habs,'T_abs':Tabs,'maximum_integer_coefficient_bitlength':max((abs(x).bit_length()for g in groups for key in('H','T')for row in g['integer_row_lattice'][key]for x in row),default=0),'maximum_certificate_integer_bitlength':max((abs(x).bit_length()for g in groups for key in('H','T','S','U','V')for row in g['integer_row_lattice'][key]for x in row),default=0),'runtime_coefficients':'integersandhalvesonly','runtime_odd_divisions':0,'program_counts':dict(counts),'ADD_census':dict(addcoeff),'monomial_primitive_census':dict(primitive),'scalar_tariff':scalar,'controls':controls,'input_sha256':sha(args.input),'program_sha256':sha(args.program),'checker_sha256':sha(Path(__file__)),'oracle_sha256':sha(PH),'scope':'ONE actual112-row sourcefanout LEFTcosetclassification and upperprogram/cost; no native/provider/helper-class census/global/price replay. No newkappa or universalminimum claim.'}
+ dump(args.result,result);print(json.dumps({k:result[k]for k in['status','leftcoset_count','rationalrank_sum_Qqueries','query_savings_vs112','program_counts','scalar_tariff','program_sha256']},sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/fanout-optimality-support/retained/swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json b/research/fanout-optimality-support/retained/swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json
new file mode 100644
index 0000000000..54f13583c2
--- /dev/null
+++ b/research/fanout-optimality-support/retained/swarm-coupled-caller-sol-high-20261024/agents/caller/PARAMETRIC-HCODE-v14.json
@@ -0,0 +1,16327 @@
+{
+  "complete_caller": false,
+  "counts": {
+    "ADD": 896,
+    "MONOMIAL": 240
+  },
+  "extra_owned": 0,
+  "formula": [
+    [
+      "C",
+      "-W"
+    ],
+    [
+      "Z",
+      "I8"
+    ]
+  ],
+  "gaussian_calls": 0,
+  "inverse": false,
+  "operations": [
+    {
+      "field": "x0",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            11,
+            13,
+            14,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x1",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            19,
+            21,
+            22,
+            8,
+            7,
+            32,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            2,
+            0,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x2",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            35,
+            37,
+            38,
+            8,
+            16,
+            7,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            2,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x3",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            67,
+            69,
+            70,
+            8,
+            16,
+            32,
+            7,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            2,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x4",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            131,
+            133,
+            134,
+            8,
+            16,
+            32,
+            64,
+            7,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            2,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x5",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            259,
+            261,
+            262,
+            8,
+            16,
+            32,
+            64,
+            128,
+            7
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            0,
+            2
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x6",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            13,
+            14,
+            11,
+            7,
+            16,
+            32,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x7",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            21,
+            22,
+            19,
+            8,
+            7,
+            32,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            2,
+            0,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x8",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            37,
+            38,
+            35,
+            8,
+            16,
+            7,
+            64,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            2,
+            0,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x9",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            69,
+            70,
+            67,
+            8,
+            16,
+            32,
+            7,
+            128,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            2,
+            0,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x10",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            133,
+            134,
+            131,
+            8,
+            16,
+            32,
+            64,
+            7,
+            256
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            2,
+            0
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x11",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            261,
+            262,
+            259,
+            8,
+            16,
+            32,
+            64,
+            128,
+            7
+          ]
+        ],
+        [
+          "D",
+          [
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0,
+            0
+          ],
+          [
+            2,
+            2,
+            2,
+            0,
+            0,
+            0,
+            0,
+            0,
+            2
+          ]
+        ]
+      ]
+    },
+    {
+      "field": "x12",
+      "op": "MONOMIAL",
+      "word": [
+        [
+          "P",
+          [
+            41,
+            42,
+            4,
+            35,
+            16,
+            11,
+            64,
+            128,
+            256
+          ]
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+}
diff --git a/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py
new file mode 100644
index 0000000000..4959f78b9f
--- /dev/null
+++ b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/agents/algebra/phase_exact.py
@@ -0,0 +1,110 @@
+"""Independent nine-bit signed-Pauli and exact anchor circuit evaluator.
+
+No submitted or source evaluator import. Equality is the complete 18-generator
+Pauli action plus the full image of |0>, which fixes the scalar phase.
+"""
+from functools import lru_cache
+
+N=9
+
+def parity(x): return x.bit_count()%2
+
+def mv(rows,x): return sum(parity(r&x)<<j for j,r in enumerate(rows))
+
+def transpose(rows): return tuple(sum(((rows[i]>>j)&1)<<i for i in range(N)) for j in range(N))
+
+def invert(rows):
+    a=[row | (1<<(N+j)) for j,row in enumerate(rows)]
+    for j in range(N):
+        k=next(i for i in range(j,N) if a[i]>>j&1)
+        a[j],a[k]=a[k],a[j]
+        for i in range(N):
+            if i!=j and a[i]>>j&1:a[i]^=a[j]
+    if [x&511 for x in a]!=[1<<j for j in range(N)]:raise ValueError('singular map')
+    return tuple(x>>N for x in a)
+
+def rank(rows):
+    basis={}
+    for x in rows:
+        while x:
+            k=x.bit_length()-1
+            if k not in basis:basis[k]=x;break
+            x^=basis[k]
+    return len(basis)
+
+def freeze(word):return tuple(tuple(tuple(x) if isinstance(x,list) else x for x in e) for e in word)
+
+def adjoint(word):
+    result=[]
+    for e in reversed(word):
+        if e[0]=='P':result.append(('P',invert(e[1])))
+        elif e[0]=='D':result.append(('D',e[1],tuple(-v%4 for v in e[2])))
+        elif e[0]=='C':result.append(('C',e[1],-e[2]))
+        elif e[0]=='phase':result.append(('phase',-e[1]%4))
+        else:result.append(e)
+    return tuple(result)
+
+def conjugate(word):
+    return tuple(('D',e[1],tuple(-v%4 for v in e[2])) if e[0]=='D' else
+                 ('C',e[1],-e[2]) if e[0]=='C' else
+                 ('phase',-e[1]%4) if e[0]=='phase' else e for e in word)
+
+def polynomial(e,x):
+    Q,alpha=e[1:]
+    return (sum(alpha[j] for j in range(N) if x>>j&1)+
+            2*sum(parity(Q[j]&x&~((1<<(j+1))-1)) for j in range(N) if x>>j&1))%4
+
+def pauli(word,x,z,p=0):
+    for e in word:
+        if e[0]=='P':x,z=mv(e[1],x),mv(transpose(invert(e[1])),z)
+        elif e[0]=='X':p+=2*parity(z&e[1])
+        elif e[0]=='D':
+            q=polynomial(e,x)
+            z^=sum((((polynomial(e,x^(1<<j))-polynomial(e,1<<j)-q)%4)//2)<<j for j in range(N))
+            p+=q
+        elif e[0]=='C':
+            if parity(z&e[1]):x^=e[1];p-=e[2]
+        elif e[0]!='phase':raise ValueError('unsupported gate')
+    return x,z,p%4
+
+def rot(v,p):
+    a,b=v
+    return ((a,b),(-b,a),(-a,-b),(b,-a))[p%4]
+
+@lru_cache(None)
+def signature(word):
+    tab=tuple(pauli(word,1<<j,0) for j in range(N))+tuple(pauli(word,0,1<<j) for j in range(N))
+    values=[(0,0)]*512;values[0]=(1,0);den=0
+    for e in word:
+        if e[0]=='P':
+            out=[(0,0)]*512
+            for x,v in enumerate(values):out[mv(e[1],x)]=v
+            values=out
+        elif e[0]=='X':values=[values[x^e[1]] for x in range(512)]
+        elif e[0]=='D':values=[rot(v,polynomial(e,x)) for x,v in enumerate(values)]
+        elif e[0]=='phase':values=[rot(v,e[1]) for v in values]
+        elif e[0]=='C':
+            out=[]
+            for x,v in enumerate(values):
+                # ((1+s*i)*a+(1-s*i)*b)/2
+                u=values[x^e[1]];s=e[2]
+                out.append((v[0]-s*v[1]+u[0]+s*u[1],v[1]+s*v[0]+u[1]-s*u[0]))
+            values=out;den+=1
+        else:raise ValueError('unsupported gate')
+        while den and all(not (a%2 or b%2) for a,b in values):
+            values=[(a//2,b//2) for a,b in values];den-=1
+    return tab,tuple(values),den
+
+def frame(U):
+    r=len(U)
+    if not r:return ()
+    if r==N:return tuple(('C',1<<j,1) for j in range(N))
+    basis=[]
+    for q in list(U)+[1<<j for j in range(N)]:
+        if rank(basis+[q])>len(basis):basis.append(q)
+    G=transpose(basis);gi=invert(G);cols=transpose(gi)
+    Q=tuple((1<<j)^sum(parity(cols[j]&cols[k])<<k for k in range(N)) for j in range(N))
+    K=(('P',G),('D',Q,tuple((Q[j]>>j)&1 for j in range(N))))
+    return adjoint(K)+tuple(('C',1<<j,1) for j in range(r))+K
+
+def equal(a,b):return signature(tuple(a))==signature(tuple(b))
diff --git a/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json
new file mode 100644
index 0000000000..bca92c222c
--- /dev/null
+++ b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/coded-native-caller/NORMALIZERS.json
@@ -0,0 +1,126 @@
+{
+  "clifford_sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962",
+  "code_sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0",
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+  ],
+  "recoding_bill": {"forward_prefix_component_l1_upper":57,"forward_update_coefficient":"-1/4","inverse_output_prefix_component_l1_upper":"69/13","inverse_prefix_component_l1_upper":56,"inverse_update_coefficient":"-1/52","monomial_field_maps":224,"output_scaled_adds":448,"owned_fields":8,"owned_initial_clears":8,"owned_terminal_clears":8,"signed_mode_adds":448},
+  "schema": "coded-native-real-normalizers/1",
+  "scope": "Exact physical central ABI and local gauges; not full-controller or multiplication admission.",
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "status": "PASS_CODED_NATIVE_REAL_NORMALIZERS"
+}
diff --git a/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md
new file mode 100644
index 0000000000..5cbfc4fd02
--- /dev/null
+++ b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROOF.md
@@ -0,0 +1,236 @@
+# A source-bound backward provider with eight coupled rank-eight outputs
+
+The construction has 632 arbitrary original inputs and nine arbitrary owned
+inputs. Its paid native profile is
+`{1:2193,2:412,3:510,4:127,5:40}`. It returns 400 unchanged native helper jobs
+and a coupled block on the 224 main and eight remaining helper owners:
+
+\[
+ X=Dx-Ry+RW h,\qquad Y=Dy,\qquad H=D(h-Zy).                 \tag{1}
+\]
+
+Here `R=DQ` is the full native rank-nine Gaussian, `D` acts on the eight
+noncentral axes, and `Q` acts on the central axis. The eight `H` outputs remain
+coupled; they are **not eight autonomous H8 targets**. No complete caller or
+new multiplication exponent follows. All nine owned outputs are zero.
+
+## 1. Exact source and the changed word
+
+`SOURCES.json` pins the main-branch source, code, normalizers and Clifford
+compiler. The native source's decompressed SHA256 is
+`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`.
+`WITNESS.json` retains Ali Romman's PR5383 candidate verbatim, with SHA256
+`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`.
+It supplies candidate sites and rational rows; it is not a proof oracle or a
+pending Git-object dependency. Every used identity is checked again against
+the pinned main source.
+
+For witness row `i`, after the indicated original `cached_event`, CLEAR owned
+`C[i+1]` and COPY the indicated persistent row into it at its actual chart.
+Every cache precedes every removed center. At the original center event,
+replace the H8 call by CLEAR `C0`, then COPY `C[i+1]` into `C0` at that same
+rank-eight chart. At the indicated later H1 call, replace the call by a
+`zero_retag`: this is physical identity on the **exactly zero** field, with
+its bookkeeping chart changed to the old call's output chart. All other
+instructions, including inherited physical metadata, remain unchanged.
+`WORD.json.gz` emits the complete resulting backward native word; the verifier
+regenerates it from the canonical source and compares its parsed content.
+
+The replay begins with one independent formal column per field, including
+all nine owned fields. It tracks exact rational coefficients in the free
+group on the source's native warp symbols, their inverses, and actual chart
+tags. Every ordinary operation is checked at its true chart. COPY fills only
+owned zero; CLEAR acts only on owned fields. Before each of the eight retags,
+every one of the 641 input coefficients is zero. All initial owned dirt is
+cleared before use and is absent from every endpoint.
+
+The source's ten `phase` records are named stage annotations, not scalar
+Clifford phase gates; its 448 `adapter` records retain the predecessor's
+physical entrance/exit bindings (there are no `residual_adapter` records in
+this backward word). As in the pinned predecessor normalized-row semantics,
+these do not update formal rows. They are preserved in the emitted word,
+not deleted or priced away. Their physical interpretation and native cost
+are inherited; this package separately verifies every new physical boundary
+identity including absolute phase.
+
+The same interpreter replays the original source, obtaining its full
+632-row normalized backward endpoint `(x-y,y,h)` and clean original temporary.
+It separately replays center deletion to derive the native coupling below.
+The changed word has eight fewer H8 and eight fewer H1 calls than the original
+source, with no additional Gaussian call. It has 16 extra COPYs and 16 extra
+CLEARs. This is a changed source construction, not a constraint such as
+`Delta h=0` on otherwise independent inputs.
+
+## 2. Source-derived coupling and an ordinary helper basis
+
+Use the inherited 112-by-8 matrix `M`, stored transposed as `mode_columns`.
+The verifier checks all entries of
+
+\[
+ M^T M=56I_8,\qquad A=I-MM^T/4.
+\]
+
+Fresh replay of the center-deleted source gives
+
+\[
+ X=x-A^Ty,\qquad Y=y,\qquad H=h-B^TM^Ty.
+\]
+
+The verifier derives every entry of `B` by projecting the actual 408-by-112
+helper-to-Y coefficient matrix onto `M/56`; it then checks the entire
+factorization and all 632 endpoints. The eight candidate rows `Delta` satisfy
+`Delta B^T = S`, an exactly checked signed permutation. Put `E=S^-1 Delta`.
+Thus `E B^T=I8`. Fresh original-prefix replay also binds the candidate cache
+rows, their chronology and their actual rank-eight charts.
+
+In these coordinates the changed word has normalized endpoint
+
+\[
+ X=x-y+(M/4)Eh,\quad Y=y,\quad H=(I-B^TE)h,              \tag{2}
+\]
+
+and its canonical mode-`k` cache is
+
+\[
+ f_i(E_kh-M_k^Ty),\qquad f_i=\texttt{zero_factor}_i\,S_{ik}. \tag{3}
+\]
+
+The registered check composes all changed endpoint rows with the following
+basis, rather than accepting (2) or (3) from a saved endpoint registry.
+
+The union of supports of `B` and `E` comprises 122 actual cold H9 owners: each
+has ground entrance chart and full-R exit chart. Choose the eight original
+mode owners `[224,225,227,229,240,241,256,257]`. Define `L` on these 122 owners:
+its mode columns are `B^T`; its other columns are `(I-B^TE)e_j`. Exact
+Gauss-Jordan reduction constructs `L^-1` and verifies both inverse products,
+`EL` selecting precisely the eight mode coordinates, and `L^-1B^T` embedding
+precisely those coordinates. Every coefficient is dyadic. The emitted
+`input_basis_program` and `output_basis_program` execute these two maps in
+place, without extra owned basis storage.
+
+Both bases mix only fields sharing the appropriate physical chart, so scalar
+owner operations implement them ordinarily. After entrance `L` and exit
+`L^-1`, every one of the 632 persistent rows is checked: the eight selected
+helper rows are zero, the other 400 helper rows are unchanged, `Y=y`, and
+`X=x-y+(M/4)h_mode`. Each cache is exactly
+`f_i(h_mode,k-M_k^T y)`. Thus the cache fills a vacated original direction;
+it supplies no additional productive input or job credit.
+
+## 3. Literal physical boundary maps and ownership
+
+Backward frames use complex conjugation of the native frames, as in the
+pinned source convention; they are not silently replaced by adjoints. Let
+`Kp` be the 112 inherited main normalizers. For each actual cache frame `F8`,
+the verifier constructs an orthogonal, phase-correct monomial `Km` from its
+unique missing odd noncharacteristic line, and compiles a monomial `N` with
+
+\[
+ N\overline{F8}K_m=D,\qquad K_mR=RK_m.
+\]
+
+`PROVIDER.json` contains all eight literal `Km` and `N` words, signed tableaux
+and nonzero zero-column phase anchors. The compiler's output is checked
+explicitly even under Python `-O`. All `Kp` commute with `R`, including
+absolute phase. Every boundary word contains only monomial gates.
+
+Apply `2Km` to the eight original mode inputs before `L`. At the exit, apply
+`N/(2f_i)` to each cache. Use the inherited **fused compiled** backward main
+input/output wrappers. The verifier checks 336 main diagonal/shear blocks,
+896 nonzero main/helper coupling blocks and eight helper diagonal blocks,
+for 1,240 exact physical equations. Comparison includes the signed tableau
+and exact zero-state vector, so an undetected global phase is impossible
+within this Clifford model. These equations yield (1), with
+
+\[
+ W=\operatorname{diag}(K_p^{-1})M\operatorname{diag}(K_m)/2,
+ \quad
+ Z=\operatorname{diag}(K_m^{-1})M^T\operatorname{diag}(K_p)/2.
+\]
+
+The main code is the predecessor's `C=diag(Kp^-1) A diag(Kp)`. Exact word
+cancellation and the scalar factorization give
+`ZW=14I8`, `WZ=I-C`; `W` and `Z` intertwine `R` on their respective banks.
+No commutation with `D` or `Q` is assumed. These are finite ordinary code
+maps with exterior scalar coefficients, not additional Gaussian calls.
+
+After normalization, SWAP each cache's **whole physical field and chart tag**
+with its identically zero original mode output. The original owner now holds
+the normalized coupled output; the owned slot holds zero and can be CLEARed.
+There is no persistent erasure and no attempted free chart conversion of a
+nonzero field. `C0` is already zero, so all nine owned outputs are zero.
+Ordering the coupled input/output banks as `(y,h,x)` makes (1) triangular
+with invertible diagonal `D`. Together with the 400 unchanged native jobs,
+this proves preservation of all 632 original input directions. It does not
+emit an inverse schedule or establish a same-cost inverse/transpose.
+
+## 4. Exact local bill
+
+Relative to the original raw backward source, the selected schedule adds:
+
+| Ordinary operation | Added field operations |
+| --- | ---: |
+| ADD | 1,644 |
+| SCALE | 40 |
+| COPY | 16 |
+| CLEAR | 24 |
+| Whole-field SWAP, with chart tag | 8 |
+| Monomial field map | 464 |
+
+Each basis direction uses 822 ADD and 12 SCALE: its three elimination swaps
+are expanded into three ADDs and one SCALE each. Eight input scalings and
+eight cache scalings give the remaining 16 SCALEs. The source rewrite adds
+16 COPY and 16 CLEAR; final cache consumption adds eight CLEAR. The 464
+monomial maps are 448 fused inherited main standardizers, eight `Km` and
+eight `N`. This counts the newly installed boundary schedule; all unchanged
+source warp/phase/adapter traffic and native child implementations remain in
+the emitted word and retain their inherited costs. In particular, this table
+does not assert that a field monomial map is zero machine work.
+
+The original source has 16,273 ADD, 1,164 SCALE and 16 CLEAR. Including the
+new boundary scalars, the schedule therefore has 17,917 ADD, 1,204 SCALE,
+16 COPY, 40 CLEAR and eight whole-field SWAP, plus the explicitly described
+monomial boundary maps and inherited native operations. Nine owned fields
+suffice: the original center temporary and eight retained caches. Their
+initial values are arbitrary; their final values are zero. The autonomous
+helper profile is `{4:28,7:7,8:47,9:318}`. The physical implementations of
+those unchanged native helper jobs are inherited from the pinned source;
+scalar identity rows alone are not a new proof of those implementations.
+
+For an explicit local stability bound, use the maximum of field Euclidean
+norms. ADD by `a` has norm at most `1+|a|`, SCALE has norm at most
+`max(1,|a|)`, and unitary Gaussian/monomial maps, COPY, CLEAR and SWAP have
+norm at most one. The verifier sums upward-rounded base-two logarithms for
+every scalar operation in this finite schedule, obtaining **18,996**. Hence
+every suffix amplifies an injected field error by at most `2^18996`; at most
+`m` injections of norm `epsilon` give the conservative bound
+`m*2^18996*epsilon`. All dyadic constants and word lengths are fixed. This
+establishes local bounded amplification, not a complete coordinate rounding,
+tape movement, recursive precision or outer multiplier budget.
+
+## 5. Every positive fiber width and verification boundary
+
+A free-group identity evaluates in any assignment of invertible native warp
+operators. Therefore the exact rational row equalities and zero-retag
+premises hold uniformly when native operations act on any positive fiber
+width `f`. The scalar owner coefficients and scalar `L/L^-1` programs stay
+outside the tensor product; in particular `ZW=14I`, not `14^f I`. Each
+compiled monomial word uses the inherited prescription: `P` and `X` act
+columnwise, `D` sums its Z4 polynomial over the columns, and a `phase` gate
+contributes its phase once per column. Each address-operator identity is lifted
+columnwise; an absolute phase `i^gamma` lifts to `i^(f gamma)`, rather than
+being confused with an exterior scalar sign. Exact one-column operator
+identities, word cancellation and rational matrix identities then prove the
+same physical boundary composition for every `f`. The inherited native
+uniform implementation hypotheses remain inherited.
+
+The registered verifier performs complete 641-column native row replay,
+exact scalar endpoint composition, and the 1,240 physical boundary checks.
+It does not claim a separately flattened 641-column physical-matrix replay,
+a formal-kernel proof, independent human approval, hosted CI, or a complete
+caller. It rejects a nonzero zero-retag, a single changed basis ADD
+coefficient, a changed saved-cache coefficient and a phase-only error with
+the correct tableau. Normal and optimized runs use explicit checks for the
+new claims. The caller must close all 224 main and eight coupled helper
+outputs, preserve the other 400 jobs, charge every added child and ordinary
+operation, and discharge precision, storage and outer-budget obligations
+before any new target credit or exponent is admitted.
diff --git a/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json
new file mode 100644
index 0000000000..0afd30ed01
--- /dev/null
+++ b/research/fanout-optimality-support/retained/swarm-provider-audit-sol-high-20261024/repository/research/native-rank8-helper-provider/PROVIDER.json
@@ -0,0 +1,13105 @@
+{
+  "schema_version": 1,
+  "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd",
+  "candidate_witness_sha256": "24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591",
+  "word_payload_sha256": "05490717144b3e6c69c0cc9e5c5df5c69d841ca13bf29aabd1b0db180628f038",
+  "basis_roles": [
+    224,
+    225,
+    227,
+    229,
+    230,
+    231,
+    232,
+    233,
+    234,
+    235,
+    236,
+    237,
+    238,
+    239,
+    240,
+    241,
+    242,
+    243,
+    245,
+    246,
+    247,
+    250,
+    252,
+    253,
+    254,
+    255,
+    256,
+    257,
+    258,
+    259,
+    261,
+    262,
+    263,
+    266,
+    268,
+    269,
+    270,
+    271,
+    272,
+    276,
+    280,
+    283,
+    286,
+    287,
+    288,
+    294,
+    296,
+    297,
+    300,
+    302,
+    303,
+    306,
+    308,
+    312,
+    315,
+    318,
+    319,
+    324,
+    326,
+    328,
+    332,
+    333,
+    334,
+    335,
+    336,
+    340,
+    347,
+    350,
+    351,
+    352,
+    356,
+    366,
+    367,
+    368,
+    372,
+    379,
+    382,
+    383,
+    384,
+    388,
+    390,
+    391,
+    392,
+    397,
+    398,
+    399,
+    400,
+    401,
+    402,
+    403,
+    405,
+    406,
+    409,
+    410,
+    411,
+    413,
+    414,
+    415,
+    416,
+    417,
+    418,
+    419,
+    421,
+    422,
+    425,
+    426,
+    427,
+    429,
+    430,
+    431,
+    432,
+    433,
+    434,
+    435,
+    437,
+    438,
+    441,
+    442,
+    443,
+    445,
+    446,
+    447
+  ],
+  "mode_owners": [
+    224,
+    225,
+    227,
+    229,
+    240,
+    241,
+    256,
+    257
+  ],
+  "candidate_mode_permutation": [
+    2,
+    0,
+    1,
+    3,
+    5,
+    7,
+    6,
+    4
+  ],
+  "candidate_mode_signs": [
+    "1",
+    "1",
+    "1",
+    "-1",
+    "-1",
+    "1",
+    "1",
+    "-1"
+  ],
+  "canonical_retraction_E": [
+    [
+      [
+        1,
+        "1"
+      ],
+      [
+        160,
+        "-1"
+      ],
+      [
+        164,
+        "-1"
+      ],
+      [
+        166,
+        "1"
+      ],
+      [
+        167,
+        "1"
+      ],
+      [
+        168,
+        "1"
+      ],
+      [
+        173,
+        "-1"
+      ]
+    ],
+    [
+      [
+        1,
+        "1"
+      ],
+      [
+        3,
+        "-1"
+      ],
+      [
+        5,
+        "1"
+      ],
+      [
+        7,
+        "-2"
+      ],
+      [
+        8,
+        "1"
+      ],
+      [
+        10,
+        "-1"
+      ],
+      [
+        11,
+        "-1"
+      ],
+      [
+        12,
+        "-1"
+      ],
+      [
+        13,
+        "-1"
+      ],
+      [
+        14,
+        "2"
+      ],
+      [
+        15,
+        "1"
+      ],
+      [
+        160,
+        "-1"
+      ],
+      [
+        164,
+        "-1"
+      ],
+      [
+        166,
+        "1"
+      ],
+      [
+        167,
+        "1"
+      ],
+      [
+        168,
+        "1"
+      ],
+      [
+        173,
+        "-1"
+      ]
+    ],
+    [
+      [
+        6,
+        "1"
+      ],
+      [
+        100,
+        "-1"
+      ],
+      [
+        102,
+        "1"
+      ],
+      [
+        104,
+        "1"
+      ],
+      [
+        109,
+        "-1"
+      ]
+    ],
+    [
+      [
+        3,
+        "-1"
+      ],
+      [
+        5,
+        "-1"
+      ],
+      [
+        8,
+        "1"
+      ],
+      [
+        10,
+        "-1"
+      ],
+      [
+        11,
+        "-1"
+      ],
+      [
+        12,
+        "1"
+      ],
+      [
+        13,
+        "-1"
+      ],
+      [
+        15,
+        "1"
+      ],
+      [
+        100,
+        "1"
+      ],
+      [
+        102,
+        "-1"
+      ],
+      [
+        104,
+        "-1"
+      ],
+      [
+        109,
+        "1"
+      ]
+    ],
+    [
+      [
+        64,
+        "-1"
+      ],
+      [
+        70,
+        "1"
+      ],
+      [
+        72,
+        "1"
+      ],
+      [
+        73,
+        "1"
+      ],
+      [
+        76,
+        "-1"
+      ],
+      [
+        79,
+        "-1"
+      ]
+    ],
+    [
+      [
+        17,
+        "-1"
+      ],
+      [
+        19,
+        "1"
+      ],
+      [
+        21,
+        "-1"
+      ],
+      [
+        23,
+        "1"
+      ],
+      [
+        28,
+        "1"
+      ],
+      [
+        29,
+        "1"
+      ],
+      [
+        30,
+        "-1"
+      ],
+      [
+        31,
+        "-1"
+      ]
+    ],
+    [
+      [
+        33,
+        "1"
+      ],
+      [
+        35,
+        "-1"
+      ],
+      [
+        37,
+        "1"
+      ],
+      [
+        39,
+        "-1"
+      ],
+      [
+        44,
+        "-1"
+      ],
+      [
+        45,
+        "-1"
+      ],
+      [
+        46,
+        "1"
+      ],
+      [
+        47,
+        "1"
+      ]
+    ],
+    [
+      [
+        1,
+        "1"
+      ],
+      [
+        17,
+        "-1"
+      ],
+      [
+        19,
+        "1"
+      ],
+      [
+        21,
+        "1"
+      ],
+      [
+        23,
+        "-1"
+      ],
+      [
+        28,
+        "-1"
+      ],
+      [
+        29,
+        "1"
+      ],
+      [
+        30,
+        "1"
+      ],
+      [
+        31,
+        "-1"
+      ],
+      [
+        100,
+        "-1"
+      ],
+      [
+        102,
+        "1"
+      ],
+      [
+        104,
+        "1"
+      ],
+      [
+        109,
+        "-1"
+      ],
+      [
+        160,
+        "-1"
+      ],
+      [
+        164,
+        "-1"
+      ],
+      [
+        166,
+        "1"
+      ],
+      [
+        167,
+        "1"
+      ],
+      [
+        168,
+        "1"
+      ],
+      [
+        173,
+        "-1"
+      ]
+    ]
+  ],
+  "input_basis_program": [
+    [
+      "add",
+      257,
+      397,
+      "1"
+    ],
+    [
+      "add",
+      225,
+      397,
+      "1"
+    ],
+    [
+      "add",
+      224,
+      397,
+      "1"
+    ],
+    [
+      "add",
+      257,
+      392,
+      "-1"
+    ],
+    [
+      "add",
+      225,
+      392,
+      "-1"
+    ],
+    [
+      "add",
+      224,
+      392,
+      "-1"
+    ],
+    [
+      "add",
+      257,
+      391,
+      "-1"
+    ],
+    [
+      "add",
+      225,
+      391,
+      "-1"
+    ],
+    [
+      "add",
+      224,
+      391,
+      "-1"
+    ],
+    [
+      "add",
+      257,
+      390,
+      "-1"
+    ],
+    [
+      "add",
+      225,
+      390,
+      "-1"
+    ],
+    [
+      "add",
+      224,
+      390,
+      "-1"
+    ],
+    [
+      "add",
+      257,
+      388,
+      "1"
+    ],
+    [
+      "add",
+      225,
+      388,
+      "1"
+    ],
+    [
+      "add",
+      224,
+      388,
+      "1"
+    ],
+    [
+      "add",
+      257,
+      384,
+      "1"
+    ],
+    [
+      "add",
+      225,
+      384,
+      "1"
+    ],
+    [
+      "add",
+      224,
+      384,
+      "1"
+    ],
+    [
+      "add",
+      257,
+      333,
+      "1"
+    ],
+    [
+      "add",
+      229,
+      333,
+      "-1"
+    ],
+    [
+      "add",
+      227,
+      333,
+      "1"
+    ],
+    [
+      "add",
+      257,
+      328,
+      "-1"
+    ],
+    [
+      "add",
+      229,
+      328,
+      "1"
+    ],
+    [
+      "add",
+      227,
+      328,
+      "-1"
+    ],
+    [
+      "add",
+      257,
+      326,
+      "-1"
+    ],
+    [
+      "add",
+      229,
+      326,
+      "1"
+    ],
+    [
+      "add",
+      227,
+      326,
+      "-1"
+    ],
+    [
+      "add",
+      257,
+      324,
+      "1"
+    ],
+    [
+      "add",
+      229,
+      324,
+      "-1"
+    ],
+    [
+      "add",
+      227,
+      324,
+      "1"
+    ],
+    [
+      "add",
+      240,
+      303,
+      "1"
+    ],
+    [
+      "add",
+      240,
+      300,
+      "1"
+    ],
+    [
+      "add",
+      240,
+      297,
+      "-1"
+    ],
+    [
+      "add",
+      240,
+      296,
+      "-1"
+    ],
+    [
+      "add",
+      240,
+      294,
+      "-1"
+    ],
+    [
+      "add",
+      240,
+      288,
+      "1"
+    ],
+    [
+      "add",
+      256,
+      271,
+      "-1"
+    ],
+    [
+      "add",
+      256,
+      270,
+      "-1"
+    ],
+    [
+      "add",
+      256,
+      269,
+      "1"
+    ],
+    [
+      "add",
+      256,
+      268,
+      "1"
+    ],
+    [
+      "add",
+      256,
+      263,
+      "1"
+    ],
+    [
+      "add",
+      256,
+      261,
+      "-1"
+    ],
+    [
+      "add",
+      256,
+      259,
+      "1"
+    ],
+    [
+      "add",
+      255,
+      257,
+      "1"
+    ],
+    [
+      "add",
+      241,
+      257,
+      "-1"
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+          ]
+        ],
+        "signed_tableau": [
+          [
+            127,
+            0,
+            2
+          ],
+          [
+            253,
+            0,
+            2
+          ],
+          [
+            251,
+            0,
+            2
+          ],
+          [
+            247,
+            0,
+            2
+          ],
+          [
+            239,
+            0,
+            2
+          ],
+          [
+            223,
+            0,
+            2
+          ],
+          [
+            191,
+            0,
+            2
+          ],
+          [
+            254,
+            0,
+            2
+          ],
+          [
+            256,
+            0,
+            0
+          ],
+          [
+            0,
+            127,
+            0
+          ],
+          [
+            0,
+            253,
+            0
+          ],
+          [
+            0,
+            251,
+            0
+          ],
+          [
+            0,
+            247,
+            0
+          ],
+          [
+            0,
+            239,
+            0
+          ],
+          [
+            0,
+            223,
+            0
+          ],
+          [
+            0,
+            191,
+            0
+          ],
+          [
+            0,
+            254,
+            0
+          ],
+          [
+            0,
+            256,
+            0
+          ]
+        ],
+        "zero_column_anchor": {
+          "index": 0,
+          "gaussian_numerator": [
+            1,
+            0
+          ],
+          "denominator_power2": 0
+        }
+      },
+      "output_N": {
+        "literal_word": [
+          [
+            "D",
+            [
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0,
+              0
+            ],
+            [
+              0,
+              2,
+              2,
+              2,
+              2,
+              2,
+              2,
+              2,
+              0
+            ]
+          ],
+          [
+            "P",
+            [
+              127,
+              252,
+              250,
+              246,
+              238,
+              222,
+              190,
+              254,
+              256
+            ]
+          ],
+          [
+            "X",
+            384
+          ],
+          [
+            "phase",
+            2
+          ]
+        ],
+        "signed_tableau": [
+          [
+            1,
+            0,
+            0
+          ],
+          [
+            253,
+            0,
+            2
+          ],
+          [
+            251,
+            0,
+            2
+          ],
+          [
+            247,
+            0,
+            2
+          ],
+          [
+            239,
+            0,
+            2
+          ],
+          [
+            223,
+            0,
+            2
+          ],
+          [
+            191,
+            0,
+            2
+          ],
+          [
+            254,
+            0,
+            2
+          ],
+          [
+            256,
+            0,
+            0
+          ],
+          [
+            0,
+            127,
+            0
+          ],
+          [
+            0,
+            130,
+            2
+          ],
+          [
+            0,
+            132,
+            2
+          ],
+          [
+            0,
+            136,
+            2
+          ],
+          [
+            0,
+            144,
+            2
+          ],
+          [
+            0,
+            160,
+            2
+          ],
+          [
+            0,
+            192,
+            2
+          ],
+          [
+            0,
+            254,
+            2
+          ],
+          [
+            0,
+            256,
+            2
+          ]
+        ],
+        "zero_column_anchor": {
+          "index": 384,
+          "gaussian_numerator": [
+            -1,
+            0
+          ],
+          "denominator_power2": 0
+        }
+      }
+    }
+  ],
+  "ordered_schedule": [
+    "Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.",
+    "On each mode owner apply input_K and scalar 2; run input_basis_program.",
+    "Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.",
+    "Run output_basis_program on the 122 persistent common-chart helpers.",
+    "For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.",
+    "Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y."
+  ],
+  "paid": {
+    "1": 2193,
+    "2": 412,
+    "3": 510,
+    "4": 127,
+    "5": 40
+  },
+  "autonomous_native_helpers": {
+    "4": 28,
+    "7": 7,
+    "8": 47,
+    "9": 318
+  },
+  "owned_fields": {
+    "count": 9,
+    "initial_values": "arbitrary",
+    "final_values": "zero",
+    "productive_credit": 0
+  },
+  "added_ordinary_work_vs_original_raw_source": {
+    "ADD": 1644,
+    "SCALE": 40,
+    "COPY": 16,
+    "CLEAR": 24,
+    "whole_field_SWAP": 8,
+    "monomial_field_maps": 464,
+    "monomial_breakdown": {
+      "fused_inherited_main_standardizers": 448,
+      "mode_inputs": 8,
+      "cache_outputs": 8
+    }
+  },
+  "local_error_amplification_power2_bound": 18996,
+  "source_original_scalar_counts": {
+    "add": 16273,
+    "clear": 16,
+    "scale": 1164
+  },
+  "source_changed_scalar_counts": {
+    "add": 16273,
+    "clear": 32,
+    "copy": 16,
+    "scale": 1164
+  },
+  "physical_phase_bindings": {
+    "main_diagonal_and_shear": 336,
+    "two_coupling_directions": 896,
+    "helper_diagonal": 8
+  },
+  "exact_zero_retags": [
+    [
+      15608,
+      92,
+      254,
+      1
+    ],
+    [
+      15894,
+      9,
+      624,
+      1
+    ],
+    [
+      15900,
+      11,
+      621,
+      1
+    ],
+    [
+      17269,
+      240,
+      280,
+      1
+    ],
+    [
+      17280,
+      81,
+      619,
+      1
+    ],
+    [
+      17288,
+      57,
+      274,
+      1
+    ],
+    [
+      17604,
+      288,
+      281,
+      1
+    ],
+    [
+      17746,
+      224,
+      279,
+      1
+    ]
+  ],
+  "formula": {
+    "X": "D x - R y + R W h",
+    "Y": "D y",
+    "H": "D (h - Z y)",
+    "W": "diag(K_port^-1) M diag(K_mode)/2",
+    "Z": "diag(K_mode^-1) M^T diag(K_port)/2"
+  },
+  "failure_controls": [
+    "nonzero zero-retag rejected",
+    "one altered basis ADD coefficient rejected",
+    "same-tableau phase-only cache error rejected",
+    "one altered saved-cache coefficient rejected"
+  ],
+  "scope": "Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change."
+}
diff --git a/research/fanout-optimality-support/verify.py b/research/fanout-optimality-support/verify.py
new file mode 100644
index 0000000000..95cad222f3
--- /dev/null
+++ b/research/fanout-optimality-support/verify.py
@@ -0,0 +1,143 @@
+#!/usr/bin/env python3
+"""Unchanged-source fanout replay and scoped-proof custody; no extra engine.
+Chris R / Clear1nsight, substantial OpenAI Codex assistance; Apache-2.0.
+"""
+import argparse
+import base64
+import copy
+import hashlib
+import json
+from pathlib import Path,PurePosixPath
+import subprocess
+import sys
+import tempfile
+import zlib
+
+ROOT=Path(__file__).resolve().parent
+BASE='1a3ced60b2f7a46bc70280a04f2eeb8ca027c700'
+RESULT_SHA='bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7'
+PROGRAM_SHA='5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7'
+CHECKER_SHA='b824bf066999887b96fc386678ce44fb2269dc30406b06d65a9aac43a0437ae3'
+LOWER_SHA='cfa9f3df855f96a3e73bcb8042a750a3aa41d18ec098d6a34268370f3e84d782'
+LOWER_PATH='retained/race-kappa0033-sol-high-20261024/consultants/astra-query-sharing/EXACT-FANOUT-MODULE-LOWER-v1.md'
+INTEGRITY_SHA256='1f94365b800cf480c49904f7056ddc6fb788b4b915ea8ea8353c5b15aed65f92'
+
+def require(ok,message):
+    if not ok:raise ValueError(message)
+def authenticate(data,digest):
+    require(hashlib.sha256(data).hexdigest()==digest,'SHA256 authentication failed')
+def load(name):return json.loads((ROOT/name).read_bytes())
+def inventory():
+    return {p.relative_to(ROOT).as_posix():dict(sha256=hashlib.sha256(p.read_bytes()).hexdigest(),bytes=p.stat().st_size,mode=oct(p.stat().st_mode&0o777)) for p in sorted(ROOT.rglob('*')) if p.is_file()}
+def typed(value):return json.dumps(value,sort_keys=True,separators=(',',':'),allow_nan=False)
+def compare_json(actual,expected):
+    require(typed(actual)==typed(expected),'typed complete JSON differs; zero exclusions')
+def must_reject(action,label):
+    try:action()
+    except ValueError:return label
+    raise ValueError('negative control survived: '+label)
+
+def scoped_claims(claims):
+    upper=claims['upper'];lower=claims['lower']
+    require(upper['full_137_field_physical_endpoint_replay'] is False,'selfalias checks promoted to137field endpoint replay')
+    require(upper['endpoint_basis']=='COMPOSITIONAL_SOURCE_FACTORIZATION_LITERAL_COEFFICIENTS_AND_LIFETIMES','endpoint evidence changed')
+    require(type(upper['paid_H1']) is int and upper['paid_H1']==112 and type(upper['query_savings']) is int and upper['query_savings']==0,'upper call count/reduction claim changed')
+    require(type(lower['minimum_total_gaussian_field_calls']) is int and lower['minimum_total_gaussian_field_calls']==112,'scoped lower count changed')
+    require(lower['bound_interpretation']=='TOTAL_STANDALONE_NOT_INCREMENTAL','total bound promoted to incremental/global charge')
+    require(lower['width_quantifier']=='ALL_POSITIVE_WIDTHS_OR_ONE_CONSECUTIVE_TAIL','unsupported restricted width family')
+    for key in ('fixed_finite_program','fixed_exterior_coefficients','finite_columnwise_ordinary_group','ordinary_initial_span_only','fixed_common_field_capacity','central_scalar_M_shared_right_Km','arbitrary_independent_originals','exact_per_column_phases'):
+        require(lower[key] is True,'required lower proof premise changed: '+key)
+    require(type(lower['paid_output_rows_per_call']) is int and lower['paid_output_rows_per_call']==1,'paid output capacity changed')
+    require(lower['weighted_recursive_invoice_claimed'] is False,'call count promoted to weighted invoice')
+    require(claims['full_physical_raw_dual'] is False and claims['complete_caller'] is False and claims['compiler_precision_stock_admitted'] is False and claims['new_kappa'] is None,'component/proof promoted to admission')
+
+def object_id(kind, data):
+    return hashlib.sha1(kind.encode()+b' '+str(len(data)).encode()+b'\0'+data).hexdigest()
+
+def origin(proof, raw, expected_commit, expected_path):
+    require(proof['commit'] == expected_commit and proof['path'] == expected_path, 'origin identity changed')
+    commit = base64.b64decode(proof['commit_bytes_base64'], validate=True)
+    require(object_id('commit',commit)==expected_commit, 'raw commit hash failed')
+    require(commit.startswith(b'tree '), 'commit tree header missing')
+    child = commit.splitlines()[0][5:].decode('ascii')
+    parts = expected_path.split('/')
+    require(len(parts)==len(proof['trees']), 'origin tree depth mismatch')
+    for part, row in zip(parts,proof['trees']):
+        tree=base64.b64decode(row['bytes_base64'],validate=True)
+        require(row['oid']==child==object_id('tree',tree), 'raw tree hash failed')
+        require(row['component']==part, 'path component mismatch')
+        entries={}; cursor=0
+        while cursor<len(tree):
+            space=tree.index(b' ',cursor); zero=tree.index(b'\0',space)
+            name=tree[space+1:zero].decode('utf-8'); mode=tree[cursor:space]
+            require(name not in entries and zero+21<=len(tree),'malformed tree')
+            entries[name]=(mode,tree[zero+1:zero+21].hex());cursor=zero+21
+        require(part in entries,'path component absent')
+        mode,child=entries[part]
+        require(mode in ((b'100644',b'100755') if part==parts[-1] else (b'40000',)), 'unexpected object mode')
+    require(child==proof['blob']==object_id('blob',raw),'original Git blob failed')
+    require(len(raw)==proof['bytes'],'source byte count mismatch')
+    authenticate(raw,proof['sha256'])
+
+def verify(replay=True):
+    before=inventory();raw=(ROOT/'INTEGRITY.json').read_bytes();authenticate(raw,INTEGRITY_SHA256);index=json.loads(raw)
+    require(set(before)=={r['path'] for r in index['files']}|{'INTEGRITY.json','verify.py'},'package inventory differs')
+    for row in index['files']:
+        path=ROOT/row['path'];require(path.is_file() and not path.is_symlink(),'input missing or symlinked')
+        data=path.read_bytes();require(len(data)==row['bytes'],'input byte length changed');authenticate(data,row['sha256'])
+    for row in load('ORIGINS.json'):
+        require(row['authority']=='canonical','unexpected origin authority')
+        origin(row['proof'],(ROOT/row['retained']).read_bytes(),BASE,row['proof']['path'])
+    for row in load('LOCAL-ORIGINS.json')['files']:
+        data=(ROOT/row['path']).read_bytes();require(len(data)==row['bytes'],'LOCAL source length changed');authenticate(data,row['sha256'])
+    authenticate((ROOT/LOWER_PATH).read_bytes(),LOWER_SHA)
+    runtime=load('RUNTIME-INPUTS.json');expected_result=(ROOT/runtime['expected_result']).read_bytes();expected_program=(ROOT/runtime['expected_program']).read_bytes()
+    authenticate(expected_result,RESULT_SHA);authenticate(expected_program,PROGRAM_SHA)
+    result=json.loads(expected_result);program=json.loads(expected_program);claims=load('CLAIMS.json');scoped_claims(claims)
+    require(result['status']=='PASS_EXACT_COMPONENT_NO_QUERY_REDUCTION' and result['program_sha256']==PROGRAM_SHA and result['checker_sha256']==CHECKER_SHA,'original result/checker/program binding')
+    require(result['group_sizes']==[1]*112 and result['group_ranks']==[1]*112 and result['rationalrank_sum_Qqueries']==112,'retained singleton class/rank outcome changed')
+    require(result['all512_alias_columns_checked']==57344 and len(result['controls'])==13 and all(c['rejected'] is True for c in result['controls']),'original coverage/controls changed')
+    require(program['queries']==112 and program['positiveQpaid_profile']=={'1':112} and program['runtime_odd_divisions']==0,'retained program tariff changed')
+    compare_json(program['ordinary_counts'],claims['upper']['ordinary_counts'])
+    guard=load('evidence/RECEIPT.json');require(guard['exit_code']==0 and guard['termination'] is None,'original guard did not pass')
+    authenticate((ROOT/'evidence/stdout.log').read_bytes(),guard['log_sha256'])
+    controls=[must_reject(lambda:authenticate((ROOT/LOWER_PATH).read_bytes()+b'MUTANT',LOWER_SHA),'changed_lower_proof_bytes_rejected')]
+    bad=load('ORIGINS.json')[0];bad['proof']['trees'][0]['oid']='0'*40
+    controls.append(must_reject(lambda:origin(bad['proof'],(ROOT/bad['retained']).read_bytes(),BASE,bad['proof']['path']),'forged_canonical_origin_rejected'))
+    for label in ('cached_initial_observation','width_subsequence','changed_field_capacity','incremental_bound','physical137_replay_claim','width_dependent_coefficients'):
+        bad=copy.deepcopy(claims)
+        if label=='cached_initial_observation':bad['lower']['ordinary_initial_span_only']=False
+        elif label=='width_subsequence':bad['lower']['width_quantifier']='WIDTHS_DIVISIBLE_BY_FOUR'
+        elif label=='changed_field_capacity':bad['lower']['fixed_common_field_capacity']=False
+        elif label=='incremental_bound':bad['lower']['bound_interpretation']='ADDITIONAL_AT_GLOBAL_CUT'
+        elif label=='physical137_replay_claim':bad['upper']['full_137_field_physical_endpoint_replay']=True
+        else:bad['lower']['fixed_exterior_coefficients']=False
+        controls.append(must_reject(lambda:scoped_claims(bad),label+'_rejected'))
+    bad_result=copy.deepcopy(result);bad_result['query_savings_vs112']=False
+    controls.append(must_reject(lambda:compare_json(bad_result,result),'bool_for_zero_result_rejected'))
+    bad_program=copy.deepcopy(program);bad_program['queries']=112.0
+    controls.append(must_reject(lambda:compare_json(bad_program,program),'float_for_integer_program_rejected'))
+    if replay:
+        with tempfile.TemporaryDirectory(prefix='fanout-unchanged-source-') as folder:
+            temp=Path(folder);work=temp/'work';work.mkdir()
+            for row in runtime['files']:
+                rel=PurePosixPath(row['source_path']);require(not rel.is_absolute() and '..' not in rel.parts,'runtime path escapes mirror')
+                data=(ROOT/row['path']).read_bytes();authenticate(data,row['sha256']);dest=work/rel;dest.parent.mkdir(parents=True,exist_ok=True);dest.write_bytes(data);dest.chmod(0o444)
+            checker=work/runtime['checker'];authenticate(checker.read_bytes(),CHECKER_SHA)
+            fresh_program=temp/'FANOUT-PROGRAM-v1.json';fresh_result=temp/'FANOUT-RESULT-v1.json'
+            argv=[sys.executable,'-I','-Werror','-B','-X','pycache_prefix='+str(temp/'cache')]+(['-O'] if sys.flags.optimize else [])+[str(checker),'--input',str(work/runtime['input']),'--program',str(fresh_program),'--result',str(fresh_result)]
+            run=subprocess.run(argv,cwd=work,capture_output=True,text=True,timeout=30)
+            new_program=fresh_program.read_bytes() if fresh_program.exists() else None;new_result=fresh_result.read_bytes() if fresh_result.exists() else None
+            # Lossless compression is transport only; scientific equality uses original uncompressed bytes.
+            evidence=dict(command=argv,exit_code=run.returncode,result_utf8=new_result.decode() if new_result is not None else None,program_zlib_base64=base64.b64encode(zlib.compress(new_program,9)).decode() if new_program is not None else None,program_raw_sha256=hashlib.sha256(new_program).hexdigest() if new_program is not None else None,program_raw_bytes=len(new_program) if new_program is not None else None,stdout=run.stdout,stderr=run.stderr)
+            print('FRESH_FANOUT_EVIDENCE '+json.dumps(evidence,sort_keys=True))
+            require(run.returncode==0 and not run.stderr,'unchanged upper checker failed: '+run.stderr)
+            require(new_program==expected_program and new_result==expected_result,'full raw program/result differs; zero excluded fields')
+            compare_json(json.loads(new_program),program);compare_json(json.loads(new_result),result)
+    after=inventory();require(after==before,'source bytes or modes changed during replay')
+    digest=lambda value:hashlib.sha256(typed(value).encode()).hexdigest()
+    return dict(status='PASS_SCOPED_FANOUT_OPTIMALITY_SUPPORT_PACKAGE',canonical_base=BASE,immutable_files=len(before),fresh_upper_checker=replay,optimized=bool(sys.flags.optimize),result_sha256=RESULT_SHA,program_sha256=PROGRAM_SHA,comparison_exclusions=[],fresh_program_transport='losslesszlibbase64; compare uncompressedrawbytes, notcontaineridentity',original_upper_controls=13,wrapper_controls=controls,minimum_total_calls_in_fixed_grammar=112,upper_H1_calls=112,query_savings=0,full_137_field_physical_endpoint_replay=False,lower_proof_execution='hash/scope authentication only; retained independent static review, no formal kernel',incremental_global_bound=False,full_rawdual_or_compiler_admission=False,new_kappa=None,pre_custody_sha256=digest(before),post_custody_sha256=digest(after),inputs_and_modes_unchanged=True)
+
+if __name__=='__main__':
+    parser=argparse.ArgumentParser();parser.add_argument('--integrity-only',action='store_true');args=parser.parse_args()
+    print(json.dumps(verify(not args.integrity_only),sort_keys=True))