{"accepted":{"artifact_digest":"sha256:001a8d7459dfec08b9e04cebc2ce71e514dd01360d8f228c90d6141349021601","candidate_id":"sha256:e685160615f4c5c1fd9ab4104178a04efe5f39cac79ac03bc357d4af16eea51b","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-8, 9, 4, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:8228b55e09f7f493b53832c12bf4681a67fd0a54bc099610cb247a5ace9c3f8a"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:74da9551cf0acae0065927905bf4a1c3880ec4a6b22387f7b9d09fb7108b9b70","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -35}, {\"input\": -3, \"output\": 6}, {\"input\": 3, \"output\": 7}, {\"input\": 27, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (9, 9, 4, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:875eca8bc527f65b787edb3e93829e12f1ca157dbfa64d156d4269dd16671e7d","sample_id":"sha256:1c79fe429ae3300061bdfd31befdcc978d6349cea488843f57826e3f7d1aa76f","source_transition_id":"sha256:c1d34ad27abb1164e363170f64a7c85b4491babfe1fa647853799bfa3b324b9e","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-8, 9, 4, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000000","trajectory_id":"vlr-formal-v2-0000000-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:acc8fbd9ac31cd30a51b609e08b7eefd510982a5fa3b71307ab08b519dcce8f0","candidate_id":"sha256:a08a3927b6fdf8a6a3d2a64d1f93b5b2f568b43bfd28e571a0eb2eb1065a553a","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (7, 5, 3, 0, 4)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:b8c2c8d794a5797898661e8e06390e37d70a94475c4142c38c641232f197aff5"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:b27ea1ced12b86171074b9ab0326ec785428678a6ddde440c84f59715723f95e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-7, 5, 3, 0, 4)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b6329b4061771de1710f54a26e2c5b0dd6d53141f1c1091ee256772bfe5238bc","sample_id":"sha256:41c95234e78d820058b134495ddceae0f36f17c4d48e6dbcf4a73c77258782e9","source_transition_id":"sha256:62a697b9819d673704ff3db8e71dc0549adb8df5574eb88161865b7bf3f6bcd6","split":"train","step_index":2,"target":"def transform(x):\n    bias = (7, 5, 3, 0, 4)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000002","trajectory_id":"vlr-formal-v2-0000002-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fc5a19812e8271a2093481d8fea1d85b4fb1374f522d079d9c78f39b411d4586","candidate_id":"sha256:e55d4aafd8bc7d79e4fc142e91c18995693fb6bcff287c5608898de1b04b460f","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (1, 2, 1, 8, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:0dd06f76b057bf65bdb7c8cd23955510e306f241d5208499343504ad7787188a"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:b9bde48604e0d196315546d864bbb1ae72ceee2cded6a74f4c2ebbda27ce0745","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 24}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (1, 4, 1, 8, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8d921243142ab4a8142a06474f08ab454308abde95aca07b2ef1830a1fe8a142","sample_id":"sha256:d6353fba85d8342024d3b8623f8e1c9481cfa6c50d17879ab071639da01816dc","source_transition_id":"sha256:35c970a7a2def0a990053c40d648e024d26a033b7fac63aaf48bb1a686c32174","split":"train","step_index":2,"target":"def transform(x):\n    factor = (1, 2, 1, 8, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000003","trajectory_id":"vlr-formal-v2-0000003-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e543996ddbd1b8cfd490cea33f73df5b570f2a3ff9d080fb103fb8ce0e575108","candidate_id":"sha256:00c249964319f5a825263f1678c7d99ceaaac5e6c19473a4d3b72d24f84ce04b","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (4, 2, 3, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:5679cda41ec309b78e6b3d6812c2df2a32da58a9432faca7e42e4ed02c0f8b27"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:981837d7306508681ab618dde3b78281bc7156d9afff76dd59a08e2f369e2ec4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 2, 2, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:65b667d0e1f62b848bfc7d46da4aa7b77071da6bdab36e9143f77d1068425a04","sample_id":"sha256:f1ff4ceb8b76150e51c51ccb6a6825c624ecf38ed4598be22c287f705301ecbb","source_transition_id":"sha256:f9d784cf729001e850084cfae4c0c4c7353958453eb1b982f8a9616dd95d46c4","split":"train","step_index":3,"target":"def transform(state):\n    delta = (4, 2, 3, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000005","trajectory_id":"vlr-formal-v2-0000005-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8c0a62924ff54f6cf552f686c5ce2d6bbdccd8e6c0117dc855609c9f6cf3389c","candidate_id":"sha256:2667a107593f316110bc28873d0b393f6ce53e935e9d0e66416bb41d39cf87df","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (7, -5, -5, 0, -7)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:2a1a95eaaae309b7acb7abb838a83c3521b7910294fd73ec10660f4ce06e3c83"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:149a8afdfaa08b629b0ad3cd3a778a69d2ec31cb270df5bd6c833b368318060d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 2, \"output\": -3}, {\"input\": 4, \"output\": -1}, {\"input\": 6, \"output\": 6}, {\"input\": 8, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (7, -5, -5, -7, -7)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e00bdd987640517e071370f3a5274f2c6a2c8921c1712ea5c633ae41ad1382fe","sample_id":"sha256:7dc8b58be20666ca07784d5d1d5875567cf8be33feeebaf1e7b94a13cf57e391","source_transition_id":"sha256:33245f3ba5b5c066bad7bfc766a2b343b4d8207469d7be975fe7623b38bd403c","split":"train","step_index":1,"target":"def transform(x):\n    table = (7, -5, -5, 0, -7)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000007","trajectory_id":"vlr-formal-v2-0000007-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e90bddbd4ad6cbbba0b45b0d1c4a2a28d950a0ea756629034f37006ee5604556","candidate_id":"sha256:e38b6207b4dcbe50a1405c9cdc46f143c1c5cafac4b00a85d16f6df4c572194b","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-7, 3, -5, 1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:6aa5b6a6e17224059c9b3e1e0298223da556f0352932624d2b20c209b0ca6ef9"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:4075d2b760cc25c80f8f423b38817d520e96a9008791e91436cc52956d2f77aa","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -34}, {\"input\": -3, \"output\": 0}, {\"input\": 3, \"output\": -2}, {\"input\": 27, \"output\": 28}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-7, 3, -5, -4)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:4a524487f5230fb1881c1e358b46051138851e791e8829fc6c22a375e17b942d","sample_id":"sha256:a141f9eee069019d5d71b004971eb13bdceb65d241bd23402e8173a0890167c4","source_transition_id":"sha256:dfc506e179fac380905382d4770ad3d8708d7fa8411aadcf31bbd60bd309ec2d","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (-7, 3, -5, 1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000010","trajectory_id":"vlr-formal-v2-0000010-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ad8fdd631491766012abfb61ee169e88975e99665d2df362a6b466e895a32e8e","candidate_id":"sha256:c6729494035b2d0f43c3a72c062f967c6b7c8454e4a142145b7955b299cfa248","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-1, 7, -1, -1, 4)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:33fd6dfae9289b2c7859059924b2cec92456c34ad7af3ca8defcea27f617d5e0"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:a8885835b7d5220f7d191542d4406c7b1eb0a9f3fa1049e3a5973140672661a1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 2}, {\"input\": -1, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 7, -6, -1, 4)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:98dc7418d92291cb7d2f893f6ecb74bf977fafae426619211a8e38c1babd48b8","sample_id":"sha256:18772458c198986fac9967d76b02303910f62ee84f4a4528cc6d6ab98fdbb62f","source_transition_id":"sha256:986bad7351cca4cea41f5df009bf764b799a2eda78fd1905cec1e70da24fb1b1","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-1, 7, -1, -1, 4)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000011","trajectory_id":"vlr-formal-v2-0000011-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1933d648eff93bc846e368fd96adae51aa87aa31eaaf6d268035b1af64d9ab29","candidate_id":"sha256:d7829a01d3c645d07cc78628d617b53ee4fb487d1170cf86383d846c1c7ac237","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (2, 4, 2, 4, -6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:d7c3d0ad943741a0a124f47aa835aff0c5cc278de3ed4c940d066c44c3d53689"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:a7ccae005d40cada86dbd8ef5bc5d77716d5514fd166440a2fc892a9863b9b90","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 13}, {\"input\": -1, \"output\": -5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (2, -6, 2, 4, -6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_003\", \"quadratic_residue.protected.case_004\", \"quadratic_residue.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a16345a3ad17f4bb97ce868f85e3e0f48664905adf9d96dbae3b51b7cda020b9","sample_id":"sha256:bc889de72490cbe626e59b527875c44587c094b63ef0ef01736668fc5ce05f5b","source_transition_id":"sha256:b5d006dd79efd1503b16f2b904321f0aee65430ac44f6b05164d58430f617ebc","split":"train","step_index":1,"target":"def transform(x):\n    bias = (2, 4, 2, 4, -6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000012","trajectory_id":"vlr-formal-v2-0000012-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e39b2452decf1b14a6e8c537ebc5da72970c41d790f9d35869c463883fca8791","candidate_id":"sha256:8876de54b2866084b91811d0193872a57759dbe9fc2432034a1eda322e5a9ffe","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 4, 3, 9, 6)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:d8a51e4ccfa2abdad960b9fa4cdcd669713e2b159faa7c04cbf18574842f8ca6"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:25c48d57cc792f3d368f9a421a8ec1c9922537030f8813421a11522c47964438","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 27}, {\"input\": -1, \"output\": 23}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (6, 9, 3, 9, 6)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0f8c15551339fc52130f0d7cbfc8cfe98421f32971c33e21ba90b2fc89f26d8c","sample_id":"sha256:fd641a9f792bb8394b3ab140c28e70884971ca01179af5e7ba4f891f6526c23a","source_transition_id":"sha256:d0320f7a002e20b5d2d39eedd94cc4b4cf0a66f23196d59bbd415915934582e1","split":"train","step_index":3,"target":"def transform(x):\n    factor = (6, 4, 3, 9, 6)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000013","trajectory_id":"vlr-formal-v2-0000013-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:069958e455aa6d6b5f1acde3b54b1435d2c41e95c1a765dd264c65c028c376af","candidate_id":"sha256:e1af980386a28efbc1836a3df23a58bf5ad969f4a797ef0ed1acf6a6bc83f4ef","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 1, 4, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:51bd6f78e4a5e1702d463bb294afa949b153e6926bdccdc277e398eaa9b56a06"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:3fa93449c9880fb56a785d13f5f9660b8f7c7bafb5bbdc8432eaa27ec702b870","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 3, 4, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_003\", \"fsm_delta.protected.case_004\", \"fsm_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f0e6d6f6b7c068a18a8d5b69e53aff9ac19469f4b534744262a096f6225441bc","sample_id":"sha256:02d19f61bb58bfcb66f270102ad7d8520625702b3ee6c8b0b9ff024005f5ea79","source_transition_id":"sha256:2490da4815c978c35ca4ea98bacfafa6ea57921566e8a3b6c49425f431fa49ef","split":"train","step_index":2,"target":"def transform(state):\n    delta = (6, 1, 4, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000015","trajectory_id":"vlr-formal-v2-0000015-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:132cebac342f8b46c040074b57dd1e99a5e4a3887e8cc94e0bf9e57fddb42ddb","candidate_id":"sha256:2db504811374823c9306fea467bdc24054fa7144f9ab31abd350d949c249add5","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-3, 0, 0, -5, 7, 1)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:4b7f08e30580347d4df72e01b7a289dbc3ea3ed0d26ccefb60fc0adc5eded5c5"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:286fb5d0f64cf228be4c686bcbe770204875484203a9839ec5b9ce444b318a4d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": -2}, {\"input\": 4, \"output\": 11}, {\"input\": 5, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-3, 5, 0, -5, 7, 1)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2f39f3aa72f69f1d01eb086eeb5d88802333f8f0887b38c6747f92f725aac7d8","sample_id":"sha256:7073faf443aa9e60da3ad49c8a3fad93aa6223218ccd0e3dc5215f2648a056bc","source_transition_id":"sha256:cf6a894964b0f1ab8d7b6f7e0b3ff3569980478c7f1f92388a9102ceceb254f7","split":"train","step_index":1,"target":"def transform(x):\n    delta = (-3, 0, 0, -5, 7, 1)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000016","trajectory_id":"vlr-formal-v2-0000016-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8f6b059a72237ad21dfd4f34ec4b0b30768843e619c119f5f06f4576173ceae6","candidate_id":"sha256:bd13a9cb2d49a41254d7f5c06c4393ed003099953059fac93ad29dc97e230569","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (2, 4, -8, 4, -6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:f5de8da61951dfe77d0e0d8aa72bc5ad309822186349d49ffb6f830e6b2752d1"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:b4f03caafde0363e8c0019a3c007ccf38e762acdd9807db2f2534b60c41e631e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 2, \"output\": 6}, {\"input\": 4, \"output\": -4}, {\"input\": 6, \"output\": 10}, {\"input\": 8, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (2, -1, -8, 4, -6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:bd7100fbd860a7de80d082e039ff83905dc709c4d33c25df79b2f43923b16cd5","sample_id":"sha256:9df50c8450b6e5e43e2b21a1a31ca87b56be7d2c25a623f5191e1e6d426d21ed","source_transition_id":"sha256:4307beaca5e881e2add002f334e89f7f5bd5afe4e087e2b992a1ba26a3c7bffb","split":"train","step_index":3,"target":"def transform(x):\n    table = (2, 4, -8, 4, -6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000017","trajectory_id":"vlr-formal-v2-0000017-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:52246edacf3c4b22f1d8821783a09cd9cc58d93b324d2388ed7728572b554122","candidate_id":"sha256:1dd8de9b2894faa58cc68b0fb73d09de05e3fe0acfdc001b78b655530ba1c4ed","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-5)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-9)\n    return x + (1)\n","verification_digest":"sha256:0806dc1c483e689f3c9d0fc77b8c3b6a923ebf001d4b8f887c8f4cc441ea8dea"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:648e074ede99e05483f1e84e2e5a0c88c756ae9271178d3b1451eb0066856047","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -32}, {\"input\": -3, \"output\": -12}, {\"input\": 3, \"output\": -6}, {\"input\": 27, \"output\": 28}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-9)\n    return x + (1)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b8724ad0d67128402ffb9cb75df18987945a4bc5dd037b3008ded307eacea6ce","sample_id":"sha256:885ac74db61183baa0f2c82332e8f50a1ee381ce86c53505bc84c83ae1b360e0","source_transition_id":"sha256:58434032f779119b3a6c974971813fda7d2b45a75fa9025c24f2a1a9c7813b9a","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (-5)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-9)\n    return x + (1)\n","task_id":"vlr-formal-v2-0000020","trajectory_id":"vlr-formal-v2-0000020-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:72653c8aec1c83aff05c4eed810a25cdee708d1836055043adff85742a25ecf8","candidate_id":"sha256:0cac70feafef0eaf3bb133ac3e62c4ea8e8dcdf2d4801eb46f3195412e12afc6","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (8, -4, 5, 5, -3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:3bed16e7abdd4cfb32fc90ced43c949696ed16e7f963cc94d47ab8d4ac29ba52"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:f3eaa3435231c52500a5ee1185ff9dd968eb616a37daa9f03feb7590511c0555","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": -3}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 8}, {\"input\": -1, \"output\": -4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (8, -4, 5, -3, -3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0017b8bb1d99f410b4bd808a25b832b57ae2d47d11d4cf64b300a657a6be39dc","sample_id":"sha256:3ef6d07c372f80d4f27af59cacc260feeb10aa196601140fc96ac1c1c6c7ba1b","source_transition_id":"sha256:204db14139bf5d6ca355fbd6dc5988b1693b685e888aba8728e4c39908f13c1e","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (8, -4, 5, 5, -3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000021","trajectory_id":"vlr-formal-v2-0000021-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d34c87e388b2411294f48ba71bc427e2d07fa30eb6543de013e7aaea1c2d6e54","candidate_id":"sha256:f93d323901af5435a9e1fc21b6f08e40e524a60a832d050b82ea5b04981d42a1","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (1, 3, -3, -1, 5)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:ad91be7a4814eb27c46983bc90ec56eaccb10a6495bdb742c4b4bf9f3a1cedcf"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:a85d127d94b869e92a1c4af0cb3ba8296bf34f961305a9f52ec0495cf642c1c3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 8}, {\"input\": -1, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (1, 3, 1, -1, 5)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6bf779bcc67942d37027ac0f2db485610fd572782fe77aab8043377805bd88d0","sample_id":"sha256:f60ef827e1504381501d62543690ce8eb182894c49f407c46e905ab36a336fe6","source_transition_id":"sha256:474d855fcd61b816b95c0117529aca4de7232126adc9e730756096258594b0e8","split":"train","step_index":3,"target":"def transform(x):\n    bias = (1, 3, -3, -1, 5)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000022","trajectory_id":"vlr-formal-v2-0000022-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:eda606a6115fbcc2166cbe489669e406191b99b9dbf0fd2fd9fa85281ee2be7f","candidate_id":"sha256:0b09af9cbd4908a51d5173ceb89bb6ecc0b2dc3a380f8a0e209504089cfc6607","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 6, 4, 4, 8)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:1048674dcdef0651e212618630fac0c177556ca6f7d7a77553d6861fb6c79bae"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:52034f93cd21df83083a6380c254fa6766b7f12cc69d5bacec7ef258ecadc020","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 21}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (6, 6, 4, 3, 8)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:584b58dab15f1220ae0cfa08cae33e49e1f7a367b54d06fc35d9d06a29249e59","sample_id":"sha256:4f26b629af42e7dfb36a7b5fd389d6c25d7b9ea5951bb30519560029199afa47","source_transition_id":"sha256:1daa0ab9bf39cf15721945fe3c279a93c019d4f833bf33918913c21f86ff41de","split":"train","step_index":4,"target":"def transform(x):\n    factor = (6, 6, 4, 4, 8)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000023","trajectory_id":"vlr-formal-v2-0000023-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8601c469f006bd273555328f668064e57623e7683de4ba1637b24c0883f51997","candidate_id":"sha256:b969f12e3bf808b3448d43d8ade010dc1ee5ad38ea4a426d68a3cd09fa815f6c","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (2, 2, 5, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:2072643e066c38e1c408c9d1da0818c00f52cd9c671064d96f38d3618d2b920c"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:06d14911883053f32c4804e6a9bfc94c62a213df7f60dabced7614477ab183bd","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (2, 2, 5, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:4c03434a61e62fc3a1c82994a709934cdb1175c5440f01c68576d7c88d5fb602","sample_id":"sha256:7e622c5044d02c109a28920c9363e8d9031745fffd245132df9e2955361b082e","source_transition_id":"sha256:d7c69fd376ee5b60f8b399bd6174f7223e7222d2d1727be88e48e13d31bad944","split":"train","step_index":1,"target":"def transform(state):\n    delta = (2, 2, 5, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000025","trajectory_id":"vlr-formal-v2-0000025-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:086d356c3a87e61beeab4006e85a630bc0395d3505a4b8e5c66a03c0fbf06f45","candidate_id":"sha256:a907d4c9437f1c5b4eda61eaf9bce963c591bf4e113a83133188efdc1f9c50eb","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-3, -1, -5, 6, 3, 7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:976d5ef6746bf4b534f894669b2b25895e469b202c4d16c77b2668d5f96acca9"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:3db49de55a918ab2ced2ebed1e569e264bd108f2ccf9cf99103b2b343d0deb1b","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": 9}, {\"input\": 4, \"output\": 7}, {\"input\": 5, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-3, -1, -2, 6, 3, 7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6355fd5e009fd48d20bb3e5e35366ce78e8197d7a932e4b2624c558b034c3cc4","sample_id":"sha256:37e844eab2bf1ac75c52de3cd44334201baf9f11cabbbd795ee42be4bdd2b43b","source_transition_id":"sha256:9acf92947a345c430fc411e7614edb7d44052b9ce367f52749ff341db5b97ff8","split":"train","step_index":4,"target":"def transform(x):\n    delta = (-3, -1, -5, 6, 3, 7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000026","trajectory_id":"vlr-formal-v2-0000026-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9f72a5dd094ca217c363840ee4c9702a2fa5d1a49d330ee0e001332a7f04318d","candidate_id":"sha256:871ee0cef40016129f8f8c646135d7a2577eb41750868a7f64f96ac6924a13ef","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (6, -6, 5, 3, -1)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:43378537c1f805069afdcc5d0afc3b11bb23db5072d44372d870cc3618868e0d"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:c63ff24290406aff4fac8c88ec9361db4e550b7bd6e6e8e9db1dfdedc428a316","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 2, \"output\": -4}, {\"input\": 4, \"output\": 9}, {\"input\": 6, \"output\": 9}, {\"input\": 8, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (6, 1, 5, 3, -1)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9a49d0f3e7b079a268724a35ea9a54d43086bfb02bd32e1f8269696ccab4a5d5","sample_id":"sha256:de587254e1e3d79aa9b72b52ac52414dc48d942e7c4c8d96447da839b6d4bd36","source_transition_id":"sha256:7758f02cfc8c6688c6578065452f45c344be8e4f7d96e048afa26504b36f60f5","split":"train","step_index":2,"target":"def transform(x):\n    table = (6, -6, 5, 3, -1)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000027","trajectory_id":"vlr-formal-v2-0000027-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a74fc6d2428fdef6f9660fe5ebe175cb813997e1661fc15f75845c689168a12e","candidate_id":"sha256:81b2bbf05f5d6cf4d125bd129d36104a041bf5233d7f6d2f12ab6bed8627de95","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (2, 3, -2, -5)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:1e0fd7cb8a1d8c1eb9ca513aa9b98629279265291e310fe731e08491ec538639"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:298ffa20b3ba20fbf83e34e8b3d345bf501ab38cd06ff5c31b1ae07732c6d016","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -25}, {\"input\": -3, \"output\": 0}, {\"input\": 3, \"output\": 1}, {\"input\": 27, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (2, -2, -2, -5)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:af6a1c514d056c9b9af5829a52a75004fbc5dd116d400cf934b785f81847981b","sample_id":"sha256:14b852c9b4f8828208063cf0bb5df6d7c57da72ba78d11f9ca7f291007979859","source_transition_id":"sha256:6c6f9b5a312017e3d028e1df8d2749d374dd81bc7d1fcd11aa0b5842d97f948c","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (2, 3, -2, -5)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000030","trajectory_id":"vlr-formal-v2-0000030-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ef5299c523284e80bb9979bdbb3a450e123cc3a8fdafdc3ab004b42d71fc4df3","candidate_id":"sha256:2a2f5aecf6e7d2d0c95c50b8a4d516f8ce89c65b613980931a94820c931f5bd5","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (8, -2, 6, -7, -3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:fb2449218b06cb35eba48a149ea04e6735f705ea73e0f21a54f97656901faa00"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:a0f82ee01041564f74939e428ea757cb421125b78bd8e4480d1736854bed4d28","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": -1}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": -4}, {\"input\": -1, \"output\": -4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (8, -2, -3, -7, -3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:435af411791ec128e52345cb845b5a1b777be7025a6ba2b67210cd7488c276a6","sample_id":"sha256:9b8553354a3b22956f6bd3801817e88897b0583e583be3145ec8b0eab727c111","source_transition_id":"sha256:a6574fc28a5f38009cc18e6f1d44c9deaf372ed40ae297710b956d99d1e26f3e","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (8, -2, 6, -7, -3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000031","trajectory_id":"vlr-formal-v2-0000031-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:4d11e121881666d50d0a222ced42d70b42bbd435653f84340a11a5f35eeff1e2","candidate_id":"sha256:8f54f14cc1b24f519c3f8316d2a64b19e57a5246026a4b20e545937a2270c978","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (4, 5, 7, 4, 4)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:726ebeaa99de540a1c2f16161989e539a94069bc8e6b685884a4a8893905d1c4"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:c0ff6314d7aba2f3be7b5fdd6817fb778d2365e767adbd3f5c4b06e73021211e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 25}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 5, 6, 4, 4)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c885714026cde814593449c5c7bd6e0e73c268c4ac15ad61cf619b229b2639cc","sample_id":"sha256:6bec68f540f1cae166a7c2b180231ec5ae48e726eec6bef7b724c7ed83f86d82","source_transition_id":"sha256:f7a66adf864fdc9182f854f129c8939b046e7923a4b6165e9fbafb18758a0b2c","split":"train","step_index":4,"target":"def transform(x):\n    factor = (4, 5, 7, 4, 4)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000033","trajectory_id":"vlr-formal-v2-0000033-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:4cab7b1c2e24c12d7f6de1ca20c5750cca19ea5753e1980620ea28816f54ca7d","candidate_id":"sha256:ee14cd955a8ef5cf3cdc82b80d993566cddef441d0c83cc295b1a0ffb6d5ac0c","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (12, 1, 9, 8)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:b9fd50967c57a02c8533481a026b38f9dda9656ce706de7351005b5419a933cd"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:b9a5c29b19dbb5d79b8f2420be3cbf8a3578979af424088aaa46514323497595","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 12}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (5, 1, 9, 8)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2e75120b9b63f226279884a27649ab02f62401ac8a64aa6746d6907d01b2d8e4","sample_id":"sha256:cae09922323fce07bac6867e6ae765cfe380f7f4c412707c44e35cea0507a9b9","source_transition_id":"sha256:8842edc50223423b99bce93e1d1d0d7ae464d7e64eb407edad2e84a480a81a45","split":"train","step_index":1,"target":"def transform(x):\n    masks = (12, 1, 9, 8)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000034","trajectory_id":"vlr-formal-v2-0000034-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fd877645cbc3014acc33c3891281763f05b1b92b4483288a8c9b294cf5ee9c77","candidate_id":"sha256:ffed1eb03b5bb790e553ba726671235573ef43cecd5c3d8889dfdc925077eee6","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (4, 4, 2, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:6f2c27ca713ef5ccfb36db1bfdac3dc94390dfdeb96179697962c674c1dc037c"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:102ef389e6cf2de248fc87eb6c59270287c48e9665a0c8ca5d37d0ab2b2a3930","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 4, 2, 5)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b4975a36512bea99712d9a4b9b5c4fb2b52962d50ba7220f748fa789ac76548f","sample_id":"sha256:dfd073c0e706bb88ba98aaeccc23abcbe2ab3c452e77168d742b7d6e75d0cec7","source_transition_id":"sha256:cab8f025045a2f9f01652b07ae6782fcab884397031ce0e2d7f93cf402a608cc","split":"train","step_index":3,"target":"def transform(state):\n    delta = (4, 4, 2, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000035","trajectory_id":"vlr-formal-v2-0000035-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:52ffc3a85a2db51c0f3e884c4aa0058b2a55f2c611a84081f64175047d07f0d5","candidate_id":"sha256:759212a79ed3880979b563f014c0d2c804bdfb257fa43049b81da82400765bda","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-6, 1, 7, 4, 4)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:77915dc571d3106904d78088cb850a508cac687c6294b2cb073c3933849b1efd"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:fbd9f0da8600c737d51a8ae6b8a159513434cb45bf1e5c1e2120d3c54c323ace","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 2, \"output\": 3}, {\"input\": 4, \"output\": 11}, {\"input\": 6, \"output\": 10}, {\"input\": 8, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-6, 1, 5, 4, 4)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_006\", \"signed_bucket.protected.case_007\", \"signed_bucket.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6fca8cac197153be95d1346d2c7ea0e0bf4373532ee3d346851a7b4b8877e744","sample_id":"sha256:b0aad975106fc14bd23aa323eadaa5dba530e7124646966204a429dbe4ecdaca","source_transition_id":"sha256:cd7f5c128cc2ad56d86c7c44379ec21e9035dc049bead67f2c56db68041d311a","split":"train","step_index":4,"target":"def transform(x):\n    table = (-6, 1, 7, 4, 4)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000037","trajectory_id":"vlr-formal-v2-0000037-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8847c4ca027d07cce1b57c42f263419457591a8e2e54302c376bd728bd1e5b65","candidate_id":"sha256:1ab7dcf1bd4bacf5f66cf1ab04ba7dca47ebd61f97809422d38a1ef75d431c2f","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (5)\n    return x + (-3)\n","verification_digest":"sha256:a279589024977a0fa29356a9609146a4e2b05952f6ca6cb7a294b273e01200c0"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:333a4acf487d23aa4099104255f9d650bf623bbe57c3c288c0e7f9f1ff7c17ba","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -18}, {\"input\": -3, \"output\": -12}, {\"input\": 3, \"output\": 8}, {\"input\": 27, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (5)\n    return x + (-3)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d95e4179082ce110bb82a1f525ea7366497dcacc3af5e763c5324b2855003a7e","sample_id":"sha256:3751e1e2e137fa6651e92c1bc11e15645710095c6a12975ae30065318c421aab","source_transition_id":"sha256:e9e11ec5cbae93d4223b04488370d202f75e42f77060c48a3013f3326d6cdb33","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (5)\n    return x + (-3)\n","task_id":"vlr-formal-v2-0000040","trajectory_id":"vlr-formal-v2-0000040-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:abcb2b3a51903f2363dbaec7345e455a72ecbe66dd085085c1b4f20dafade0c1","candidate_id":"sha256:81ff883df049e68a9a3de5bd69960354cc1ccdf186bd650decf8a8f3964a9db8","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-4, 4, -1, -2, 3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:167a02cf4196f56982d547d6b4c3e8cad1d761fac069936e50c97648c33cf5a6"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:7c80956b22b6bc31ec73f4e2341e3a194ed31a4f3e4acf1f70a2a28b41bc1698","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 1}, {\"input\": -1, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-4, 4, -1, -2, 4)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ae7e9517b9a34be83bc1734721d92d1ae8d00621a7d01fdccb9c4cd871cb4ea6","sample_id":"sha256:d9bad51625289af3e79f4a7ede1b7adbc98851cd8a0cd0a35f1258ce5ca2c634","source_transition_id":"sha256:c1e7546b1cd36892220d4149032067c48b02c0739ecdce7d269835ee619f0bb5","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-4, 4, -1, -2, 3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000041","trajectory_id":"vlr-formal-v2-0000041-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d718e27a3b1c0a32ab8a4374d541cdfc76949bbefcad64341fda94edf1e7ebd9","candidate_id":"sha256:af4f2502c382f8e242b39bdcd0f8861b61feb5165d5c6c29459e30ea5de46e38","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-6, -6, 7, -2, 6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:46aa6b745316ef5676af272a4a09c69ef8b6316ae0a3593d7f73da93e69fa273"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:2b98cc8546908dcbaf153edc338ad22e0621750a9fe3fe64c08255061918e44f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 7}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-6, -6, -7, -2, 6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ee3fafb8db13f446dce64e7739005d994598d06919a51d0590024c8e4cf78c95","sample_id":"sha256:7710f75ee819aacdff3de03eda2f76df1d534cfff67726326e7f6a19f1c8e7dd","source_transition_id":"sha256:ecfc30a55ff3d2f79421848c19b43d3fa6b5d47a4d6a550867c63e6fe35c16de","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-6, -6, 7, -2, 6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000042","trajectory_id":"vlr-formal-v2-0000042-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:bb6b4227495f40002022357a4919c50a43e7f0eeb8f771ed887a77cf6aa1fe45","candidate_id":"sha256:9af34cf301cd6e4b7eaa5650ac102c979f8df7f1d5b0d21bb258f2990a21ffdf","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 3, 1, 8, 8)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:3cf68c7c92adcc2315146c6533735805e1f2f5003453a31153c6f999273572a6"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:68f05ea2b49805241d5411e5e90400b591faa656061b64bb727eec9d5c378fbd","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 24}, {\"input\": -1, \"output\": 21}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (6, 3, 1, 8, 6)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_012\", \"mod_product.protected.case_013\", \"mod_product.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8436a7ad505091a4ebb2ed254f09f1715644650b5750ca9fa5ea731d7e72adf8","sample_id":"sha256:e27685248e06be0994e86b294112aea2ecf03a68dd491e0615472849a3eb7cc0","source_transition_id":"sha256:982ed57b04d82044889714b7e5d29650ed087436a15aeabf0407235d72806a8f","split":"train","step_index":4,"target":"def transform(x):\n    factor = (6, 3, 1, 8, 8)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000043","trajectory_id":"vlr-formal-v2-0000043-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1f8c7da51694f6cc09cf754e328b4c8732c6bf71f45b400bb214f9da457609ed","candidate_id":"sha256:b758ccc7df489f1411498310847cd0bbf1242b75e69f6f89c7ea34fce280b950","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (5, 2, 10, 14)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:9bd42215ba4831f13cc4cd515592d56c39fba94ced8f650a24c51607caf60c8c"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:66ab7d274c9130e13a18ce1583912fa001640b98b968f7c274e26bcc32299a1e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 13}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (5, 2, 11, 14)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d7b10fe6e1329c19facecc8fa1da41e21550e981ae94bb534bf9ed8e92a322e5","sample_id":"sha256:7add7b24c009aee3e36613fd8c8cba58e372a95adac143609f128d19e28cdaa5","source_transition_id":"sha256:f35b02ffdc7ba5d150edfff9d86a446cd63a801ec85e9137bec2763ae094f7cd","split":"train","step_index":3,"target":"def transform(x):\n    masks = (5, 2, 10, 14)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000044","trajectory_id":"vlr-formal-v2-0000044-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fb2162222e9ef602c858a83b028ffdf0a4832a51eba935c1630067f2f4be3e9e","candidate_id":"sha256:25473cb7f0a6b01b3f5e14d8118af1e4b7ae188496cf78429e3c6636a2dad6a9","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 4, 5, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:4571ae812c799f0d6f47c83511acb9099e025da7a74241b4af168db8bbc363da"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:7d8b9b293f9842937a4993db30707ff57820502b5a3b95d1eeb3315c9149d316","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 4, 2, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9fd05c70748dacf3d16902c563c86e6d4f6f7e9859fcef367fe9b8b2fc49c0d1","sample_id":"sha256:29c09dfb5dbd9bb6785dd22e11346f2e1b8731592702a695a05797a058313fb3","source_transition_id":"sha256:7b5b8822a4f3fa83f0b44b3f6082a2704d29bc17a081ea329d5ff8b84df176e8","split":"train","step_index":1,"target":"def transform(state):\n    delta = (3, 4, 5, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000045","trajectory_id":"vlr-formal-v2-0000045-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a2c03e3b461aff846596fddd40b0d771671baf768b75fb48ddb794ee1f59514c","candidate_id":"sha256:2841bef71ab6caabfd94ac028e9d7ce523a71d8ea0ceb10e3255e6d35ee302e0","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-5, -8, 6, -1, 6, -8)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:7e79c6600d0e8e64495258b6a219c07f217aad87192bac0e7c7a70ec78d3ed1a"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:e324b55d121bf3e608886aea58f985ada5d81047675a6d6ef3c453f264207d27","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 1, \"output\": -7}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 2}, {\"input\": 4, \"output\": 10}, {\"input\": 5, \"output\": -3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-5, -8, 7, -1, 6, -8)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:faeaa8eeba40227bec9526aeff11cba3a32cea914ce0e3fe1c1096dff3f2c4d6","sample_id":"sha256:1d0434650afe426a23fd216b8afcb710a385578bb812ff9b83f4bca423ac15cf","source_transition_id":"sha256:c5005b6803dd4d337c320509496771aa9bad8d9ebab30856e76e30c9dd48a4ce","split":"train","step_index":1,"target":"def transform(x):\n    delta = (-5, -8, 6, -1, 6, -8)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000046","trajectory_id":"vlr-formal-v2-0000046-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9fce06ea24a2e5eae25441559af8bbe601050fb0ca9cb5a5310216c5bdbea5a5","candidate_id":"sha256:24910c7c07a0ac31fe568c92607c0ad07211837442db80450e75d5aadc0dd2b0","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (6, -5, 7, 6, 0)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:acfcd940fe2f04ac2b891c203d4224f04085b540355ff1722f02bde2a47930f2"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:72cdd3a513e0074d1f6372e39ef11138065c5d3f1bbc7ec59535f31052047bab","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 2, \"output\": -3}, {\"input\": 4, \"output\": 11}, {\"input\": 6, \"output\": 12}, {\"input\": 8, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (6, -5, -2, 6, 0)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_006\", \"signed_bucket.protected.case_007\", \"signed_bucket.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e0b76eee62348b0c9197280a0fef71dba6ed32b6c6596163736c2b218dee1877","sample_id":"sha256:3dc1ecc00c84c8f1c1eeb6b342dc2ad2c0f0b06bce83336a8de9f32219aa8035","source_transition_id":"sha256:6cae6f2a97e277824b33ee4478eb833c26419ab0d5430ba6858a0aa00faaa4e0","split":"train","step_index":4,"target":"def transform(x):\n    table = (6, -5, 7, 6, 0)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000047","trajectory_id":"vlr-formal-v2-0000047-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:494a3f406bec180e50ae1ca8a04c92f751b65080c505ffb016f29c73ada7c79a","candidate_id":"sha256:0b7e78e5b653274e16486ac5595425b2848009b04434822b46a30664bd09a718","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (-8)\n    if x < 6: return x + (-7)\n    return x + (3)\n","verification_digest":"sha256:01ef8676b239be6162b4d2457ecaeafeff455f0d0778e03bde7a0b173d23316d"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:d4a0e0add93c34b8600db96da31b6629f35fd45bd3b2ed88f67bdcfec151c833","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -21}, {\"input\": -3, \"output\": -11}, {\"input\": 3, \"output\": -4}, {\"input\": 27, \"output\": 30}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (9)\n    if x < 6: return x + (-7)\n    return x + (3)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a35015c879310d0e38abe67060dd594979edf3faf88d30e2b753a9db1dff03fe","sample_id":"sha256:9146e615f495ebc29bb258c3de799126b24003d6e755cc86e443e4d8bdfd7d58","source_transition_id":"sha256:72e234a345fff7a65dcefa56a8d186d5d1d0478dd706048388f480f5f1393030","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (-8)\n    if x < 6: return x + (-7)\n    return x + (3)\n","task_id":"vlr-formal-v2-0000050","trajectory_id":"vlr-formal-v2-0000050-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b85342582547e3647d9fe567f483c12aa7a1be8fc0274a89268ee459be20e962","candidate_id":"sha256:ba6689e644f44ad2d809a17efd550950e627a3ad433b147e7d4aa5e3817d806f","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (8, -9, 3, 1, 3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:7efc8bc7d4337f9798d9d5cf9eb532198b08da32adc58604ce1ab65b89c4af44"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:a0415f0b4cc4ee6c97e3dca42696fb31a1cb30f125995ffe37750c23c1877187","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": -8}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 4}, {\"input\": -1, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (8, -9, -4, 1, 3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cbae2fbff887d6ec893ac97e1c016d84acfbbb51090f85ba8343778b7e171364","sample_id":"sha256:1613a22d875a2255072d0878cc999a2b35a2da3851923f0a5abe1209c3edf440","source_transition_id":"sha256:9fc1964d9bef06561e9032a82f20d450a56f525a4b720c68c24b1a5e3d563825","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (8, -9, 3, 1, 3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000051","trajectory_id":"vlr-formal-v2-0000051-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e3ec055c7c0069bcf0aa771a5b1f7e3f6b9ac5a1b959832ce190e0cd0606b105","candidate_id":"sha256:74cfc727dc7cf6796b8d852f94c545877b55125ab002f99855b33fa54473c578","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (4, -1, -7, 4, -3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:e148dcf9643cf5b85033615980791e8382c6aa6184aec3b4f79c7d8a5f6a8db1"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:6b9c93db04c44031906b148c8413f5858f22bba573bb83032b8bd64237e8358f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": 13}, {\"input\": -1, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (4, -1, -6, 4, -3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d8ba742871f035c1596e1201b20b81139abd7b7d463f245ad26be2969d4a302d","sample_id":"sha256:1469a029d73cc98a1524f01e6ef40eb8f8a24f3b083eb5b997a4e210372c8590","source_transition_id":"sha256:67ba946f874f8193e58931c82db18b1ffaeeccf29b693e48568548259167a785","split":"train","step_index":1,"target":"def transform(x):\n    bias = (4, -1, -7, 4, -3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000052","trajectory_id":"vlr-formal-v2-0000052-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ac22d35e280018ea7a86376617caa3441944d6925d2f8d2b8577e7234fd4444c","candidate_id":"sha256:76e4ea6cd2964361d3654990384e225d75e02868f787257f76cffc2290cdc5a4","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (4, 7, 5, 1, 8)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:fff461e08daca6659d0d458bcc6dd04d9d7567d3af232577fe243d7b8fd1e19d"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:e69982852722727394b5d8594bdc1e35b2c8ab2aae57d9cf6891254073db0fe6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 21}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 7, 5, 3, 8)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d9248e169504a502e2476b29e20b6415af3a5b125829f2c40b461d0668e7ada8","sample_id":"sha256:f9ce33740896c3e364fb5c6e3098fefd62175d3b7c53e84a38ab3b6db3e2a210","source_transition_id":"sha256:64fe43648020cdd5791b4aa751107af9c8b93432c3663c90d122ac2bd99ba502","split":"train","step_index":2,"target":"def transform(x):\n    factor = (4, 7, 5, 1, 8)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000053","trajectory_id":"vlr-formal-v2-0000053-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1372e6ffc715f5b03e8a7b2d8083d35de5dbed6d76b5b7c1ee1e2dc3b0107619","candidate_id":"sha256:3d863399c1cbf1353371790204f0d781b67aa6ede43e9f71efff971be1d97b02","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (12, 9, 9, 11)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:375533a1e28d518d901bff35f09b86d108f5791c407b470274c83a4936487528"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:dc5c0fabff7a8a3112963947ad763527de479b9532e5e2f9e16beb58f2ca62f2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 12}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (12, 9, 4, 11)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a1d0eeab5765df6f18f2fb78f791086533a6806c5eca59bc0730ff91ee88dd28","sample_id":"sha256:5a9ea593e2f75226a90eee4b279d28d4473eff82068f3c88b2a2d135fd1cba58","source_transition_id":"sha256:8e91eeb5ad780b7593aa629a9ac451491774d6a98a54fd81c215b5e073d9b497","split":"train","step_index":2,"target":"def transform(x):\n    masks = (12, 9, 9, 11)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000054","trajectory_id":"vlr-formal-v2-0000054-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e3d0a8b738aa3599367fac0b49447ffba2d2871a2e87d365c9fbd03446443820","candidate_id":"sha256:ce2925ade92bd68cf1e76677763389bcc06a9197681c528fecb4e5ba6101a0af","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 1, 5, 1)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:d47d2e8654cb8adf9d84b097cb604da9903aa21f716897b927048f89df3f9459"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:206083dbfeb6dcd7dad0e4f57c220c18e88fae43a49acf014b082f79ad834f87","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 1, 5, 5)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6cdb1136d99f757c3f77070d69a23c2771a7e0e9b3fc9352353a0a2b22b317c6","sample_id":"sha256:6c940dbea986ec8b92899e7bc4c31300f94c8f3c214ca7155eadc3257194e623","source_transition_id":"sha256:5c23fbd74d09d6999858369ee551f57a06d4725744250e73418ba15239495181","split":"train","step_index":2,"target":"def transform(state):\n    delta = (5, 1, 5, 1)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000055","trajectory_id":"vlr-formal-v2-0000055-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:7fe56b17a961761feca7b69f99c04e880a27bc71b50726bd16476ce6f2fba1d8","candidate_id":"sha256:800c57fac5cd0547903ef9b4225ed3e2ac12317d96a3b6a02e30ce1cddf2d4b2","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (8, -1, 2, -1, 8, -3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:3b2bddfbd290b4135a2af3e8819b6b9c4a10d0c415c1df85f088562fec27afa8"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:22f39c52d5ac924e6544c295fd3e0da51ac8164b87aeefe3a9c0dab7256ade1c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 2}, {\"input\": 4, \"output\": 12}, {\"input\": 5, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (5, -1, 2, -1, 8, -3)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:aff6042dfaae7287e453c12ce27a9883f8355d78bc225a0cc3b126fa8550a35a","sample_id":"sha256:2acbd0c73170e3216a4d358f07500e86a3d0b64efd20b142365e3eec175c2432","source_transition_id":"sha256:296f2e4c19b13031fac240d89d04744919bdada31897949751564680b74dd1fa","split":"train","step_index":3,"target":"def transform(x):\n    delta = (8, -1, 2, -1, 8, -3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000056","trajectory_id":"vlr-formal-v2-0000056-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5bc795a16cb881c4ccfda0ed138f3ef6f0337104fa85584c6f12d954a06e28ce","candidate_id":"sha256:0fbec7588322098f12263c72449703ae88438bb1f9fb03ef7a018d4dba431a28","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-4, -6, -5, 1, -2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:4acfc92fc91fa002b2697ec9e2221e520848e2cdf0afc7921a97a71ff79d68a7"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:e82de7663c86eadabd2a4018188572e4a385214b142e628f39b19be34433972b","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 2, \"output\": -4}, {\"input\": 4, \"output\": -1}, {\"input\": 6, \"output\": 7}, {\"input\": 8, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-4, 0, -5, 1, -2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a6d88e89c7fb26fae5710d936b07849ec15306e94b73f98d8a3a7bcd65f545e0","sample_id":"sha256:e90ccda481fd6943c60e3df43606121e83e4c54f65a2011b770eada9b94cdf36","source_transition_id":"sha256:74e0e2a4cdd0992457555fe2b831dde654039f117dc2206087fb33cebe4964dd","split":"train","step_index":3,"target":"def transform(x):\n    table = (-4, -6, -5, 1, -2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000057","trajectory_id":"vlr-formal-v2-0000057-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d3e1a128455dac688f275331511927b291f35c14d0106aafacd077bb2a6f419c","candidate_id":"sha256:083a2b50fd06d2781fcfc614939e369a0ff4c0487a6e5cb71b3daa8336730b12","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (3, -2, 1, -2)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:665b69446deec2eb92f242e0fca53a28f70c86c32270871ac6243ba724f9fae0"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:7f33c58d8471f6ef053fda338b19ded0f651f703462f320a44703a6f5ff9bd18","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -24}, {\"input\": -3, \"output\": -5}, {\"input\": 3, \"output\": 4}, {\"input\": 27, \"output\": 25}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (3, -2, 7, -2)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ea91d4d615496b2724a0aba588d8b074d12685d2cf8d8a79686f9613df12b4dc","sample_id":"sha256:e598205a7d9e8e0818c0cc91cefec708c8550993c225c29609aa5d4934d565a0","source_transition_id":"sha256:cc5dc75c959df5fa29b9040d2c98f4d49c21b2f94cfb20a746b306c7a513c0f4","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (3, -2, 1, -2)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000060","trajectory_id":"vlr-formal-v2-0000060-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:47faa291fa76698575ee484862d1f62d547782e09685faaeeace08ece4098d05","candidate_id":"sha256:4e6ce743f5e028a6e8c2d54f0d5c18afec0273938aac085dc298af9dcf3f3d3c","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-9, 5, -9, 2, -3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:2266c5e708c3a446ae3e3a9d1aa6b456eacd09b3b853a0ff36811164253d38c6"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:3b70462225d1deab4b0a987955777a55adfcb510410ead525d38ecebc18fc757","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -9}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": -7}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": -4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-9, -5, -9, 2, -3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7c01b46d60700de09e042f786c29b61fa09466211325ceaf35e921266d87642a","sample_id":"sha256:912e83ea6d6cbcb1bd0d0ea1d66146b75122739529a4e992b0aba7fb24d18f84","source_transition_id":"sha256:63d66796d9e7fbff4508e9ffbbc0d8e2b138baa1ed0914f022bb283944fa7261","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (-9, 5, -9, 2, -3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000061","trajectory_id":"vlr-formal-v2-0000061-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:892311828da0a386f17b649598554dfa54c1f9809e4b95a616e96ea918d3437b","candidate_id":"sha256:a35cb20a6888d4887011cb0a7d7f03a344746a6b6b2ec1f7b640641a7dbee3a2","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (0, 5, 4, -7, 6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:532baae2893f72c1924e97970e5b86cf3aa37a22321968ec0bfca98a3cf06956"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:6ae24a21fc67aa6ed7d1b86c29e13ed39b85efdfbbb27d36fbf74e29130094f1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 2}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (4, 5, 4, -7, 6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:57bb7cc8e5f7f8375db44523f0696d4f5d683712f1bd2a76b09b716ef551a878","sample_id":"sha256:fd6fa80a1ae1c3e157e823bd8895ae8ad46c09e3fbe5a9f2576af4733b11be73","source_transition_id":"sha256:fa78786482f320d9ca0aeb9198ca68abd50fab475e03c8452ca3ba47a477cd89","split":"train","step_index":4,"target":"def transform(x):\n    bias = (0, 5, 4, -7, 6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000062","trajectory_id":"vlr-formal-v2-0000062-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:01635b965e276aa323c3273644718790e66af39e05c0a1ae0f9b58070bd9861f","candidate_id":"sha256:d499fbe859def4d02d373d57e58554268836e7028a444c1f6ac0a6c775d5a027","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (8, 7, 7, 7, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:2e1b4b092a502762dabfee51c0795a476d47afa11f572494cc4dd0728865c67f"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:ddd45986f21745cea64e1a978222d3351546da1c7ed52a0c73bcbd35f1c10b78","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 21}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (8, 7, 1, 7, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8b1e53e059b0c68a98e85ae84b5f8207244ec3591df0abde19492467570ea3e7","sample_id":"sha256:9fe3661c94586d6dd004b5852c397961569cc7a007469350970afe863f5a6de5","source_transition_id":"sha256:ffc73c21b6ca4d3532906f41c8dcaaa10aaa9d7f474df9360e1580a6a3a859e3","split":"train","step_index":1,"target":"def transform(x):\n    factor = (8, 7, 7, 7, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000063","trajectory_id":"vlr-formal-v2-0000063-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1b6aab1b1a775e29018198de07d40716455f97d82627ec0759d9c29d0111bb0d","candidate_id":"sha256:1d2ca3cf8708c729e627abcb27d7bc17b26eb82d612ec6b43d07cf2a79af552e","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (1, 5, 12, 8)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:0bee98a3db96339002f71d5f6fe3b6afef8d2b8188406c52af97a2a09171dcca"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:9fbc0dc21a859f04da48f975b1475acc8f6dd4ddc40ea360b947be5c78e524aa","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (1, 14, 12, 8)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5491c24cbc5e19220f89771c7d5a4e61fbd07b0b64e37914105aefaea8058ede","sample_id":"sha256:faaf09af4063cb33c20f64ad0bfc4480086a191a51bdd53197044989763090e5","source_transition_id":"sha256:864612fa4af82a8908fb99c0ad403e4c87937fbf696a5abae4cba356ed24122b","split":"train","step_index":1,"target":"def transform(x):\n    masks = (1, 5, 12, 8)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000064","trajectory_id":"vlr-formal-v2-0000064-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:97aead5313348e7d26708579e47391770cade4e1229b7dd32041733b8b9c9b82","candidate_id":"sha256:1f4e714a22d4ef33d9a0569c353a6d2268833f22915a093f3bc643cbac805051","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-2, -6, -4, 4, -5)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:4ff45e4adb533c5ae61dcf3a667a60e0f0213f08d5f20e048e896aff1ca1c6ce"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:1b848cc003f8d3fe6135c6b33652ce6ce03a5e6dc3093b9c28cdc3e97ef2f18f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -2}, {\"input\": 2, \"output\": -4}, {\"input\": 4, \"output\": 0}, {\"input\": 6, \"output\": 10}, {\"input\": 8, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (1, -6, -4, 4, -5)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:df5d7f52125474230576dd88e80a69ddc9183b73e3e1453797f47bb98fc9426b","sample_id":"sha256:b7ac32898180154047c882c90496ef936cd8e7b8d1998e4c32fcdbcc8f1cf736","source_transition_id":"sha256:138e018a2e09f12f32b3f8c1d198b92bfd2197682748ff0a9f8ac005e7385af7","split":"train","step_index":2,"target":"def transform(x):\n    table = (-2, -6, -4, 4, -5)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000067","trajectory_id":"vlr-formal-v2-0000067-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:cbf63355a78b3e5f0ab7e7e35bd245b0242b378c773ac5da0bbc49789beabf38","candidate_id":"sha256:5435cdf33ef809f691d3fe0c41fa04eea900b2d5ab030633dd759b64ff9f864e","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (0, 0, 9, -8)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:33184b0bf7787435b8cb1512064106a9d51babe895c422fdecc2ace0f66c0b3e"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:03ce41b3e539cea654ca8dd9c299d5627416830a708c29fd121cc68ee91906b1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -27}, {\"input\": -3, \"output\": -3}, {\"input\": 3, \"output\": 12}, {\"input\": 27, \"output\": 19}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (0, 0, 9, -5)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:21babb4c9dff675a553cec019880046e77e233a29edc322951885c14ee51e693","sample_id":"sha256:d239d056e3f8e7b24b8e733882a1457af88722bb73cf3a5390cc69a751a3d0f3","source_transition_id":"sha256:a774710affe688c208da4948b01f707ceb2928ab0ae0cbd531c407a9625a6687","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (0, 0, 9, -8)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000070","trajectory_id":"vlr-formal-v2-0000070-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d0098410fa9b13a130f861c2e93f29f5fecb42ec39ffb7a3634fe960c9825b71","candidate_id":"sha256:2daa97714d33e1063ade6d59d51d34df761674a5a66c14ffdb310815f4dfb37b","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-4, -6, -2, 6, 2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:b00507e0d7ac28c4ced9ef5592abe26773ab477c928e932421684a76ef2c91ea"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:57852e00ed45b05ea5635c37556f18392d1077a18f1b41a068cb1a0f3f102341","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-5, -6, -2, 6, 2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3abd5522582f18cc355aca65b3fca63c1b0935e2340c3425cfd554f4609d0b6c","sample_id":"sha256:4ec679a55bab82a4df1c74e5dd80c06ae0cb0f74fc04370260f747075a1cebf7","source_transition_id":"sha256:bbeff95f47e0fa7c66a3a6ff33934511b7514d0bfa89e0cbb3e3dfdbc94e6dcf","split":"train","step_index":4,"target":"def transform(x):\n    bias = (-4, -6, -2, 6, 2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000072","trajectory_id":"vlr-formal-v2-0000072-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:185a98ea2c699e4196f409b6b68eedbf2658a15e4698fb216da1848b4c6c290b","candidate_id":"sha256:d24cb92a539696420712ba4667b76d50e52cd4105f6cb1955e51d162d38c00fd","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (14, 11, 5, 1)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:d7abf05208b59214a7e4880fd07fcf5402e291c5b41005243cbc73fa317fa722"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:7a08762afd94648358805e8e6160aee27718e512ff68e975d32a70ccea03accb","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 14}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (14, 11, 5, 2)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ace7c4725d1ac2ad53960f36b7658597585ca47aa503237967654cd7e6c092a0","sample_id":"sha256:6c6d8fa6276f6435e37838736f9bc6ee50d98b3f97b220fbf16ec922dee1f975","source_transition_id":"sha256:c7735cf13d42f26c4ebfe58f8b4afefcc5b9b09daa3fba3551197635df0943cd","split":"train","step_index":2,"target":"def transform(x):\n    masks = (14, 11, 5, 1)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000074","trajectory_id":"vlr-formal-v2-0000074-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:28373056d16ba3bbb85b0bdab96d25a0f8549c86ff22b57e003f9b888656ae64","candidate_id":"sha256:19a2011ca774ace4c42280b7a9d8a34abe4a6c742fcfad9ba1fb6fc0c4b656bc","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 4, 3, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:e0b123dc62937cf28f666d75c721d99d50306ba70b47b4879d34f2bb37a7bbf0"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:0007406c2c93baa2015be9d70e94b5d5c5cac4253e6aa525c2e239fbbb3de1a5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 3, 3, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_003\", \"fsm_delta.protected.case_004\", \"fsm_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cc56abd3117df39af365c1f8ea130f2b78ab9d169cad78217ce72335031ba6ef","sample_id":"sha256:ae1e98146bade6c5f65ef0aa0f29bf749e200f2ec14ba706ae80290af9e311ce","source_transition_id":"sha256:92c3c5e9bfef5aeabbfc842f9cdd4309aae55dc154fee1720add90907175c5da","split":"train","step_index":2,"target":"def transform(state):\n    delta = (1, 4, 3, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000075","trajectory_id":"vlr-formal-v2-0000075-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:52522e3217f56ed56f1597a70c66335983d667b98af1809890749b750601a972","candidate_id":"sha256:51162d55dd3eac0f1e525e0ec6942239fbc8ba93a82e989e5902b6aeb8a5b9e4","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (3, -7, 4, -3, -8, 8)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:3e722450d0895048d3ccf3ea0b22a7d21b3c46a490cee8e2dbc62ab81689b31d"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:3e96671ede9161b76eda5646f9e876cf5268f556b35ad956a3f4755b81ff8d3b","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": -6}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 0}, {\"input\": 4, \"output\": -4}, {\"input\": 5, \"output\": 13}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (3, -7, 4, -4, -8, 8)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_009\", \"lookup_delta.protected.case_010\", \"lookup_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3f60c4a439d9f38d04fe8ca976bbb9f5d16f354a43f20f845ccaafd66c945ce7","sample_id":"sha256:f430a2ebd56fd36c3b7976c5065047438f7cca4f839aea249c1b4415eff35917","source_transition_id":"sha256:ecb71af372b1bb195baaee4850b5ac6e01b3d7ee80374c3d527ba012ee73147d","split":"train","step_index":3,"target":"def transform(x):\n    delta = (3, -7, 4, -3, -8, 8)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000076","trajectory_id":"vlr-formal-v2-0000076-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8bba9c1d19535bb721e20377a351d01b570b931a9bd283d5e66c3161d3e92a5a","candidate_id":"sha256:feebfc81c8dfaab75a59c08ebbd12755b3bf5e8925804c92c9485b92521b438c","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (3, 1, -6, 7, 4)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:c512ed278835a90a9de2a12e8d25d88b41c80e3f5ddbfe80f66e658c62da91bf"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:fbfe513e2b416c4135b7352ac08a5ab691836bba52908fdad8a1b073e595f107","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 2, \"output\": 3}, {\"input\": 4, \"output\": -2}, {\"input\": 6, \"output\": 13}, {\"input\": 8, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (3, -6, -6, 7, 4)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:147affa8bc920fa2de6ca640b132bed464a9a4786b65886bf512067ee89b93fa","sample_id":"sha256:16d01db9dfbc470c3de3e735e070a1cf526e2244457b1f520406b8d1a1a17ba0","source_transition_id":"sha256:3c4b776f78dfc47883d1670fd82a427e9370c715bc94d7bc4020fd309b35ef7c","split":"train","step_index":4,"target":"def transform(x):\n    table = (3, 1, -6, 7, 4)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000077","trajectory_id":"vlr-formal-v2-0000077-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:466e979be8d2553d4e2e9b2120975bad3c54ffe80174765323a8c114881e9b77","candidate_id":"sha256:0066bcaa20fff44595b5d9b86f00f4a2bc066c776b0026f9bb9aaa84e4749292","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-1)\n    if x < 6: return x + (5)\n    return x + (-5)\n","verification_digest":"sha256:565d323493cb0d075af81c97e2ead4358649d24abe048a4bfad5ab2a6043076f"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:b29aecac740e07753e05e1d87e8ac1fa968420f674ee8877a56d5874e5a6b6f7","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -18}, {\"input\": -3, \"output\": -4}, {\"input\": 3, \"output\": 8}, {\"input\": 27, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (-1)\n    if x < 6: return x + (5)\n    return x + (-5)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e60ccf312da7764a36de87dbab6fee425b5f4d5aeb0f070cd9ab6d31d228fd9f","sample_id":"sha256:5da33fe379ce77bbb83cae0f0882dacdd180bfbad48c777283cd92d3cb26511d","source_transition_id":"sha256:7e182f3e553d0961cd6901bf376140cc793fb4fc1a3611ef01f59d73cde19855","split":"train","step_index":1,"target":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-1)\n    if x < 6: return x + (5)\n    return x + (-5)\n","task_id":"vlr-formal-v2-0000080","trajectory_id":"vlr-formal-v2-0000080-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1ab781ad740552af2c68ef35d3f6582f4bf17a18b48ac800ca63c9cfdaf812a6","candidate_id":"sha256:82b61861aeaccaae53a9e15cecb0e0b833e44467dbf8fa82277ef0329d7f2002","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-9, -3, 3, 3, -9)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:df936dd823cab88c30c599169c60ce43a07ef6e5cd0bc42b13c3ffa5700f084e"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:8c310b80fac895df80d597b50a6fca45f3dc9c6ec6f0a32d10c635143e5a40a0","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -9}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": -10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-9, -3, 3, 2, -9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:19d2502132bc361a3697fc1449a26998234524df17ad8cff0d6d93f00b61d6ef","sample_id":"sha256:b900ee33de43a55d07286520b079878e84d25b49a398b8595563022a40bcd3e1","source_transition_id":"sha256:52b356ea9b89453466f443fedf0d44858089f1cff1d7441de3b1961c803ffa39","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-9, -3, 3, 3, -9)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000081","trajectory_id":"vlr-formal-v2-0000081-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:4fde87be9f6ceedf16515fca2e305a2f643d11419787c1c6c38a0b0147a97dd6","candidate_id":"sha256:8265b0a5f9fffdb025cc729e78829f9553b86e9bb9b1592d9c5f29d664858f88","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (3, 9, 6, 2, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:5f664e91ffc99332da352841148143a0d7204ee32eff1656f60e4ad6708450ff"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:acbdb63fe7a9fc96a2d50523c975273f49cf0a81fa766128e191d01b0045c5b2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (3, 9, 6, 1, 5)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:13d872ea119d7bf1f1ff97a9ba4927909314b1e7853636d7324af569cc65ceef","sample_id":"sha256:124097b1fd61ea56c6832ed803e1f4f394af7f27fb0e7f26df09e3e87d6499e1","source_transition_id":"sha256:47d0a1e4ddb1694733a5b51e8a5a24af1490ec35b428d8590319ea407140fad6","split":"train","step_index":3,"target":"def transform(x):\n    factor = (3, 9, 6, 2, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000083","trajectory_id":"vlr-formal-v2-0000083-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d8fefe10309df772b27f996aa2236ee96ac107dfd7dc05cc55baff68b56e3320","candidate_id":"sha256:88a943fd98a09dca3a495b04917eea3b0399929d8e26cb028d6695f1706faed2","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (2, 15, 2, 4)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:13ae152501ca380d21dd8551a56e63b179a15722380f56d75528c90ea3febecd"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:c1e1ca673c60a000973b8e13256928400ec31ad924d2abd8e74aa312dbf4408d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 14}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (2, 13, 2, 4)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:913f91f7b86b0ec50f25513407eb7c71b619a2fea44bd4e2d424698494300b79","sample_id":"sha256:255127d6316e77a4f58d6a1ebdb0eddef30cdcb75fc5f4d173a7a97f79cdc762","source_transition_id":"sha256:b9feecccb15b3cd07295be1b40839cabc7f11e6320ef7b462cc8cbccc6655ab3","split":"train","step_index":3,"target":"def transform(x):\n    masks = (2, 15, 2, 4)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000084","trajectory_id":"vlr-formal-v2-0000084-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:43b97d7cf30cf3f38bb0628a267af0d092cf26a9e46717198021cf9c068f07b3","candidate_id":"sha256:6b8d4188dfdc62ab56a041cc11bdafea86e147237908a4f84f2076da3afd7cf1","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 4, 6, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:8f2f9bc6036586f04bf42cf8d8dca2eec41fe1ab47dc36b5f8cf4822426c0a26"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:21712570553c3a229a3a029e2f1781f4ee526a259ca3d4b1f36bba2f0ac02d25","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 4, 2, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:834e96b2b0f2b52e341d7746e22b153d49a3902c8dd74f39b988d032b01cb8e0","sample_id":"sha256:fa48fcb148a098f390eb6a2b28689b7a32f02d0d0e6debf16878eca85687cff8","source_transition_id":"sha256:5d14a975e37c7a540bd96d59e40aed92b1957b2262cb727a5ff92c72a85f7dc6","split":"train","step_index":3,"target":"def transform(state):\n    delta = (5, 4, 6, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000085","trajectory_id":"vlr-formal-v2-0000085-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fa018198eaf9e3b432f1ad5ee47aa21c4ec85901d7fd6f529e4eeb7202c9d054","candidate_id":"sha256:1fa46d677a5d23af0f371ea1c4a97f29470c88a0be41b673442e7b6a0e36d22a","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-6, 1, -2, 1, 1, 3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:8fd38ff3ac99e1cea827be6c13c1370dd4b7ca99c709e8657f9968fdde749675"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:0df59afb498ae10a705b0b138295fe2d1fa11735e0cada4e53e50d5fc07f8a5d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 4}, {\"input\": 4, \"output\": 5}, {\"input\": 5, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-6, 1, -2, 1, 1, 7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_015\", \"lookup_delta.protected.case_016\", \"lookup_delta.protected.case_017\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:55289b9c3a745ea904901d1b5626dbc0e10a70db64508dc0519f94f58e3ee783","sample_id":"sha256:0d8821e5db32c6099d9bac56a8d0b2967f5047042c61e0998926acce2e51ad7e","source_transition_id":"sha256:c8213646809d84b2b22df3e74c2065f38861d0f42780a1c3cc9db899d0442afd","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-6, 1, -2, 1, 1, 3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000086","trajectory_id":"vlr-formal-v2-0000086-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e3ee5ce64d2e5c1cd1e22da399d2081c871f89ae8669b2ad647c6f04ec717ec4","candidate_id":"sha256:0c1dda05e1c5e457752968f59ba44b5c92e91351d2254d5d71918d262ff17849","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-5, 5, 7, 7, -1)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:a1489fb72d44ccbd1fec8a126063bdcc3861d3380c5c874eaae84223510220d2"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:ea7cd49e3d55b8325e43595d06b0ba20fb6bab9f7253cce07443762e124703d5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 2, \"output\": 7}, {\"input\": 4, \"output\": 11}, {\"input\": 6, \"output\": 13}, {\"input\": 8, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-8, 5, 7, 7, -1)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6e672903beb0de011cef350d1d6868f5c8bcfd6eec9335edcdba28b487f493ea","sample_id":"sha256:0fa26d7286574bb0c3e90062dbf917832ccfad127392817fcb8a1a2394a292d4","source_transition_id":"sha256:74b1d4c0d2805b12c86b6b544305b12ad0c41f739183b717c7cda4a623e93b1a","split":"train","step_index":3,"target":"def transform(x):\n    table = (-5, 5, 7, 7, -1)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000087","trajectory_id":"vlr-formal-v2-0000087-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:24d2d094ce392882c8a666a9c37169d4b18abf20332d1c6f6a1bd75fca9a49d8","candidate_id":"sha256:1907212c903ce4b14a4a93759f6a8c8309459793aff6f924bedeafdc6e5abf37","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-2)\n    return x + (-7)\n","verification_digest":"sha256:42bb96c211510df32512e5d6e93ed2e99176c14a622a78bbfad7d8f0f35d828c"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:02086847b5bd42827b645e9883da00933ef2e50e137fffce64258fed1452acd7","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -28}, {\"input\": -3, \"output\": 0}, {\"input\": 3, \"output\": 1}, {\"input\": 27, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-1)\n    return x + (-7)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b0db8b545f5420546039981aaf6db8c73f0a2a2316933749a4fc747ee6664cbf","sample_id":"sha256:c1db8f066539822c835c2c6375cff0a9a7b49a0fc073d41f50f39e689ee0723d","source_transition_id":"sha256:8a52def24e68797ab3b0d4890cec0a74684c5f40259cb8492251900044e8b6f8","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-2)\n    return x + (-7)\n","task_id":"vlr-formal-v2-0000090","trajectory_id":"vlr-formal-v2-0000090-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:271952a1f479be16284c893723e1db3ee07988873f04a68c4b194e17b2d5e59a","candidate_id":"sha256:1cec464e7a7d30094facb9ad214cab0ceebf011634680732af99b85699c5a582","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (8, 5, -2, 5, -2)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:7cefce3f69c1a1a7074b5984528295ab671fbb2c85628f87e06596c9e9d9674c"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:916d1cf8713d1cf908a1dfa7886e9c6b6abc11d647ade3a859093ec285b7cc8e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 8}, {\"input\": -1, \"output\": -3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-5, 5, -2, 5, -2)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_000\", \"residue_bias.protected.case_001\", \"residue_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:71a211e5244344c1e88ed317ee0d29d86e27bc52d9f733b14da0ce1f4307d2eb","sample_id":"sha256:33c29c7a0ac35212ad2ea7ebe259c766c1d63ee7512aa288e144d0b99194af1f","source_transition_id":"sha256:d0165230b2b44bea3d18fa7e912d0d48cfe69c397940b33d654d7c69dcf858df","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (8, 5, -2, 5, -2)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000091","trajectory_id":"vlr-formal-v2-0000091-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5b0fcf75f537511c7109e6577876ce1f9c15fe675fa281b9c0215a9bddc65eb0","candidate_id":"sha256:6e3250c71bb6dfd353a48fa9393f17a2534f6e790d0a01f95e414294bff05246","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (3, 4, 0, 4, -3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:bd3d0bc8e5b80a4599c530a503a9dd08409caa43716eb38ddbac8063922d5722"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:d4cd2d2ddc7bc3f3ce86a2d5e01bd8212db8d62cd1511546fcdc17d9e64f2828","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 13}, {\"input\": -1, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (3, 4, 0, 4, -5)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0047e4ac7c41f5ba712ec0be926f6831f9e6cd5952d088e1d9cd5f7ac5b0e549","sample_id":"sha256:aa144096d76733b89c3e8f1e8c2a850977d94b799c7755bec6c4138e724b4283","source_transition_id":"sha256:3feed6084538879e96c23bd978a5ac4e62d79f6cbccb2cb817e3a11dd76e9e8f","split":"train","step_index":2,"target":"def transform(x):\n    bias = (3, 4, 0, 4, -3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000092","trajectory_id":"vlr-formal-v2-0000092-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6a4e75b46e2bc697a54b32114db42bc98be820aa6fd6175138ed33307a967852","candidate_id":"sha256:01f225ea3956f2aac8371fe4081d82ff669ca1f68099eebda70c9a23a07bcf06","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (7, 9, 1, 2, 7)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:b6e932fb471f6fad4c204e4a4474c33c7871ac592cb65b23e9e2460e3558a40a"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:c6d8a73bb19717ebd1fdea7edbbaa471b7d72bb1533d235e7090dad3c3608872","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (7, 5, 1, 2, 7)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c08778929d7fa5a27c84c024e345aa8e8e4e7b0c301263c3a058ecdbfa4ac937","sample_id":"sha256:0b1d3073c4be2c1e55e9e72a5613f3e92b42ff84be1def1058b0bf00af434b66","source_transition_id":"sha256:753d5762e493928d280759301d148a6818336bf72f0e2d440ca0582eb24b1dc0","split":"train","step_index":2,"target":"def transform(x):\n    factor = (7, 9, 1, 2, 7)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000093","trajectory_id":"vlr-formal-v2-0000093-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:754ed4bd2b290083dd6aa6465893cacc43f80acde5ad6e50f6c98f8c8b310a77","candidate_id":"sha256:25af67452023246737d0f1b6f8aedb9f699d6003d237ba2e39fcc98a1afdd92c","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (2, 15, 12, 6)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:e36d74270bd107fdb9bdd609f31340a4675abe9e1136919eaeb4d2d8b76aa993"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:3cb9e774b490b1e678ba23a78ac8346cdde1d608e95ec590e8667fc5d2f15bce","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 14}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (2, 10, 12, 6)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:da2a21709370b091404bd0c9c16c96986ebee9ba58efadae86ed58832797ddc3","sample_id":"sha256:f067d4734740c292d9ace0e32c04b88a2c91d1a583d4f0dd4fa4c5c396d4a7b1","source_transition_id":"sha256:cf88add9ce65f7637306d7863dbaabba0cc9824cb10cb47afce835b1fd493eca","split":"train","step_index":3,"target":"def transform(x):\n    masks = (2, 15, 12, 6)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000094","trajectory_id":"vlr-formal-v2-0000094-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:4914e4ac435c6226bb8d92f7818a31bba6b4140b60dc9c970fcaad42812e494c","candidate_id":"sha256:a7b67946aa02ecc8e56a925599cdb73d9d9f00e9403f478fa8440d876d02f5e1","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 5, 2, 6)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:618bd5ddb9e121feb1c2072d7a09a868c3fb4eac492d16db98926a237ec0c001"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:177ea2e1c83bc9af1ef1dbf65bdad1ba7d1aeb5b5b0a78f9ebfe7f5d69476446","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 5, 2, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:56e7264ad9ac6128e7ecbae6676b6684cb1ccec314dbcb384cb62957327cad71","sample_id":"sha256:878166d93dbdeff4a70b49222724265bde19b1236e27391f8937b4ec4b553b67","source_transition_id":"sha256:1c785e3bd479ce1b5a18cf483772e1e546bd8028b4d8d620292ee07f0289232e","split":"train","step_index":2,"target":"def transform(state):\n    delta = (3, 5, 2, 6)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000095","trajectory_id":"vlr-formal-v2-0000095-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b52b1b57f4ad20776b3028ad90677db0da4bc5eca1531638171fc628691c93e8","candidate_id":"sha256:f2b01cd5ea733d83a2053f77d764f49aa74dd1739cf91418235f32dc49f55f03","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-1, -1, 4, -2, 2, -6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:a03e32fccfc0d8988ec40bcdea6f4327c4b8a9dcce6adae1173bd0583e9fa454"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:af57c40285173e4bf7d8ec0e4344b8654f05c36a28c1c89f7ebfb87934fe8e6f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 1}, {\"input\": 4, \"output\": 6}, {\"input\": 5, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-2, -1, 4, -2, 2, -6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d67ea8f8fbc1ceeb306d9d61ac36b28b70cdd646ffebfffbecf5008193ee7eef","sample_id":"sha256:8fb49f279fb80a1c08d23cd5d323785b4726f77028f222bca7963eb8385eeb06","source_transition_id":"sha256:540548895a812e8c837266af4c3d9a3289009d3a5827a5442e4ed62805638b13","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-1, -1, 4, -2, 2, -6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000096","trajectory_id":"vlr-formal-v2-0000096-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:87c1db69d8adeeed091fc7e1785c9de0c4243f07056ce0faa231787f106583fe","candidate_id":"sha256:f79a5d3f84968eb61de20044a4a4088b36ecec04392e21df05b576bfe7a19749","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-2, -7, -5, 3, 0)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:2f014a35dc5979ecb6d0938fa95afdcbb2ba19bb3cb3fc45a154ff5e5fe97714"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:142103f22a73bea1ebd30cb36d2e0bf7625d825f056bd5684da9929355137686","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -2}, {\"input\": 2, \"output\": -5}, {\"input\": 4, \"output\": -1}, {\"input\": 6, \"output\": 9}, {\"input\": 8, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-2, -7, -5, -8, 0)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:367bd7f8a75ecf48fb7931a9e87672f1889dff212e4efe1340f70932462f219e","sample_id":"sha256:5bb5be98e7a206f3b09c2e4fe57685d1a6d1220adb30f8f817da6074bf477fa2","source_transition_id":"sha256:ec3540daba3c2cde59b7a0009b057e0c2f3d849c3861fb5ae67a4b0db59526c2","split":"train","step_index":4,"target":"def transform(x):\n    table = (-2, -7, -5, 3, 0)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000097","trajectory_id":"vlr-formal-v2-0000097-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1c5c778fa797c52ecad34b0f94af99bc258514f589fede1f186d70887f0fcc29","candidate_id":"sha256:119e8516e8e83f713c524278e2a792bb53309c25cbfb788789ea068fc19d68c7","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-4, 9, -6, 7, -9)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:114f2aa8b119583254bc044685826b6d2b5ff1fd7a9aca0163dca055ee300803"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:7c6a316e44b119db91f7a648ccd5381f4a941e8748a1ce4f48c7001ffcc35907","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": -4}, {\"input\": 3, \"output\": 10}, {\"input\": -1, \"output\": -10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-4, 9, -1, 7, -9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3f442f602d39258123f4083a446ce755263735ea888e8bde6fbef75c5184b992","sample_id":"sha256:2cee1d54412313ae121d9d6bd4fa87d2a78bfa436d64d56247d84cbd53cfa01d","source_transition_id":"sha256:6789f8bd8635977852e2d392f0831fb51383645f780708f49959673980705d10","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-4, 9, -6, 7, -9)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000101","trajectory_id":"vlr-formal-v2-0000101-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b8a5b4f9a2cb4c7d4239d5068bb917b2da41cae70ee7fa937b1ca12487eab820","candidate_id":"sha256:36b2bb4022c02f1a528634393ec3dd89cd133522b35ee9a3e7a094ba1afe7a09","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (0, -7, -6, 5, 2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:5a3c4285eaac14668d0c9e00fe1c4d1d8a7fc2eb247ae75ba9b2a68c934a16c8"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:febdf86ae2223e74bda51a44a6b2f84fb8a98e7e393292ad43fc56da3894e7e8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": -6}, {\"input\": 2, \"output\": -2}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (3, -7, -6, 5, 2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9d09d6e11d3e57c168f76cb33018572422663a067d95bcd9b994d03eed61b5f6","sample_id":"sha256:c56133c8d74064ef4a60cfbaf065144c6de1c0708cf8a73a340e41dcf015e19f","source_transition_id":"sha256:0c0964173f8024b73b9385aefe617ff153d28f3a8f80f10066b206f132ac97ae","split":"train","step_index":1,"target":"def transform(x):\n    bias = (0, -7, -6, 5, 2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000102","trajectory_id":"vlr-formal-v2-0000102-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:571dc47ab5178d0017584d83cb4e32baefadcaaf7402c25f2f51d61f688b5eab","candidate_id":"sha256:0f390a9eefecc8114dad134ad22a39baa8d466c7ac6f63e5bb74b885c8c43b8b","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (3, 3, 5, 7, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:d15fd2d2b65f71d13ecc14d566167b7cda7ef85d76e686a38eb4f38568eb52b6"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:49ebd719ef3f614bd6245e00d8f0904bc6c30c6b71490feeca1ece1160f58b12","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 21}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (3, 3, 5, 7, 2)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_012\", \"mod_product.protected.case_013\", \"mod_product.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:58002e826ed8396135dfea5c97f57bb30d563e884f40012e0690589b02dde8d7","sample_id":"sha256:66986667ca180a61695b278acafa610aa48d4891188cb7509bd83df58b105306","source_transition_id":"sha256:9ebcd5ddeb1e8f475a005ee05ce996c60168d52530681623be24d3171ea148dc","split":"train","step_index":2,"target":"def transform(x):\n    factor = (3, 3, 5, 7, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000103","trajectory_id":"vlr-formal-v2-0000103-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1672d9aacbe7e11e31a6429bb40025e07087f139d1b8e257791adb93f891487c","candidate_id":"sha256:d58b906d7a8e0385bafaa2f5c0945b427a9c888948330685da0c7de313010694","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (13, 1, 8, 7)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:b751cac995f4055360d5fe64e61a9f65767dce43f19558f0d10d0d22323ad98f"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:cc13341046087ef5ccf48812bef706d7a4784af423d29216c024880b78b9b106","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 13}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (12, 1, 8, 7)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c65ae022fc088646a7afe9a3fc7ebb133947c75504f03eeebfb1a298b4977fc9","sample_id":"sha256:3aeb151f60dfe81b264fe4c15f1b09d32c8e5bbe4f12108ae5fa63044dab42d0","source_transition_id":"sha256:d2ba39c1d6082e7b0e4ad37bb98d430048122c8992f7f74adc51345e34f13374","split":"train","step_index":1,"target":"def transform(x):\n    masks = (13, 1, 8, 7)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000104","trajectory_id":"vlr-formal-v2-0000104-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b15fea8eca47e2b873820166f87801e071f961465ee0f1b6283056e442a83b65","candidate_id":"sha256:71848b17ca324b89c497f93d3dd943ed440826a126697e9da55b8590fbd4b13d","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 3, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:d79a6d311127b0b53824e77dbe6303376562073609b49336beb6b2e514ab306f"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:6fb5a4a21281f0f0fb85689a3d7c0541b8f0a526a83d9af108c1106aa4b48338","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 6, 3, 1)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:83f2e7f7920d7c621d7dc90cb6fc25714da2e63b05b71cefa7e22862f4c87b26","sample_id":"sha256:ef419adea66945a5695eb7057521783ab23cc034fd71417d3c9ce86c95713a8e","source_transition_id":"sha256:fd54e2fd1ba289932686cbc2dafa0f93949335bd6ffc764370a9442f0c3576e3","split":"train","step_index":2,"target":"def transform(state):\n    delta = (5, 6, 3, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000105","trajectory_id":"vlr-formal-v2-0000105-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0f5fe8cd365b01e33d45db076b1d63c90c432528b95419cd96efc4e0b12537d5","candidate_id":"sha256:3b7a38639c0a8efb82ef35575f766ef00a0059351ae42d069806a1c2cd6a7175","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (5, 7, 5, 8, -8, 1)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:7388086f5333b48d83deb29e9b73f1340802166f0bdd3a44d869dd12a4898fc4"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:d28378408919221bd5ea4271886c20e162c7f6b50049859248f35e947be8a0bc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 11}, {\"input\": 4, \"output\": -4}, {\"input\": 5, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (5, 7, 1, 8, -8, 1)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:61cbc72f62658a5fe5459113f2388d5b93486aa8972d91caae72b1b1d983e0b2","sample_id":"sha256:fc26e9a92ad6a4e49a6373be16f3e121e5cb964162f546e1e187573010d98720","source_transition_id":"sha256:bdafc2d792421ab0d2b6a2cf5ea81ae93988e005a8136b037912aad151ead60c","split":"train","step_index":2,"target":"def transform(x):\n    delta = (5, 7, 5, 8, -8, 1)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000106","trajectory_id":"vlr-formal-v2-0000106-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:eda11ff08e951003b610096aae3dafa439e6b78557495ecd5b14268747546bfe","candidate_id":"sha256:6cf00ee954c56edc23370ee2f2e255412a8ff2e0b0f1ef56d423268bb775ec1b","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (3, 6, -8, 4, -1)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:c7542ead412b8c88b09d2ad473be5f5687bbbc3e65809ba57898c66989b5baf2"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:cd39d3e4132e2d1795c8a9c66bf8c5b6e6fa978e3b49a9c900dde5506774cee9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 2, \"output\": 8}, {\"input\": 4, \"output\": -4}, {\"input\": 6, \"output\": 10}, {\"input\": 8, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (3, 6, 5, 4, -1)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_006\", \"signed_bucket.protected.case_007\", \"signed_bucket.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1d31d41cbb1a6c09c6777ba51c8a898382e585871fd90fa9b66d580da3c79dbe","sample_id":"sha256:1c1c7b6b47696dd56757024f881705a827fdb9e10fe5d9d0713d3613f029fe62","source_transition_id":"sha256:ce5206a256866e966cbe5d4a47dc6fe5358af968e760ba9321d8c016daf8ba04","split":"train","step_index":2,"target":"def transform(x):\n    table = (3, 6, -8, 4, -1)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000107","trajectory_id":"vlr-formal-v2-0000107-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:612f2a0360a2610b0427ee63f1885ef339ae3c74e2df81f547da7ef9fb4de46b","candidate_id":"sha256:05db254ad73b092967d2af85893362fb68db7382052cc1c47bbad8943b323931","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (7, -8, 3, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:f90a7e5fee7721b7aeaacd20842ae4c7aea2d60462f3842e5900715306d79374"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:cfa360b7e6c70634e7f007cfdef920e3164e77c3658cc84fcec8a3936991b3d1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -20}, {\"input\": -3, \"output\": -11}, {\"input\": 3, \"output\": 6}, {\"input\": 27, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (7, 0, 3, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:357b3f38bb0d1556b62fedb9def6a1270bb0de69631c27963e6db0e6e41185e2","sample_id":"sha256:fe12b12151146c6c9d6e498b5e4189bde1e702f6b7fca89bbc751513e134eff5","source_transition_id":"sha256:c1b37a321e1766179d788efdd3d4cef3bef52bb56aa7682c801126f33e44227f","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (7, -8, 3, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000110","trajectory_id":"vlr-formal-v2-0000110-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:08459af28b3bef5d7dd44420a47e9ba01360daaab0688615e6ac4533c64ec051","candidate_id":"sha256:93679cf347ed8fa97eaea101894aed4abbaefa3a04f605ed44e82129eec875a2","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-9, 0, 1, 2, -6)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:f58c7ea73614afb80ceaadc034c94979705e44fb6a1c3e1e8ae3ca4e60596a7f"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:603c4949ae2a7620a3cae86142c320f74ba29284ea7e6541c423d98f24844ec5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -9}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": -7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-9, 0, 9, 2, -6)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b294fe51478a40fac92a3e0995657f05d2f825bcdb2e9041f052cda6200d10c2","sample_id":"sha256:ad058be9e483811a4e68548cd46d7a6e85992e636aaa39a0db32bc5f34bbc041","source_transition_id":"sha256:d50d0a2eb8e62b8034d3f381f9bd0933ed727784fc26c270ff71091a843f6f6b","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-9, 0, 1, 2, -6)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000111","trajectory_id":"vlr-formal-v2-0000111-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:97e39b38d3b666c6d138807a335470f249e462756cdea5c2ce28fca619b57677","candidate_id":"sha256:77e94c3625758faff66f76059de0a0f95ce2ee1d1f780f97d26fcf6964f649ea","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (0, -3, 6, 5, -3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:355bee4d4da8d7c0c4025e9f1c46ca0a61213c4a05d0af1921c3b2163107f929"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:c79b2dc1be639215fec953f833366b2509385069c768e850f5d80c6bcf7301f6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-4, -3, 6, 5, -3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ac987dd393f3b945f6e5503f6b22a214f4552d28201b78e5c531c5e0d6e1c651","sample_id":"sha256:f4fa28b669a89e6c4b06eb6f4381a87b294a386485dbff555b76b27815ad835c","source_transition_id":"sha256:afa4c51340cb9a35ca466d3878eb443c1a4d35fccd7383ab5b2ff19e7ed415cf","split":"train","step_index":1,"target":"def transform(x):\n    bias = (0, -3, 6, 5, -3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000112","trajectory_id":"vlr-formal-v2-0000112-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:886447219a7e808e4c7b7fdd92b64acb39e55d685ddf14977ba91650a9d1b650","candidate_id":"sha256:166757a71343d851a4be87ef21ef8c2834f5bbd3f68982c22459dbba81c51ba1","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (1, 1, 8, 3, 4)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:f050766af44b1f135d092afc557ad27512ecb7f999ace3936dd902605901cec1"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:4803a10d7d2e308b866523737cf4e6177e3b2a9e97845faffe6f6584fcebbce8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 16}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 25}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (1, 1, 8, 3, 1)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_012\", \"mod_product.protected.case_013\", \"mod_product.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f2f10bfbe0e4c9f86696e245b84b6ce16b3f1fc09ed8f44f01009d123bc54f1c","sample_id":"sha256:b828d7d67463cd945e093e35db8d6afb7e8065669c9e3451130b49ea7f699167","source_transition_id":"sha256:cea4a44a99d35a86737d8cdd8766e0135f84c0fd2aafe1bce0e40730902cf46b","split":"train","step_index":3,"target":"def transform(x):\n    factor = (1, 1, 8, 3, 4)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000113","trajectory_id":"vlr-formal-v2-0000113-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:13e68a2afbc6e36bd50517b17c8e32cfded90c642675bb79b9fa552ff6a74b5c","candidate_id":"sha256:efce0548942415d64ecd13bca49c412a6f803aae20021c902bf3ad23b35dc09a","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (15, 11, 4, 8)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:2bc31a303a22cacf4a5ef032b006e6ee2314f8c67a42e17694bfa27c356112ec"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:61ab2c726672597e675fda78cdcb269528fc8b54e81762ccd209e449dba35856","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 15}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (15, 11, 10, 8)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:825a2518c19e87167773f29246c3cb78ee7590cf28d56d130beabb5a4249391d","sample_id":"sha256:5d577be856612ccb5fd37576e669651f75467f57366525fbfaebcbbc4f2756f7","source_transition_id":"sha256:7995a71af94ec06465e916cc1d6b60e57036aac887c9297ac6f63af306d17f1f","split":"train","step_index":1,"target":"def transform(x):\n    masks = (15, 11, 4, 8)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000114","trajectory_id":"vlr-formal-v2-0000114-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:09f9919714cb534bd7469db371b2e9e08a2322e833bc2e78f4594538a9b7bb84","candidate_id":"sha256:d4882a536114133f6cab2cfd2ba4efd8abf1baf3d4ec9cfc4a096b095aacddc6","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 5, 4, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:126bfd9a81de9d3afa0e9b5a4849e8d8c7b3f6d7f90cdc601d9ece1ce182625b"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:eb5250774ef13e00aa78b11bf5a8fed3995e5ea84dc22c93b8895babfe2b8aae","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 5, 4, 1)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1d711191f49ce4140e3dca174d6b721580054a7808fc23321de501b4b99dc50f","sample_id":"sha256:aa34f0fb3cbe4624f1f49a1170542c3acb19515d99d69aaf29888f2d3d47790d","source_transition_id":"sha256:a3b378d541cb97281e779ca1cd4c0cd9ea2af8bab241547fcab1b03f1383e484","split":"train","step_index":1,"target":"def transform(state):\n    delta = (1, 5, 4, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000115","trajectory_id":"vlr-formal-v2-0000115-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:932c01b0e43efa7e9662a7f3a0000615530518dea90e985edfe19e2d1f3d7a94","candidate_id":"sha256:22fa6d712831c497909ebababf2ec0c067eb2a1da4577c7b940aa3a101027e09","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-5, 4, 1, 4, -2, -4)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:9b0e5c1f397e5010e871e0c215288f34ad9f50c4a899ca22a73ea86e74981ed0"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:27402d1003fbe7e2ac3acd634cb77be5bbdf695d4ccac9dcb8dcaaa7c5044ab9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 7}, {\"input\": 4, \"output\": 2}, {\"input\": 5, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-5, 4, 1, 4, -7, -4)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3b7746cd2115f9444e004c4b65f23b1d030c0a4ed31bb1b4251ae49ab76c62ad","sample_id":"sha256:0f97a59df0775097081292bf2be78c2945dd6455ef3c7d30fcd21ae1d5e4d9be","source_transition_id":"sha256:b3accf36e53649f5688d012e5c6dc3713aabe54b357f32fd9ea1c2bd43067809","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-5, 4, 1, 4, -2, -4)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000116","trajectory_id":"vlr-formal-v2-0000116-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a49783d0cf177ff5f27930488568e7263bff719e2541658b9d415537318b418f","candidate_id":"sha256:81f63b08ddae8232cd08d63c10fa0113657bc13aa162ff793c100d04ba9926a3","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (6)\n    return x + (9)\n","verification_digest":"sha256:274bd04c2e9fbd361a75779d20d140bb06761cd6314d4b6b14678d58affc7743"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:7a42e74c7523c06f16b597b439ea537507548b0d9b2765a8f48d8a3954264e77","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -23}, {\"input\": -3, \"output\": -7}, {\"input\": 3, \"output\": 9}, {\"input\": 27, \"output\": 36}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (-1)\n    return x + (9)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:baa7e2c91ea6babe6e9adb86a607b0b95a5e0a1aa8662c4166f98690f853beda","sample_id":"sha256:fb046dae40c1d1a9f79ce7d27b6d0b05fa6ae99ec8a9d8ca5b8dd55a3a5619bb","source_transition_id":"sha256:d59e6b7d612e6fe89b3949a265898757ddd9cc5e085e7696381751d3c422fa0c","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (6)\n    return x + (9)\n","task_id":"vlr-formal-v2-0000120","trajectory_id":"vlr-formal-v2-0000120-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:15a03ebbb9e58f4c08f76bc420e899793cc1a1829f9de85cc559f643582ec3c6","candidate_id":"sha256:6d26c599e98f4b6e5c7aa27399477a716b784ec9ef24227d7f0ff07819b53ade","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-1, 7, 1, 0, -6)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:1c7260de4691cb4000350e320d7eebb3b821991316285a31211a84e1c0baee49"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:7d7726399d7ee3ab98ac803cd363799b29041f0fadfdfda464997fba4fb99141","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": -7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 7, 1, -9, -6)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:976dfddebc73a6e0bee165d6797318dcc0be764b324b874b8d87893b2dec4b1a","sample_id":"sha256:7d57ca4139787c29e8f87bda3931fb17ea38480a73f9dcf7a44f0e6bcf02a8dc","source_transition_id":"sha256:6722733fe3c0eabfc96361809a20262a9d92d42b3065ae2a1414054e78bfc84e","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-1, 7, 1, 0, -6)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000121","trajectory_id":"vlr-formal-v2-0000121-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2a956d455beb92dcaa59da20d8310002ca6fc138c1cdcfc829df6fc1514ceb77","candidate_id":"sha256:9e3587d16cb686ef1a6308545f2d8fce4ac01fe9b44ebbfe50fec85f72875e45","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (1, 1, -2, -4, -7)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:a9ac79ca7e8890b629afe4b468b4bee744a8a94df8eb64915fc5dfed11a2891c"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:f0b9fdd2c1c508aea073d282bac549f0eff0b526b037ef73016d1f96b8b75ee8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (1, 4, -2, -4, -7)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_003\", \"quadratic_residue.protected.case_004\", \"quadratic_residue.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7f7d1113e4a4ffabc8f2ee22e772cf9f624781b2375a50bc17a4e02c7f14f2ef","sample_id":"sha256:080ea9f4704a57a01b34a16170324ef2bcdf83525ca0eedf1475d4a8da60eb98","source_transition_id":"sha256:46be0db84086668ad6b8df3e4cda1237dcff6b6b02fd22b1b78b58bba3f5c17f","split":"train","step_index":3,"target":"def transform(x):\n    bias = (1, 1, -2, -4, -7)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000122","trajectory_id":"vlr-formal-v2-0000122-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:74ed7a98612fce6abbe3d3e6f6ddbbc5ed0bf895863bd63194f003eb857b79f8","candidate_id":"sha256:26a7025c48d80e4b9ed59adc21180e54ac02283a009388e913207c29e0cdcd91","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (8, 12, 9, 4)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:116793032698cb02f095176b45f17a903ece799aa6fbaaf02213f2f95f4667db"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:d850c9ab0d54df7e604745d382f7eb6ffd814b2692a014e6a67390accd5e2e2f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 13}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (8, 12, 9, 14)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c3f7af3143e5ed7bd479a6f68af6e7237b8afa754626fa11b961efd7a317a3d1","sample_id":"sha256:16ba9048295a05e21b71e68ab67914841fcbb47720347e9c69cf325fce6040b0","source_transition_id":"sha256:27a732206400879fbffd2c78cc4b036d201b6a139c1b35f28a8028ea6c8ce2c7","split":"train","step_index":1,"target":"def transform(x):\n    masks = (8, 12, 9, 4)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000124","trajectory_id":"vlr-formal-v2-0000124-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8b2571dcefc6deb12bb5072e4b2fd61b7866d455f09669f437022f02474a3210","candidate_id":"sha256:6a4dbda0811c6fc5a199630e491e40e3510287387ab7871d49544e11f0160ec2","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (4, 2, 3, 1)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:4abc77617b21d7fbea4d0b70e7a77711acef4a0d473c1870ae4f930f21efda42"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:8b6147d65d9285c1327f8c12675559496b236656e68758fbec2be9b1d13538da","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 2, 3, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:19123458b15ae8e80ac91f987d47b0a3dea0eed867bab9c91215b4db6863070d","sample_id":"sha256:6c211c263d07987d60c7daf3517bb4bdbd9bbe58443ee438ad467858be35422a","source_transition_id":"sha256:1accdbabbb956e35f0c2395b9fc3cd7c1e9890ba44407c3215adb82144c4132d","split":"train","step_index":3,"target":"def transform(state):\n    delta = (4, 2, 3, 1)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000125","trajectory_id":"vlr-formal-v2-0000125-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b3376254893b6064407e445390ea9cef329ad03f3f2dc212490b4c5e2cf6079b","candidate_id":"sha256:983a291bb3301e5e09e05240e5db08993031412114bd4c1eed6f5e7b52d9bd66","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-5, 4, -4, 1, 1)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:f4e4a2c6bf7f373d63e99a4058d6df80d200a572a9e821e920b34609d0da1ceb"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:26e13c7bd2678ea51973bfa9333b4ebb6136c68b94a6bc7fe380cc1d4cc95dfa","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 2, \"output\": 6}, {\"input\": 4, \"output\": 0}, {\"input\": 6, \"output\": 7}, {\"input\": 8, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-5, 4, -4, -6, 1)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:645a7c7a7952cfe94c1b1b053a6abe35a4bf5dda94b4c0b12c44260f603220b4","sample_id":"sha256:00db6cb62bc85c68fc98595563419c7e32a7fe621a5f7aa882a9bd0e960950a6","source_transition_id":"sha256:0aa118026fca141eec214e9e99c47f15c780776f27270a31e61535b4504cf9bb","split":"train","step_index":1,"target":"def transform(x):\n    table = (-5, 4, -4, 1, 1)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000127","trajectory_id":"vlr-formal-v2-0000127-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3507c5c00f5cab38f2e8845e6ec521acca559a9a3813229fd7a60393112fffc6","candidate_id":"sha256:a1535d7835fa023807c4187ab0543e765ed27ddce008d9ce8602841050d72756","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-1, 7, -6, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:75332ff51be4e21b27b5d3d48c978c476a7b064cf036d5bd093b1415a02e0fdf"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:e0ce47021803a29ae11857e929f81b80af2009bcd809b004ee95aa4a7f64d7ae","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -28}, {\"input\": -3, \"output\": 4}, {\"input\": 3, \"output\": -3}, {\"input\": 27, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 7, 8, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cb720fd451cba6dbd98058d0f109cc5cc02f80472a2b89a85779d7d90594bc94","sample_id":"sha256:44964dc3dbdc3f37e50f400f199e759f0482c0681bccf2f5ac2d583adf40b064","source_transition_id":"sha256:95160a43a84e8750474b52b8cbc86ac7f30d91e2cd21f1c20ec8dbb1a1dcbb36","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-1, 7, -6, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000130","trajectory_id":"vlr-formal-v2-0000130-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:79e94e18f9449eff4488352ace4b277bf170689087b74c5337b403012079244f","candidate_id":"sha256:8d36e791e9c2720263d635f8479ef5a8be32243183eea84cd1b4f67993f74694","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (0, -4, 6, -8, -5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:88fef32bcb1635b3d79c8c081dc88629908f4f52340a83e007087db210c747d6"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:1373f2c9986e69f57b2b96a67d27d3d76c0a897d91322b7c20f61868978d61d2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": -3}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": -5}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-5, -4, 6, -8, -5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_000\", \"residue_bias.protected.case_001\", \"residue_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:4046d66d3d4654a11fb008cf82b98e77574aaba8cdeb9461716a4b5cca592094","sample_id":"sha256:e798bc8b6fa8db415469930c4c4dd9663cb08a45df1c58cc6be525c4809a5a5c","source_transition_id":"sha256:053bd21bf07b696618b66ddd4cab2d5dba5d55f4c90b9e2b9135e1ef15c5bf2b","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (0, -4, 6, -8, -5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000131","trajectory_id":"vlr-formal-v2-0000131-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:84dd34dfec00ceb734a63ed497af20a41aa83e682d55045c4d6cd897a9427766","candidate_id":"sha256:abd83c2ade90d9c3852082bd48010ac3c30e240fd9e6b17e48d9cbaaf4f1328a","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-2, -4, 1, 5, -5)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:9889834e74d1d1965e96700e90550b283b3644dffa2d4945440c14727fd0b1c2"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:4e2ad948aa7f3effad5d16463617920d7a8cf688a0773b9200bdd5fe52f5a71a","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -2}, {\"input\": 1, \"output\": -3}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": -4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-2, -4, 1, 5, -4)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b245393a787c8c0e8aa7790e97414aacf9f3b75384f76391944598ac27c83373","sample_id":"sha256:92ff2ee8cbad59ef0156d65f6041bc7697eda51e3ed3c9037566609224cf2ea8","source_transition_id":"sha256:fc68b35378c04d600990ebad25e6014f5d83a2ac6b8948e18b664318bb75280c","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-2, -4, 1, 5, -5)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000132","trajectory_id":"vlr-formal-v2-0000132-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0b497efac3c52c26a2c7e4806834f362a9d9804423b7fde812ba468fb1fda9b8","candidate_id":"sha256:e45bdb73f92db735f004f973ef39f4692025341e46dc139b8484deb3ded08eb4","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 3, 2, 4, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:db5115188dae5a5657e87da7667dd291c96842b4cc60f3af8dca16c8fd5e75db"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:24ce606e2a603440845ad18bf7dd97e0b8d7c9be192b47fb496e08e963991184","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (2, 3, 2, 4, 4)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_012\", \"mod_product.protected.case_013\", \"mod_product.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:fd790d162a1885390bf06e3515d3951dfb1507bf975ada3f3d323c95816103b5","sample_id":"sha256:aa74dc8d51efc2c2c858a408c199f1e0e1c7842bf342fa8d39bff4972e5b61bd","source_transition_id":"sha256:9ec4a740075c739a61a0f07ab3f930f67040676c79d4f430a8ec946f75494e10","split":"train","step_index":1,"target":"def transform(x):\n    factor = (2, 3, 2, 4, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000133","trajectory_id":"vlr-formal-v2-0000133-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f0a7563a784b88dcf22957ed5c32ce36e90671b5317e3377fd1305a3f08b55d9","candidate_id":"sha256:fccf19a2bb7ea8c515b2934b319cb599011a4867b045da41a7f37c1d000dd900","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (13, 2, 7, 6)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:a00b37bc05766d5b7a207dc328b24700ad432412f45d918809ec2f9361892e6a"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:00029b0e26c66992100f25a98a4c165e31d96f5fb86a536240c9c77e24b0bc47","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 13}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (13, 2, 4, 6)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d9dd610dd8b4317fa5b3c86a7fe48b7912399fed432f20cf263211c3d81d6550","sample_id":"sha256:fc85c657394d40a0d839b7607d3399edd458f05d0600d89b5c2cd5b76fed8e1c","source_transition_id":"sha256:963395eddf498bc7bb6444434df77924f4081286d0e80d99e3d412a194fd5605","split":"train","step_index":1,"target":"def transform(x):\n    masks = (13, 2, 7, 6)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000134","trajectory_id":"vlr-formal-v2-0000134-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:344419084ddd14f7f4268bab67df29c7d98c74b64c29df08b249a45f652fe25f","candidate_id":"sha256:48b5500f8b9d11f6cb9f4a3ff19d7fc35ac46543c9fecebf5945f346293eb0ed","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (2, 6, 5, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:2fc0fc4cdc52d885b37910746489534e9fac8d417e6bedc203d9902908380619"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:d756c7b8e7f968b148aaf756f3a70e81c5900db28f395ab34022a83e476282ee","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (2, 6, 2, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:38e7f2d13730d556ca1685226559b87967a6bdbbdf6fef192d1362c50cb65553","sample_id":"sha256:7cf390440d41a744978bd2f47a5282036cbf917dec98b10ad88f79295cc660a4","source_transition_id":"sha256:ed711c56e6a6c36279ee8fc804e7469fe3eb4071888dcfad1e9856d7c73f9d6a","split":"train","step_index":2,"target":"def transform(state):\n    delta = (2, 6, 5, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000135","trajectory_id":"vlr-formal-v2-0000135-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:13cf2c6098314caedbf2ec94ec1fedd1e7fe25c9d4b674882ce8f3857b969db9","candidate_id":"sha256:74c3d933a032ed8b3715344166cee075dc9e6570661a5108f9805a235f1bf4f8","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (5, 3, -6, -4, 0, 7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:ac848121df7a73cf6ba4c4561e1fa95c94b2eeb8252aab15729c61e4ceb26acf"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:2f7574ada10a3ee70b19021e63953c409235bb5f823705e7c8b6ea93afa1db32","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": -4}, {\"input\": 3, \"output\": -1}, {\"input\": 4, \"output\": 4}, {\"input\": 5, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (5, 3, -2, -4, 0, 7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:86ca7bf8c2b9eefa54ce773bb8706fb523daf06858a52c20ec193ca2d2578317","sample_id":"sha256:64c0fff6df78c039db10fdefbc82e9d329dd204acec1e04f5d110c1f4d5d8457","source_transition_id":"sha256:31a18965f2fce854d4098fbaf5dc3ed590409829946f568ef6296378689c54df","split":"train","step_index":4,"target":"def transform(x):\n    delta = (5, 3, -6, -4, 0, 7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000136","trajectory_id":"vlr-formal-v2-0000136-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e1bafbda31313aec595d6f4715b3bd327b33a99475b47db9d1ee8f54bc20afa0","candidate_id":"sha256:49cf1d47f9788522495de443412c7133caab487b0c28a165592fa54fab50056d","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-3, 3, -7, 5, 2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:07449f7337bdb48fcd011e070f715d25c1fcdc73186d4d010a1cad8d701a44e6"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:9fcada330b0a7ce7e4435183def8850787cd67c69f300ddbbc40285c43c7b21a","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 2, \"output\": 5}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": 11}, {\"input\": 8, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-3, 3, -7, -8, 2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:89e3a2f947003b5feb669ac44b1b35884557e309acf107919e24a4c8d5c638f3","sample_id":"sha256:2e15e1f9c98c522ad67fd2063516cbcfc1426886129e926ee24c096d33c6f1e7","source_transition_id":"sha256:0f2e98f3c7b84efa4915e6e88eb5a9b702cdf2b5e6f571a160e83cd2d0a2cac8","split":"train","step_index":4,"target":"def transform(x):\n    table = (-3, 3, -7, 5, 2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000137","trajectory_id":"vlr-formal-v2-0000137-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:60c4a7c948a9a8e8344aba7e3618e530bdc1e42dc79631ee6fb0f46434e2c458","candidate_id":"sha256:55f9096fe4ca2a079afcf841c7b77ccc78edc1eb60c7a633f5ecc02e23a081c7","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (0)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-3)\n    return x + (-5)\n","verification_digest":"sha256:d0db091fb701346894e73e626bfa6d3989fb66c6d2c8fb0a2cfa0490f11a43f8"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:99dc2d66ce37e1db2e72a41081b4db07ae04f5934efc33e402da64ada84ae996","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -27}, {\"input\": -3, \"output\": -5}, {\"input\": 3, \"output\": 0}, {\"input\": 27, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (0)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-3)\n    return x + (-8)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:64f420c27234a9d5a9edb26b6b8ebb461595b133167367cfea9df6f5dddfd56c","sample_id":"sha256:a8fc7b36f86171887f69951d05f541601a3bc6566ec2739f14ab9fb399004a41","source_transition_id":"sha256:cff512799e3943f55b4f33a6e216e5d42401651d0317e40d681b8506db66395c","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (0)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-3)\n    return x + (-5)\n","task_id":"vlr-formal-v2-0000140","trajectory_id":"vlr-formal-v2-0000140-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:37a78899fc913a916c054ff81eabe0f4c750d359cafead53f0a7dda7fe5355dc","candidate_id":"sha256:ad1507627ad50b511dea90fb5bb6b0299bec164b2416ef5e5693972f79fb80c1","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (5, -3, 3, -8, 2)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:ac40c895dc0ac66a1aee457de2903e6e28dddc5b35650dcbac236efbdaf15a13"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:c523ebc276e3235dcb7fb817ee7d1986dae46549d6a7768008cb0258ba987761","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": -5}, {\"input\": -1, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (5, -3, 3, -8, 9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1fa324b5c9ae527b44a08b74a2253584b6b47306b48b3a6107166462ce996b65","sample_id":"sha256:dab647bf92fe7e6e4e84af4f489d6964d429703e199e17e244293e6098b3ae4e","source_transition_id":"sha256:7e4f73ca1fa4f7235b5e9d81eb405174c138d14f388d78732526c87de0da68a4","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (5, -3, 3, -8, 2)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000141","trajectory_id":"vlr-formal-v2-0000141-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d1b150dcdf6d51a50633aec63d061fe5abac074a4d2894cf5d6acb7755b2a196","candidate_id":"sha256:c060ffa02ca4076e9957593ae75dfcb7e02e7c541964051538e60c63f2fbf926","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-3, -2, -5, -3, -6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:f9511e0717896081d8ab1e504ed0bec41a2f431758dc9e3f746d85971ed1aa2a"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:f8415e38bcdb60964bac74e7d3161641c4a64472990bd31ad51e32670fc7a29c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": -1}, {\"input\": 2, \"output\": -1}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": -5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-3, -2, -1, -3, -6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1735b1ce2d7ab6c503d756c1f3096ba83076afe6ad7ad1c87c2ca167bfb9587f","sample_id":"sha256:c615d38a1b94af948a991b70de7a1f06f5e401097295fbd34e77cee01b17fc92","source_transition_id":"sha256:45c0eefc0a1fc9ff4524287d855715886d18e1ec367c3bd07911b6c5320a3105","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-3, -2, -5, -3, -6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000142","trajectory_id":"vlr-formal-v2-0000142-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e13e9b031262c1c40cad085661bf46047a5576bbb6412bbee58344121553709f","candidate_id":"sha256:12a1281bc4c1d793f6d386282ee9030a4e388091020d1a755029dcb9ed8a9e6c","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (4, 7, 2, 5, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:95c8628d8959f89a6ee90d4b97e0b1d2771f5974f1e2eb26bd05ec2d997f74ec"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:86572af10c57c59e12d008a60104c355de6bf1a1f2b19815c64457ae1a4e2c2c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 7, 6, 5, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:886ef28920cdcf410b6d58005671087be31f1ad60a9b88d87a27613f5c7bd321","sample_id":"sha256:919204321664845ce4df3a293ff0d4378ba91c575625b8776332632698e95287","source_transition_id":"sha256:5aaf21634ff2c4605234e686717728609a31cb1ac7e3bf6bfe9ee087090148ac","split":"train","step_index":2,"target":"def transform(x):\n    factor = (4, 7, 2, 5, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000143","trajectory_id":"vlr-formal-v2-0000143-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:23db1517309dea8ec68ae75ed73833c9a0e449d006e3d0ffebd73ab8818345fd","candidate_id":"sha256:3293286191e1cef15048de75f8504e6f4523dcc6ad433c9a9adbefd5b17c9161","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (4, 2, 6, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:6216e7932fc27406483079c234d2d97dc2de48d79db5cc6ae63428992b6346d3"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:3978299e01f533713199af84014f557b4245e8eb4973ad4d5ce99b36c601a9f9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 2, 3, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:389ada566fc07bda5ac26f3f395d7a9fd72abd5e58f4ad36e684112a78a9f3f2","sample_id":"sha256:95d271271e76f9b7f2826497f873814f8b019d5d1d2535b276d37e2537e5eb3d","source_transition_id":"sha256:72b4151698b3bc2e97ee19f28d7f15b8c30e54ae2ef358d772bdf47209257caa","split":"train","step_index":3,"target":"def transform(state):\n    delta = (4, 2, 6, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000145","trajectory_id":"vlr-formal-v2-0000145-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:89b1cd41f5aa4ac2e6dfcb8c2e9a3b09f0fa2da9aa16d4862dae4c017475d27e","candidate_id":"sha256:417fb09f7a1199d4e6cd8a668bf896bb2e3eae3c36bc943543655d727c8b7594","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-3, 6, 6, 5, 8, -1)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:673fb6d29ef8cd3255c37aea28a0ca3fff5e5255f4f5f36720d9f6a1d957ceee"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:52149cba85e8d7600c8a8031bd1c2de14d4a90ab4c51322f9bd90f24248a86be","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 8}, {\"input\": 4, \"output\": 12}, {\"input\": 5, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-3, 6, 6, 5, 1, -1)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b7e96d09d831940268c6ff469171324fb950a810bc41950ca76d3c48c306fd53","sample_id":"sha256:2eb9c960ee2563a264c4824dadaff546704cdf6da084cf70ab237dd2c3741f69","source_transition_id":"sha256:ea46f4975ba3c1694b50da02d01479f12d311780ece0f535adb7bbe98e849b74","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-3, 6, 6, 5, 8, -1)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000146","trajectory_id":"vlr-formal-v2-0000146-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:7b17ad95de53585193dc548f6bb3a7efd73da64ab1871540ce3d06d823cf95cb","candidate_id":"sha256:b1903f8fae60cfa6acf0e12ad01ad5d1e8fe0d5b0f13fc59131322ef648fafbd","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-1, -4, -7, 3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:d6cb7628a8bb744e95241f0cd2e8f1662bc714d10cea07b40e5c5fb17f38474d"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:31d5eee0feaa16b7b85f412125b6b77c9e1d2db30cb39bccbbe46ba39041d247","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -28}, {\"input\": -3, \"output\": -7}, {\"input\": 3, \"output\": -4}, {\"input\": 27, \"output\": 30}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 2, -7, 3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:db5174f2f6a578cf085b666b0ce624c79538cbcac0b6624f30b7ad15ee6a9c3e","sample_id":"sha256:41fa9a081e4d8875b810198123b8e8128f3a6572178c18c1e8b7d211449de68f","source_transition_id":"sha256:9c7fa5ba750af6ca86cf13ce178831a82929e4d1623ccd976bc9f366e70e3dbc","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (-1, -4, -7, 3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000150","trajectory_id":"vlr-formal-v2-0000150-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:cb223c2b3f421f8ca4ce18f38864482171ffa3d6c48c931575963bf55855c8ae","candidate_id":"sha256:946ecd4a64b431eda297d4ebdffbdcd2af3d886cd25a009d2538ef50c781af24","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-9, 3, 3, -9, -7)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:e50b918421c2647dc203288fe8f2e9640b9bab04e0bfb4836dd2f47d158de424"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:55baa502432426cf4eed04331192a28e3212da38580044142ba311856a89cab2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -9}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": -6}, {\"input\": -1, \"output\": -8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-9, 3, 3, -7, -7)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1627642b15703c7297d177e352e9bdf726cf5e1e669a1b51cb038b2f8cae46d0","sample_id":"sha256:a9ad4ff85d9f1e4da0640f33c749dde3b8597315797454ac824d1fcc7c9bca3d","source_transition_id":"sha256:f7bad1596cff587fc77cd22c354e7ad9371bf91de3c7ae7108b162dc9d6abc9d","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-9, 3, 3, -9, -7)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000151","trajectory_id":"vlr-formal-v2-0000151-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c8c73fe446d4aad3a84f50c3dc266dfa3f052f18c321951b7fa3d8b4565e7cdd","candidate_id":"sha256:e62a90a16a4b631c6ac6f93e2aecba31cd8c506dac84b8ce3fa9647cad3399dc","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (7, 0, 2, -6, 6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:6e8ac939bdd5b66d8a2d064acf658e87b23f490d49320ba04acda0f7a82dbb58"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:e12cdfe9a3938460ec368c39abd3a059d891611b471b86145cef509118aff3ce","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (7, 0, 2, -6, 2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:137b3c5b35dae0552301655ce1b1e61360690ccd14773d4c89d46a30738a01ef","sample_id":"sha256:890b244c3b3888cf66d3a047ae90070997f19cd5458eeaecbb9e1cd857c59292","source_transition_id":"sha256:42a8594011240597ba203d94b00e58ea3e4c0effb4475f5a48c97af8fb1ef127","split":"train","step_index":1,"target":"def transform(x):\n    bias = (7, 0, 2, -6, 6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000152","trajectory_id":"vlr-formal-v2-0000152-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:90f1527bdec720306d639e203acf2a5734f0bee7bcfdd3d53c4393c6a5fb7983","candidate_id":"sha256:6bd9ef2bbad8388cd5f60e4521bc33ab3a850ab9d1383f5426802a3eafe25b6f","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (5, 7, 2, 2, 8)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:cc67943db30514c40aea730d8f19264eb7a8c218678becf094e2697ddca5db1b"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:eacd7cd4290d86361675eb1a0a0ba7ca14de593acf238967474c5b9d1f3d863c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 21}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (5, 5, 2, 2, 8)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:68302d30ef5c6fbfd9395b0c2baa71e002c9f3d38bc60c6ac8b38ae7b10da4cb","sample_id":"sha256:13f79af2d8baaa633724d71661596c8d446101b549792df00e1ae3b11e8a1bdb","source_transition_id":"sha256:0ef1ed3d47701244c27619032ce8d6c23ec8aaa7c330267bd3065bc58fdd39b1","split":"train","step_index":2,"target":"def transform(x):\n    factor = (5, 7, 2, 2, 8)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000153","trajectory_id":"vlr-formal-v2-0000153-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c4bd97328dd34d621adfc7595e4298a95d5ac74bb1ee8d828e3d9376240e8491","candidate_id":"sha256:6bf8e9dc2699b594e21818b2990c9c8410f8ad0245ff51172c082e0dfdc960b9","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (1, 4, 2, 2)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:b47bfab7c2576c703c69a3bacedea8112dcc1a5f3bf42dea428f7ea5c96ee349"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:8f2f2016d5932ca71836f229d59dabb6ad09b24e46b073893019af8a98673877","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (8, 4, 2, 2)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9870f7cfa824aa580fa500b3690389d1b03e16dd11a82c44c11ff08cb6cb6c6c","sample_id":"sha256:7bbb94ce9d6f19b21fa30d0457e6a2bb56b753caccf526d11e73e7a14ddecc6e","source_transition_id":"sha256:90199b7891889f530a41945e70424f9c2c2650a0ff0b2dfc0ac864a2122308ce","split":"train","step_index":2,"target":"def transform(x):\n    masks = (1, 4, 2, 2)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000154","trajectory_id":"vlr-formal-v2-0000154-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:57380466b62fda981c79ca1a85e074799bd5f5297db53baeedc92462eb62b3bc","candidate_id":"sha256:da4a22275b0aa93a5e1fb689953aa4f335e29e57d8c55ebe9bb59a94a365734a","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 5, 5, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c4bfb77f9c8f7a19b8b60928e5d62a6da73f5d1770e0ef6e0f75a4b62388e78d"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:5ee2909eca8ccf8b373e7f757e13e3152892eba84a18c039a0dba1922aa97871","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 3, 5, 5)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_003\", \"fsm_delta.protected.case_004\", \"fsm_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:38bbb520d5b8d1dfa3ebe16f182f61af9fac0a15225521d999abecd315cb6591","sample_id":"sha256:4e09448ee1b3e573bf4249df198813e88c2b418618f6ab48253eaf0e838aaf7b","source_transition_id":"sha256:a3e28e3008296d33eb011a27c72539f40955b5129bd8cf67f6b226f0e81486fc","split":"train","step_index":1,"target":"def transform(state):\n    delta = (3, 5, 5, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000155","trajectory_id":"vlr-formal-v2-0000155-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:014278d67f2d95539881663f9a1d5a802e734b9e602a96d1d76c30a6e5f532b7","candidate_id":"sha256:f62c55a4748e07087fab202c3c5b55fc71342ca1f0cb12af97f044ed9d04681e","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (4, 8, 4, -4, -4, 8)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:cf7ce9b19ae97fdc8f524183f4936321d726596430d652f22651ddb7a77c0846"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:515445f1c4a87091b0d4b790f12599baa3e8dc76f0de9c167a0550eb686a684a","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": -1}, {\"input\": 4, \"output\": 0}, {\"input\": 5, \"output\": 13}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (4, 8, 4, -4, -5, 8)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0af6975ba8a53c8f6d8a65bea615a1f2cf7399913a8f80af26e5bd98e9d5dbe5","sample_id":"sha256:ede43a16610529b0bffc92d03fd23e2b47d26d80d8b7f975d1f20bbf2138452f","source_transition_id":"sha256:5d439ca945eb6ad27d229fb13eef1a005cfe7c8ddeb8790928267a0d74a7759d","split":"train","step_index":3,"target":"def transform(x):\n    delta = (4, 8, 4, -4, -4, 8)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000156","trajectory_id":"vlr-formal-v2-0000156-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1ec5778e64e5050af8c8c7e7000b8f3fa300a5ad7b14b890e2110f235d4ce4a0","candidate_id":"sha256:345eabd2b1381922746a08623994a2620a81d1caf6df10f432559a1ab75d6eef","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (6, -5, -7, -3, 6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:f31c7434530fdfdcac42a02ef90a084e9b92445482355cc6c35a6c422a86a18e"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:5ae3bafc7098236e64c27ada2db47fe931ec142b9d0fde649aef5ffdcb62160f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 2, \"output\": -3}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": 3}, {\"input\": 8, \"output\": 14}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (6, 6, -7, -3, 6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8bf4ea2ef135b59aea53fc25a7b55f865b8d4fbfd6369d2b3769b86b3e1f67e9","sample_id":"sha256:0afab0ac3a2f544eb39c2f64bfd2d0b8f4ef6331fd8cab4f02b2e6d93711af03","source_transition_id":"sha256:8e274b2ba6643e38fbbb8ae5742137182cb58672822455393bcb5d289cbe1547","split":"train","step_index":1,"target":"def transform(x):\n    table = (6, -5, -7, -3, 6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000157","trajectory_id":"vlr-formal-v2-0000157-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c59b51f0145085a9a6a125d6a05a873927d509f774a40c8f062abc13adde67cc","candidate_id":"sha256:f6dfbf91b8919af7323c3e8896958576e741bfa62f909d01b02af54fe88e2216","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-5)\n    return x + (-8)\n","verification_digest":"sha256:9976b50ba3240b5ba6b0e7ea956c0011f299b5bc9555cc3b3c1ff2bc38a6e142"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:24f0a38fec92c7b036af45e95cb92aba474d92f176cb6193ed802cbd7307613c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -23}, {\"input\": -3, \"output\": -5}, {\"input\": 3, \"output\": -2}, {\"input\": 27, \"output\": 19}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-4)\n    return x + (-8)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1a6df7519f8fe8e8adb9dd2c0bf6353c77bea9657dd08b8fa54edf2fd03d7688","sample_id":"sha256:aad5533400116c837e87d98b3ca6e8e0e6b28f57bfe0183431aa6db8a4e89ed2","source_transition_id":"sha256:a6e37ecd6b04e973068e04073614b91e2145e02d50c9696ed9c057e7c517bf26","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (4)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (-5)\n    return x + (-8)\n","task_id":"vlr-formal-v2-0000160","trajectory_id":"vlr-formal-v2-0000160-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:32d7e53af74211f422129167a165143c312f5dc05044479a15cb4a4e27e2c415","candidate_id":"sha256:a0050ca77c94175909731576a3cfa042ca901b4e313f4ca582bd50adc4dcbe70","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (9, 4, 0, -3, -5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:667054d86e3c3456e3754dc41583961995243c655054f6a5e17d22b017ff198d"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:80c90bb573c9626989a3ac231cb27d3f66d2ae8ea3070e040bc50f7a6157f9ea","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 9}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 0}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (9, 4, 0, -3, 6)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a4e4e3a455c59372abb03478514bd2496976c83f605fe752308bbd2a77311c1e","sample_id":"sha256:1e6d3f423dffb4213cce42d00ed223148c6df874ac1775d304b499fd73c4053a","source_transition_id":"sha256:0f7cbbe49eaf3e4030f93001ff4138fbd459f7435660683e73602b79ca9351ba","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (9, 4, 0, -3, -5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000161","trajectory_id":"vlr-formal-v2-0000161-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d3311edc502a5267aed97fffe098b5515bd28122dde67b3b88df7b5dcfd821ec","candidate_id":"sha256:ae1d2fde22de7b87aea5cb90b032e2f4fae23c7a2bd0bc1e1fa378568a761f72","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-4, -3, 4, -6, -2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:3436564101a4c35c18804042155615a36e5e9f8e8f7e5f821b0ae2319917c953"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:029f5429f9d63395d5ec1f2d1716e8ae635d450f4ebdb7e17754b998cfbdc49c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-1, -3, 4, -6, -2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cb1f05d4ac8178e67f45ef8d1eda652f41e76ee9a158cdc84656b9d1347237e2","sample_id":"sha256:3a249c819b171e1c047b0b60ed9711f9df54b11a9a7dd51ea5dc2a2daa0a7515","source_transition_id":"sha256:1b07c7be178971fb6499d537541657ef9a89013bcd46191db4af95c60057e07f","split":"train","step_index":3,"target":"def transform(x):\n    bias = (-4, -3, 4, -6, -2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000162","trajectory_id":"vlr-formal-v2-0000162-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d8d1cbf136378299234dbc325e6a80b3fded027d945fa4961d3f6ee7d872a170","candidate_id":"sha256:2fde46f7064168fac1ee155459a68006369d0ef60dc473e891155fdf5f4d2fb7","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 8, 7, 1, 3)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:309cd8bc32eb835d0429f0b81945ab2b4ac736cbbf43a91d1f4a3c740b786845"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:095db9e222b30fa1bbc3db72b8873f567d8a1dd78401c7fc09327070c0c9a8f8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (2, 8, 5, 1, 3)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c21955ea73701344bea70dd0f5f0849109fb0deeb1c0ff6ef6e7e82aff9f67c8","sample_id":"sha256:9e780de4e8242295a061cb733aee3f94e9320915f1d747613e6296381dd974f1","source_transition_id":"sha256:873fa2068f87c13a9de4c8dd840ac96794fd438abd4ce7eb9e565211a3b8ea22","split":"train","step_index":1,"target":"def transform(x):\n    factor = (2, 8, 7, 1, 3)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000163","trajectory_id":"vlr-formal-v2-0000163-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1d6e539dbaad22b0ca482e364e7ce897d04f79f4571d87ff30bc1f9e0aec3152","candidate_id":"sha256:e17dec09bedca696bd9796e2bed50f7b9d3b8b0d5fcfcfd18488e631d4449d34","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (10, 11, 10, 4)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:4333172c1b32abd1fdbc0fa0ca111f54589ead1b891d10e898748a0d52aeff04"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:e4f3c1e77ca911be08dee657807c51631820de7315e7c249b2f8814cd40497e1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 10}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (10, 11, 10, 5)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d1dda4eeb389c16b7ec3130c8c1d258de72b801463bb53a45276cdc98d0981c7","sample_id":"sha256:7f8f5319e60c39fa3387f4e9625a0aa24ce8898a6c60d1bea8ad17cc3461fc18","source_transition_id":"sha256:76fc76e909716b5ba7a9a695b52cc850a014d8d2daaf22972302251e851566c6","split":"train","step_index":2,"target":"def transform(x):\n    masks = (10, 11, 10, 4)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000164","trajectory_id":"vlr-formal-v2-0000164-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c695057dffa3af61bcced23e078566efcf62b9e42a4d401bab560ca747eedece","candidate_id":"sha256:9b752488671f23f6786b3c5acfa74581ed6c338c30924280aa22c1042d3e9124","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 4, 5, 1)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:a6780be488887acfdccf76ff19ce1a0822cd1da58a16b70e3a80aeb16dc709db"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:dbe8a4c7be36db2b8780f273026ad0c46fff3aa39aad46ed15353f949a51ab61","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 4, 5, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:986082d65986d946c910d05e9a9b8e642d0a04f42a6773e5acff6caae5488fdf","sample_id":"sha256:fa11e0e78845a931edb6eee615dbb94d06d8f4bf823b22ed35aa197ecb0eba81","source_transition_id":"sha256:be04d1ac205217a3b4345ee146b450f980b1209879bebfc565b0100be28bcee6","split":"train","step_index":3,"target":"def transform(state):\n    delta = (6, 4, 5, 1)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000165","trajectory_id":"vlr-formal-v2-0000165-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:680c43bda26bad2aba79ff80f8ac3f58272e2f9df273930e622c6eed8ea61732","candidate_id":"sha256:483f2526e33aac5fcc4aabe58b24a1615bd7fa6c29d63e645193130369b3fcfa","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (8, 3, -5, -1, 0)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:0be563901575b4601e130443f2dcd2639ac963832ac9ce29201ebeca5b1ef644"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:d621099acecda9ad50fd0e804618822be393a0393ea2d45b83d90a11f9dc8c1f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 2, \"output\": 5}, {\"input\": 4, \"output\": -1}, {\"input\": 6, \"output\": 5}, {\"input\": 8, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (8, -1, -5, -1, 0)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8ba571ba6b7684cfafa240ef51d283c06ccec96430e6e71a1c7dac3f1c6aa1de","sample_id":"sha256:6000ace760e4009e1fa405a3a87f0251a965ea0e336f48d879e6b1dfea7f671c","source_transition_id":"sha256:dfd173f87343dc5eb8882225d7c3c687942226393884840484bd9cdde0318c5f","split":"train","step_index":2,"target":"def transform(x):\n    table = (8, 3, -5, -1, 0)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000167","trajectory_id":"vlr-formal-v2-0000167-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3f27bf84f82f0a576289b014a9cabfa86d7975251a099bebbe21e83ef393ea36","candidate_id":"sha256:6e64a4050954d5f455a39bfdaef4ce980fb8ecf038519ec92b6ff0db58af1f6f","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (-7)\n    if x < 6: return x + (-6)\n    return x + (3)\n","verification_digest":"sha256:2455d7e02c1c281cdbcdfe14004d48d57f0f7d4ec1bac9c1cfb61e4443ab1489"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:f567e44a7e70c5b205828676d5e422db3b9719e15e98d926b4461313064f1b1d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -28}, {\"input\": -3, \"output\": -10}, {\"input\": 3, \"output\": -3}, {\"input\": 27, \"output\": 30}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (5)\n    if x < 6: return x + (-6)\n    return x + (3)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:931fd5e42768127f18a9cdec3b85eccd8dcb4ebee9b9873eb3a3f04e284977fc","sample_id":"sha256:cb72bd87c1f7071ef2b86a51747fbd00cb4f4400a0e67afd55a2e9b95e525041","source_transition_id":"sha256:922a64a04f332da1b3f858e808f4abecb547bb6f8f0d9cc6de72c3e3f9fa2529","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (-7)\n    if x < 6: return x + (-6)\n    return x + (3)\n","task_id":"vlr-formal-v2-0000170","trajectory_id":"vlr-formal-v2-0000170-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3aa40f895e11112dfe1ff62abeaf82e04991eb9f958ae315e64572dcff0dc852","candidate_id":"sha256:fa289ea1ce5ab18dbffae0215c6c991f21208c02beab30a7015b0fb723d93b99","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (6, 9, -3, 1, 5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:eb21a85c701c0f73b162d1b0debe96589bdcd3d560f55d88bef549b55771bc26"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:1e112a929f0cbcf2df0ea6f32e67c4c28f1b1d71e2eafdd2d5c9e562187e8b7b","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": -1}, {\"input\": 3, \"output\": 4}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (6, 3, -3, 1, 5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:740d773e59a321ae3e5e7e871a4b0fa09dd77d8f799a4e24eb66f03dc7c8d503","sample_id":"sha256:a6abd1be5657ddb570b9ea058a1464a494efd886dd5e63f141e2fa64f5f221c1","source_transition_id":"sha256:1fe195c11862720713ef7a4aebb33cf84c6fc90f9b990c62f83e384984cadba1","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (6, 9, -3, 1, 5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000171","trajectory_id":"vlr-formal-v2-0000171-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fdde7a3d9ccf55f255d8aceeb89b114ecd869fdeae0c2145f1071aa30e3ff2f2","candidate_id":"sha256:98be619d9b0e9b8e57e09325ccea40ccc9950a7633a8a28239fd93c08c8a5be7","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (5, -5, -1, 1, -1)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:9d790046409b8bdd4242d3615742376c54d8fb5e192133621a61c6f98f2b1d7f"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:697b76868d942309a697f94b976ca1e2921c1fb8e7405aae9369a705e9ce9d1c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": -4}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 10}, {\"input\": -1, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (5, -5, -1, 6, -1)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_009\", \"quadratic_residue.protected.case_010\", \"quadratic_residue.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:56a87c0de3e9e3cacc9c9502e93a5eb41fe23df377beee4f31c2b21f995fecc2","sample_id":"sha256:4d8b733feebca72cfabd25600bf4669b3a000a693139f968fc45e58c6f460f82","source_transition_id":"sha256:460228555fdf5534d01ff6f99a61155a71f44298886cfe5f2713287524bade0f","split":"train","step_index":1,"target":"def transform(x):\n    bias = (5, -5, -1, 1, -1)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000172","trajectory_id":"vlr-formal-v2-0000172-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:31b742ab1a2bef8cf8daf2fc5dac4b06808e97487326b3f4251589dbc06e4ea1","candidate_id":"sha256:f57b6222526b05c7a3b013139cbcb93ba448826e2a0a9a435e8431123a874f4a","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 3, 4, 5, 3)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:84cf685366bd743460468c61b78d163b5ae1f0fa766f52c225cabb7f46f288d4"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:3a3829d621e41767779429b158c603fa862cc2867b4ffcac7ea96fdef63ef1ce","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (7, 3, 4, 5, 3)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=13\nfailed_count=2\nfailed_obligation_ids=[\"mod_product.protected.case_000\", \"mod_product.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cf9d8cdfa489207c815f1b5009a2462379eb9ab2f3b216cdefaa45f0d2fb32a8","sample_id":"sha256:88188cf35530b0f3eaa393d08537d4447c47a5056d21f3db483e35c571e12388","source_transition_id":"sha256:75700139213951e9de2807288ba5244f9545f77a1f69e5173ceab82315772c2c","split":"train","step_index":1,"target":"def transform(x):\n    factor = (6, 3, 4, 5, 3)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000173","trajectory_id":"vlr-formal-v2-0000173-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9a03fb31bcc58b4e0b3e07bdc9a70d0fdd7b29a8437c86e7024adb18550433da","candidate_id":"sha256:aef1a81384bc864f82d246136bff1a00bd9cebabd24a8ac0fb97a9c0474e680a","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (9, 11, 4, 5)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:d9e117adf98b9d8d6c390377a338dcb2385405a616da73f2589624f9de684dea"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:fa58b9ba2be7c56d4658d24b858631f2d99a67a643d4fe1f2ae707bf9e9fff89","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 9}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (9, 10, 4, 5)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:33e79e40e5b8b6348f43454b9e34a65e011360aca6bcb0d80b3529b3a41f2589","sample_id":"sha256:cee1a7a7c13b3e49100164b12719c3ab35acf6beb1aa5533c519f8d3ba1018ab","source_transition_id":"sha256:8866cc1929275a53ee27494ec9531a5b68c1bdec5f408e2c6c0bef65a0f0723a","split":"train","step_index":2,"target":"def transform(x):\n    masks = (9, 11, 4, 5)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000174","trajectory_id":"vlr-formal-v2-0000174-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c9454e363901c02ddc7c5db947e8fdf8732ef3df7de14fef0b9e8a3afa5e7fff","candidate_id":"sha256:3d2f9d50c99f866e1fc5705ff11e882c6c3626c4c65862bd0cf04c58fd31c101","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 3, 1, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:3ae4359caf22ec7fc3d5340a62b052a7d6beaded4db5760035a7c5b7d534e487"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:42c67b45f93f83222106753fbfbdf5a731fd0cb32e874f088ce5f2abcf1d72b2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (2, 3, 1, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:bfac4c9b2cea76f2bcf53a4de20d3c8d382036cafdbdf1cefc437284ea4033ae","sample_id":"sha256:ca42a14766b6293488894a4c9182dc0a727ae5d6f509912e0e6fce205435e209","source_transition_id":"sha256:f7798d2c97dbc7db80dcaf0b4f94e3527a7c8a95859f3c356a5288d040938422","split":"train","step_index":3,"target":"def transform(state):\n    delta = (5, 3, 1, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000175","trajectory_id":"vlr-formal-v2-0000175-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fcd6577c1e101d0c5397e468cb638bd9ba063d406c4e8c2c9e69c2f2cfbc4526","candidate_id":"sha256:b246016c3a376f80d46475895d94dda1ab63cd992be518c832fb6b56d76df86e","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (2, -6, -2, -4, 3, -6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:0100691f8ab836dbc91eee056a3c1069a440fbb30cee5898c05a42f200c140d7"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:b885ddf4fe2f5e86f0216a79cf65841ae5be276f0ae874e9b3ec381350daba2f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": -1}, {\"input\": 4, \"output\": 7}, {\"input\": 5, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (2, 2, -2, -4, 3, -6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:90c91af644421fc8e81700e15eefe9d1aff429cdd4c23a4479a744e6765ba5ed","sample_id":"sha256:fd8f3ff38888b21f845f0804873da94c2e708ee9f0aeefcadb2de114e3039545","source_transition_id":"sha256:c91d3fe1a64dca76b06977920587574b08f92a7be50782878b8129d22a804381","split":"train","step_index":4,"target":"def transform(x):\n    delta = (2, -6, -2, -4, 3, -6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000176","trajectory_id":"vlr-formal-v2-0000176-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:54c63a6df4c09bb472fc9cf8ae0152491be446e34046e401dfc23830070ab8c2","candidate_id":"sha256:d592fe86f2fe1c6cde154430e02178f19062eddbd8b678a7f8f04e9ae8163553","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-2, -7, -8, 0, 2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:11c3686ec5f82630525922c407b999af80a185c8b898b1bdd00e76a3aeb022d2"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:7145b6f5d40b7172098406a00317b18e41ebcfd38e6f59aa6e50bf4de7e10717","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -2}, {\"input\": 2, \"output\": -5}, {\"input\": 4, \"output\": -4}, {\"input\": 6, \"output\": 6}, {\"input\": 8, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-2, -7, -8, 0, 6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_012\", \"signed_bucket.protected.case_013\", \"signed_bucket.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3b4fde8ca1a7a0efb929885bee5afd63f703ccf39b0ec157af133f055c6c4a3b","sample_id":"sha256:9dc892637917f1ccdcf24959f82d2f34670294465134581634e3e239dcbb60f3","source_transition_id":"sha256:f2b7253f2ea5644939c1f4c994667f422cca3c44bdc9db69c4d6a2628f2bd6cc","split":"train","step_index":3,"target":"def transform(x):\n    table = (-2, -7, -8, 0, 2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000177","trajectory_id":"vlr-formal-v2-0000177-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ece22b787ab7065409f0da2a5acbb3982bff3a5be4317232f1e3b840559d14b6","candidate_id":"sha256:2ab717bf2985dbb8e066f8413e26d8fe2a0694d2e6c660cd332242386ec30dd5","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (1)\n    if x < 6: return x + (6)\n    return x + (5)\n","verification_digest":"sha256:e1c6c3fc6a4d2024c7468af6e80dd3d53fe725b0daf5d60d2b7fbabb54d15ec4"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:0bd5d4bcdd8c57698adf574f8ddc21fc45dcb3c1f0c551d63e09db2e35e42d54","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -34}, {\"input\": -3, \"output\": -2}, {\"input\": 3, \"output\": 9}, {\"input\": 27, \"output\": 32}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (1)\n    if x < 6: return x + (6)\n    return x + (-4)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f2bf3383fbe1305ec3b70fbf7914d043f4619d6689ac5305af5887d3ed85b945","sample_id":"sha256:6e638d828d0813061dd9d23121c74df0203af29a4d5c5f04854bd2b17a836660","source_transition_id":"sha256:2bc87e6a3c3b979fed6eeeee0e23656b68e06b217c1eeb7767bf1258c69cfcfb","split":"train","step_index":1,"target":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (1)\n    if x < 6: return x + (6)\n    return x + (5)\n","task_id":"vlr-formal-v2-0000180","trajectory_id":"vlr-formal-v2-0000180-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d19e401cf22be766b88f5dc07b1dd41e5142d8be018931b60cfeb73f5f36271b","candidate_id":"sha256:87f71e6e079b81fe6cc273f21281c2110ddb4240cf4d3a6596146034a35b2118","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-5, 8, 4, 1, 9)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:ad15163310861ab2a4d1993197d01b2614fc2af279ebb6ab479178a1a91c0f19"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:96e1fb07f4627eb80a8e0d062e2fa8f96b9889a4ee76c9bd3683847951150dca","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 4}, {\"input\": -1, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-5, -8, 4, 1, 9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9a41725a146f84c52c60337d3f645df2383f4af9bb806730a09980cba53d8bba","sample_id":"sha256:02b8156fd01a037b943f45a225776895851ce9f577f17cc0e9a425d07ec114b1","source_transition_id":"sha256:124a1e60ed0597ef9316f38f581dae2a2fcdf3516a3269705738838b17fa20a9","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (-5, 8, 4, 1, 9)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000181","trajectory_id":"vlr-formal-v2-0000181-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f1af7a67c7672d6a113d4656917ad1cc349352e8722e036d8f867f70018fe5ce","candidate_id":"sha256:995728f1e656f41de6f87714c6b0a2a74cbe79a0b6877e47a1bfbdce04637bfb","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (7, 1, 6, 1, -2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:b9d9c6ec1825756b58e8845301f0fb5e55879a9b05318d54e799da9af446c415"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:8a5be23dc149b1d7d6788a2479d4c30c4603a39019d522f7fa417a1b2d303a12","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 10}, {\"input\": -1, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (7, 1, 1, 1, -2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1f85feaea38f007ae46b0bec2b3a400556648ac9b545bd3325f2dc63eba35726","sample_id":"sha256:48844dbab261a4a5b84ad3e8bed8c799b2c686d74a0e319e68b92011b4a70664","source_transition_id":"sha256:39f4c7f081ef785663cda4ffbdc9859eb0dda837b076c077c23bc22d21c4acad","split":"train","step_index":4,"target":"def transform(x):\n    bias = (7, 1, 6, 1, -2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000182","trajectory_id":"vlr-formal-v2-0000182-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9a2028fb7ae315c265f4ed1135df0970a0521b5a9f81e9f1fbb0f9cde0672661","candidate_id":"sha256:d3a51704b642b8565083236928089625367a3df86fd14e837bfeeba04b632b5f","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (7, 9, 7, 2, 8)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:9e3cd4c7a87dd53ca3c65858ddb95c4204659d29cc9ac476fc41a55e9722c6a5"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:8c885b2b92bc9060bde56b6713be89690eb42f5b8c6ee6544f700d49c4543320","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 21}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (5, 9, 7, 2, 8)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=13\nfailed_count=2\nfailed_obligation_ids=[\"mod_product.protected.case_000\", \"mod_product.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a8675066d807157e0598dd76f9f798e526d804fdc15d666c3c0e5534f23ca1ee","sample_id":"sha256:ef3de6ebc76384f43a39ff9503898b496c6f525b0c1e49ee754c86467634690d","source_transition_id":"sha256:4b1fcd984bc1e7662c88b65dc7c33c05f7f456e5b748f2f19e261232a15a094e","split":"train","step_index":4,"target":"def transform(x):\n    factor = (7, 9, 7, 2, 8)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000183","trajectory_id":"vlr-formal-v2-0000183-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c1ea0ff0b497138e49ef5bbec75c548a129c75ce504d0401ee2aa574b1d9747b","candidate_id":"sha256:0c17f03c05145075412b80884ac276f150ece484fff02fadcae9833e52811523","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (15, 1, 12, 3)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:8ec107338e6fb178fef9ebf325f09f993fff7a13a77c3bed78625598e40ab1e7"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:9a6af0e6e6d8869f56229d8be3b1dcef65e4922415bfd8bfafa4e9a8725f3722","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 15}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (15, 1, 11, 3)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:79785efc33482a0ee233d94cd1b899d64c740603115411bf2cec354d8c8e4e37","sample_id":"sha256:4302debbc11ec964a9f7aef857e28884526d2e646d53e981e10cd8448e301253","source_transition_id":"sha256:20196f1eb4dcf7889fd464ba97bf33f69a1757b5cb4c12d242fe1de9a05d2cc8","split":"train","step_index":2,"target":"def transform(x):\n    masks = (15, 1, 12, 3)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000184","trajectory_id":"vlr-formal-v2-0000184-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:355acea99817e5f99e9ac7d0bb73ae33dd16e9f401a67b3e220a345daa01548e","candidate_id":"sha256:38c393c1db949bc605fba067df0c50843fd0ffb3a7eb4009e7fc6356dc08fee0","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 2, 2, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c478aad32e811efc83b1dcf07989a22f3bcbff1da54597a58a2dfae739f0278b"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:141b8edd23b3f89e46862c6948fd5b23f6f3f10040db263bfa607ad20858ba0e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 2, 3, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:97eed694eab16abce5c400b012deabc345199e40039275dd353184b97605ecc9","sample_id":"sha256:be086b58911cd54dfba955a674bdd923a1e8d042aeb31097a0eebcd94c91b8f2","source_transition_id":"sha256:8768c626ca43ff1375e9e5801664191dbd237cacf39e9dc197940875da3b42e3","split":"train","step_index":1,"target":"def transform(state):\n    delta = (3, 2, 2, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000185","trajectory_id":"vlr-formal-v2-0000185-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d1b4ba20a5d19f919f9db18e396f50b143a8203b0de0a70ea8cb5db9e3ed1853","candidate_id":"sha256:c6cd22b4aa54f5bbb710ced7ac7d1800c2d220314076d2d6add016890b1c94be","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (4, 6, 8, 5, 7, -2)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:3252d2791182e9b28eeb31112d0c8e51e943af184c55579aff7980592c7acb50"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:071b5c9a61dc54f4241cba90158bf60c9f9fad43e068e83480d37758a05ce350","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 8}, {\"input\": 4, \"output\": 11}, {\"input\": 5, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (3, 6, 8, 5, 7, -2)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:56d7527cf78719bcb2481c2bd2c8ed6d991b0360283e10fea2438e91b6b0a718","sample_id":"sha256:6ca319697c7ede1779575f5caf80d82046f316eb2ad337b03b30509061a89450","source_transition_id":"sha256:2bb8a3bc69c256725cf792ca61ddcac8a09698287986d7b02900201da1bdb409","split":"train","step_index":1,"target":"def transform(x):\n    delta = (4, 6, 8, 5, 7, -2)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000186","trajectory_id":"vlr-formal-v2-0000186-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8f62606770199c5f11a4aea66a653faca09bfbf53fdf0a159547003d3113e819","candidate_id":"sha256:b0be4348fa009f890a1a091a0a9898d2e394d5c5ae4bd7d4aa88a71946ff6031","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (3, 6, 1, -3, 3)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:557f8bb17054f086c1bcecd70a5bdbd71f0da0a30d5005658d423cf892e1a95d"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:3750c90d564485c666a44ae8820e9a6ddb22ecd010761d2e589f0f8dbad310a8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 2, \"output\": 8}, {\"input\": 4, \"output\": 5}, {\"input\": 6, \"output\": 3}, {\"input\": 8, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (3, 6, 1, -8, 3)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:81249731a29463fc4775d652b6ae68f4c47e703557428577b4615b7c62ec57fb","sample_id":"sha256:5d082a41e44afa7414f03b4f3b7a172ea1025bba2275c290207febb283045b60","source_transition_id":"sha256:06ef5f06d119932a6da74053cdb18dab95e115496e46fa25673d45983efe599c","split":"train","step_index":2,"target":"def transform(x):\n    table = (3, 6, 1, -3, 3)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000187","trajectory_id":"vlr-formal-v2-0000187-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:575856c58a31dba1bbaafc6d6e51a9988664605a4a97b7faed2ee79ea74ec963","candidate_id":"sha256:ef1c44246abea46153da2c49ce2d4df1b9993910835784acfe9ec5cc0d555f7e","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (0, 7, 8, 4, 8)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:ab650b152f48a66acf3960991b76bea300bc409b0097ee994045c519d50fcee8"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:b0d3b33854cbe6946c35db6295e4c8e2b7448b0102251b883fd48c0143ae9887","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 7}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (0, 5, 8, 4, 8)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:00ee7595d63cb66e9898b2e5c7d15ed9925706d8201c1648f22553e514454004","sample_id":"sha256:8b9a4ff2f62d45137d2cca37668e642d3bb9b615abda8f2f60ad8d3650cf64c6","source_transition_id":"sha256:8fc2aab4e86c925bb73e81c5a9e149bb404ae4f17a2cbe32f7022e39d5909ea9","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (0, 7, 8, 4, 8)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000191","trajectory_id":"vlr-formal-v2-0000191-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:986170e8befb83dbc0dab77d9c8f3eb249357227e0184725e12a68d4c5692e70","candidate_id":"sha256:a178fc799377472d05e536f45f790c7b5b46d0fc968f16e08c234391a778ed89","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (5, -6, 0, -4, 7)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:7c485549d01f16ad67efb784d00ea6a082747a672c903fa06366674eefb22c7e"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:b1ea145310c1ed398fe7197e5a84b716036208f32a6ec9dc56eecc670fc6ad80","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (5, -6, 3, -4, 7)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d7bb226b6712fce72a8821620a6c2ad504d0d47df3770d941384e28f14fa464c","sample_id":"sha256:1a6816a1bbde5817e43de63e53f01affe993bf2edeeefed8a4371ad980bb263c","source_transition_id":"sha256:93a4c1df913585ff98a9becbbe572ae2b97739ab9933928a36656513e4802216","split":"train","step_index":4,"target":"def transform(x):\n    bias = (5, -6, 0, -4, 7)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000192","trajectory_id":"vlr-formal-v2-0000192-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5a9d2c312bd4d1c4a99c874c40adbe4c51521a1d4cb250981bf178a28cdba901","candidate_id":"sha256:31064b3de308878ad3ae7fe98b03655bf68570626dfe89c2a0f2ad5c83627aea","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 1, 3, 1, 2)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:2f63add585033c61ee980b298d5adf3a7dfa8210d5906bf054607d4bc2b2592e"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:229d2f74b22d4c3c0d73ce30b6f8233684746c0a55b80956fe892fc74baca2e1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 27}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (6, 1, 3, 4, 2)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:091086e14672eb6d79d07c3c2c962a0c8ec36a4d2c424e69a65df2f09428f9f6","sample_id":"sha256:5425bb67ac06280090e63d3efa2f3e0b7c1cfe4ed29453350e82c2bd98603401","source_transition_id":"sha256:bea89108fbc8f90abd30bf26b9fc8fa1e02a038b889caeb6f053767cf2a4d857","split":"train","step_index":1,"target":"def transform(x):\n    factor = (6, 1, 3, 1, 2)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000193","trajectory_id":"vlr-formal-v2-0000193-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a94244fccbee9d1132de79d45edec3fc1fec7f19bf08d56280baff9df13afe49","candidate_id":"sha256:b7883a48776a1a3d2ad2681132fb0404bd5bdd80a6c3a25275dcc63b664fc772","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (8, 5, 7, 15)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:45211f38b5d6784daae96ece9f071fefb6ac19d5cc789f02f4ced8562a76b8c8"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:5fa7b1f02f79a969e50226314f4456ac07b28273db88ef309c3a86bfc500726c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (13, 5, 7, 15)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:42102919774f3aee9d1a3d9e2cda874cc057dde077081631836268ab8c7572d5","sample_id":"sha256:c2c6c30b5a4868a51b160818c73efcc32b2ee8a9e855170ac16997f41318335c","source_transition_id":"sha256:079eb796026565e8b220390908d33227328e6261e3b7cd15f34f10babe30d6c9","split":"train","step_index":2,"target":"def transform(x):\n    masks = (8, 5, 7, 15)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000194","trajectory_id":"vlr-formal-v2-0000194-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f8839db3ed437e5b3a8934b8359f1ade9935c68a8b126ab34dcf89aca418b850","candidate_id":"sha256:ea5ec90b7417096fa8af79563c5f02db11eab6c1861b5bbbc6ac9d5b99c67934","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 1, 6, 6)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:066383df95fd69fa172e4f812f5ea22d5d0a2b3657bb79d943b755285007803e"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:21cef0270a6c3a9049490f27570c8d5840f0079a25a41e6807b831562cbb7e8a","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 1, 4, 6)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:40b59dac48133fcd394beb36ae76fa6796954c41cd8cf561657ce3c4004d462e","sample_id":"sha256:f7e8992dff01dad4e2227679eb5d6d134d0c6d23af0c413494b715c1f59caabf","source_transition_id":"sha256:187b7e438d88ccd60bbf4fed6024ccd97697a9b3d9ff988974496968062d608f","split":"train","step_index":1,"target":"def transform(state):\n    delta = (3, 1, 6, 6)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000195","trajectory_id":"vlr-formal-v2-0000195-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:355e27ba054eff42ad88ec81b941a02887a705773dd9d6da376186c39a4f44ea","candidate_id":"sha256:f2d515bfaa3ed7f1d0ee3bde15b6e459a2e2da65be89af3e6532c2f3ebd0d5b7","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-1, -8, -6, -3, -1, -5)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:a2af5f2120bfcdd50d968d2dd28ab17f89ca163426494eb914c2b5cb8d5c0c25"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:75ad68afd4cb1321c3dcbde6fc634c943fb8cc820481e241927b346372997ba6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": -7}, {\"input\": 2, \"output\": -4}, {\"input\": 3, \"output\": 0}, {\"input\": 4, \"output\": 3}, {\"input\": 5, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-1, -4, -6, -3, -1, -5)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a526bfd8a1d414d51d841a0e4db06163ea3565d759532bda3635606a96980b4c","sample_id":"sha256:9855d630218af17a46572cd1777696e46b5c0a494890e2ddac9b95977fa13c25","source_transition_id":"sha256:b600a5084f6ecaf8d7afcbc66cf6ea60c73d670cb5b6b77b606f8d6e13c15185","split":"train","step_index":2,"target":"def transform(x):\n    delta = (-1, -8, -6, -3, -1, -5)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000196","trajectory_id":"vlr-formal-v2-0000196-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5f7b7e2edc9951e41159283f8fe38925aae1663f1cffab84dccaa62bcb881f6b","candidate_id":"sha256:c9e6fc758970375abcef866cc9b7b8a02f3481a314bbc36a6ff8fe1545534b0a","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-1, 1, 6, -1, 6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:2e981c7adfed028c75820784c8aba37628fb3fefd37abe9adb0933fbf8af9937"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:f492aa6eec5210b52ab31bf5d2d8b992ee0554bdf2f9ddbf0828d83306407d02","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 2, \"output\": 3}, {\"input\": 4, \"output\": 10}, {\"input\": 6, \"output\": 5}, {\"input\": 8, \"output\": 14}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-1, 1, 6, -1, 7)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_012\", \"signed_bucket.protected.case_013\", \"signed_bucket.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3b18c4945dba7cb3876e90b215c43fd179c86fa9761e5c4729ac5362802ef57a","sample_id":"sha256:b1a2d3a603742fd747948aff05a287bd3616c8aeccc3b6c47cec839117d2bdc2","source_transition_id":"sha256:9d7e21e9745813ad39e9a959ede3d213329d1b6e887c4cc8c9e9b47f2545f9aa","split":"train","step_index":3,"target":"def transform(x):\n    table = (-1, 1, 6, -1, 6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000197","trajectory_id":"vlr-formal-v2-0000197-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:28fbfdcdc86ff4d798abc56eddd031dd4ece2a9eaf2e6e09065c99df0c0f0572","candidate_id":"sha256:5a1b7143c87294aaba5ef49ca6bc2d6fd137c59d194dd5d29fdf5fe2d4adbe25","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (1, -8, 2, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:7e07bee53fbfc59dafb01dc5184ff09f398a31e57293f54b6a95906a59a7d445"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:4b4297db67377f837d77f084f96a65eedf30201f448fde2a17e5a4ac1811eff4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -26}, {\"input\": -3, \"output\": -11}, {\"input\": 3, \"output\": 5}, {\"input\": 27, \"output\": 33}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-3, -8, 2, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5d30651d9da3499c8e3799ebe7f106b6e052c98cb69676fbf3d3b5b852fdc649","sample_id":"sha256:73a2b65d80ac3c73d5adf34ecc5b0a1e740ca997f5710e3863c22a15f3885e9e","source_transition_id":"sha256:d4b864d83870976b1df5b60107742360c5756308d25d1594e7a7d98f3a9241ac","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (1, -8, 2, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000200","trajectory_id":"vlr-formal-v2-0000200-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6b77b51d0331223a792f09ae23f1f9216ea2d40a54fd47d7d53c90a87f416f2e","candidate_id":"sha256:98a8e3a62b5be7901bfb2416634ba49916ef3cf15658d332f893f09c5fa9fd03","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (0, 7, 8, 9, 2)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:bbc21a6cd7a9b4075524c1436504d2b2cfe9fdac900a4414d5e9f307e6f65d00"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:042fbe1a46eb2d45a0f8fb2828d1b6548e48951a51081f6da7d685ff12789ae5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (0, 7, -4, 9, 2)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:538799032c96dbc04aea67c4e4a264da3ec0925aadfea9604d00a08f639a2c66","sample_id":"sha256:e682ffffb737e0c9dd795afe6e3212951190b8b4f905f46e6dea7627753dcc15","source_transition_id":"sha256:668b6c252e95d558516720be7062aad73d6ba6096a92929ec148e62ca55dc9ed","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (0, 7, 8, 9, 2)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000201","trajectory_id":"vlr-formal-v2-0000201-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3ae9adb08608f0f9d36cfd3b7f0938c61fbb0944003bf006d4fab9d2a9b33998","candidate_id":"sha256:fa63a4f3f828e97168c27d720cf67aec11f4e4488abbfd39b086095ad94a57b8","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-3, 5, -4, 5, -4)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:d188ce4b9b629c7cd00e3a46fef1a969aaecb2a88d248185ee69f0a2ede0f23d"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:79637f8e4b8c4b26f13236594d29c2099ecfb2d1b45e3083a6b38164aea534b6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": -3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-3, 5, -4, 5, 7)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:33fa145f3d2f870822779a2cd717c3c58ead26eaea6aa36b7543615e203552c8","sample_id":"sha256:5451dd830f2b059726f8e4beea487ecc69754a6ea91108a44458b312de8b1e67","source_transition_id":"sha256:11bcd2420a281788ce4d8fd19587f94ec999e0a2302cbdaa756405748355728b","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-3, 5, -4, 5, -4)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000202","trajectory_id":"vlr-formal-v2-0000202-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:276cd04398b7ddc62082a3503a146b26fb63a47c65ace1bbff895cf9968512c4","candidate_id":"sha256:f4c90c76dfe3145b42b84dd6075cffc33f378e117d427e5f65d6f0b8aad039b4","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (4, 6, 6, 3, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:85703f0d97228996a91ecae326f1531ce95c1d8f76e8a83c2438befa87d0f2a4"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:e25b6a1b36dbd206470ae34e5f6667e634a3f3c7d52fbd4385d1fc9bcde48a73","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 7, 6, 3, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7041b66e49e5d1f869ed9c57848cc8931038fb126187d844a673460e2580e019","sample_id":"sha256:9ae9ad69df9f1243fa749ac21f20f4c869291149ba9aa8ad37e5d10daea2f5b2","source_transition_id":"sha256:690bd77210d1eb6115114f048f6d41db721d7e9cd5df656d036591a1c86cd55f","split":"train","step_index":4,"target":"def transform(x):\n    factor = (4, 6, 6, 3, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000203","trajectory_id":"vlr-formal-v2-0000203-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ca7bb0435ab74d04d454a5e2fcc9502416cfe5114d342be1a787f8e83f3beae8","candidate_id":"sha256:8848705dfeaf89c62ce0b2e4a8292c990980942c32e45f8ca740bb99d8d97c26","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (10, 7, 13, 10)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:25bb76c2c07c88796cbf55065160115b9b9cf63727e903ceda0eeb176ba7f445"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:5fe5e3186049b141e2afdee8472a4d74ca41a2cf943a20970e1f708148fae2be","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 10}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 15}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (10, 13, 13, 10)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ecd738faa7fc4670a779bcba34f1cd12d5a5070f34cdee7c0948b4c22b33b9f4","sample_id":"sha256:f71665b6040be9cbc16747cb80a21456523d7f0010c3c6c41a60d734166a0c7d","source_transition_id":"sha256:c7aafece56a25013d308eaba4b786d6c6a8c0ed75bfaafcf3e260dc1f9c1257e","split":"train","step_index":1,"target":"def transform(x):\n    masks = (10, 7, 13, 10)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000204","trajectory_id":"vlr-formal-v2-0000204-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0083df8495f358b0784340685adbb148f9c20460f2fc65d5f258c03e35b53541","candidate_id":"sha256:781886ecc66159c758f56183a35f5d5e8980a4a18c1ada1935250588ea388b24","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 4, 1, 6)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:a57c1a8a15d12b4de2d6c713d78aaffe643558656b8b918c97c9e63df7223b5d"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:e44cc377a7deb0ab21cee3c336e7959d447e87d01c4277f42626dd14b290cc42","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 4, 1, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:81994c57c96180897bb842aa7b77919b295aeb009e2806e7b46cff293072961f","sample_id":"sha256:c1bbcf7f66c1f0662071618c4ccf17c94c946e882e98cb2122d1974ab8460597","source_transition_id":"sha256:e4617e2983a04a20fdd4fdac3c35bf75d64fa7ac8dbfad3e72a91be345b1cea4","split":"train","step_index":2,"target":"def transform(state):\n    delta = (1, 4, 1, 6)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000205","trajectory_id":"vlr-formal-v2-0000205-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:61542048f19f2f53afd552af82a7cef34ceca41dfa1100064dad43c470933a6a","candidate_id":"sha256:1f13f0a8bff20185b7c81baf65f68b7d68cecd5b5f7a359e3dd40bdcd74a3a84","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (0, 1, 1, -3, 5, -3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:bd0cecfd4a308e4e5ade638f3d31def37bb3c5143d9671a8c6d8fc8020c9c785"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:86a0acf1f8db1a033cc355160eeb886ad17026e47e237bb81e7b97a3d4333630","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 0}, {\"input\": 4, \"output\": 9}, {\"input\": 5, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (0, 1, 1, -3, -6, -3)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:bff88fb8f5887db9e1d388813ac177c271d21ccc431cbcb8a14c758a1184b7e4","sample_id":"sha256:101d90b26cabc8ec9e7e7e77ca10fa600993cd4cff8fa4736ebfb5a19bdec7ea","source_transition_id":"sha256:39142bd54032cee916bd102ff521b402100ca6297c9bd099819058ce7a17aefa","split":"train","step_index":3,"target":"def transform(x):\n    delta = (0, 1, 1, -3, 5, -3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000206","trajectory_id":"vlr-formal-v2-0000206-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9f5cf357accf385bb0611c75c3ce6624d42e619868c19a6e6af3e3523a115263","candidate_id":"sha256:95097e5a547fa398e9cb11b902620c53d3713ac0e865432c8622bcdced667dec","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (3, 1, -7, -8, 8)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:c566af23a228e0ddd71ee551f1f4e36fcd7112f235261dc28850778e953b4ba9"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:4508b49a10d1d84d1a48fca53b76ebbf9b996014ff1f1be1f874836c1b2e86b6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 2, \"output\": 3}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": -2}, {\"input\": 8, \"output\": 16}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (7, 1, -7, -8, 8)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cfaea773ea2edcab17aaec623d6f7e700cf26b13782f2c9fb7f9b48599193048","sample_id":"sha256:e1b7d8838be5db669ee6d643a67cb13c107e522b8230742b57f4c952c3d4578f","source_transition_id":"sha256:7762084e5a903347988980e46cfda2e3ea9e9d45b36f1749d099c48853ae7d9e","split":"train","step_index":3,"target":"def transform(x):\n    table = (3, 1, -7, -8, 8)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000207","trajectory_id":"vlr-formal-v2-0000207-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:bbbb0a76277230afe8ec57249c257a70cc7758dc81913b2964d2e97bb46b3f36","candidate_id":"sha256:202b0d9cd84a18690dc28f3f0698ea17c4e3f943d05e617efddede7c90ca3153","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (8, -1, -3, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:bd1e9aebc4f7b2a4be64e9fc26791591eb53767dfb51b09ad80915bb444860d8"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:1c4b84d4360159dd2dbe31f7a2ccf426970c56fdb20b2891876ea2ebb09f7409","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -19}, {\"input\": -3, \"output\": -4}, {\"input\": 3, \"output\": 0}, {\"input\": 27, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (8, -1, 6, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:71c0750cbb39eb13934c8a3576c6f970851cb49c44bddec712e832457cbb5dfd","sample_id":"sha256:668499f82fbe979b82e0614598ee408d7f6a7167c9153ad4b00fd7ace4e7190c","source_transition_id":"sha256:61a92d9982d635c801bf627a88b285b1c15b5bb2d5578b9dea60949ccd1c975b","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (8, -1, -3, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000210","trajectory_id":"vlr-formal-v2-0000210-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:33b22f6198f9b1cad9bd2fb476a0ec553268911548a45e34b4bee6e84e8b16b2","candidate_id":"sha256:acc7f6b406794cdd6fd5303bc4eab5f1f91f78d685d74b785e7cd3926211446c","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-1, 3, 3, -4, 0)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:275d9ba6c192e9b91339d20f4a09a8a20192557156ad037b906bd035a9f2b5a9"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:8a6b57751f20a8bdfbca365ca6f0c38f9642e6015d5862cca140123c50e198dc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-1, 3, 3, -4, -3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:10a30acc0a9eca3def09af4dd25cabd45b1cca3fb73a6906d8aabc5b4c5160eb","sample_id":"sha256:1c0db0ee628698cc79a3950802927b4e9741a0a4af54dc07f035826c53940d68","source_transition_id":"sha256:837d10fe2ed72978b767dc710c6aac4be6277d91c687424c7e225b1689f22b73","split":"train","step_index":4,"target":"def transform(x):\n    bias = (-1, 3, 3, -4, 0)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000212","trajectory_id":"vlr-formal-v2-0000212-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e4606d1e94321c5e5568fde2d232f84c3e07509e5a0553231318b06ab650597b","candidate_id":"sha256:acfcc399f3a27207f3760e7bae7750f84ce384cf6ca50167f05ba8e59c5cc102","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (1, 9, 5, 3, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:f0f66861f9f492c7b335238141d659c4afbe92eb56726bdd5968ac504ee485cc"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:9960291121c8690c432a3f5d47173410d3d9c27ecd943c759d77e408adc64c89","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (1, 9, 5, 3, 6)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_012\", \"mod_product.protected.case_013\", \"mod_product.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:333d09b9b75c49fe230a6879bc5d5c815bf276fe7c3b82dedb7b440322ae6ff4","sample_id":"sha256:437ecbbe2593a0293548894eb616a00d5092afde4038488f599875b09a8c7039","source_transition_id":"sha256:f9a202e8e77f5c385761b3874ad1927deacec89308348d3c61f107fd0bc242c2","split":"train","step_index":4,"target":"def transform(x):\n    factor = (1, 9, 5, 3, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000213","trajectory_id":"vlr-formal-v2-0000213-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fbb35e623be5ef98a146053b12d23f3a4c7f8b2e7af7d14d0a9b7fa511f01615","candidate_id":"sha256:098318b6039ca4b22639345d739f061ec20037435b1284151804641dd5c96072","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (11, 2, 13, 5)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:273b651cfdc207aa4c0987ebb9664b68f988f058a5bc079954067cb82483f70d"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:de6da4325fc09dec5d9783fef6ae4c93d0f7f2a374bb81d29b6dbd9cf2ea89b4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 11}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 15}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (11, 2, 13, 3)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0275a402021b8f629c7e4ab35ebc19a38ba950ce232298121c0e296c551120bb","sample_id":"sha256:403fd31037a8f85e77b1148d11f957cfe9fa9a69f15fdb807f57367f26e306b7","source_transition_id":"sha256:0842fb817c352a06f6f08323783e4867e81dbd7f9a1723a6e7e9b791e757b9c4","split":"train","step_index":3,"target":"def transform(x):\n    masks = (11, 2, 13, 5)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000214","trajectory_id":"vlr-formal-v2-0000214-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:55c7a351883516016161fa769edb8416bcec53bc33aeb0d966a611c95067d085","candidate_id":"sha256:bd2163f2ad3a22f847278baa136b0823989479ca334480e3b40c8e8933fe1ae0","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c0b9df6c6b24ad580777b1d601fd26462d8a3d9e42efeb6625ddf7d6364c4443"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:12a78277cd8312e620b5a8b6672060ca3898f7650ab3d6bbb9c7be292bf655d6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 6, 2, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:dc886df09e7482ab64a78e7821d0cb473e71dbbe97e3e189012c1f26e8a87359","sample_id":"sha256:442bbb741d88a24803dff64b6edd7e0e86522f3f40fed683eb3e873b69b1dc21","source_transition_id":"sha256:07dd4f769f1ab5e5ec943d9258848dd764b776de8619537df6cdda12cd5e9538","split":"train","step_index":2,"target":"def transform(state):\n    delta = (5, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000215","trajectory_id":"vlr-formal-v2-0000215-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f0f536f393ebfe2df3956d94e5e92620cb8056f150145d277583c25f0f249cd1","candidate_id":"sha256:e07cc71f29a2dd20b7cc5e75ea2ef0a5c0c595dfc40e1044e8458e8871ee5f31","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-8, -6, 7, -3, 5, 3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:7666518d2ae07f81fd320d7edc040a111380e3e648c10844abe8d5e573e73f6b"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:4e48e98718b0c7028f8501a06abcc8b663313ca0f2f66029ba4719fc36129ec8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -8}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 9}, {\"input\": 3, \"output\": 0}, {\"input\": 4, \"output\": 9}, {\"input\": 5, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-8, -6, 7, -3, 5, -1)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_015\", \"lookup_delta.protected.case_016\", \"lookup_delta.protected.case_017\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b7c2b1ee1db56acd46a7949c9e05d2dfdc01a260634318a21876ccfac849e629","sample_id":"sha256:e27df0cfbf4b36267e9c31172d5e562aed9303cd2bd01a7cc73e74e3e05d17d6","source_transition_id":"sha256:f5e7c3e83ce7c0553019a82d7db27bdbf4b779ef26a37c44b3119782ae89e019","split":"train","step_index":1,"target":"def transform(x):\n    delta = (-8, -6, 7, -3, 5, 3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000216","trajectory_id":"vlr-formal-v2-0000216-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:dac4b8a7a1f12e0788e32c135e4929a3a4ae33bec1f8b534175b58dba276bdee","candidate_id":"sha256:6cc68b1e44d52b2991991fd10d9f18ae7215296987bb7f3c4644583d8ed500f4","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-1, -7, -7, 1, 6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:3343b4315de5acb81d1eef437bd019f3b1dfbc2409b24b59a2419d1e14b397b2"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:751f94e44f14d7108a1b6508d7ea7b91dd1bdbe71a732407033261c846c1f90c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 2, \"output\": -5}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": 7}, {\"input\": 8, \"output\": 14}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (8, -7, -7, 1, 6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3fe36e1a96e0cc3c47a1ce262ba7e1e1cb5e9793583f03b6375c5eb2236c37b2","sample_id":"sha256:49fceb07e803ad675c5430d1333b8ad41b435ee0e39d1430548015f64765ad9a","source_transition_id":"sha256:a91db1bf29750c03e1d506faac35660f9aeff462d4e9f2bab86525f854ccfb65","split":"train","step_index":2,"target":"def transform(x):\n    table = (-1, -7, -7, 1, 6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000217","trajectory_id":"vlr-formal-v2-0000217-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:dd40093a754723d6c3b85b0185a3a15c6216d57f5ec2a1b5a8d2896fe172dcb6","candidate_id":"sha256:467960f4e09ccc3fc4c52658eac8cef71e53871f607d931e271b3f0fb798f16e","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-6, -6, 3, -4)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:fb954bf5f02e958e35dd7c68edc787b9db4e5845b92803512d3ff0d078485f99"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:2e80738323ca9ec46192a73b4df0142e50c2af4f0d8319cd7e7e08e04fbac4cb","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -33}, {\"input\": -3, \"output\": -9}, {\"input\": 3, \"output\": 6}, {\"input\": 27, \"output\": 23}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-6, -6, 3, 3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:067c725112adf0a37eb181f9ec4dfc771914a0858fc5d875424408727adf30ce","sample_id":"sha256:8dee87af33c8bc2bdd480329ba1497285a088608961333d8169db95d9da22e26","source_transition_id":"sha256:f5a8295614781aab5dd0b11966b75caed279764e51c038ab4f545ded763b8019","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (-6, -6, 3, -4)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000220","trajectory_id":"vlr-formal-v2-0000220-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:79e5fc4bfd52e8939f9be84c118463d4607021d86a3446ac7e953305585202f9","candidate_id":"sha256:36350f9b168766c10bc3e7b2d3fe5ab82396b6875c6e66713633bb38cafd2d8b","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (0, 4, 1, 9, 3)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:b15ead410c9c40ce9fd7544e035db3c5fe3c9a49f3df11a66f903302d8a9d5bc"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:d66f8a6216c039101759ea61e00a995c274a206cf3bdd4b2429f5297eb4d3521","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (0, -5, 1, 9, 3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:67666791ba653084e7dc9e3c26766c7190ff57ef325981d53f50217fb2e91347","sample_id":"sha256:fdefa2669e1e5c2793661b2bb5ccfb1bc5479a12aa77c00fbec22bd5d21e982f","source_transition_id":"sha256:7111f85f99ec97f665035368a896a800b7a099c052ea3e0771eb6a0bc1e4c231","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (0, 4, 1, 9, 3)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000221","trajectory_id":"vlr-formal-v2-0000221-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5d9fcee3dc495aec3651e9f74ca16a469e0e20bf6e6437e76d7068b5a9398405","candidate_id":"sha256:a05f881ff798e6dde79690ed341c4fab96a0a26812f64665a4e9acd3e16d492f","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-6, 7, -4, 4, 7)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:02313b4f05b49e5e51f2d366fbae9a34b3d8d695807702c4587503e76ea9a6ea"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:b31127effd85019aacf088b20697b142050ecd191cfafff4f06168869f1d646e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 13}, {\"input\": -1, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-6, -1, -4, 4, 7)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_003\", \"quadratic_residue.protected.case_004\", \"quadratic_residue.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:20a92164d8fa30565e8591e36ea2158440e1f5427c9fb6467050d5934780783b","sample_id":"sha256:b48fdd3996c03845945f64d128665c74056f53f44c9f269de30bebca3f9ca649","source_transition_id":"sha256:8f76e8106369d99250cbf08f16246bca8a402bcbaf717a803d384d3c3849d482","split":"train","step_index":3,"target":"def transform(x):\n    bias = (-6, 7, -4, 4, 7)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000222","trajectory_id":"vlr-formal-v2-0000222-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:92c2e582f10643f45afcb2c3e07524c36832fcb3349b75bacf3419015a6b2466","candidate_id":"sha256:ebce908a7f09a973bdc6ba8df20cfd50ab24a56467cce11f9774c58e86e3531c","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (3, 8, 7, 3, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:6c150c26abbcb1947dd30ed350a80f9d35f1b21493bbe5b98d35265888346975"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:cb771f2afbdc4add6edfd4f5bee3ec114e903fa1308abccc2ca3c3c84fda0312","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 8, 7, 3, 5)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=13\nfailed_count=2\nfailed_obligation_ids=[\"mod_product.protected.case_000\", \"mod_product.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5976398cd2bb9a9389854cc8c36e547715a896b81c2bdac0786fc27f6e26083d","sample_id":"sha256:a195e5ce922f45901e6374873e1dd69cbd34c6d79e927564c32f50e1714a36cc","source_transition_id":"sha256:738c1bfd86b7146b40d289f61b726fbe6ed8caaf3fe33268cfbb2ed00cda339f","split":"train","step_index":3,"target":"def transform(x):\n    factor = (3, 8, 7, 3, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000223","trajectory_id":"vlr-formal-v2-0000223-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:beb353b45382f96b9aabb6a66a7fc89280268e4bced9c78f8b559cb9f3272e9d","candidate_id":"sha256:c6e8737147f4d4d9b0dc99919f1c47baa3c4cdbe86530ca6bbbed77c9f5e793b","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 5, 4, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:dc234921ecf099ae86e28e5e5681039ca7ed8be1119b3601b0872e90d9bb06d4"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:ed1db736ca6e5bb4c98c9e5391a675037b6221da3d6db1212e10351bde9730b5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 5, 4, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:eff87242bc38e1af795cf6fdf7b08ea92d2306813de248401e9d063ede752a59","sample_id":"sha256:5b3de8e03da25fa2f6c96b3b64ab60b72b0c15048b5fb794de8bc8263ea50e84","source_transition_id":"sha256:1ce290c9f6f1722f97475721cc18803dd460ee43a4a9b566c0ace65325a87f99","split":"train","step_index":3,"target":"def transform(state):\n    delta = (6, 5, 4, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000225","trajectory_id":"vlr-formal-v2-0000225-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6a49599f1ffe638a113c4e0610ea21b032660a8dd71bfad08f15016a02644a43","candidate_id":"sha256:19d5c271490d580119c22fb1aa8fdcc25fdcd3664a5c214a8d3d210d91030f04","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (3, -4, 8, 4, -5, 3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:23e2d0b19a02b6c1dcafe18b028f3ce65455f9fa2157c36812d1561cd5471001"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:bd75ff16860c1d80f45de49429387af6393cd4b354d0521a1b964c484b4cf6cf","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": -3}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 7}, {\"input\": 4, \"output\": -1}, {\"input\": 5, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (3, -4, 8, -3, -5, 3)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_009\", \"lookup_delta.protected.case_010\", \"lookup_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1b2f7b13c2782554fb03f1447299567f6d3840df4db08607495eeb0a16e59c25","sample_id":"sha256:27c2ae45fe8c2614dac37228539e30309fde2cbabd3ae50b355ce62e7d8aab08","source_transition_id":"sha256:770c487e22027711a9b7d7b9267257d5c9fe5467e71076f2dced5a670daafdf0","split":"train","step_index":1,"target":"def transform(x):\n    delta = (3, -4, 8, 4, -5, 3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000226","trajectory_id":"vlr-formal-v2-0000226-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b0b43c1a72f818cdc900c256391645284c55eb2bbe5d6fd6879243f4757720bb","candidate_id":"sha256:4573c8efa608700be5a135d0193a693b5ed9da493f6a45f63aef66fa0aaf86e6","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-1, 8, 2, -2, -5)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:e046cb27eb5b5583775abaff26c5af6c3281d72d4853efea03985905b40b5f81"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:16951abdb516f177d3e3141005c5a16b760cb84217e46035ed146f344f5ccfd6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 2, \"output\": 10}, {\"input\": 4, \"output\": 6}, {\"input\": 6, \"output\": 4}, {\"input\": 8, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-1, 4, 2, -2, -5)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e744803b9649620660b353ab7b879647eaa4cd179a51f4a8bf21197d4f187113","sample_id":"sha256:1f5c48c5dac977e6e75334e58d120698bded7ccfb3c73d3e2e478e3514dc6241","source_transition_id":"sha256:93ee6e07e48dec9f7d901890b6aca7343f161bac7700372b64c6321e731e5b5d","split":"train","step_index":1,"target":"def transform(x):\n    table = (-1, 8, 2, -2, -5)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000227","trajectory_id":"vlr-formal-v2-0000227-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3d1cafaa424af07a3eac0ba0c273cb0be2f3cb2f551562384b903b70999fd28f","candidate_id":"sha256:b4d23a61ed59a74e26f3d8c2f07a272d23ea9aae729ba15ca9f0e2c2e1c84e75","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (7)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-2)\n    return x + (-9)\n","verification_digest":"sha256:0e0635ac37ae150b61e81b641a87276e5f466a457e05a6d2eea2f7152bed6df2"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:4bd3af33f0105478a9f54e78d07a5914fbe50081334974c93a528fd38202991b","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -20}, {\"input\": -3, \"output\": 0}, {\"input\": 3, \"output\": 1}, {\"input\": 27, \"output\": 18}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-2)\n    return x + (-9)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f7ab0e6597387dee367413d2d22751bf694ba506167ddad80985b7da1158d527","sample_id":"sha256:23f30d1b7ca922ff6432f480ee5e44fff4cc706222834eb4c6bb6ead80e3dbdd","source_transition_id":"sha256:8e263301b30e1e01c2bd537d3be1912ac46832e740686c345bc4e39157e86af7","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (7)\n    if x < 0: return x + (3)\n    if x < 6: return x + (-2)\n    return x + (-9)\n","task_id":"vlr-formal-v2-0000230","trajectory_id":"vlr-formal-v2-0000230-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f0a39530c42cf81114138b70b04b6ea522f9c115cb91627ffe5dd9a7ef04de40","candidate_id":"sha256:0f46ddf635d969e2427c8d5e01c0ccabd2a74e733e125b6da8319b8a272e7cf7","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-1, -8, 8, 1, -5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:ff3c370b78dbc89bce6460aad41b740d62ed3e20901bd6b11ea05c145bd51eba"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:88c67cda66c29490bbbec587c79fbd9517b295772b094ccff7ce200dadae7d3f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": -7}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 4}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, -8, 8, 1, -3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0fb2774ccac691aee0a1521a02676e9375b3e9e52f0d9257b35f786f2bef2671","sample_id":"sha256:61dcce8a4baff00180747e613b8fd7dc7779d4929be85ec2fd9572c6efa47bbb","source_transition_id":"sha256:a70fae9c0088bf16a86c0c121b91095e25a84cbc6b48a24d5f5ccd8bdfaae288","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (-1, -8, 8, 1, -5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000231","trajectory_id":"vlr-formal-v2-0000231-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f706bb2a022e914a435f424eff317eb5f5571828e8b68422c3420962047ca252","candidate_id":"sha256:725f45ef93d8ebb3ca435014ad090bfbfe322d35a6333e0ae192fb4c9e9f728f","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-5, -1, 2, -7, 2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:01fdb73259cdae5c52ae32a69962e91c459671fa6d5160c97f8074cd30d48bcb"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:7e6a856dc7faad6e8ef85e2c0ace3379f8118067d33083bbcf9ff3559e56aae9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 2}, {\"input\": -1, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-5, -6, 2, -7, 2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_003\", \"quadratic_residue.protected.case_004\", \"quadratic_residue.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6fcb2741dab1caec4cdb7d97efbe39df76a9065735a557b3678016e5329aaeec","sample_id":"sha256:1c5b623ce7efe61d8e27acd330598835031d944dbc539f13757259563beb30fb","source_transition_id":"sha256:31c2c388ffa9cb5ead9adcc7dc7e3fc8d357df190122239e922dcfc0deffc269","split":"train","step_index":3,"target":"def transform(x):\n    bias = (-5, -1, 2, -7, 2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000232","trajectory_id":"vlr-formal-v2-0000232-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:f3404f9f4d37aa75bb92282d019e09d0f8b68c90f280d2fe8ab25dfbd9a11104","candidate_id":"sha256:7cb90cce2e096490616d4a51e9deacad89ce236353c9f29190f383d4b219576b","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 2, 8, 9, 4)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:0ffe99314bd6853e24810dce422360c08dd742707c19147aa8b6a1320e8b3d0a"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:de1e8c7a6c14dc0cf7db342d7b16d2bc4b030b1a11ac99ea23e2f8dcece657fb","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 16}, {\"input\": 3, \"output\": 27}, {\"input\": -1, \"output\": 25}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (2, 4, 8, 9, 4)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8a262ea14c55fa70d42c44211d06364bedd705ac4a029002c43f68ceb78ad039","sample_id":"sha256:4faf23aaf916eae73b5fe5762352bfdcfa7e00156496f90069fc8f5d701bb174","source_transition_id":"sha256:df3927273940465888ab96f6c289d6ad9addc8a9107bc8d928b39a26f17fd4fc","split":"train","step_index":1,"target":"def transform(x):\n    factor = (2, 2, 8, 9, 4)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000233","trajectory_id":"vlr-formal-v2-0000233-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d23f22100ed6607003c940a291d3ca999a4aecdc3b3729edbe6b31716e986a29","candidate_id":"sha256:5e1532633e37c31126b0ddd4f574299b8d100b66159e7242ab747b7ccafe01cc","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (12, 9, 14, 13)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:c4c5714b6e156891f5ae5eb9400379eb045939cf1966fa7a5a73d8fdca336db6"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:8b47e41e1ea98b37b8e18d9a87ccfadd25f5c4ae111261e0fc1796133df69244","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 12}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 14}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (12, 9, 4, 13)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1a421fc45a7ccf6d7bef424083ed61c69b35559c1dcb8eac932716d8a5deb7cf","sample_id":"sha256:26f096b901b2e7d27da5a231fcdc95220cbdc4a3a69d080d9ddc0aaaa1a98d63","source_transition_id":"sha256:dba13a1198c3c57840012c48b94c3b48b8a08031faecc0a22b994b96a04f378d","split":"train","step_index":2,"target":"def transform(x):\n    masks = (12, 9, 14, 13)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000234","trajectory_id":"vlr-formal-v2-0000234-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c28b3fc395d63152342fbde61af752ecb8740e17ede7d0cebb62eadd82b534cd","candidate_id":"sha256:4fea09a4e2f9f7d536276e5d7b610cf46484d38e19bb3cd94eff0b7df83b4559","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 1, 6, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:0daa8bd06e902e841be1e5979578b06a2bbaa40316193fda750b46231955f9df"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:497b822d9536dc74c8df15d7a42de408bd624e3d87b7c1e62c3a29dcf9350316","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 1, 6, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7e682e1aca7e9474c63c19f19034049c19935269f8a16fc7e9addce4cef0f7b5","sample_id":"sha256:527717909a5b9c88b2d0495a43a7efe1951d2533d1d770beb74e7faeda151063","source_transition_id":"sha256:fec09cb53e653dbf2071a852029a83b3f1fecd5a2ce9a64fcfe0fdce1fb59b66","split":"train","step_index":2,"target":"def transform(state):\n    delta = (3, 1, 6, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000235","trajectory_id":"vlr-formal-v2-0000235-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:76c95ffada8c07e32ae52cf20432abbb37c10f3a2e0eaed9501d1db205024001","candidate_id":"sha256:78f8a14a8eb46321fd8a84815991924ffca6ec2bcce7ff82ffae4418fa47e33a","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-5, -5, 2, 7, 8, -6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:1ed08254adb5acc9b567d730c6c92be0ae47e938b61bd549ec91122395b9501a"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:f674ed2f4e784dc92fcfa40efe52b66ccd002d48f1c5340c803dc2b9f3d028ab","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 1, \"output\": -4}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 10}, {\"input\": 4, \"output\": 12}, {\"input\": 5, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-5, -5, 7, 7, 8, -6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:eef06812c9af0b80342922e9f89104ae3cd30c660c901cbb4a932a87f743e453","sample_id":"sha256:1dfbc61d8cd9196f1d68a78a8ccc3d6f5d3eae34e0359eca9d4190ae6f339555","source_transition_id":"sha256:31213225a3273bcb7d972556a71d81b43d3f7bf6d060089527bcfc5c1e8ce361","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-5, -5, 2, 7, 8, -6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000236","trajectory_id":"vlr-formal-v2-0000236-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a91585ec5035a0bf3cb7f58469a1ce2e31c6f58683420d78645b25404e967480","candidate_id":"sha256:c50dda8f497e37a3130153b6b6448b72dc9a6c8aa1bc2aae8cc31f3004be7843","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-5, 7, -7, 2, -8)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:27d443f0daa06896b82f7ecc4b3630d1141baadcdf02c939902d6983ceb7b8e3"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:bbe6baa4ea395f4252ed1e27fb1a5238de80b8fd56d8c6f8baf23a77b5797d96","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 2, \"output\": 9}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": 8}, {\"input\": 8, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-5, 7, -7, -1, -8)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:39ecf16afcc929948e7e9cf0f69f18894c14069a4195decae61a27f1724f5894","sample_id":"sha256:b3266a134706b1508098d34fff30685161294fc66bf00859dc02adbd582305dd","source_transition_id":"sha256:52ef2fd5ee369499166f056c94ec9d91983e76347a6735323b6e51a206a5e73a","split":"train","step_index":3,"target":"def transform(x):\n    table = (-5, 7, -7, 2, -8)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000237","trajectory_id":"vlr-formal-v2-0000237-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:304b6c38fea6ed2f2cbbdfebfe059be4c12bb4cdf27e803473955e68136c4827","candidate_id":"sha256:e4f3696cd2ba2eb87af2e8266d827bec6879dbaf8103321719e12eb58cabbf17","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (4, 7, -6, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:71c515b63a0e5a3c0da6f0a57f1943a8034cd83025d988fdaac1357302c41702"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:ad7de562213bbf3995e2f32e743849f5edba15db7050fe1ea70b58cb793880ea","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -23}, {\"input\": -3, \"output\": 4}, {\"input\": 3, \"output\": -3}, {\"input\": 27, \"output\": 33}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (4, 4, -6, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:10a18de128b73b690112720824c2dbf3b0fcd3cf7db27ed3494b449a9315015c","sample_id":"sha256:59e010eaa2d14c3b888239b043d9b988a2daecbc69cbf968458c41e34f63c307","source_transition_id":"sha256:fe31afe8229d8d22a21eb679d75be861c8a98be99cdbb36a234c910c1d892933","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (4, 7, -6, 6)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000240","trajectory_id":"vlr-formal-v2-0000240-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:323be372244120f7491c67ab08659b5f124e92e5e7ae99e9eebf50da763f127b","candidate_id":"sha256:ae5e8500a4a025733a7fd2c61792f22f055641ea934d29714f109327cebf36f7","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-2, 0, 7, 0, 0)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:6d2af72431f50c2a423b37004d8046753589b281e8a29faa8a4c8582148d9bfe"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:353abed0a48cde7e5036b5611211f4279f29825f310474ab228632a77f21b0ca","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -2}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-2, 0, 7, 0, -6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3898bdff768c1c90c1ce6d87f26372d51f438a2a07eedf09f24ce4731be85520","sample_id":"sha256:4a34c27cc3753c33a032a4cc33c331d4240ccd1c39f9a148d00a77d278ced05e","source_transition_id":"sha256:043831bd9c24e6969e7ddab3c69ed1b449ccf252b125ab2a84406918fedad788","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-2, 0, 7, 0, 0)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000242","trajectory_id":"vlr-formal-v2-0000242-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c796777b4bdb414648dc11f478c5f3ca93faec1fe77a6f3d1e762ff55f1ca2da","candidate_id":"sha256:7b987e9c057bca12194ba67ca747cae45725bc8332f460005f4e2608c31e4253","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (8, 2, 2, 5, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:f86c92662c2f61c76be017e385a225cfb37aeeed0079148eb848ac83e68ed90a"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:01ac2098da4f56c17dbccc29fce23f442b409f096ac75e20ceac375a7661a92c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (8, 7, 2, 5, 5)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5f870221186e59eafcf30b44b0232b12e6489937ba59ba2d6aa23ed51adede3e","sample_id":"sha256:2c870c00e7166af1b77adf9f052101ff351348d3fcfba355b7602cc3b4c39585","source_transition_id":"sha256:6189933d9b3213c0151d6b3d3a5240448e01fd6460c3fabf1ebec4850029a529","split":"train","step_index":3,"target":"def transform(x):\n    factor = (8, 2, 2, 5, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000243","trajectory_id":"vlr-formal-v2-0000243-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c41a69c1f53b69d3c40c524c2e88148a85348dea13b2e3d4541d014d920f959a","candidate_id":"sha256:1d526ee4bdf9a2babf5dc338b777849f53c2945a76ae3ec1710104fcd4b99f6c","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (12, 10, 12, 2)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:e752c94c1c721aa172199bdb8507f8f723ce0dcc1e2af74d0d9a85a8c4177f10"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:4b400d8a8afc67d41410a9498d0282273f6eeac734d3d891484511a979572537","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 12}, {\"input\": 1, \"output\": 11}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (12, 12, 12, 2)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_003\", \"xor_mask.protected.case_004\", \"xor_mask.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1fa5d2faba84c5ad24c8f92f7c09adb4478a7c87bfff64a0468c206adb02748d","sample_id":"sha256:3338f2294254eab6a08ae579601053f2f0febbfdd67a385431d7161fa26e3f25","source_transition_id":"sha256:b8ec942750c56a6749a0fa005be97c771d1b5b10f8cde0864890294316ccd413","split":"train","step_index":3,"target":"def transform(x):\n    masks = (12, 10, 12, 2)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000244","trajectory_id":"vlr-formal-v2-0000244-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2064109b39a17abdfdef629dff7e2272c6ca00fd1c968677200389e636578365","candidate_id":"sha256:eb210761111bfeb6a50546b68a7306193534102d65c8e3cd6e898001ac7ed317","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (2, 3, 6, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c21c4df53a1539480fa75f20d5476154be5ebf45d972a88f6b9b0ece617e5fa0"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:79240aac10bf59c2e92c2d55fb0e0fb8ada462cc114c768e349ce4f8c9620039","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (2, 3, 6, 6)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1768a62f29acf8d3babde89e07ce5abf26306e2fde3da7287d1fc6eb7ff235ea","sample_id":"sha256:d82781d908b764fb4935d1125a9f9149d2bb09b80d8c174641df43d8f70a1746","source_transition_id":"sha256:5b31b1c900f227db798062e04a2a0d1b089281b8d548a5e2eef3cfa3263155b6","split":"train","step_index":3,"target":"def transform(state):\n    delta = (2, 3, 6, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000245","trajectory_id":"vlr-formal-v2-0000245-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d92bdd13bfc002a4d8d7f7927234d53b8b492fc038eae15aaff0f0b250c2e8f8","candidate_id":"sha256:005f055f22d545c8366d6e8b00c0b1232ec4986921cd2316c871edac4556dc8b","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-3, 3, -5, -4, 2, -7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:c0c694718401c64b911ae6deca9d1ddb7ac0e6f67c20e810bca4c04bfd0a3ca5"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:f6a996a4c48c55bf4da9a71de6b8fec4eacc1fdd414bdff198e154185e2de2cc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -3}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": -1}, {\"input\": 4, \"output\": 6}, {\"input\": 5, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-3, 3, -5, -4, 2, -8)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_015\", \"lookup_delta.protected.case_016\", \"lookup_delta.protected.case_017\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:253cb9e28ec5a0eca2f527c515c0c1006b164cf32fc001dd3bd3320fcc6208e8","sample_id":"sha256:7b86f3399917d7557c4765c2778260de5eb1dd0766cf86bb105603aea3b5a7b4","source_transition_id":"sha256:cc96e3623a83803636153f18a40d4664a85c7e8682adf8e08aedc111af450cc7","split":"train","step_index":1,"target":"def transform(x):\n    delta = (-3, 3, -5, -4, 2, -7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000246","trajectory_id":"vlr-formal-v2-0000246-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e74f67609c4653b29e4a0cb0255bd309ab4a0a54ec21937890b3f5a994d90fec","candidate_id":"sha256:088ecc7a6793dd3120dc05fa11cb8a1803810bd71cddb565d59bd399fc707dc8","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-6, 2, -7, -4, -6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:c2b65ea88df94115d428dd0ee3c825d2f78cfd9bd66a7c14831a3b7baabf7539"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:afa122dcd909a8e5aedc05fc553543d809f9f749626878eda386652d31c18f67","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 2, \"output\": 4}, {\"input\": 4, \"output\": -3}, {\"input\": 6, \"output\": 2}, {\"input\": 8, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-6, 2, -7, -4, 3)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_012\", \"signed_bucket.protected.case_013\", \"signed_bucket.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2fb9e21b2298cbcd1defdf720e69c096b82ef9c8df354f1c4b6c8ef15614d6ea","sample_id":"sha256:451e1c721ae85ca58799bfbc3742f7bc3dac2569294fc0c029e05aa994a6c6f0","source_transition_id":"sha256:ca79ca990badb08864174b7e12ebc22cfc2e1784c803a39b695de1cdef05e0e7","split":"train","step_index":2,"target":"def transform(x):\n    table = (-6, 2, -7, -4, -6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000247","trajectory_id":"vlr-formal-v2-0000247-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:309beca606a31851a70a04045ff575fc30a6317ae66909250f5ff7dff5a736c2","candidate_id":"sha256:7ed04114bacdbb4565a625b7e0b7f5020bbdd3a56f0db9bc043f23201dd8ce79","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (4)\n    if x < 6: return x + (9)\n    return x + (-1)\n","verification_digest":"sha256:32016c7720d7c4099219e070be66bbdb1ce8da6f1267898a80fbe5a310cb04f6"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:52e138c61788cf4feef4ec3f6136937081636bf77cd2f52987a2aa4ea04b3942","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -34}, {\"input\": -3, \"output\": 1}, {\"input\": 3, \"output\": 12}, {\"input\": 27, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (-5)\n    if x < 6: return x + (9)\n    return x + (-1)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:4563cc2e11e5c0357a610e5ce7a419f8eed3dc912b39991e6a92187a8aa52bf9","sample_id":"sha256:97e9d3c8081317c99e299046658d97e14d5bdcc6c0a8a0ee0c944da09243080c","source_transition_id":"sha256:0493451c15d0435c7e7b2f7894617d2275d94080e033887395cba9cd187eb427","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (4)\n    if x < 6: return x + (9)\n    return x + (-1)\n","task_id":"vlr-formal-v2-0000250","trajectory_id":"vlr-formal-v2-0000250-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b7becc4179d237f3e999091a8ff38b35f5e21f279eec7f509033fe530b06f23e","candidate_id":"sha256:76f94b751fe2646d49ec1da982d139e02239c1d0ab76cc4cead823c74b771006","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-7, -5, -3, 8, 7)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:a18d0a88e7fc4a82035c60aa2b9576d24b0ee92d61babb4669793e1512af3890"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:ab3d5c2d4141bd020531948ce373ab9721a81423ad8f2369b42f04f8fa094574","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -7}, {\"input\": 1, \"output\": -4}, {\"input\": 2, \"output\": -1}, {\"input\": 3, \"output\": 11}, {\"input\": -1, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (9, -5, -3, 8, 7)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_000\", \"residue_bias.protected.case_001\", \"residue_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cb1b9046d17c6fd89099c7f56cb086ef4a22f752cefe3ad66c00de7294e965d6","sample_id":"sha256:8c0fa28319004063ae73f21ef5f81914d5c7676336beb2c229ed7e7ca4c0a188","source_transition_id":"sha256:2ef084d3769ae236563fe0b58e064af229d04615a5a9eab6d395b5198c0bb4ca","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-7, -5, -3, 8, 7)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000251","trajectory_id":"vlr-formal-v2-0000251-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:316a23404d1a3d611ccad19be537b482174ac2b5fdb7fd0a4a948e78b6749ae6","candidate_id":"sha256:611690d4946d928c278976345fe022a328cd16d30f05a542b83ca073e8d33855","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-7, 5, 0, 2, 4)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:df8a2d2fb8ad69135c436ed5776f3b090952574b0438fdda0c2d9bba03a00bfd"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:2b2d6aa05306f816949ad449ca6cdbc034e28c99d68797411d33777a88c3bb95","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -7}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 11}, {\"input\": -1, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-7, 5, 0, 2, -3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:85fd82a6e2e2a0cebe7b8f16646142622a723ee1423148aaa7831ab2be41ec06","sample_id":"sha256:b3e77c279fd6bea9a719e55176dc5e4e6ed26a5b913367afe2a698281d873511","source_transition_id":"sha256:1d545370a692733f75e3a21db4cf5d68e787d026a864137e7dc8ddbdfd966de4","split":"train","step_index":2,"target":"def transform(x):\n    bias = (-7, 5, 0, 2, 4)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000252","trajectory_id":"vlr-formal-v2-0000252-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e7902434771b5ac32994941146a9506ddea3c48b568d9151b0414047ccbbc8ac","candidate_id":"sha256:9487bc036bb61e626b7ad389c4d9d7dda148d32345c9282abb4d6f7bd8d9814e","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (3, 1, 9, 6, 5)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:ee28ce3f36309b1687046b0eda500f5ea77e735712de5f17793d5fd5093df4fb"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:e33bcfffa38c119ddd6062077f3ba619dd7dbdec41fb37edcb93e97830590f3c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 18}, {\"input\": 3, \"output\": 18}, {\"input\": -1, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (3, 1, 5, 6, 5)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6cc8d8c47f306f99f355ab60f59761363bc387c2bd6c71c63a7926ecd80c0c95","sample_id":"sha256:d0e44041d20214cd573258c4a920582878700ef84f83ad7793a5de6894ba0071","source_transition_id":"sha256:8711e29ea28955cbe6d07104eb41d23cc8d7812870b84db2999a9058a11a9ac9","split":"train","step_index":1,"target":"def transform(x):\n    factor = (3, 1, 9, 6, 5)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000253","trajectory_id":"vlr-formal-v2-0000253-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:34a382293cdd2b0ff5e421321b3ba3d0f40f4d8f16a20558c9319669526c25cc","candidate_id":"sha256:0475708f9a7f102d8e9a01f131d1a166c74f74416bacaa4ede8b9ad9e2002357","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (11, 13, 10, 3)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:1b3939b8acc5219670687c9cc34b754bb55aab6ec43030455d4b14a70a10dd36"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:37acc3f79692d2ae53ee8785aba907a14ad60465d63717a4d5b3ef09247b23ee","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 11}, {\"input\": 1, \"output\": 12}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (11, 13, 10, 7)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7216f23c16970b44c9fdff104dbfed43c2e28a1146ea7f84809303ac37f8fb20","sample_id":"sha256:b2ec9edbc247fd19846639e330b8e03dbbaf80a58c0a5052fc67b0760a9a10c7","source_transition_id":"sha256:b6726a7b37be26325e40f74f8f05c970be3ff8bb6f3f8babc6492614912244d0","split":"train","step_index":1,"target":"def transform(x):\n    masks = (11, 13, 10, 3)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000254","trajectory_id":"vlr-formal-v2-0000254-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0bb5c530b39149b33cc3e07ad08023668a09ddf112eb63738b9ddd9abeecb235","candidate_id":"sha256:4c3f40c15a9a69a71e87eedcad583e4298b89b049d247cedb44742d3d6195edb","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c3dade0ed28be91040e6c007bc127b3ead0ffe927c7e94edd929ebffa2288047"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:cdbd93f7fbc3f07be834b4807e8257fda824461c6f9fa139cb087bdf2e6a8f57","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ca96686df527fac9f39572e2150e7a299874370bb0b1ba1c4c29ec824f526769","sample_id":"sha256:7124ee9a78f3fd0fa1be853d45ac0416c498d03bbe4184e7782ef62ef8032fd4","source_transition_id":"sha256:76a74e2744d719013eefc62051622d1377e9837579902bd8a96e559d044fb201","split":"train","step_index":3,"target":"def transform(state):\n    delta = (5, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000255","trajectory_id":"vlr-formal-v2-0000255-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:71778dca9080de03d1ae2b70ae8982e9e012fd2e6d0528573232327ac0d3854b","candidate_id":"sha256:2fbae559afcdd4c9aa22e91d57a991e44dbbe478d05d0c0688d61c958d56f187","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (3, -8, 5, -4, 8)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:7a3e5c96b61e7576fed45f68a25face9976d78b9275c71dccc23e37aa5b77b6c"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:98b1185b43612c3b84a4fd1c5868193d7631757187c64e19f7034ed237a3a1d9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 2, \"output\": -6}, {\"input\": 4, \"output\": 9}, {\"input\": 6, \"output\": 2}, {\"input\": 8, \"output\": 16}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-7, -8, 5, -4, 8)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:719d9cbf3c2314ed093ded5b43b9549f513a6ef551419974ec2248661c62e7c5","sample_id":"sha256:ada322852e38c9852f312e8cfeb7acb014ac053a474e5223b1ae513a992e3a08","source_transition_id":"sha256:2af931d4122013a46a2d11ea92804857368fb4a644451e98c0c09f234c0ca577","split":"train","step_index":2,"target":"def transform(x):\n    table = (3, -8, 5, -4, 8)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000257","trajectory_id":"vlr-formal-v2-0000257-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:abe35272c55deee447381f55e4926f81d21c6083e48b197b3607e3bdb38eaccf","candidate_id":"sha256:a54599d96ab53a6171626dcd39fbe44137055e29d4429ddede27013880c2bcfe","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-5, -3, -3, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:0468a1e696bd4396f3d1e130504066a9fd823e659ed0e829d54cb18367044b60"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:e052837813247c558e4416def7a19411fc68451c478cc0a9ce17194140c697d3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -32}, {\"input\": -3, \"output\": -6}, {\"input\": 3, \"output\": 0}, {\"input\": 27, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-5, -3, -5, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8a2d4173867594b3d38ce508f4a9a196049cb4a62a64f0d63a56ef4cdaf8b81f","sample_id":"sha256:6d3bb73623f5d293514f869c5fcebff3e65d3f1ba917a0ef8e37f733f314124a","source_transition_id":"sha256:1c178427e7ce04f436b48d1ef14a2ed6511558a9c9261ad62782886547505f5a","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-5, -3, -3, -3)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000260","trajectory_id":"vlr-formal-v2-0000260-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:bfc386da01cb0fe0009d14c1f466f5a87d0fe4a68312dcd556bcc0f2defefff2","candidate_id":"sha256:ccf7a6c426dfae2f93c9d65265f474a8b045e04c2ddf0593da557ce26c483c0b","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (5, -3, 5, 2, 5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:2d1a274c56c24238da3cce39b7731d20f7245c989cd98523d24ec35052e504cb"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:2ed91665cc9c3b0333b791e117fcd183271d94e52180af8158f3177485074a54","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (5, -3, 2, 2, 5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cdb07baf772e92bc29d9e923be21b8a0cd86835c3691ab9e9e597fc261b66877","sample_id":"sha256:4f4923060e409126138ada5c9b26df32d13ba34e71e1ae06a35535518e426384","source_transition_id":"sha256:b19a252a6c458c1207bc680e6619ff62c4d4e4273624c33b593638bd358dd3ea","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (5, -3, 5, 2, 5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000261","trajectory_id":"vlr-formal-v2-0000261-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:56ad61ada6c39c2299fe713487512e99f66cba56de04855e307e944c89009e23","candidate_id":"sha256:3e4ca7150b28cb688187a10ee144c39df1eebc47c365931d33aaf73343e91e60","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (7, -7, -3, 5, 6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:d1b3ce5994d21b897ed6c4e4ea591939ffa4e51ee2fc3865f0e7cc346924fa38"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:6c5da72d01b941710444a1062c47905eccae77fbaab534d09bfc4ed0bbbc6817","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": -6}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (7, -7, -3, 5, 1)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5c8f53b708addd2f4153e24be1a37bddafb3828ee374bdc8012ac2a34bfc8c1a","sample_id":"sha256:13d591106b69c749bae52ab0e82ae0b137eb285c5289d2bf7ecbce0b407d853b","source_transition_id":"sha256:62a3bc2a0a976ebbd49b1490cc3f7b2283cc365fa34c659e4190eaca728fccd4","split":"train","step_index":3,"target":"def transform(x):\n    bias = (7, -7, -3, 5, 6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000262","trajectory_id":"vlr-formal-v2-0000262-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5983f7216d2f52be500c992685cfca5a88438d885baab2cb22669af8f40b7768","candidate_id":"sha256:2eae509aefaf342dd62fe0f01021a87086e7d19c9896072578c24567b14ed1c9","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 6, 3, 7, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:2730d1ef58422994fc8e333a5c196e8aad3a2d47ec5e3e620fe9af0dbf43191c"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:480d36740cab7e4a088b32798fa6864fa2f062bcbdab70f36b1b5551f4726125","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 21}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (2, 3, 3, 7, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1b9a599fc66a7463672fe183f3ae217d57d5870d924401482a91bc1f7b50780a","sample_id":"sha256:28ffa567739fb5f26eaaf15642102f704fdc2e0192cad80b7322bf1e3ef87cf5","source_transition_id":"sha256:01671353fc1d07dbcb7dbb432876dbfbb4465c3cc52f8c68aeb66559d98facba","split":"train","step_index":3,"target":"def transform(x):\n    factor = (2, 6, 3, 7, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000263","trajectory_id":"vlr-formal-v2-0000263-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9c9659e77e6494be247beea7ae9faa98c9a93e8c24549011f1c70833a092aced","candidate_id":"sha256:782b65376d4f94d0259d75fc794f47321f3245fb37862a6019f53e18f36a51c9","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (15, 4, 13, 2)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:f90a4e70972feb98f37a0ae770135213d6bae669a98f93a02f22ba256e387c05"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:48ee270f30917262e6b43f00fea603e069bfd327dc15e944d81cb3eb225f9de6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 15}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 15}, {\"input\": 3, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (15, 4, 3, 2)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b75341ea05ed5f9427003d5a8d178d385beac49a68e1a08c23613933e3a6ebdf","sample_id":"sha256:77b9139159e226387119b2e3be36ac30c9e0303cbc8a143bfb5f61b0f821bf1b","source_transition_id":"sha256:f3b506e1c18768f339baa27516429977dd4cf3282e2d61c73dcbcb2f4c2288e5","split":"train","step_index":3,"target":"def transform(x):\n    masks = (15, 4, 13, 2)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000264","trajectory_id":"vlr-formal-v2-0000264-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:54c2f559443a35cc681e70d235ff823f405b3ed4cef56eacf70fdac7b417b2d0","candidate_id":"sha256:5e9b40246317335c9149b55d9612c7846241fde5803364af0627a7a2a3d2516c","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-6, 8, -1, 0, -6, 3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:d11962f200feac2b0665704f1f6944066ab63f511bf67436b14da1442286cf4e"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:e64c13df55501f7e5f95e0ca0090a04c2acf3ddf50803b704b9763769efa6b1d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 3}, {\"input\": 4, \"output\": -2}, {\"input\": 5, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-6, 5, -1, 0, -6, 3)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:64f33768dd1304dbf0f1c0a1c62110c181dba6d101f360ceee382aeb432c0178","sample_id":"sha256:597638dbb752b127dd080c7d3b0f64fecb31c862902eab6c17769f908cbd73dd","source_transition_id":"sha256:8bf8519a9d32e0e055b037c4eac4214ec3646ff60941d63437eaa8c4007dcbf0","split":"train","step_index":3,"target":"def transform(x):\n    delta = (-6, 8, -1, 0, -6, 3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000266","trajectory_id":"vlr-formal-v2-0000266-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:7b77c4fe4abe90b3ad54afe5905ccad9150d5fab9e08fadf281decb90ecfb559","candidate_id":"sha256:bfcfc6cbaf15ca93d0ef5064b6e01a0829d0aed879114bc4e29df0aca63d001f","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (4, -2, 8, 5, 6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:597d32aa5f9bedd0352715259643764fbbca682f4ad1add5c7b102ebfaa8ebdb"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:3063fea0b94d032efcf16b41d415bda097e9f4b7e6a717066a6059eb658b6ac7","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 2, \"output\": 0}, {\"input\": 4, \"output\": 12}, {\"input\": 6, \"output\": 11}, {\"input\": 8, \"output\": 14}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (4, 8, 8, 5, 6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_003\", \"signed_bucket.protected.case_004\", \"signed_bucket.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2498f91a5219b4e33013e4faa9cf3d99aa33d5b611d2d60b4c86b0e3f2121376","sample_id":"sha256:4c56e8b0b9205e88a77aef7ec4481293c344351e645dc72af100b4ef510e132e","source_transition_id":"sha256:31152d649e6bc342054c7a5bd6e1c6040abe425adb1db161fc39807a9cb8f732","split":"train","step_index":3,"target":"def transform(x):\n    table = (4, -2, 8, 5, 6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000267","trajectory_id":"vlr-formal-v2-0000267-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:dc33dd89288313b298421434f2318db227d2895e5b560d7f465ae39a9524894e","candidate_id":"sha256:d91ff253e778cba64092625e4f70eeaa402870d712b6560dfa2d4e1574508ba4","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-4)\n    if x < 0: return x + (-3)\n    if x < 6: return x + (-1)\n    return x + (-1)\n","verification_digest":"sha256:5f2ebb9457a1db4bd8ecb85fcbba9e77066ffc97ab38d46f0df52d6959fd5ea3"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:959649656387e87fb0d4471476ee43b58f562537a0f019a8976b7d1908994897","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -31}, {\"input\": -3, \"output\": -6}, {\"input\": 3, \"output\": 2}, {\"input\": 27, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (1)\n    if x < 0: return x + (-3)\n    if x < 6: return x + (-1)\n    return x + (-1)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:51d42a7cc40989f22b2f5f1de314aedbbc283422514805d7d2f32810e278ece9","sample_id":"sha256:3ab165282e588b1bf5f995abaf6d7e1e2a112b59175c237ec0c57edf43d7fa44","source_transition_id":"sha256:610ca6a21a7f849f1d4280cdbf267ae6b28429c7e09e490844750387d8d8c8fd","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (-4)\n    if x < 0: return x + (-3)\n    if x < 6: return x + (-1)\n    return x + (-1)\n","task_id":"vlr-formal-v2-0000270","trajectory_id":"vlr-formal-v2-0000270-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c31da818098af25f4d3070a65480dbfb8e6e576f90ee3db89466c935380e759d","candidate_id":"sha256:333a8e28d022507d96efafe69a4c99f543beafd180c68adda3aa184f65828791","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-7, 9, 3, -3, -4)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:174ec6783c1017f2ae2d1dfde80c5e5a802c12a6f4409f33b9be7f4baefdf2ad"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:a73f59c907eb4213df3c767fa81b23d73bcdb20f989b0f827aae1f6a6f7984f3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -7}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 0}, {\"input\": -1, \"output\": -5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-7, 9, 3, -4, -4)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d17387164cf697f9450e2b1384e617c1f9549cc8a813ef1bd05b1f282bb6bb7d","sample_id":"sha256:87cc255557bd53398aa3ea94db6e1017a8699b34202cb5e3a6c907816c45161b","source_transition_id":"sha256:8e913ddd33da3c3d0162818aa27d3b77e242f640edaa79b8e2fbd2727e2002df","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-7, 9, 3, -3, -4)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000271","trajectory_id":"vlr-formal-v2-0000271-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:137e8823a52a323c73d9e7ba11680334383a44d38d6f5aececee1a11a1ea7ea4","candidate_id":"sha256:3a2ca25830ee5ba4a65448ae3a7065edc9b97cbb3b7f8aa751fcdb3ef2e19c8b","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (1, 8, 6, 7, 6)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:8a847895b905171627b1da9ae1a99f654eed1a0d86fed97e5fd29bfe4e4ac55f"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:9575b7ee8dc2e833ba8c3074fe98569b01f746a8ef3121aa011c6c11504c26fb","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 21}, {\"input\": -1, \"output\": 23}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (1, 8, 2, 7, 6)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:68ced8d09c3321a67a0a66a5018409258bab0f21ab339296c6da91c8b5f3aff9","sample_id":"sha256:79faf3bebac85b1a8174458ba115a2d0ab3838e8161a2ee9674222d01ed8033b","source_transition_id":"sha256:62bffe86abdd99078efd89e128bcee6564d6a50631e3e17174aedd179d72c23f","split":"train","step_index":2,"target":"def transform(x):\n    factor = (1, 8, 6, 7, 6)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000273","trajectory_id":"vlr-formal-v2-0000273-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:86899520d635bb6f7d92e622c8cd5891c3a45a2b6aad2ff1497a9bf0e7cd07ae","candidate_id":"sha256:9e5613c7f41cde9911aad477ea3cb52759901ec82a9bad47279e1c6a2365b1d5","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (2, 1, 13, 11)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:8b8138f822030a6c8b53dcd2f88882ffa1a0ddf78ccc6e2104b6b03383caf511"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:927562aad8b8a2c3dc4c73df954be551f69c30a26556da1d31842e60643c55af","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 15}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (2, 1, 2, 11)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b8ed1126ad1299f5fac93b473b9e97a7804825629d1a4c6dc7edecf9ee001c20","sample_id":"sha256:e677c3613eab214c95d76fc1542885fa2d13733c4447ef403e24cf6bda8378b4","source_transition_id":"sha256:858cbcc13b45797d90639e01cbccfade993f8d879e995ca5749726518063fe63","split":"train","step_index":3,"target":"def transform(x):\n    masks = (2, 1, 13, 11)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000274","trajectory_id":"vlr-formal-v2-0000274-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8823ecd7b66315ca4b409e8f655903b16ef2a8a399b25b66a50f19f06ea2d06b","candidate_id":"sha256:2080a853a64a4baf22bd7e3255add919a1a9d2ae651c74bda828dd82429e68dc","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (2, 6, 4, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:26c49c28182cbc5c0aa7e2ed2d1ac8c33dec0dc789fd2780bd050fc8dff11cb1"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:255ab3d21e8583451972e60226735edba61d57261b7f98955cc8dd1ca90f9fcc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (2, 6, 4, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2db1bf50cb1378d7f77e93fa9b908c88c00633b806ba0eb0f34ac0ae6b559759","sample_id":"sha256:4fc752c1d2bec491e2f49adcbfc057e948a69e98b8cf1c1ebcfa7e4adac7b120","source_transition_id":"sha256:4b2551735032d78c0b3be924c206d9205a080f873afc865945d12f21fff568f0","split":"train","step_index":1,"target":"def transform(state):\n    delta = (2, 6, 4, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000275","trajectory_id":"vlr-formal-v2-0000275-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6e377c8aab3cd023e2d386f0216acf9107d079d847438706c4e539e8162d97ba","candidate_id":"sha256:b6b73e70ec411f87394283735d98ec12da5098a4a10130fc77283ffc23687145","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (-8, -2, 5, 3, 7, -5)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:99de69f9ed40af0d1ad5cb2b9fc6bf5df5f46c3b2023c9f2d050d5cab9b32f8f"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:4b35696384c674be3a7ed90685dfe2f3bd4e98ba462b50079c8fbd34789f9bb1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -8}, {\"input\": 1, \"output\": -1}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 6}, {\"input\": 4, \"output\": 11}, {\"input\": 5, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (0, -2, 5, 3, 7, -5)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2382d9bfa40d08eaaecbaab360373a752ab2c146ca084868a6a7b44b2f18d382","sample_id":"sha256:c58c649cf6654c24a99cdb32482be777011966d76c8b3ddc7097b131e19ff910","source_transition_id":"sha256:0acc8f9cd9b5cefd4b0437c7014dbb5b199aafd68b4ab4aa2a721fb93016c4c3","split":"train","step_index":2,"target":"def transform(x):\n    delta = (-8, -2, 5, 3, 7, -5)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000276","trajectory_id":"vlr-formal-v2-0000276-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5e28f36603812660b23e77caef3f0b7fcb4bbca38b97b509e34ec3dba1b21172","candidate_id":"sha256:5e388f8e829dd3e84ed9ce84128abcd88a9fa32915585dbf9a63e257fda76705","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (6, 3, 8, 5, -3)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:16836c940d6e703865392bcc9724942067ddaa869a2197358f44554798d3c6a4"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:bc16b4cea20401cacee3c4d7278e07c700459dae0e5a32a6c941e4c1c85d78a6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 2, \"output\": 5}, {\"input\": 4, \"output\": 12}, {\"input\": 6, \"output\": 11}, {\"input\": 8, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (6, 3, 8, -4, -3)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1016077dc42bb45e07b94f0020e7f809c4272ec9ae9358c66d128a919e9c6ae9","sample_id":"sha256:61dd27d7f2d228b30f7126ab5e663f32c35dd09758e091e486d0761e0f390382","source_transition_id":"sha256:cbd155f9d728625fe5dd946136bf9904bb41d1140503cd610abcec53bad3bce8","split":"train","step_index":1,"target":"def transform(x):\n    table = (6, 3, 8, 5, -3)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000277","trajectory_id":"vlr-formal-v2-0000277-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5868030df166873f44a3d3253a7d3073dab308836adc72f0b24b1d0cd549bb2a","candidate_id":"sha256:9d6dd9433852877fb35e9a37bb61a153605d4ee20bb25cd13495bfc705387695","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-9)\n    if x < 0: return x + (4)\n    if x < 6: return x + (-3)\n    return x + (1)\n","verification_digest":"sha256:8e6ee7c9a1fdb4d3aaf5856530f73a8d4d2b62be849557783016b276b34dfbb8"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:553cd42f16109c1558aeddd5ad25263eb9f71bf084ded75c4fe8dde1e44f7ba3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -36}, {\"input\": -3, \"output\": 1}, {\"input\": 3, \"output\": 0}, {\"input\": 27, \"output\": 28}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-9)\n    if x < 0: return x + (4)\n    if x < 6: return x + (-3)\n    return x + (0)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9426a5a504e36885b86c3b056afa43d9bdce39db5cf3547b0f8519903e1b54ce","sample_id":"sha256:14a9cf0965bee417c17bbcc6649e7639d931cb9ceec0caeb1f8d6f954ac94df1","source_transition_id":"sha256:2d25bcd554743fd5e9a0542183a37bb01d575a2c9725c777fd9aa7f1d68d580d","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (-9)\n    if x < 0: return x + (4)\n    if x < 6: return x + (-3)\n    return x + (1)\n","task_id":"vlr-formal-v2-0000280","trajectory_id":"vlr-formal-v2-0000280-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1971d3b0a7a6ffb57806e77173a68a84f61d8e6ebb4f8f33c6a31c54edfaee79","candidate_id":"sha256:136a176b68e18819c7af940c7b3d51c462a85724ec85223dabadd8726bc5c80c","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (1, -7, 8, -9, -2)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:452ac4f20c52fd64e43f4515ba92c92ada367663a650dcb648fe081811d7952b"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:dc3565a555e5370ecef0d995b4cbbc447ae86e1a6ca8d4c5ea938e1571023573","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": -6}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": -6}, {\"input\": -1, \"output\": -3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (1, -7, 8, -9, 0)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:df5e215a33b9620028f4b42b65fc6815870f6dbae46d0a3c7a89e548c2d6a622","sample_id":"sha256:3b80cbac0ea6d6232d161066a8433e6d4842caa236322665c8c5d6da48e9825b","source_transition_id":"sha256:c67bec91361030051568394fdf7f8692d2c4c405c9fe3f700a773466fa42a675","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (1, -7, 8, -9, -2)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000281","trajectory_id":"vlr-formal-v2-0000281-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:028733ade05c544a39da0e1876835714d45a0178bf21fcc845ee494e3c125c7b","candidate_id":"sha256:3b6aed64fe1fd7826cf4ba10f47bf0d2ae299f0e0e3cf9d44e3c8ac47ab2852e","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-1, 5, 2, 4, 5)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:cd57649bd2f7d37384ee37843570e280e2d0d9766941bfc2c1947f626f5a490e"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:4640f0f69fde6c3ce9fa070ee9b548d510a1a5cf50c6838c72fc0c523c383f29","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 13}, {\"input\": -1, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-1, 5, 2, 4, -6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:488b151d20f2ceb035b4ddaf244e5e770df7e78be7420d7966fa3b8e1ce8408c","sample_id":"sha256:8c70c7bf1e1f1a3fda35feb194eb2d43b008128611d3bb1fbd4dd9ebfb1abfad","source_transition_id":"sha256:3e0589c04540abcb8701838a236b11221daeabc24bf7bfe0689e4c5a2771021d","split":"train","step_index":3,"target":"def transform(x):\n    bias = (-1, 5, 2, 4, 5)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000282","trajectory_id":"vlr-formal-v2-0000282-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:85212a764571d3ada8bef3c19b0d947ebe1e6b8e734571db7059071aa7b5b194","candidate_id":"sha256:7b305e5b02f2643646938642fd34c3b628c73a15f682f85f6f631261e1c7a5ca","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (5, 2, 9, 4, 7)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:8507e8b1274e6c92558d709679407b2248324d3ce6dbbb6933ddef7fb62fa6c3"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:50fcb11a53b595f4a1e76e028acd8e14cf84388203f5af6534c218ba1e2d4cd2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 18}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (5, 6, 9, 4, 7)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a8c12e1a1c240e80b74ade3966e072dc574ca0e57793fae3efc59a071c7ad1e1","sample_id":"sha256:86ccff9895a1a9f6693a607350adede60169b44578955aca94219decd5ef9239","source_transition_id":"sha256:312aa9f2ac76df03a8acc0b70336f23f3e56bcf2367c1a901da631376b6eaf63","split":"train","step_index":1,"target":"def transform(x):\n    factor = (5, 2, 9, 4, 7)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000283","trajectory_id":"vlr-formal-v2-0000283-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:58f9adabd57b2c15c36bd9a32c88af9d773aeb38c7c7205bfb6f36b37ccbbd31","candidate_id":"sha256:134d3aa0df0d989db193d53b7c0fca3a781d0b252ef5aa4a2f70f9fc0c1db7e2","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 2, 3)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:8519c8ebcf25e1d8446a04e71f1a809404c64354c9fc8141ae70b30f5c8e6e19"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:5bf075cc4345dd95dba6fd62185cf48977373324a7e0359426d1bb7fb1338176","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 6, 2, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:95a5bd75436db0b7074fcc2a275d66b1ea15ab19f1277fd4f085ded3015679d1","sample_id":"sha256:eaf41f4c0020adf29189714e0c92a8f036b1d766400e43401fc82956b3c434dc","source_transition_id":"sha256:a31e9bec154de02234e3748dfd25a85df7216bf0c0a5b0cf42ee960571a61642","split":"train","step_index":3,"target":"def transform(state):\n    delta = (5, 6, 2, 3)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000285","trajectory_id":"vlr-formal-v2-0000285-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2702106a1a41e814a60284786667cfab8743d9e0fa7bc36a668add3753779cf0","candidate_id":"sha256:421a6f54e2e23283cd5228ea79fc385ff839e6b3c847fa5361bb1bab2ca53e12","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-7, 4, 1, -5, -7)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:9321b5002adeb2d7b9d0661ae4fa1a2e4e2446a2ad36b88492bced6d8be447c7"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:403de5c667b4d75c99987a9e5aa599f634ed917ff7e660b67c6c914b7ada62f2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -7}, {\"input\": 2, \"output\": 6}, {\"input\": 4, \"output\": 5}, {\"input\": 6, \"output\": 1}, {\"input\": 8, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-7, 4, 1, -6, -7)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e5de1a9de80ee702cc1464b1b4bd7a29b2f01caf9796f6e04060f4f9412ffe97","sample_id":"sha256:c189403526078ae0f5e8e2518574962c03af152539e38f3759ed2d992e42c1d8","source_transition_id":"sha256:3168434c676158ea158594f10116bafd19b88c70e84818b2b15863b506fb2b68","split":"train","step_index":2,"target":"def transform(x):\n    table = (-7, 4, 1, -5, -7)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000287","trajectory_id":"vlr-formal-v2-0000287-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d3e9fe9380e202c5107b5d7d74d421b944fff171ca98f4605b82bd8fb008b7cf","candidate_id":"sha256:3534c57b34fecb31511c764f43e88b705f7504712f9d9bf3cc2139e81a54f257","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (2)\n    if x < 0: return x + (1)\n    if x < 6: return x + (-7)\n    return x + (-5)\n","verification_digest":"sha256:fb18badcb72b2bb669e93be079f40c4de984e34c4a9322a60b29ad9a3c549f7b"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:3f5b396f8a7091dcf84e513f017e90697508c859df6443cd3d94684c70dcd118","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -25}, {\"input\": -3, \"output\": -2}, {\"input\": 3, \"output\": -4}, {\"input\": 27, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-4)\n    if x < 0: return x + (1)\n    if x < 6: return x + (-7)\n    return x + (-5)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ec76eb74d59f558c200d8cc61206ad2a98d9d0d3fd0368a9d5ec07fd25d20925","sample_id":"sha256:b6d89a393262e43ec0fa6e41a7d919c4ac8bf046131e890de0d7e7eba734d9c4","source_transition_id":"sha256:158f69b2bae89e50677db7ef7e3badc4def061042dc18016fd5a6c835359af82","split":"train","step_index":1,"target":"def transform(x):\n    if x < -6: return x + (2)\n    if x < 0: return x + (1)\n    if x < 6: return x + (-7)\n    return x + (-5)\n","task_id":"vlr-formal-v2-0000290","trajectory_id":"vlr-formal-v2-0000290-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:58934d7336a608e876c942904319ab0cb2b587c0ec84491220cbc9de35f18dd3","candidate_id":"sha256:3cccdd8eb61825164521ce6aa13d2660f5271cbb00146f6a7535e27ca08dba96","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (2, -4, 0, 2, -9)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:034894d39f2c09b48354914c6493d71b16ec13e1bc6f07dfafdc052354bed8c1"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:a813dfd9d81e4a9d12fe09b5fb7d25d3fc9b0d54868bba6a0e71d17ab5aec52e","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": -3}, {\"input\": 2, \"output\": 2}, {\"input\": 3, \"output\": 5}, {\"input\": -1, \"output\": -10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (2, -4, 1, 2, -9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3e18dbb458c2c15d1f9344d3b7bf336671e4f40111d4c1ce96fddc3c5fa2b90f","sample_id":"sha256:3bc1500fbf1c10441cd4542301ba5f44c9ccbf48af6c4e829fa907d041656796","source_transition_id":"sha256:2e025525d9808bff96ab4037a5aefb24aeae332518e702f11a6700ca19b96647","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (2, -4, 0, 2, -9)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000291","trajectory_id":"vlr-formal-v2-0000291-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:1c5f5dff5759b8bb407059565c9486d304a8b20bae9a0406c37fbd0ba05d5a5b","candidate_id":"sha256:296e702dff64568bd0a045940a779343cec23d8abb70c97a3cd1e80dd1fe8426","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-4, -2, -5, 3, -2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:f195168b18609f4b69472da5807aa29bfdbc3be7896404d0d3814d32d0981077"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:30d23f053265ad945d278f69e51eee2b361743f7cad18424e38e0903a22afbd6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 1, \"output\": -1}, {\"input\": 2, \"output\": -1}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-4, -4, -5, 3, -2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_003\", \"quadratic_residue.protected.case_004\", \"quadratic_residue.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:619c204568dbe36c0ad1e75bc4e2e1b660d64dd7cd474ac82b7488b868c7c462","sample_id":"sha256:06917c5c7dfada32bfe8f4c74014dc75ab218773ba6430fad290e8726081ef0d","source_transition_id":"sha256:436e18430cdf886abc387da41b5c51ae43be5b63c5c47f731a58ece96eb69667","split":"train","step_index":2,"target":"def transform(x):\n    bias = (-4, -2, -5, 3, -2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000292","trajectory_id":"vlr-formal-v2-0000292-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:40a39eb0c793bc44f06b36c3d5c3724f17c4fbb52dff9d058280b3838a44ed46","candidate_id":"sha256:903752b20e773be6f2f8ea47a9bb0d04275c7f644e0b69a882e1ef22fb27b071","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (7, 6, 4, 3, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:afb6dd80dd650f444bb17ba94b8b1fd7a55f0b10adaa90695b7d9978e2baab5e"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:3716a65363eadca25e213bbff09142818f2fe3373bd1ce3a5055ba26257d119c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (7, 6, 3, 3, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_006\", \"mod_product.protected.case_007\", \"mod_product.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:cb794fb3da32d462c0925a91ec132132deabb3595e4f7689900b063cf4b9eb16","sample_id":"sha256:8751253c70b176060fa4d8ab8337b8913634aa649f199ca8d2aca1bc7e120593","source_transition_id":"sha256:f3c0318547f64eff4e874ac241989989411113d7b294d9990837c43631d9ae23","split":"train","step_index":4,"target":"def transform(x):\n    factor = (7, 6, 4, 3, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000293","trajectory_id":"vlr-formal-v2-0000293-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:803114953f6569cff1fed18768f61620c744921a8c06f14e1d2412386bf9079d","candidate_id":"sha256:e627f3a2b644f6f60fab59ad20613af938ef4906a43a569351288e87ce5848c2","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (9, 2, 11, 9)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:c2f75740102f576c7c8ae34e8bc956cf1682fe69bafc3d4cc330c4f80d48ad38"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:bb3b60e31631ad4490d8f27c8d1a6fb55a3ce686540c1a7761f5bb2854988259","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 9}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 9}, {\"input\": 3, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (9, 2, 11, 10)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:46f517963fec61c119ad14b29a81a5cbbcef112beaf9cceab6f63e45f0295e24","sample_id":"sha256:3b326941b0dbe13a34e71db8f79322c5ca6ef5d8adec6de41e5c6f00a4c72b05","source_transition_id":"sha256:ebd260b0898dc8de6d571609fba9c2380ad744bb44b2165a31ea922a01a8152c","split":"train","step_index":3,"target":"def transform(x):\n    masks = (9, 2, 11, 9)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000294","trajectory_id":"vlr-formal-v2-0000294-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2ed84b0d87f8ba0751f1705f345b89fb847b2d774e94c4359ee3895ee86b5e77","candidate_id":"sha256:98648fab41746346eff376ee54a6aae236e9409f1eed25640a12bf043bafda7b","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 4, 1, 1)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:67bfc1a89c0d81abfac0be87404c71119c606463577347224821c17b3bc3e615"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:e0ac0fa6cb27d73d2d173c2de1fac8a6954b8bc600529ef43399d8003fb6b4f7","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 4, 5, 1)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d4836a7727132ee7485ce9e9e78d42d7612cc11ca71f90c4615f7a15600f3f36","sample_id":"sha256:57ae657215f19cbf5a22a159065751cf2e3ae3aa5f036520d23ae14986a2d674","source_transition_id":"sha256:67ff837e20d33500c031912929308ecf3de64b2811d15b8425f7423ce14833e7","split":"train","step_index":1,"target":"def transform(state):\n    delta = (6, 4, 1, 1)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000295","trajectory_id":"vlr-formal-v2-0000295-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b31759424777fa83b2fb7a6460d287ba9429d2dc5159b5e79c3eef240da234f6","candidate_id":"sha256:19951a094f1e0fb83491923e6b5a4c72667044f9c528ca884b88abb8b1c219c2","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (7, 8, -3, 5, -2, -6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:83eaee7b77c4f45fa9e6cc0ed915568e78f103b374965a0915912bf7a9712a2f"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:6b800b5a58431a9e555914a74e2771339a26cc05f2325c53e771d2062f020d9a","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": -1}, {\"input\": 3, \"output\": 8}, {\"input\": 4, \"output\": 2}, {\"input\": 5, \"output\": -1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (7, 8, -3, 5, 1, -6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:904b36a32099d123a2d0e218ecb00b0278e53f0976357b1eb6a9f6f2012c8193","sample_id":"sha256:f7d446e93e518e526fc7090a4750dedb845bb6a33b512f30bc6712a188af7e6f","source_transition_id":"sha256:9f39c14bad16e32faf2375758d4fde4933dbda461261c7e3dc6ef5e69db131eb","split":"train","step_index":3,"target":"def transform(x):\n    delta = (7, 8, -3, 5, -2, -6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000296","trajectory_id":"vlr-formal-v2-0000296-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:d12743e39ed75d67d25160cb209435962b593b1aff54759cfce0a493b9abbdbe","candidate_id":"sha256:11d8b5cc48cffc76028bb13f1172ddf1748564ab82725418d9c0b4be49e985ed","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (4, 4, -3, 2, -2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:79dc0a235e68a0a10ada5eaf4c44e2583980c17f9e30ce56cd7a5c5a0019cda1"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:d9a76c0ba374f34ec832510e1cde33b94f8d508c6a57c9ca6941759bdd8c2f18","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 2, \"output\": 6}, {\"input\": 4, \"output\": 1}, {\"input\": 6, \"output\": 8}, {\"input\": 8, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (2, 4, -3, 2, -2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0b4aac2576a4686cef25007632c25746ff513041f38c57ef789c14cc381ec333","sample_id":"sha256:3f76fba42d088ebdc0cf21d2f4b8c21fd8ccd12a6a40839717c182a6baa5c572","source_transition_id":"sha256:126fa8ccccb4b5755a18dd106064d1c9d33b42870e5bf964c61ab6df61139f29","split":"train","step_index":3,"target":"def transform(x):\n    table = (4, 4, -3, 2, -2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000297","trajectory_id":"vlr-formal-v2-0000297-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:16a65883e6e004a5cd9e86619841b7f8a3fcefad65f9bda6d1cd36a8dd63a0b9","candidate_id":"sha256:0599d8e0d0cd82fe6e11cc4f36318d62c88545f403f90ea7c6ec251664d9705e","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (1)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (2)\n    return x + (-3)\n","verification_digest":"sha256:746b6e16b0eb8224bb9a41f9c68064089827cadbd98e65a54962467a80110b60"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:48e4d2369fbb3fbc04b8109db18d9e77749fe96b8c03a6db2048a0d834e22184","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -26}, {\"input\": -3, \"output\": -12}, {\"input\": 3, \"output\": 5}, {\"input\": 27, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (1)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (2)\n    return x + (-3)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d6224103a13dbf667e5f596afbedd64ae17cc8c62c5dfc911ea4ac3c2729b566","sample_id":"sha256:e1eb2db4a11d87ec369c0199812d76250d4772c4879a83a6472b84119fc46807","source_transition_id":"sha256:5ff6253fa59e6804c251717316854a2ac1e117a407fd19544d921f3f034b6b14","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (1)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (2)\n    return x + (-3)\n","task_id":"vlr-formal-v2-0000300","trajectory_id":"vlr-formal-v2-0000300-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6664f5fa9020a1dbee9c0b8bdb0554e285df74331fdfe647d9d76b9d63686a94","candidate_id":"sha256:ae614fe2bf8e49cd16c168c8116cf490cf36396744d3b0fb8d14cf6a4ef4a167","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-6, 7, 9, 6, 6)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:89b3738e1ca19b462eb8575c795fd3883a3381f310de59645f2973ea6464f800"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:504a2d03fb3b74fed3704133131a0e098e109c8cc6ec7e089b877527795a1b59","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-6, 7, 9, 6, -2)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f42055fa21816e100c36fb451add9cfa9bf6c874a1603702cc940087914099df","sample_id":"sha256:c6e8d1322f716df537888432b3457d4a1c018b0b1ad6619a758abce06a6b4540","source_transition_id":"sha256:b1ced0fe1000148386bf9212676537c401a46126d93a01cc308141e1fbda7f0e","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-6, 7, 9, 6, 6)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000301","trajectory_id":"vlr-formal-v2-0000301-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:cad00634a1cf63539dbcd4ee31a3655543d92f85aa87cb1bfb5c254e5fae9827","candidate_id":"sha256:145b0f63486c1f820fa9aeb966bef76b78f1b87eb200a36159e1aab850ce92ab","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (1, 6, 4, 2, 3)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:b7b57a7353dd1bd5a43ee157c45790c0da52c35a908b9aa3e44aeaeb7e2da091"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:bdabfa41a7e45ea5971bae64fae218b3a5d728c11ba82d8a68bf77909659e9ff","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (1, 6, 4, 6, 3)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:53db78f5e2f64ddadad948602912213aceafcdb0adbb045d90dba6e080f1528e","sample_id":"sha256:2c739bef8cf96668337e5b2abd3b8f34fea4d768cc6bb6e28c36c069a362f5db","source_transition_id":"sha256:0069c9f230486ef0f5a211c0f0fc94d369d857208e85b7702ac10461d06c03ec","split":"train","step_index":2,"target":"def transform(x):\n    factor = (1, 6, 4, 2, 3)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000303","trajectory_id":"vlr-formal-v2-0000303-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2bf13bf73374d7b5418816c1ef93c8d6d42a3d18a084f51ae28ca73c183f4b8a","candidate_id":"sha256:f40b7ff9db1b0980017860a87e5738faa4242cca576d9142e1a76802f7b3b488","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (9, 14, 2, 5)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:4d4cc12cb8a1d4dca2c4f206167698afd9619213985fcd077ff738b81e3e3121"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:17fc90cae9b98ffad73d447c6b288eab85cd2e5fd13ac844b86d9c274786d05c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 9}, {\"input\": 1, \"output\": 15}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (6, 14, 2, 5)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9f7445ba2723b00a94858b1c146f3b908f1996cd92268bd5919d9b0bf13821e3","sample_id":"sha256:9e8137dc176406306b4c9676af422a1c87db4a2a1b9ffa6467b26cfbcf76b444","source_transition_id":"sha256:3f078cf965092a1787f862dfa6ed6c0ca641b5024eba36973785fdd6287c9547","split":"train","step_index":3,"target":"def transform(x):\n    masks = (9, 14, 2, 5)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000304","trajectory_id":"vlr-formal-v2-0000304-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ecb4ca560a2383c6d9248a10f2a291cc9802105df5a9224bff954c496cb26c21","candidate_id":"sha256:d2e803b8ea795c796076ca42c90fdbabcae62eea1c2f0af2891c960de2bd1030","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 2, 5, 6)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:00df73b74b793e085e0fad39cdd93184ecc7b1b2c3be001877bdbddd2f540053"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:bc4d76dc144b9470d86c2191bd0a8cea8333d5e0accf9761f815e6015d1593a6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 2, 2, 6)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f67f8b4992747dd85cd1ed1f1d4fcec1d236922f27045f97f16ae8e479026737","sample_id":"sha256:ec9025f32450f1d005a8e5e97a465a0a5ab174191230b6d8fa99c329e5fbab1d","source_transition_id":"sha256:ff0544cc6754a25fcfcc1f925c1e0c81f24c4e2e37d027987ad318b844e0fa0c","split":"train","step_index":1,"target":"def transform(state):\n    delta = (1, 2, 5, 6)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000305","trajectory_id":"vlr-formal-v2-0000305-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:359a8bdf5dfb470c28687cdaf1ee2262bfb076d79d020e04b68b876e6e39a887","candidate_id":"sha256:4e349228fad4307470ae96ce8e286906528295df67ae2750f0832cc9b4c909e0","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (2, 7, -2, 3, 1, -5)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:015f4015e2ef327568c3c21312d1189b223e4b426dad9836bad4b4036c07425d"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:2486d5ac8f3e53d1136ac628555fd69d379e5b73a0dbcffc716cb64ed0d16c00","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 6}, {\"input\": 4, \"output\": 5}, {\"input\": 5, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (2, 7, -2, 3, 7, -5)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_012\", \"lookup_delta.protected.case_013\", \"lookup_delta.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:807faf3a8aac9ff3ad34a97702eb5d77b8ed88bb34fc441b50e97fc3548767e6","sample_id":"sha256:f2853ea4eef36e5e23955169f5215535337b4c73f0a5102224fe3c2b10e83be9","source_transition_id":"sha256:359587599eec47365bf606a8649ca7664c63dc2d1b76aaedc4ba2d31ffb2ada4","split":"train","step_index":2,"target":"def transform(x):\n    delta = (2, 7, -2, 3, 1, -5)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000306","trajectory_id":"vlr-formal-v2-0000306-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c3af8883fcbe6976df4e8e02f038e3a037be1e2f5ed9e75bbac7db1eeb6c5c95","candidate_id":"sha256:e5056953e3f213bb72413610338defd4ff6db6c65648dd2cd6185778dafec935","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-6, 7, 8, 7, 8)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:9b17538041d8928158d90ead8e77f029a69e71efa0f2148a5ec3593041f4da7f"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:18900fdf13187c67951375785f6c6517ec754be6d3939e4e3b2b990e3b3f3bc6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 2, \"output\": 9}, {\"input\": 4, \"output\": 12}, {\"input\": 6, \"output\": 13}, {\"input\": 8, \"output\": 16}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-6, 7, 8, 7, -6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_012\", \"signed_bucket.protected.case_013\", \"signed_bucket.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a8b9a4b16a4a3c4d0dc7ca037f966c7c90f5b78e5a825744a0c2fd5dbf988d5e","sample_id":"sha256:2142952259dca6fd10e02c3f571cbe3a8cbedd526febd8f1d6c78b47326b4279","source_transition_id":"sha256:1ac02ee018765ffbac7c5a42ada185dbd1232b23962680e28fe5bcbea9b11cfa","split":"train","step_index":4,"target":"def transform(x):\n    table = (-6, 7, 8, 7, 8)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000307","trajectory_id":"vlr-formal-v2-0000307-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:16f64d7536bf5a7d44ec18d85a8878ff04cbfd3a32c5a405de7c8ccf3030a9bb","candidate_id":"sha256:22a6be97d49daddb354c60bf0cee3b5460082e1d1f7d9d8fe119e2bba6fcb809","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (0)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-7)\n    return x + (0)\n","verification_digest":"sha256:efa06b6a7db6da89be81a45b24d54a51c8b891849936c66904abb2f6509f0d54"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:fe2f642232b83e420c3314916d9a4ed6a4d1fd4a272527e2d7c6ce734575ad31","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -27}, {\"input\": -3, \"output\": -12}, {\"input\": 3, \"output\": -4}, {\"input\": 27, \"output\": 27}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-3)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-7)\n    return x + (0)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7a33b99a151660518fffac824348e399f90ada7845746dbc1f9b8fe3e76eab87","sample_id":"sha256:ba66a646e153756c44f9b112f332e95190f97a8bfd0718a47c9b2c1d194a5256","source_transition_id":"sha256:d52872bd03396455a105f1103ecc1530c78a6e5478c02419ba61f62b4f1c3621","split":"train","step_index":1,"target":"def transform(x):\n    if x < -6: return x + (0)\n    if x < 0: return x + (-9)\n    if x < 6: return x + (-7)\n    return x + (0)\n","task_id":"vlr-formal-v2-0000310","trajectory_id":"vlr-formal-v2-0000310-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ee51ed316e30204b4b82d3f4e60f7397e6a1818b748a4ae7b6b467aebde52ce9","candidate_id":"sha256:64c5d7ad126afa11ce2ab03ce8e97466f04f646cb4c4875e3418e42f9256f30c","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (0, 6, 8, -4, 5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:1824a49df93e01d8976bed9246884bbc4505bbc678a18e822606e7def998ef61"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:5d7b0dfb410ee66f6f97bc45e818487a6b62780c62ddd96a09697caa153067f9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": -1}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (0, 6, 8, -4, -3)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0c8ae568533b34401364ab0e51bcc68e81d1b8ea480073bea7fd4c6056044c41","sample_id":"sha256:d2085aed10f7345840f9f233761e15802a40cac2eef9c373fc15066cce83070c","source_transition_id":"sha256:046238dcb976857462c93ddd0571f6cf7923dac0c1d39c4a8a33b010b21c9b10","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (0, 6, 8, -4, 5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000311","trajectory_id":"vlr-formal-v2-0000311-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:e97a4417969f3f3c1305598977d4544a744e75ce9fc939aa1fd876c9da869ca8","candidate_id":"sha256:0360993938aac6203a73d51f7afaae0c245023a958fe61dfab7a42c08698e571","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (3, 1, 1, -7, -7)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:841b86760a329f4639ab488404302c6b8a1fb6883e8ad411d4bd43e851f0773c"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:7bca7b4a58b288966091bae9f592c0b098aa9c815b5ecc3d588f7324af082265","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 2}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (1, 1, 1, -7, -7)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:df3a5721288764ef49aad1b1832a1c247afc932079ce42eebf2b506a219e446f","sample_id":"sha256:64312616b4ce029b7323c6cae7aad61c8481e7096ca611635e98dffc41ac5dde","source_transition_id":"sha256:ce34d32c380d3438bb25a4c78bae7f12fd969211931ff19c0cdd44cf1c80da57","split":"train","step_index":1,"target":"def transform(x):\n    bias = (3, 1, 1, -7, -7)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000312","trajectory_id":"vlr-formal-v2-0000312-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a83bdfddeb9135f29aab67b80b91d6187b9673ee9f57dc608daba17e1743eda1","candidate_id":"sha256:565286ecddce3f3f2810b4c6c1390af4bf37cbfefea4f6351d0019414c5b295b","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (6, 3, 3, 2, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:67d39c07697b787fbdddd661bcb0f423421c9f4f54a6ec3a904832f6bc2ef774"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:21dbebc1039767e5ccb90f10352941c2e0cbf342d1d2fb15f20aaf64cba4d989","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (6, 3, 3, 5, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1c83279f66459f738a315d24dae6dcd9063b8d7a2913bca106f9440047ad9352","sample_id":"sha256:5c261641d5ed018e09e43d49e8f0a21189b4ad16f1013bdaf40c3d7e6439364e","source_transition_id":"sha256:3468ce5aefd5ec8c44f1c9880fe56c3cc611f4674b8016bfe7ff521f11eab7ef","split":"train","step_index":2,"target":"def transform(x):\n    factor = (6, 3, 3, 2, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000313","trajectory_id":"vlr-formal-v2-0000313-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6208e0b762a76572ab08eb0b97446dd1ae2fc7c6af76b1f9cd42571d7755dbb4","candidate_id":"sha256:2fbc6cbae75a5d8b6bdd57739e13324126b226a6a5dd0c233332bc5ebc008657","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (15, 14, 5, 9)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:b613d607e08e3065f5a72cf5acd03cd342e0f8ff7612e6b8115d747ae62e4bc5"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:22aa3aab25246665cd6883be37e8385db2bcaf602a4efc76154e9cdbad223167","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 15}, {\"input\": 1, \"output\": 15}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (15, 14, 5, 7)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3820149509f0066b45e62ee9520a7b599dda10dde4afafea6b75a9bdf43ea92f","sample_id":"sha256:d9659bc3ec78fb03a388b5bfd74c44d94439361c4f32c9e1b997dacef90d01b5","source_transition_id":"sha256:fd0aecb4f8b019690696906e28b1c02aa7510c28d2d9eacc5dd9ecadd8e81aa2","split":"train","step_index":1,"target":"def transform(x):\n    masks = (15, 14, 5, 9)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000314","trajectory_id":"vlr-formal-v2-0000314-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:56939718829176aa194e86bff2acb2fa96a442096d2373b2a1802a77374f4373","candidate_id":"sha256:a0fab668b8298f30d3a6b1982d14b1611d664ba9a498206b1c70e6a5477160de","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 3, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:5673e1ec6ef81f7fbba26b9fb053da86d742836447cfa568c731eb16ee9fef1b"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:47d0c97c1be05c51981da6ea2302c5d0067a07e6af77a843e26f43da63b9c8d5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 6, 5, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:7195d60f4db4534d1041dc6033d883067446de4a54ab0430780c0c001fde5a31","sample_id":"sha256:5e8724cc0b46491d33bcfbba4fb8bdd494c6e161655f23cf7fe0722c61337d21","source_transition_id":"sha256:416c7447cde7abeb953b513faf0f3a401e52a01cd8f46638e610292f99108d2c","split":"train","step_index":1,"target":"def transform(state):\n    delta = (5, 6, 3, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000315","trajectory_id":"vlr-formal-v2-0000315-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a99107110ca4759f2e6fc03a37c85dc0ea961ab5b8eab0c8523db001a3524877","candidate_id":"sha256:bfbbb383eaf413f2f42323d504be3776737f3f17b4dbcc22d9db5d5702f3594c","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (1, 3, 2, 5, -4, -1)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:4538fe0e09024e3de21124e8ff7c741dda4ff2a7a184209c105dfd5ea395eaa7"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:0d1752563edbd8485b2f96af612af294bd595076fb3ac01bb55efbd7fc1f78db","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 8}, {\"input\": 4, \"output\": 0}, {\"input\": 5, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (1, 5, 2, 5, -4, -1)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f1439a420d8f148ae7a3acd7ca17ce3275eb912d514032e2981a4184452c8dee","sample_id":"sha256:9545a9cc89c3204ae9c456c20034e5ba824efff9aea2ce89b6ff5f7f61478219","source_transition_id":"sha256:c3bb2ccb403cd453842d713b1239bc498b207ddb4b6657bf2ad8f5c3d1857233","split":"train","step_index":4,"target":"def transform(x):\n    delta = (1, 3, 2, 5, -4, -1)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000316","trajectory_id":"vlr-formal-v2-0000316-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:803bbe35075161e1a77cc9b5fef55331486d786197120d06f4fc958339304bc5","candidate_id":"sha256:ac471712ebd7c9b928a7de957bb4328bf1cde9c7d43af20788cf9d0f2b92a23c","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-5, -8, -3, 8, -6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:30dfd53f5fc59e2a3590223e83f80b2db31761fd1b2ad38a066da0ee79072c18"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:a1b96b478612b3243805d70c8c3a979f33297c746c93007769ad14df0a5f3062","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 2, \"output\": -6}, {\"input\": 4, \"output\": 1}, {\"input\": 6, \"output\": 14}, {\"input\": 8, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-5, -8, -3, 4, -6)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:caf960e8cdcfa4630d58ed2ab81b25488ea3eb2af9902a695691a5cceddaf9aa","sample_id":"sha256:963df51ec4f7d14d1346622e99c94fc738ab615ea1a8d725f26e0def429b2bea","source_transition_id":"sha256:eb57580df9c7256103faf4d5d1b46bcf2bd2b0ab567baeac7d0bf396141331d1","split":"train","step_index":2,"target":"def transform(x):\n    table = (-5, -8, -3, 8, -6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000317","trajectory_id":"vlr-formal-v2-0000317-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:6d955cae4b8b19dcfd7ba2cbe32bfa4f7d0eab49cc7c2e6103e87f9abe063a87","candidate_id":"sha256:719f8f6cf25a2fe358689cc7acc44e28682b92494d87b2741d74475aa99d3d6b","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (5)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (1)\n    return x + (-4)\n","verification_digest":"sha256:610ac6bc242dfac068c417e690bd9e44c377f858eb8d3b5baa3c361087f4b98a"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:8e807d3c192fe0b37765974aff05a5518a0b9b7251a7cd18027d739f6d856c8f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -22}, {\"input\": -3, \"output\": -5}, {\"input\": 3, \"output\": 4}, {\"input\": 27, \"output\": 23}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (1)\n    return x + (-4)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c5b7294e531eb62aaf71f8d6833cdd8a1dfb0a3965eb1814c8a734ea4faf8d37","sample_id":"sha256:ff2d2500957dc4e2fd74e32cc8782f89ed4af6f0cb10c192b2cdfe8903374aa5","source_transition_id":"sha256:b4ddd36522c880c5b0e74131760b3722dbde942e2451d4e992c36430a162b974","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (5)\n    if x < 0: return x + (-2)\n    if x < 6: return x + (1)\n    return x + (-4)\n","task_id":"vlr-formal-v2-0000320","trajectory_id":"vlr-formal-v2-0000320-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:01128cbf7b07d33beaa91c935c965e3e542dc397b38a628882b5117da7f27c14","candidate_id":"sha256:fd4760cd634937836432006f62c13f55c72af267776802b66b4a3c4257df8b6a","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (8, 9, -7, 7, -9)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:7d14de174451b183bca661ab0a7ca9488a74e526d7d52851adaffe746914d82a"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:ffa79ecd8a81e463b4d678467fafd8c0cde47dce801ffeb465fb900d5ff17908","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": -5}, {\"input\": 3, \"output\": 10}, {\"input\": -1, \"output\": -10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (9, 9, -7, 7, -9)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_000\", \"residue_bias.protected.case_001\", \"residue_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e6e06073705b63cbcb1e0592565ac7b7db037721d00a68dd6daf1f76d767e945","sample_id":"sha256:4cc6aeca03396c55f4121338785a9e16984abb2fbee3fa83938804d86602b91c","source_transition_id":"sha256:a113dc13fdefdf8818c3793cd6595277e53840a51fa247929e9627d642beb7d2","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (8, 9, -7, 7, -9)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000321","trajectory_id":"vlr-formal-v2-0000321-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:fa47ab540915a733f4061ad40af60634cf291a9352e4386d60e59f1a146fc871","candidate_id":"sha256:1e68ca3c029e64c99362797fc38113dc75a745d7774ac7b8a2a3b06e0fd464be","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (6, 7, -3, -2, -3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:ba01fe4e0c890f0fcf8c7dd746bd4fd1cead897b7d2609527b7b00c507610dc3"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:f66fe895570210bfa4adb299a665e81fcab1a08a34070b61300c853f61f8ddf8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 7}, {\"input\": -1, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (2, 7, -3, -2, -3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3cc550872d89af2379c15e934dad52ffbdf97eb798d523157af639df7217ddbb","sample_id":"sha256:d7b38612d5422eea0f4f9bc8a6c8200e3d0b3c24805d14f0825666276723a1ca","source_transition_id":"sha256:ce3a13443945be7445d07431ff735b122d2d0f110f3a003aa48a4128f7f04bfe","split":"train","step_index":1,"target":"def transform(x):\n    bias = (6, 7, -3, -2, -3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000322","trajectory_id":"vlr-formal-v2-0000322-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2d5ab4e71f0f81fd533dd7c1191f8628bf9cc38136fe10a39c2710878aa5f228","candidate_id":"sha256:648aae7eb481d5abe4692532dda7764b38fb8167e25dd1f76010cade679382ca","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (3, 7, 3, 4, 2)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:637482dc47f8415408c1250ea615a848a1dd31ad4d4333a04ec130dd9368db01"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:745207bdfcc5189182ddcb0e9d5ea2e60f74f70f4549d4508bc717100d4a6aa6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 6}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 27}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (3, 5, 3, 4, 2)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e485a72dcc26029fa3cc19543cd91bc8283a70665b2a5e0f52500bb8e9d89b08","sample_id":"sha256:64abe03962158088edb424468d2ba08e1e2e1ea47a4f77d8ffbf90d85f9ee3ac","source_transition_id":"sha256:b22be979c3323e8cbfacb095885c5d2ac10c2e10889e75cc2cabb5369752a30b","split":"train","step_index":3,"target":"def transform(x):\n    factor = (3, 7, 3, 4, 2)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000323","trajectory_id":"vlr-formal-v2-0000323-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3eeedc4b5fe460a49b7a885462aa8c14265f60d611f26f03aeb6fbb00eb6ac3c","candidate_id":"sha256:c0d4e34f70e1954fad4c6c0079190222dbb15ffad66e16b01b0c038b07e02679","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (5, 9, 7, 15)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:4ad91d2fb83e51930d2fdb7ce9be1be16f6f4d30ed9107da93c224a7bc64e4f4"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:202878da3df4736d86e1afe99f5e6fc287d2f0f4ca411e158fe80d44c2f7b4a9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 8}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (2, 9, 7, 15)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:8bf6a2a9e8e854394b131db1ee18b09672eff297cf4d33f28ca851062a77daf7","sample_id":"sha256:7e9cd00bb13293d11bf7c558aa0d3339215066d0945a720bd61a1110db696a9d","source_transition_id":"sha256:3768f83de7af7c99e5f36b8d7d759f4ab72e660edf63d11899e483aa653a1ade","split":"train","step_index":2,"target":"def transform(x):\n    masks = (5, 9, 7, 15)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000324","trajectory_id":"vlr-formal-v2-0000324-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:eaeef99dd73ca0ed2a4325232f80d887ab4e1c8050cdd8e0626621c7aa5fe6be","candidate_id":"sha256:0b5ab806012092b47bc732fcbe6cce2e731071a3a67fef1825c9e4d3f94889f2","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 4, 1, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:e40fee05b743c52c3c53cca4c5a6fec1610a625405a98e387014e59d86fcba99"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:67f0e464edb0ffcd6623f9db43d7acf8ecfee860f892c4201794cd146282577f","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 4, 1, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3353f03c1094f8905f49d00e386a8c0d81c79601b02acf4bd9acabdcc2d1f9a9","sample_id":"sha256:3ae9fe7d7a1f00d66cbe1db542886f746fe385c4ea1083e1d52cda04d6d46341","source_transition_id":"sha256:963a683d9e399e8d75b7ce8a09c3f3988b91b94d87a31ea7901999f7fb7432c9","split":"train","step_index":3,"target":"def transform(state):\n    delta = (1, 4, 1, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000325","trajectory_id":"vlr-formal-v2-0000325-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5ced4e6c568f9519397e6682195a4d5960543a36e25d7ab50a356d6a1f7b7c3f","candidate_id":"sha256:fdb5df03ce8ac7739cdfb663f551b23f6fe97959bc3fceaeffd982fd679cd5ad","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (8, -1, -5, -4, 2, 7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:d98e9954a1e1cb7069a0a1fe1647bf615d499420beed12d978c160a3dc9f885e"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:09fde4ae00f24b5de007070db8fff5e2cee22276fe30742efc13c01ea90950a4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": -1}, {\"input\": 4, \"output\": 6}, {\"input\": 5, \"output\": 12}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (8, 5, -5, -4, 2, 7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2b2fec24fb0099305948e0cc2368264af97a72329dc99f112180c6d62a68332b","sample_id":"sha256:d0b58ba0f19d55793247869b081f6dbdb7ab59291402bfe2494f8de3b61a6919","source_transition_id":"sha256:cc79cc540215218aba8122925755ad7899ffe7592876ffd5365454c07c59bd37","split":"train","step_index":2,"target":"def transform(x):\n    delta = (8, -1, -5, -4, 2, 7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000326","trajectory_id":"vlr-formal-v2-0000326-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:442a7d2d8ae4dec0b6fd98a4038946cff24edb5cff3d794fe0109850af0a9f91","candidate_id":"sha256:55e641a49f91b58a25617b42eb47a5e2fe5521b7406c6f13c081f630949aeb76","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (0, -1, 7, -7, -4)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:6e1a7a06bf979eaea651d7d23e045c49a92b64b10fc6548dd3d16997ab33dc45"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:7e13f2e5ed537d19c964d2e8b9117e834404f00dbfb691033d1c3b42e3950b76","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 2, \"output\": 1}, {\"input\": 4, \"output\": 11}, {\"input\": 6, \"output\": -1}, {\"input\": 8, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (3, -1, 7, -7, -4)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:a653984a3584a846e8a7a7f32c86c34a070810bf38630cbb1b6db4a6295c6371","sample_id":"sha256:111dd0f87e3a61aa7bc0294806671db1ca80610b3035c74dd21964dad60f30c2","source_transition_id":"sha256:fed6932bc181145992561943b951049b1066e9d0b9f0d870c461cf27c048262c","split":"train","step_index":3,"target":"def transform(x):\n    table = (0, -1, 7, -7, -4)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000327","trajectory_id":"vlr-formal-v2-0000327-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2d4b217e90244b6f282ee676c1a4da6c88a70d9ea5cbd7ef64483027e9f128d4","candidate_id":"sha256:94a2590ddd6daa85c427e3c7cede7b91f030fac2d1a84e7fbd7bb0e6af657f38","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (-9)\n    return x + (4)\n","verification_digest":"sha256:a71dc29c0f8cee1d37880fd51946280209e79c9024a3939ff84f1d1273c08446"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:9b8f07b07837b62ec69c50a130e6795ec87d989675085681c51e50e23530ea76","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -18}, {\"input\": -3, \"output\": -7}, {\"input\": 3, \"output\": -6}, {\"input\": 27, \"output\": 31}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-1)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (-9)\n    return x + (4)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_000\", \"piecewise_bias.protected.case_001\", \"piecewise_bias.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:f7548b228f564145d41c256bb368e38446a6b2586c7c3c821ff2cfa42d24b566","sample_id":"sha256:fb04151a6f6adb4a53f1ae817c2159f424dd86f190bbc6fe3795b6cd2f88e7a1","source_transition_id":"sha256:8213e2eb11936f93a0215fa7bd58bb4de4978691ae3405eb2819ece97fe2dab9","split":"train","step_index":3,"target":"def transform(x):\n    if x < -6: return x + (9)\n    if x < 0: return x + (-4)\n    if x < 6: return x + (-9)\n    return x + (4)\n","task_id":"vlr-formal-v2-0000330","trajectory_id":"vlr-formal-v2-0000330-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:540dccc22557c68a38f9c4eaf98ef54c682dc11afefb02c6637d03f1707f00ed","candidate_id":"sha256:9b9eea824f1a90afb12df6f270bf66197202255cda88a650bafe28c51b399c34","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (9, 6, -1, 5, -6)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:27d2b56bc87995a0606837177f071bb6632861932e26df07b351ecef9524652b"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:d6a425b9685df6c282c417c84f3a7cdf1ce4f6e24cded4fdd3bc13d52d9a34dc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 9}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 1}, {\"input\": 3, \"output\": 8}, {\"input\": -1, \"output\": -7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (9, 6, -1, -8, -6)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b12c5ce78573c4497fa737c639ddde401565f0f99bfb69971882a1e04211d63e","sample_id":"sha256:b81f4ad3825e2cfe9a33f1ae420eaa2e755ca534693f4cc462bca68736ffe94a","source_transition_id":"sha256:f5c12c215b0b474fc441dcdf1821d72e2f40f71a3f88b565d7a692b26c1a2814","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (9, 6, -1, 5, -6)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000331","trajectory_id":"vlr-formal-v2-0000331-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2afdb66fe989ff1dd542f141de6276e7b2af5f07bd4284a8cafebd64b4f992f2","candidate_id":"sha256:c33e6f2713fbac0d6d7e63485d090f9982599060ddef55bda0551b0e7c88c745","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (6, -3, -1, 5, 3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:288a470c0af68299ebc2191a128a8a26b5dc20b46ef42c94ca2dc2992e31d510"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:e16406708c4ed56e56247f1770a3fbd72ad7a7ad568991d483e30b774ee558ab","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": -2}, {\"input\": 2, \"output\": 3}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (6, -3, -1, 5, 1)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_012\", \"quadratic_residue.protected.case_013\", \"quadratic_residue.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:453f7737547d742ab45f7c68d91972d35f3ed35eca62b20ad965815009eb5f99","sample_id":"sha256:76a9155366ec34cdbf260e8b1b03e66d995f19d6cdf265969e3ce13a8fbd3a3e","source_transition_id":"sha256:5d3849780682bab3caec7ad111ec986bc5ecce836e2c50d7d4c7cd64ae596687","split":"train","step_index":1,"target":"def transform(x):\n    bias = (6, -3, -1, 5, 3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000332","trajectory_id":"vlr-formal-v2-0000332-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:484a5eabe9b8ec7caa51e3a99d69dd6f17b60d0d7a9382a2ba6f42336490057e","candidate_id":"sha256:ba81c7b88ae69a9276da2983a83df40adae22639382115ad56aa76e9ccbce848","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (8, 3, 2, 3, 1)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:03bfdae890ae6cb3d7aa2550409740f13c57e6c361e51d8b0832483d81bbe660"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:cc04f8419b9024164d67021d4ac84341fbad86c553cf03bee9b05b9bc60d4840","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": 28}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (8, 7, 2, 3, 1)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_003\", \"mod_product.protected.case_004\", \"mod_product.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9b71fb1232ad05d835ac61e3fe47ca45e991984dc43c79f6515277631d0efb6c","sample_id":"sha256:e5d98442cb52663c7f6fcefbf24b43f2d30a08fe77bf09db3464ab79c2fb601d","source_transition_id":"sha256:a20c87357916ddd9a2cc4641685de93e6932876c732c9fde86e011925867e44b","split":"train","step_index":1,"target":"def transform(x):\n    factor = (8, 3, 2, 3, 1)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000333","trajectory_id":"vlr-formal-v2-0000333-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:9f46dcd9f7b03fa47855d84a8531fda396a1591c234e236a289cd030829d1c54","candidate_id":"sha256:136dd16c24bd72fddb0fab1e1ad6f241876a163e8cbb5ab5eb9fb4e63ca25d83","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (13, 6, 2, 6)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:c6c9b4d4b81f4997adf4a572a9222f8646eb06a3b9772111223268ed24e2be19"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:9372eab7d5b7b608c396292609d4f6832d1dde4d64ff0a29038d423468372422","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 13}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (15, 6, 2, 6)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6791f220c9467b2053ad7fd3a065d6cbac099a6752dd72c1ffea9d4157945c0f","sample_id":"sha256:9b04f4a4494370baed79d199e9fd355ab68bbe1b6b3c56077df051570f06d5cd","source_transition_id":"sha256:f1fb82153cc5ecb8014a51cd84293677dd8f7d87b3d0f585641d51d2c0387b93","split":"train","step_index":2,"target":"def transform(x):\n    masks = (13, 6, 2, 6)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000334","trajectory_id":"vlr-formal-v2-0000334-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:2c46892e9c59845d45c364b6f56d7785237889cca9c74910012a479a7f121f3d","candidate_id":"sha256:d755687840b02dda68f0291e7753c62f062249bab49729358b9bcba30526be6d","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (4, 6, 6, 1)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:c78d53492619658cce21a84b4a75e291b82dfe80c729cc8c0167802a51c6f4f6"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:3c635f42c5f234c818e38de23c13ee5b04986961b9f60fbe2e910ba742805323","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (4, 6, 1, 1)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_006\", \"fsm_delta.protected.case_007\", \"fsm_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:36c0ab27663dbe2c6ef01873eee28ed4ac5b148e828356c149b193bd55eae79b","sample_id":"sha256:5995fb1180d38b1cf06e12695b7a5eb730a62d77fbbec65d42d72f1bbe48543f","source_transition_id":"sha256:0fe4bd50092de9bf6532992b32470914c4beb1222361a79a9c44b07ea6e961eb","split":"train","step_index":3,"target":"def transform(state):\n    delta = (4, 6, 6, 1)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000335","trajectory_id":"vlr-formal-v2-0000335-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:b005a2619709c63ae43f0d0e33c48e64332dff526cdb66009dc0627d47f5ade8","candidate_id":"sha256:6e767e74ec1b592f49d0eefa227dd3696d1dad7d261ed3f1526a17eaf1b85dc8","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (7, 0, 6, -2, -4, -7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:cdede52a20c8aea3f556bd38fbed0a2f23232a58a209333d00b040f43294eecb"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:03ddd0d28eebe3ca10ca345409161b09b7ad0289101c3c82b68061b7d38ed90d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 1}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 1}, {\"input\": 4, \"output\": 0}, {\"input\": 5, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (-1, 0, 6, -2, -4, -7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:eacfda34e9b30a8a795f2957b912f138ae0c069231f1e01b640cf6d93ac9d7f7","sample_id":"sha256:1a81fcaef453e1ecf3a7a65d83562265a3b72794296e8a9f7e20e1c1ddb21306","source_transition_id":"sha256:a7e5784eb81d2d9cad9a8dad53fa6ed9d9afb6913476eea2207d489aa2870677","split":"train","step_index":1,"target":"def transform(x):\n    delta = (7, 0, 6, -2, -4, -7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000336","trajectory_id":"vlr-formal-v2-0000336-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ebe73aa5ecb01da7c8185e614628cbac96d936c07a6f531c9ea62cc931a14242","candidate_id":"sha256:03a251efc1cd03b8945f30ae8144c7007b14355e1edfcbc666c8faeb6d5f4111","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (7, -2, 2, 6, 2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:42186b4a8d68f94e268901da714a4217c420f803d8a13ec0ce3df66f3361c2a1"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:8a782b923d0b02548307f98012b92262516a5fc31d8d2af93716a3c86917e103","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 2, \"output\": 0}, {\"input\": 4, \"output\": 6}, {\"input\": 6, \"output\": 12}, {\"input\": 8, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (7, -2, 2, 7, 2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b3f38108e0e097e478d61fa8456c111397505a4b65503944d993117b92ab101c","sample_id":"sha256:580dc6caf5007bb2c00014bb7b495b495ca142de91d0724faeea46778df86eda","source_transition_id":"sha256:7fdf5dc934e6e28b939a3835187ee57009e75e9186b1d4d3f0927c87863f32e9","split":"train","step_index":1,"target":"def transform(x):\n    table = (7, -2, 2, 6, 2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000337","trajectory_id":"vlr-formal-v2-0000337-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5e987b30e1a89fa4fdf1aaa6c2d30da65bda18f852ac307310c14faa219e2900","candidate_id":"sha256:673765cf446e1650c5c4b0cce896b565ddf7bc1c2cf367698d4d5f4ddfed588e","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (7)\n    if x < 0: return x + (-3)\n    if x < 6: return x + (2)\n    return x + (1)\n","verification_digest":"sha256:4bd34cee331d20fd0536429a888756e27523b275cab7972f3ec0ae405dd8c409"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:7015d84986101f5427d164f1cbc3134fef0add8c13f75ac68bd0b9738d521d83","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -20}, {\"input\": -3, \"output\": -6}, {\"input\": 3, \"output\": 5}, {\"input\": 27, \"output\": 28}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (7)\n    if x < 0: return x + (-6)\n    if x < 6: return x + (2)\n    return x + (1)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:dbc0cb99fc8887998096d1dce277ee8805e8f68e49b8dde3c2855dfc7ce67038","sample_id":"sha256:3266d47b7a401d80d15a20a1120806f590a299d50d6e0bdfcf5d1c6ce71b54cf","source_transition_id":"sha256:c902f5744e2e48b05536429a438d5f06cde7d64399a8fb5810d691217d8764c7","split":"train","step_index":1,"target":"def transform(x):\n    if x < -6: return x + (7)\n    if x < 0: return x + (-3)\n    if x < 6: return x + (2)\n    return x + (1)\n","task_id":"vlr-formal-v2-0000340","trajectory_id":"vlr-formal-v2-0000340-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:705725ccd0ac098b72d1683da986f74e28e3ed2e8285f52b877dcb4598a80e95","candidate_id":"sha256:1bb7a5ef3ed9da7227e0be9b6fd68b7b4b8e4bcd2e1e4fc8b010e7c181b1f163","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-1, 8, -6, -1, -5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:6d2061b5d03d0cb9e670bf7a6871b1336175ade075a392bc53761280026ed113"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:8bb61fee88f1548a515bba3148bb8a138783e581965e07ec7772a2b57b83cd48","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": -4}, {\"input\": 3, \"output\": 2}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 8, 5, -1, -5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_006\", \"residue_bias.protected.case_007\", \"residue_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9a3e13025e9a91bbd500fb4d011bef4e0d7a76ba045375ab28cb4f87e2a3ccef","sample_id":"sha256:4907b5b192feb3bd73f8a1f241d3201787223809a0d85d2bb1ec75322d2d543f","source_transition_id":"sha256:16a77bb809d3668f0ee0dd770aead371d43ba5b563351ab817cf885d33c387f9","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (-1, 8, -6, -1, -5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000341","trajectory_id":"vlr-formal-v2-0000341-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ef31e56282bb654618a3e0d495527f3ddb9b8bca632227866bc5118f9d7cdaf4","candidate_id":"sha256:94b3c832b3eb31cf858f63eba8fec68e39189146b6d727194eade33e4174624a","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-6, -2, 6, 2, -1)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:0379800589c0dfe093a663811a273e1e8f33592fe70d498ba6ea43def14466da"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:6c1724f54fa891619e22da23a1aa899dbc03d676f3e28ff95997e189bfa65247","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -6}, {\"input\": 1, \"output\": -1}, {\"input\": 2, \"output\": 10}, {\"input\": 3, \"output\": 11}, {\"input\": -1, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-6, -2, 6, 0, -1)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_009\", \"quadratic_residue.protected.case_010\", \"quadratic_residue.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:eb71e9f03086039ff0e62df8bccdbb1fb884166f1c1701179557b0dc0bc879eb","sample_id":"sha256:aa5e420511de7add5e4ff1077717270c5558ec7ed279b5d3e956744e0d1d2753","source_transition_id":"sha256:5b2b8ffde11d37f5016bfba6a6e7dc7a50aa8d80de4b31bf337e4ed666140b57","split":"train","step_index":1,"target":"def transform(x):\n    bias = (-6, -2, 6, 2, -1)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000342","trajectory_id":"vlr-formal-v2-0000342-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5d24bc5c29e138a09f891413054cd8e0f405d07636553a10bf192e4c644221f7","candidate_id":"sha256:1469ba85f038a26594e4797bd131607e8e2b6218c7207d29925cdb8b85bb5e85","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (5, 3, 6, 1, 4)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:689ca0ea5e6a092c3601bd7df8588d7a76342c554aaef0bb436eea7e1cd1b78d"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:42f79e77dd53e384464c64d473ebe5b288efad43e82791c7b80960ecf30bae02","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 25}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 3, 6, 1, 4)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=13\nfailed_count=2\nfailed_obligation_ids=[\"mod_product.protected.case_000\", \"mod_product.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:9873545f6386564a0491be19f0728eded2976a63b734af448062eb384f680c31","sample_id":"sha256:6a9ca9b8e96020e24efb4785495f87bb0feeb9a872163bcd48dda46dc99ebcf7","source_transition_id":"sha256:5ed81eb8e268aa58ee0c0362cc5bc0b043792362c510c6cbf89f69b24f2cb166","split":"train","step_index":2,"target":"def transform(x):\n    factor = (5, 3, 6, 1, 4)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000343","trajectory_id":"vlr-formal-v2-0000343-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:8422a8a0f4a622b5cb56ed3985599e6d20ef7df6062c5d0823e5ce49180e7247","candidate_id":"sha256:5c2e974e6ab620b749f788ff1c3bb1b5d9e7179f95a649d5f188c8436d99b309","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (11, 14, 10, 8)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:4e0d6fa9738714c91eed014518de7127a2b5d144c7e82b0071ebc4c3ea504435"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:7219778c3cb6982c27e08983c2700774f4696433b4b89d4a14c91efc54504cde","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 11}, {\"input\": 1, \"output\": 15}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (11, 14, 13, 8)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:73cad34e9a3dcb7747d59f572764ecce994a4ab875b94ad840ef3361911e136c","sample_id":"sha256:6c296e51c81a1822cd9d1e5a79c8fd7024450ccd7d10f0bd171a1a0a9af2e68b","source_transition_id":"sha256:579671ce977ddbc426263e6ff9920ddb091bfd36341ce130e9affcc3b5c2f52f","split":"train","step_index":2,"target":"def transform(x):\n    masks = (11, 14, 10, 8)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000344","trajectory_id":"vlr-formal-v2-0000344-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:61d85218e4b87fbe6a1fdb5c3e9488d81a59ab1ae8217d928f4254964b36fc16","candidate_id":"sha256:19781e114a938fc40706f4d8c2241152c40f04f847c56cbf47e52afa6c3439bd","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (1, 3, 2, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:710007e2b239c1928138ed8efa4ad5727a4f9a33540ab77209f0c85ef3db6171"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:3e95504a6fdd2d2af0caa3a338a422786aca53d48e13c93ffc280553e59018c1","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 4}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 3, 2, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3648215a74619dfe3d30ee068cf8beb2c8339a65888893c10b99411840533afe","sample_id":"sha256:00b371bd70a968c5ec91866cbddf5e5df5f91ba28e18e61e0ad7aad0c223f3a5","source_transition_id":"sha256:bac586f37543b886dd3d7386debd05d6883ae7349427786e1ee13e6560e56071","split":"train","step_index":3,"target":"def transform(state):\n    delta = (1, 3, 2, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000345","trajectory_id":"vlr-formal-v2-0000345-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5c20ffbb6d5dec09d8feeefa424024a50f5bddc7ba326500862e7b0d32dfa239","candidate_id":"sha256:09561cb0ecc91a425aa6567a4cb460f0ae2cd271e78c22ddbedd40d87c9ea004","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (7, 1, -6, 7, -6, -3)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:6e20616fd258660d8b2000647a220bec0e6e977f7b0f2da906f00742f151bee1"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:b25d9d336b9ce147a47906bb4d296f8bbcd68ec067d7880d739f89c1b30a321d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 7}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": -4}, {\"input\": 3, \"output\": 10}, {\"input\": 4, \"output\": -2}, {\"input\": 5, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (7, 8, -6, 7, -6, -3)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_003\", \"lookup_delta.protected.case_004\", \"lookup_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:fd203cfcea71daeba678f6d9329a783c26d7d846a0eb3b68fc0d2e0b9ca17e72","sample_id":"sha256:d9f9695a667ccad3cf3737e880ca207449fafd0d7e663acd693b001215af95ff","source_transition_id":"sha256:e5bc10a88958b9e2941e7a7fa8cfee3b12980c7b18db0468527412701a2e71be","split":"train","step_index":2,"target":"def transform(x):\n    delta = (7, 1, -6, 7, -6, -3)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000346","trajectory_id":"vlr-formal-v2-0000346-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:621e48bcc3221a05742085649d5f20712769a2809f2a28877874f124a42dc181","candidate_id":"sha256:fd4e034ca48e222d75166470184e1d4438410b4eb2fd97dc8d4b55421e831477","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (1, -5, -6, 0, 3)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:d30824c8037266f83b0fc50c3534867256b05855f4caa2790956b92d45e0c57b"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:67d35be89f7a9938a435755154e95a77de08ae1ae515bc30b06d3cee029ca231","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 2, \"output\": -3}, {\"input\": 4, \"output\": -2}, {\"input\": 6, \"output\": 6}, {\"input\": 8, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (1, -5, -3, 0, 3)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_006\", \"signed_bucket.protected.case_007\", \"signed_bucket.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c89bfc590765e30a1fa889e52e666d3d688aafc28cc3c6fcc23094241ec326ad","sample_id":"sha256:f66263ff45dd01ba90f9a30c4eca941df9d0e42e0d24107078d6eb1b593a46ed","source_transition_id":"sha256:1e389981d0765e74ab33c3e7689da217b2d0a6fb8df38c35f9afb57527574ccd","split":"train","step_index":2,"target":"def transform(x):\n    table = (1, -5, -6, 0, 3)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000347","trajectory_id":"vlr-formal-v2-0000347-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a5b0a338712e8b4b7297c36a2af149f8d99eb63a15b55cdc5627e9e1addb2ffd","candidate_id":"sha256:2fb0abd4ba224ddd2f1e89acae9dc7d8150be72c081157b67db8625835d86986","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (-7)\n    if x < 6: return x + (1)\n    return x + (-3)\n","verification_digest":"sha256:30dbda36f9acb6db24b0c31b646df20a4c513fe8960d58b5125f91796dc662da"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:b0082ddaf6ee292adc6d8acb30143f8bddbdf5e88e3b07565c4bef4f30d21514","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -34}, {\"input\": -3, \"output\": -10}, {\"input\": 3, \"output\": 4}, {\"input\": 27, \"output\": 24}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (-7)\n    if x < 6: return x + (1)\n    return x + (9)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_009\", \"piecewise_bias.protected.case_010\", \"piecewise_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:c473f083a0f80b6a07b16bcf6ff06d756918ab4be6f7d4f7b16b6424de459319","sample_id":"sha256:fa89c7550d70f2d3b73396d653f9715ed4256e01d691829003ef27f65bf4f118","source_transition_id":"sha256:c34a8543019963a259f6055c900e4e4efdd1ec540f1a1aad767c1f96ab438345","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (-7)\n    if x < 0: return x + (-7)\n    if x < 6: return x + (1)\n    return x + (-3)\n","task_id":"vlr-formal-v2-0000350","trajectory_id":"vlr-formal-v2-0000350-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5527432e5987522f6bfae91c00bcb773f35d948a1398b5d83d939dd891d84351","candidate_id":"sha256:ff7c462db9a63902de086a23bd3017e3395825c619421876b7445b31f7aa4314","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (5, -9, 2, -3, 5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:dff12dce3f5f327a68bfddb2870f4d41a08a7be52c8612ac2537f596184e4dbf"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:2cfa9857bc4fe2a3e01771ca9dd57fe633e370425bcd00f7a840edf8719ce979","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": -8}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 0}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (5, -7, 2, -3, 5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3e35c648dc7cef3b68ffb08bb39f7cb9762af6062aa37f7ccded90fc60f14ec7","sample_id":"sha256:8190058437f2d23438cfb44cf7d29aa58e3ef7901fe2325d17b9f7394d5a6204","source_transition_id":"sha256:f5a6bcb02e235b9a7a81ee53f81f12b56349c7ee0caef13d103ad0fc26f37f05","split":"train","step_index":2,"target":"def transform(x):\n    offsets = (5, -9, 2, -3, 5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000351","trajectory_id":"vlr-formal-v2-0000351-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:cafce94d9cca66898f42fc64162af8a6fcb7f97e3518ab753c88680cff5803d2","candidate_id":"sha256:d9b3cddce551e6d7757f686510f600f6fd0428a1b5180a479a1ce76e294eff59","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (3, 5, -6, 6, 2)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:0a9f266bcde85b22fc463c59145fca3ba0d25e4adc2b85126a26f37061d36a38"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:83e827e4606c03364a8cb3c7ebfcc03e0c6ce8997801304dff5fa639f2ddf580","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": -2}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (3, 5, -6, -4, 2)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_009\", \"quadratic_residue.protected.case_010\", \"quadratic_residue.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:da474198cc4094f4d1f0ed0e0ba4fddec9a2951361ae1ca2ba9ac4e9a79d6932","sample_id":"sha256:7976585d22f7a16fe537cc6eebdeb0dd751d878b32c535b9010de26b7bdfd8f2","source_transition_id":"sha256:0ce73696210e974e6221a5f77b886423cc315565708e1874653ed3685c755d33","split":"train","step_index":4,"target":"def transform(x):\n    bias = (3, 5, -6, 6, 2)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000352","trajectory_id":"vlr-formal-v2-0000352-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:983dde54c214044acb4798d22f021d6dd695270e62bba18ec7ac56fd880a628b","candidate_id":"sha256:f9041cde9f70ec59ebb155c5218d67e3660c156a404942d10962f1cbb58233df","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (5, 2, 2, 4, 3)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:be7a6686c500fc302b25c9a280cc1556e51c9fb3a033f2cbc3d4c023dc873e95"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:3fd0461278fdf069bbec6caf0900e40865782d447c45b9f6695aa4a39860ca31","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (5, 2, 2, 8, 3)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d99a20d48cb467bbca25a8882dcc2ddbb38672efb942a1f86d2809f36370f034","sample_id":"sha256:14db48df550d2f05a4e980bc4d76130402f9fc261184ab143aa699b984019d77","source_transition_id":"sha256:f0974500b0818212532f982acd3cfed678ce52bc4d4c77f92f2f96dc0b0d0090","split":"train","step_index":2,"target":"def transform(x):\n    factor = (5, 2, 2, 4, 3)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000353","trajectory_id":"vlr-formal-v2-0000353-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a5f8319df6930776d3ef7f1a8aced6f40ff2329a756430e316e8b80b8c266d75","candidate_id":"sha256:c6c5ea57d312ea79c2d1586b98a0a98a35212320156b560f9dd0acbcba850e2e","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (2, 12, 2, 12)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:d5e35b385534b573a5f2417324db64f7c05c4001193ac250a15a09157213c31b"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:693e52e6f078c06e15cc9d97b82d77eefd5ea696f40f6cfb1071634a55e4a759","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 13}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": 15}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (4, 12, 2, 12)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_000\", \"xor_mask.protected.case_001\", \"xor_mask.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:092f599ab544ab4933d6acd34a3f4571b5a19452648e7602fdcb6965739426bc","sample_id":"sha256:81169669f57418a9e5a329814fa6a435dbd9222f0ad73c5961a905fb98c2acfb","source_transition_id":"sha256:a289e121a2f983f5a5065c27f95312b9426f9bf734a9c928a0a1258b6e74a30a","split":"train","step_index":3,"target":"def transform(x):\n    masks = (2, 12, 2, 12)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000354","trajectory_id":"vlr-formal-v2-0000354-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:a0eb13724879092853deb65d40aefbefc2990c9aad6996df55c9c00374cf8eeb","candidate_id":"sha256:c84a581ecdc234927e39a6cad7881f886085766c3b2d511b81a2bfc7d6a10311","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (3, 5, 2, 2)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:fe81dbd65e0034e8da70cfa244d73b3c181fe3f0a43640248cb645d99bc89c49"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:b6b073cb54b908878c2551190bc74d1f03af69268aa1fe6abfd6ed50fb9a9612","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 5}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (1, 5, 2, 2)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:1c31c0c8698901b5dc7d53783c159ba91b2e169adef23f3d295c25a141737cdc","sample_id":"sha256:df5fd9a697df0c4bbe1cc9d531512b41dc0a4326095ef4336e78df2110566477","source_transition_id":"sha256:5b18a50dc2ee9fbdc7fcd92a130f89123d8166e6c002afcd9264c22089c7fc1f","split":"train","step_index":3,"target":"def transform(state):\n    delta = (3, 5, 2, 2)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000355","trajectory_id":"vlr-formal-v2-0000355-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:17e8b0e7ab5df398fa4a2d8971112422a0fbbb5b45444ed75a4b7872d3329984","candidate_id":"sha256:210a28e306b7a8aaf2655e04ed55ea1479ebe3a75ed5da93a380bf0170a52cd8","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-4, -3, -8, 1, -6)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:aee377fa164d6c3739f0a1dac442c94ddeb7b17b219e235a21b539496388f73e"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:4268104d75799a097befe709f2affeb48fcc12229ed13ac375646ab5bf8f19c6","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 2, \"output\": -1}, {\"input\": 4, \"output\": -4}, {\"input\": 6, \"output\": 7}, {\"input\": 8, \"output\": 2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-4, -3, -8, 1, 0)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_012\", \"signed_bucket.protected.case_013\", \"signed_bucket.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b998da3197ca7a43531e83d3ae050b88ccf7f62ae3ba02710e8307eee736a3b2","sample_id":"sha256:517dc7ce3d06a70df284fcd56efa6fc0834102758b8eebc0783c37e73e4432c3","source_transition_id":"sha256:4bc8cf7d522808e8e395a289bbe9177163c8c1048e7d95acbe0ddc9cb29fff46","split":"train","step_index":1,"target":"def transform(x):\n    table = (-4, -3, -8, 1, -6)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000357","trajectory_id":"vlr-formal-v2-0000357-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:abb4e82f9c21a30d9f1be5f9ff052a8c7df5f3e246459424349bdd097f7c9bb1","candidate_id":"sha256:e04463a165fd2e6b6197a7e63bd1d60635d9512532d8452bfc33106346e4f5bd","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (0)\n    if x < 6: return x + (-1)\n    return x + (5)\n","verification_digest":"sha256:e3a7e3f4b8e51bfe1af85a58e1111b15818641c6700c026c4e9e579946bf7254"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:fc6e126161bd9150084009c0c1d69fcebc13e357a3b8f73d378192be8076f1c4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -21}, {\"input\": -3, \"output\": -3}, {\"input\": 3, \"output\": 2}, {\"input\": 27, \"output\": 32}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (6)\n    if x < 6: return x + (-1)\n    return x + (5)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:90908be47426f28cd3b1df75c619f1ab05fc552538d21122e1f27f8990d5b9a9","sample_id":"sha256:f64841c5f98eea08fd8b89c02a37921b2d0faa0a43ad1004f2c401bfb1757b85","source_transition_id":"sha256:d0a28fa3379c15b205766c19abf29f467ffd43fb175467f20bc350c4ab1efe48","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (6)\n    if x < 0: return x + (0)\n    if x < 6: return x + (-1)\n    return x + (5)\n","task_id":"vlr-formal-v2-0000360","trajectory_id":"vlr-formal-v2-0000360-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:80c9e3732e6f85a72c2a5ffdd6726986b873c15b1de7181803b2137c7ec28fbf","candidate_id":"sha256:47fa9ce7efa56afcee5972e8188dd794081402fd4a84f1fa6e3c0f9f13221a8f","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (1, 8, -7, 3, -8)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:300c946fd86360d6511ba7b1c1f3063fb2c0c0a346582276827be36d061283b0"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:7174bb3b35fc1250af86863febdf58adbbfe125795925f146fe88491af9ca3cc","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": -5}, {\"input\": 3, \"output\": 6}, {\"input\": -1, \"output\": -9}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (1, -2, -7, 3, -8)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_003\", \"residue_bias.protected.case_004\", \"residue_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:e446bfc3e9e662cee4cb534aa9ce6441e35bca5bc68f3ef24c1968d19143a00c","sample_id":"sha256:8df9cddf7ca489b49883809b78124358a4791fccb6ed4b9beac43534f7adcd7f","source_transition_id":"sha256:7307cd908e9292da78f3eeeeef997ebe0ad5a5f4798e19e2311aec75e4232200","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (1, 8, -7, 3, -8)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000361","trajectory_id":"vlr-formal-v2-0000361-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ea988f5ded2124c1099e3bd845d7ae73aa3ad9d998aa442b62fd907505b050af","candidate_id":"sha256:376befc132f5f975e61f9588450c7e589d4d4ecce31d4350e6a4743d73535c32","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (-7, -1, 1, 2, 3)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:af799ec960746ac4decd929b98666f2856a1af7b1415e34d1cd5125a05df20df"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:93c3fb422019db080c64a0fead4c05183dfbbb4f3ad1c337e168b84491cc791d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -7}, {\"input\": 1, \"output\": 0}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 11}, {\"input\": -1, \"output\": 4}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (3, -1, 1, 2, 3)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2829d7859ff71ffe99277b1449bcc5d76db5ebd30da741a720d5d38401402225","sample_id":"sha256:adccffdbe371d9d6a4a0cc567504b1a3562a2d81a6b603c60c036b1ef432e91b","source_transition_id":"sha256:98538fff3aef61ac9b84fabfe36f269d59d49c66520bf61a1262cc3cfee9effc","split":"train","step_index":4,"target":"def transform(x):\n    bias = (-7, -1, 1, 2, 3)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000362","trajectory_id":"vlr-formal-v2-0000362-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0f9de6bf9a48c25744cfa593004fe71122eb36a9730573ef4506deef0cecb653","candidate_id":"sha256:44f70f3233b33d32dad461ceeeb626bc45e422b0433f478f8950e282068345a7","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 9, 2, 4, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:21b8ae8fd07a4f74ede542703153ccba023e6161be74db62bb7c687459ec5215"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:9273505018b94283878c2b68469b9ead21047229fa8c77321c923083bea339b9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 12}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (2, 9, 2, 1, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:00986714f9a44c72caad19462b27b92954e1d6b905bbc65ec7a823ae0a95e54f","sample_id":"sha256:427e6b82d7bb1ce137aad0eef1b245c5c6431e491deb67b84c5248abed52972a","source_transition_id":"sha256:146556b519b923239070abda647cdda8fd0b59aa2f32c57ad2ada7496aab8924","split":"train","step_index":2,"target":"def transform(x):\n    factor = (2, 9, 2, 4, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000363","trajectory_id":"vlr-formal-v2-0000363-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:30f4d182bbe76ce6bdaa0c1ce63a3a0ea262808be893b3e48a766caf3df112cf","candidate_id":"sha256:cd83ea8e65e4548e6b7f4fe2971876109aecbfeba7daa3899057414d71f4e65c","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (2, 11, 12, 9)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:54ec72464021bb351603419cb14d064a7a958423b2f8597faf5653b32d244200"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:9320fcb28d89992d7c338083e7cf185e74ac05a4c5872697bac12bbe3771a8a5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": 10}, {\"input\": 2, \"output\": 14}, {\"input\": 3, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (2, 11, 12, 3)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6409ed3631a9a3a4ba5c674e81d66eea129386678306e42c58af2735042509a5","sample_id":"sha256:6ecdbcdfff22c49a23d0558913cf44ee281526105fd4e6968b75b96333acaa1d","source_transition_id":"sha256:6cae930b2e2a482e52c3ecbd405a29b09a2b6b9a1f91fc147a7d4088f475d37b","split":"train","step_index":2,"target":"def transform(x):\n    masks = (2, 11, 12, 9)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000364","trajectory_id":"vlr-formal-v2-0000364-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:56939718829176aa194e86bff2acb2fa96a442096d2373b2a1802a77374f4373","candidate_id":"sha256:b0516ce8a762b984e58cc5dfa52989455dce1b96ee33f453f3b598468a34bca2","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 6, 3, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:49fe9da30818823407f002d7e84c4121355b53c9cc8509561dbb3a4a385b994a"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:f4eb470577383015e1b1400fc3858025a29e7013956d9903fa8a6b42ec4fd514","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 7}, {\"input\": 2, \"output\": 5}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 6, 3, 1)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:fc0ad54ab5dd6e74e288e17eca0850c3285882be56b6f5dc546f4fac00bdb9f2","sample_id":"sha256:67fb9b57950287acf641fc006fbcb0c85a21de6bdf548fa712d0e520e009ad6c","source_transition_id":"sha256:12fa9a75866d1673ba6c983515c059f5ae8e65adbcd0c9d79dc60ab97354954b","split":"train","step_index":2,"target":"def transform(state):\n    delta = (5, 6, 3, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000365","trajectory_id":"vlr-formal-v2-0000365-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ce456f8c6400d586f4f171992ef0b79ace83241f2395c05a975782e89bdf2b59","candidate_id":"sha256:8f71fa1644cdd95ea0003823e82dc3c4263f4cd609d3c06508b75bcb8a96508b","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (2, -7, 5, -1, -8, -7)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:b8a54c82319743d153548e6481b32ea020f4966ec29b53e5141d156ce5467247"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:1b4533cb108bd9cc5bab98e3c802d030ede91ce92c4be481118c1ad5e19d8234","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 2}, {\"input\": 1, \"output\": -6}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 2}, {\"input\": 4, \"output\": -4}, {\"input\": 5, \"output\": -2}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (2, -7, -2, -1, -8, -7)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:87e3c017d8e8786a8358f3fa48cbf417e26f6820b0040ed08ea703a3a9ad727c","sample_id":"sha256:00da9f073d4850402a0c12ecc26cddf1e8f7c22bbeb404c09f47378eb67a235b","source_transition_id":"sha256:1ea2b521aefdd1fba27d70f7c3a86daaedc32ad42a249ea1455d65167a47226d","split":"train","step_index":2,"target":"def transform(x):\n    delta = (2, -7, 5, -1, -8, -7)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000366","trajectory_id":"vlr-formal-v2-0000366-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c5b64575570ecaf22dad15e6dee16baee86290e4020cb809b63f77fba44f83ca","candidate_id":"sha256:4e3b68641d61f6dc48870cbcfd206494e5c50bcf60ec8682ea89719b3d0155d0","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-5, 8, 1, 0, -2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:49b56b6a1273788ad32c5c7a4495e21c7d8b185a3f8495b19da1998545e2b0a6"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:5d74f66c67ce94fd6866759cbe9d7ad28c5a531756c1a42c9657d6e5fc4f1d09","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -5}, {\"input\": 2, \"output\": 10}, {\"input\": 4, \"output\": 5}, {\"input\": 6, \"output\": 6}, {\"input\": 8, \"output\": 6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-5, 8, 0, 0, -2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_006\", \"signed_bucket.protected.case_007\", \"signed_bucket.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:6e16c4df3b3e6498d27adf8d6da1e794138551bcd96b2dbe6b153d8ca9ebf521","sample_id":"sha256:680f3e21114c6bc92e44010ea7fa4c925ea64e92ff3e603d32333fe69cfbd2cb","source_transition_id":"sha256:01dd71f02558ec91bbdc34d15d796eb4e91b1594e9d026cbb98602bf1cb64651","split":"train","step_index":4,"target":"def transform(x):\n    table = (-5, 8, 1, 0, -2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000367","trajectory_id":"vlr-formal-v2-0000367-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:c49c9a4abc1894a6334c8590b216513ac1cdc29c20bf7ac3a228c7995f563222","candidate_id":"sha256:c2255c39e440c868ad19f9f70a2ced87ac5b3f79fc195ae9fee9911c135e9f2c","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-6, -2, -9, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:259604c5f2a7a2b1aec6489849c86842090e2a44122d2e9c789c04909a8d8768"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:31053caecdc2da3042dc89ae1a7c392c8ae96d12da58b2bd933ca53bf7d14948","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -33}, {\"input\": -3, \"output\": -5}, {\"input\": 3, \"output\": -6}, {\"input\": 27, \"output\": 26}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-6, -5, -9, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:ddf04a541e1834131f01a88a4976317c281576318de2783b4abfc75bf6245395","sample_id":"sha256:b3d20e83398e63a9e54bee8500f4b36f496535a1b1f48bdb0becf340d80d2a87","source_transition_id":"sha256:cdfe05688b71ff96322663d9acc1acfda4b0778bd928fdbb6a8dd56ed4f94d22","split":"train","step_index":3,"target":"def transform(x):\n    offsets = (-6, -2, -9, -1)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000370","trajectory_id":"vlr-formal-v2-0000370-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:20f79aa1213f8c3e734308354406e71a1264b399661ed30462797041fe5434c5","candidate_id":"sha256:d20400811e586bba46f29adca7c580fa21ff6c11172acb71ffdc03a35bef2ada","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (1, 5, -5, -7, 1)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:24b7f62c44bc7e18f7011463e4a591f270b542c8dc7cab54b4c2d3e85ac1ceaf"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:fe5558f34e4c5d859d52c54723626f6afae74fcfe6caff6cc5062b0d180fa5a3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 1}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": -4}, {\"input\": -1, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (1, 5, -5, -7, -8)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_012\", \"residue_bias.protected.case_013\", \"residue_bias.protected.case_014\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:4bc535939723a7342bca3df513e9521afc6892a4c7a371721e9c3617ee927107","sample_id":"sha256:1ef1be8447de9940ab94fca317873b85923782f77410c916abd0c64d1d5fca98","source_transition_id":"sha256:48416c6fd3162ad5dffb82fc438fb11477381debc0f657f9a3faaa29256e67b4","split":"train","step_index":4,"target":"def transform(x):\n    offsets = (1, 5, -5, -7, 1)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000371","trajectory_id":"vlr-formal-v2-0000371-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:72a5df8d9084ac0cf9d4ddf34e88057d4af18703d94d9ecbb145be8bb7e634ab","candidate_id":"sha256:8d7810ce01c3e889b1e2dd7c41c23ccf4114edf0e3a92efc6ea7b25489108fa0","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (4, -6, 7, -6, -1)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:f06fdbb14999a5c50791d0c1ee51ee8d717af87c8583a863cefc91681aea74d4"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:139a3744c6370b08051a434cf8428c85f98db3f460a9794667c7295e83963e8d","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 4}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 11}, {\"input\": 3, \"output\": 3}, {\"input\": -1, \"output\": 0}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (4, -6, 1, -6, -1)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:3f01b747aed2cef828a4c16f4d7c4ea4b1c4c9cc0354f1bd8c6b6f748cba5843","sample_id":"sha256:1a2e1516a9006cf6a1e92ae31889fc76c35db6642d214226ce56d5d55cc966f8","source_transition_id":"sha256:fa1196302727907ba3bdee21b00b962a6fc209d799ece0df26b5e86f3c3703a4","split":"train","step_index":4,"target":"def transform(x):\n    bias = (4, -6, 7, -6, -1)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000372","trajectory_id":"vlr-formal-v2-0000372-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:690bd6f3536a2128a2e3eb0bf347c283cd25d5ba73be8ae8d55feb56eef400bd","candidate_id":"sha256:caf7b27f9764700a3bd8a3a7daf53659e519c6332da7be704ce89093b13f3f36","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (4, 2, 4, 8, 7)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:58e39857f672483da1cfb968accb80f9fbf9d9e28a666aa75e3ee19f000cc1ab"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:08fb2c3d28d3d2c9ebb540dc0dacbb22bff8d8e1de0e544780b5c7e3169366e4","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 24}, {\"input\": -1, \"output\": 22}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (4, 2, 4, 2, 7)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"mod_product.protected.case_009\", \"mod_product.protected.case_010\", \"mod_product.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:dc595dfce2ec269a0b63a30fae4ce789816d9d2a150d5d113061024f5b420b3e","sample_id":"sha256:d1cf335ac1ea1d9eb510628b67e62652a54045ae133d7eeb9ba939cc55e3e153","source_transition_id":"sha256:31271f528d61332b6fe41eac88687f272c9511cd31bbf985f47850cda8efd1a6","split":"train","step_index":1,"target":"def transform(x):\n    factor = (4, 2, 4, 8, 7)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000373","trajectory_id":"vlr-formal-v2-0000373-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:df56eaacfc849615c50d86fa40ee1d2969c1a1c9049b73e1586ea5e0346b8974","candidate_id":"sha256:af940de22983ee28b342dd8ad6c2d7cf2578847764dfd16a438caf879f7d0160","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (5, 4, 14, 2)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:eb8e75db62a059bdabb35f7dd94e4c84d325be8fb07711a19d1005f92f260d21"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:cc38e400acb49cd0f3b2f191ba09bd8c7c43916f3c9b24d1777a0f32750a2d26","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 12}, {\"input\": 3, \"output\": 1}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (5, 4, 13, 2)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_006\", \"xor_mask.protected.case_007\", \"xor_mask.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:39aa94ca234d8ba109a39a6496c63d9d9145db466bd063555da3ee33750842fd","sample_id":"sha256:dedbfae8ccbbca13bb2be70496a3c38977caa9b26a39bea5a637b3868dd56855","source_transition_id":"sha256:8cd7c4575cbcecc7a5da60e95607b13aa3ef6945900cf9893c8e2d204c986c07","split":"train","step_index":2,"target":"def transform(x):\n    masks = (5, 4, 14, 2)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000374","trajectory_id":"vlr-formal-v2-0000374-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:43df099cb5ac249bbaafd9152a00fb0fbddae48f6e83dd34f8d6c81025445532","candidate_id":"sha256:ab2e30e67bd1af0c938d77ba539a2d1881872461fdca29813ff51b467bca1ebd","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (5, 1, 2, 4)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:a78436af7611f5c55c3dd963d49de77ed1d513e7a47f4ec355493e373daba010"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:b2f5cd3306e71498566924a37fac905379cfd0d77b826ede6a7ee383ed8863d8","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 5}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (5, 6, 2, 4)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_003\", \"fsm_delta.protected.case_004\", \"fsm_delta.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:0bb5100479b63ca92498b2e2c6fa0b735eece4e1f86a299cda1ece98a14aa5e6","sample_id":"sha256:e36ef197ebf08d128611afe2b8084fd84ab05282dea822a95c8556cafc0de1f5","source_transition_id":"sha256:334fb4780b013d0e87a57bb3b5afb8f7086b02a8e51a64adf7a1fc1833bdd00d","split":"train","step_index":2,"target":"def transform(state):\n    delta = (5, 1, 2, 4)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000375","trajectory_id":"vlr-formal-v2-0000375-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:5f2599c0863a9ba786d3575ccbf25083949cbfc4ea9042864776316141c0481e","candidate_id":"sha256:0db797d6425a843a048a255d7322cc1f6dd1b416044dfad3f9a2443e3affa506","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (3, 1, -2, -5, 3, 6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:eef944d3b23d20548df756ac016d909f23fa914fa0d5d4702017aab0f342604d"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:944b2b86e03351288527cd586b8a382c06be9b0c36da67c477d40ab0e81c9ae9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 0}, {\"input\": 3, \"output\": -2}, {\"input\": 4, \"output\": 7}, {\"input\": 5, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (3, 1, -2, -2, 3, 6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_009\", \"lookup_delta.protected.case_010\", \"lookup_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:fe6a484a7da7dd89acd29c7facd74359355e05ca846dfb4f754d70a06d3aae5b","sample_id":"sha256:e61d46d5ecb58efe6b97a5b53225b0197c6457301b6307e94f564821ea193de1","source_transition_id":"sha256:1513ade5697af05f976d6ce106eec357aa46df0c96e2ff8fcb75f110ce2856dd","split":"train","step_index":1,"target":"def transform(x):\n    delta = (3, 1, -2, -5, 3, 6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000376","trajectory_id":"vlr-formal-v2-0000376-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:18c5f3535352b8948199e1eb4cde62f8c6ea284284e3ff90683de40d85852a64","candidate_id":"sha256:906c5715d29db1e4ed63463e3cf68408d03f131779f5b68ae39f86548fe838dc","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-4, 6, 4, -7, 8)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:079aa96cc935ee7da4d61ac86cce1d286061fdcc66eaca35b4622dd33fa74a38"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:2ac1ed6a56a6005f70bb864a7f95d61f48b48eee50c1d112114b5bfea48d8ba2","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -4}, {\"input\": 2, \"output\": 8}, {\"input\": 4, \"output\": 8}, {\"input\": 6, \"output\": -1}, {\"input\": 8, \"output\": 16}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (3, 6, 4, -7, 8)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_000\", \"signed_bucket.protected.case_001\", \"signed_bucket.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:2d43cf83dcb6644fe23315fbaac5d52d84b78c455fc2ada876e29d7f8add9cb1","sample_id":"sha256:b47f6c909aed61d65229271635e92d306e6e4b1b8c370e4f331c4520db705447","source_transition_id":"sha256:55ed7becf46fbd290222e74c9334f4a7c194d6a77c7031ef4c3c2d8f43d99fdf","split":"train","step_index":3,"target":"def transform(x):\n    table = (-4, 6, 4, -7, 8)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000377","trajectory_id":"vlr-formal-v2-0000377-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:ac7ed4cf6b2954a36e43ac62510346633a96016669aecb5e27a5d9779b037891","candidate_id":"sha256:7413df8fe2a86912959bfb6a7c4bdc492d2ae53540ceb3793dfc8f9a448b4ba7","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    if x < -6: return x + (8)\n    if x < 0: return x + (-5)\n    if x < 6: return x + (2)\n    return x + (2)\n","verification_digest":"sha256:2b1a0b50ed8e17d2458bb1423c6b8f7b008dc0d2484aa977ab4a93c772be72f0"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:cc808367ec32b7927acc458ec568685da5b971962aba62c505dc783ec11b9cba","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -19}, {\"input\": -3, \"output\": -8}, {\"input\": 3, \"output\": 5}, {\"input\": 27, \"output\": 29}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    if x < -6: return x + (8)\n    if x < 0: return x + (3)\n    if x < 6: return x + (2)\n    return x + (2)\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_003\", \"piecewise_bias.protected.case_004\", \"piecewise_bias.protected.case_005\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:b53a70973cdfcbbdbca179a3a5586a1cc39c2a600f20c2788b255ed682027889","sample_id":"sha256:8aade8cc6753114e6efb14b92ad8225b4ef700b1d874b84196f5727435051a88","source_transition_id":"sha256:c584f78b71c1a8e76e335f1ba2d888a18f8c8d35597e6f3728dd76b119347734","split":"train","step_index":2,"target":"def transform(x):\n    if x < -6: return x + (8)\n    if x < 0: return x + (-5)\n    if x < 6: return x + (2)\n    return x + (2)\n","task_id":"vlr-formal-v2-0000380","trajectory_id":"vlr-formal-v2-0000380-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:242f42de08131041f6a4afca63a353468fffe517f2ba833eee6cbe57fdd56f8c","candidate_id":"sha256:ff33a6697de271911f885b05bc47d263c7d59689a6d8b3b495319d9b7f9ad84e","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (6, 2, -7, 5, 6)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:2856c2ec0bd994a1b70772305e39f7bf981491a476d47e1d8b357926153c5949"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:b8d78a7e32fb4ba790c9a76d081af1e3b64f720f0058672e6629d27ddbb2c3b9","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 3}, {\"input\": 2, \"output\": -3}, {\"input\": 3, \"output\": 14}, {\"input\": -1, \"output\": 7}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (6, 2, 6, 5, 6)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_006\", \"quadratic_residue.protected.case_007\", \"quadratic_residue.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:64b05b0a2a38436a0e38d9dd4d0b53a1a4ce6336a80d9e4da0839248911bd52f","sample_id":"sha256:8e9feb154cd1e082d20e9a983a1641b34afeb1048e86d675ec3c65c7c5da1154","source_transition_id":"sha256:0d1ead4cddb83516b8cdabf915b31de125715f5d3ee824ee38a77df0257ca7e0","split":"train","step_index":4,"target":"def transform(x):\n    bias = (6, 2, -7, 5, 6)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000382","trajectory_id":"vlr-formal-v2-0000382-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:bdc345a4f9c9516a4638d3c9d329ff3e15d274ca630c4b6be675d5a8ab8b1bae","candidate_id":"sha256:ae0c3e3f7e684194bb65cf4ba1d2d3bba6722b75a8cfb5d36a442f6edb9c3d4d","certified":true,"rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"text":"def transform(x):\n    masks = (3, 4, 15, 9)\n    return x ^ masks[x & 3]\n","verification_digest":"sha256:dc3665574e222fe05b6b65f3ab591f8517238d7f17b02cd62adb731fbb7d59b5"},"incumbent_rank":{"component_ids":["xor_mask.protected.case_000","xor_mask.protected.case_001","xor_mask.protected.case_002","xor_mask.protected.case_003","xor_mask.protected.case_004","xor_mask.protected.case_005","xor_mask.protected.case_006","xor_mask.protected.case_007","xor_mask.protected.case_008","xor_mask.protected.case_009","xor_mask.protected.case_010","xor_mask.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:21dfef52a6448421761b963b8691837acd262fe7cfa95d56ac83a8c9f0f3a166"},"incumbent_state_id":"sha256:d0d6210e821b45832598098a189642fbdc6851e971dd721457de642658d349bd","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 3}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 13}, {\"input\": 3, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    masks = (3, 4, 15, 3)\n    return x ^ masks[x & 3]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"xor_mask.protected.case_009\", \"xor_mask.protected.case_010\", \"xor_mask.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:d7b54c4f65d21f3483ec6ec8675dcfcbeb3c44621624e2eb5bb76776e6958f99","sample_id":"sha256:4eb2440072f03ce44af2987e8c7e65a0a9b9f9d359ffe38f49816130606aeb7e","source_transition_id":"sha256:fe93099b32f0fa585bf7d9d755bb0f28e630c1ad855b1de8ba23c9f2fb974a60","split":"train","step_index":1,"target":"def transform(x):\n    masks = (3, 4, 15, 9)\n    return x ^ masks[x & 3]\n","task_id":"vlr-formal-v2-0000384","trajectory_id":"vlr-formal-v2-0000384-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:41031ade5f56d6ff5f88cd1b4f3384770b0d375d664f322f9cc1c10673277cf0","candidate_id":"sha256:580b4abc2cd3b4f4d0efdc596ae77836a9c98164799c3e0d385d41e9d787d571","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 5, 6, 6)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:29d34ca1e22fd005ee696cf6890447c2e00576eb5ec0aaf8d5acccef9368eebb"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:376827d45f7ec00c26e1a8838501d1bff669d9eb5d683c521cb4d16eabb486a5","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 6}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 9}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (3, 5, 6, 6)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_000\", \"fsm_delta.protected.case_001\", \"fsm_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:01b7a6f8c084c20f61a58e9c7db107847e9ca53df1b6091f94755afa4c4eca1d","sample_id":"sha256:a4245eed5a8a653f83c21100d0c9a86cd144c3f8072ed95a82c911f8614f5042","source_transition_id":"sha256:fc3e126f1eaa39ace7625d1d91f4955b11b8c9c38a9a3e97ce6b3be2a480e34c","split":"train","step_index":1,"target":"def transform(state):\n    delta = (6, 5, 6, 6)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000385","trajectory_id":"vlr-formal-v2-0000385-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:0273dfef2e0f46395223483ed326fba90980057c21d4f70c5909570faae890e0","candidate_id":"sha256:c359adc2265c5ed2e1701de32aed11c2150c6feec2ac374531a7b25abe191f5a","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (6, -8, -4, 2, 8, 6)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:db30dbcd91cb95a279fcc966f34abf0c1beb32ecc8650db3e327797173b86045"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:6166c213a3de8cd9e71feae67922856ae27f4a7f671e2a4e62d2ef21030784fb","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": -7}, {\"input\": 2, \"output\": -2}, {\"input\": 3, \"output\": 5}, {\"input\": 4, \"output\": 12}, {\"input\": 5, \"output\": 11}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (3, -8, -4, 2, 8, 6)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_000\", \"lookup_delta.protected.case_001\", \"lookup_delta.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:310963ec394ace0453164f6a5e8337814e7db954da596274b241657950b4e832","sample_id":"sha256:77296bd86a7a4f26f96369a18b1485577476be064718bd0d896fcb5d0854b27b","source_transition_id":"sha256:b345a27bdad6434d4c43cb0f4decabe451cf79968e3d2106d4eb9b03df7e5827","split":"train","step_index":2,"target":"def transform(x):\n    delta = (6, -8, -4, 2, 8, 6)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000386","trajectory_id":"vlr-formal-v2-0000386-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:eab2e859ada271ac8b20d1bf4c551df6feccc9c3f7573d42462d8c4af42a0da6","candidate_id":"sha256:77b9f0f6329d3d5bd1c6fb9533085ca619f78cf4ad7e02d52d34e1bac45fb2b3","certified":true,"rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"text":"def transform(x):\n    table = (-8, -5, 5, -6, 2)\n    return x + table[(abs(x) // 2) % 5]\n","verification_digest":"sha256:f184fde3b03d34d72d1c1f298b33a5b44e76ef8912d9884d51c749355598d40f"},"incumbent_rank":{"component_ids":["signed_bucket.protected.case_000","signed_bucket.protected.case_001","signed_bucket.protected.case_002","signed_bucket.protected.case_003","signed_bucket.protected.case_004","signed_bucket.protected.case_005","signed_bucket.protected.case_006","signed_bucket.protected.case_007","signed_bucket.protected.case_008","signed_bucket.protected.case_009","signed_bucket.protected.case_010","signed_bucket.protected.case_011","signed_bucket.protected.case_012","signed_bucket.protected.case_013","signed_bucket.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:9a3417dbc60677d3a051f8b8b535d527ad5be33883c5f04914819bf8e4aa6b47"},"incumbent_state_id":"sha256:f8d8507529ecfc7fb6db7a4af0ca8fd5258b9232c3319aa3242d48f1ce743376","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -8}, {\"input\": 2, \"output\": -3}, {\"input\": 4, \"output\": 9}, {\"input\": 6, \"output\": 0}, {\"input\": 8, \"output\": 10}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    table = (-8, -5, 5, -7, 2)\n    return x + table[(abs(x) // 2) % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"signed_bucket.protected.case_009\", \"signed_bucket.protected.case_010\", \"signed_bucket.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:72e171559ed0553b7acd125676a6477a739ad1712fca986d7d11b7ef58e81702","sample_id":"sha256:1cfdacf0025aab97ee0b2ffe70661ff07a9ce61ab6a8f9e6b96eb71b70190aa5","source_transition_id":"sha256:fd57f874ce22de6c45456cd8d420e453e5fee12b6e701ae415f8d8e3fcfc10dd","split":"train","step_index":4,"target":"def transform(x):\n    table = (-8, -5, 5, -6, 2)\n    return x + table[(abs(x) // 2) % 5]\n","task_id":"vlr-formal-v2-0000387","trajectory_id":"vlr-formal-v2-0000387-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:facb014889138c26375b1ed46b5e2a29f989aad5a20e1f2303ae2792cfbef5f4","candidate_id":"sha256:655dc6bd7a1041c392c0fcb6d0387247094c0b2f6a4401c37a89cd272e9c2fa8","certified":true,"rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"text":"def transform(x):\n    offsets = (-4, -5, 1, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","verification_digest":"sha256:15fc245ccfe8d38da9f85d4ffd2f10332060978f71e93779244da98e838311e2"},"incumbent_rank":{"component_ids":["piecewise_bias.protected.case_000","piecewise_bias.protected.case_001","piecewise_bias.protected.case_002","piecewise_bias.protected.case_003","piecewise_bias.protected.case_004","piecewise_bias.protected.case_005","piecewise_bias.protected.case_006","piecewise_bias.protected.case_007","piecewise_bias.protected.case_008","piecewise_bias.protected.case_009","piecewise_bias.protected.case_010","piecewise_bias.protected.case_011"],"components":[0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:7f262bc043f35a82c9d27db790591fe95084ba9a12a95ea8ccb10fd4ae089852"},"incumbent_state_id":"sha256:06c85aebf9c3bc7dcd3ae05f239af2866e6b56f4f5f81d37e870e4613e9faa39","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": -27, \"output\": -31}, {\"input\": -3, \"output\": -8}, {\"input\": 3, \"output\": 4}, {\"input\": 27, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-4, -5, 8, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"piecewise_bias.protected.case_006\", \"piecewise_bias.protected.case_007\", \"piecewise_bias.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:215ded9e815811dff14eda985d0281296417e64c1e4862a997096fc58ca0adb6","sample_id":"sha256:db3db1221fbdc84ed86a581978216a8f5802eb39b3c553babebb65f776372de1","source_transition_id":"sha256:9a404de376b9f80fd16ffff12c63b44a3d970678414dd098827c16f8ef59f131","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (-4, -5, 1, -7)\n    bucket = 0 if x < -6 else 1 if x < 0 else 2 if x < 6 else 3\n    return x + offsets[bucket]\n","task_id":"vlr-formal-v2-0000390","trajectory_id":"vlr-formal-v2-0000390-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:3fbf5f47d3c609b0a8b6891e5af3845bc7f11146a9567c28f7953ac79de94cc0","candidate_id":"sha256:86e39a1f8d5ec1375cd4861924573415e09a07d2ba23491fcbcbc12402562d1e","certified":true,"rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"text":"def transform(x):\n    offsets = (-1, 1, -4, -7, -5)\n    return x + offsets[x % 5]\n","verification_digest":"sha256:89c5e27442addcae89a849bdfe8d208f3b3448347a701e81397273c4c14df197"},"incumbent_rank":{"component_ids":["residue_bias.protected.case_000","residue_bias.protected.case_001","residue_bias.protected.case_002","residue_bias.protected.case_003","residue_bias.protected.case_004","residue_bias.protected.case_005","residue_bias.protected.case_006","residue_bias.protected.case_007","residue_bias.protected.case_008","residue_bias.protected.case_009","residue_bias.protected.case_010","residue_bias.protected.case_011","residue_bias.protected.case_012","residue_bias.protected.case_013","residue_bias.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,1,1,1,0,0,0],"schema_digest":"sha256:62341d32785d1f40add8b7d9a2033c8b29deb0f308314d764a9e3a6ba15d704a"},"incumbent_state_id":"sha256:28717eab6b272ade6c62169031e30b575145a444f5a5b262f08cfd3ceb351bf7","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": -1}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": -2}, {\"input\": 3, \"output\": -4}, {\"input\": -1, \"output\": -6}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    offsets = (-1, 1, -4, 3, -5)\n    return x + offsets[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"residue_bias.protected.case_009\", \"residue_bias.protected.case_010\", \"residue_bias.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:5035c8ebf11bd59a3a341103f273a1b50ce75c559bd1d57e6447081416bee18e","sample_id":"sha256:135c9844a15329042dc797e53155164463d8010a0aa7750494f326be1cd6628e","source_transition_id":"sha256:8246c894f4abec60b113d35fb4f209636810cf614ac04b6da8686effa4e1375c","split":"train","step_index":1,"target":"def transform(x):\n    offsets = (-1, 1, -4, -7, -5)\n    return x + offsets[x % 5]\n","task_id":"vlr-formal-v2-0000391","trajectory_id":"vlr-formal-v2-0000391-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:771854a01718359a668fd9b4661c96f4c7b5694dda6def97e67ab992a12ac919","candidate_id":"sha256:d3a2bd4268b161228f2b3b844f1586435243598b750d3b18061772c0cc2215bf","certified":true,"rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"text":"def transform(x):\n    bias = (6, -6, 4, 0, -4)\n    return x * x + bias[x % 5]\n","verification_digest":"sha256:5fb1ec34399ebb2af51678a99376bcc725853e12355806af9315d4157d8b34ac"},"incumbent_rank":{"component_ids":["quadratic_residue.protected.case_000","quadratic_residue.protected.case_001","quadratic_residue.protected.case_002","quadratic_residue.protected.case_003","quadratic_residue.protected.case_004","quadratic_residue.protected.case_005","quadratic_residue.protected.case_006","quadratic_residue.protected.case_007","quadratic_residue.protected.case_008","quadratic_residue.protected.case_009","quadratic_residue.protected.case_010","quadratic_residue.protected.case_011","quadratic_residue.protected.case_012","quadratic_residue.protected.case_013","quadratic_residue.protected.case_014"],"components":[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:717d3ecca53d12c0ecff394dea1f6a83b72e1be21fb5aef1413f3efc53bc2e4a"},"incumbent_state_id":"sha256:8101e087c45bb5b519daa6ad8e6ed36c9bcb9c6d81c553e49a9aef821302bd11","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": -5}, {\"input\": 2, \"output\": 8}, {\"input\": 3, \"output\": 9}, {\"input\": -1, \"output\": -3}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    bias = (-6, -6, 4, 0, -4)\n    return x * x + bias[x % 5]\n```\n\nSanitized verifier feedback:\npassed_count=12\nfailed_count=3\nfailed_obligation_ids=[\"quadratic_residue.protected.case_000\", \"quadratic_residue.protected.case_001\", \"quadratic_residue.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:29c2939fa77d06412bb75547adbf0443e406142101b669c16c069d52b9f31a0c","sample_id":"sha256:1d089512c6c0f445887cbbdf0d2d5fc57f4713c159bea9bfa71bcb5321392495","source_transition_id":"sha256:4f95b4b0264e6b33fff118a9f55695b62134094bea7cee676f7ea067e3b4ba2a","split":"train","step_index":1,"target":"def transform(x):\n    bias = (6, -6, 4, 0, -4)\n    return x * x + bias[x % 5]\n","task_id":"vlr-formal-v2-0000392","trajectory_id":"vlr-formal-v2-0000392-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:77ad6366dcf0e2c1251c04e0528815dee05910865a3fb99a0ddbfb98bda5285f","candidate_id":"sha256:1f9887587863ba4376df0977192c1a1047d9e0faa00a5b620f2028656da5eb75","certified":true,"rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"text":"def transform(x):\n    factor = (2, 2, 2, 5, 9)\n    return (x * factor[x % 5]) % 29\n","verification_digest":"sha256:12c9bb4a0944f10fc50fd1d4d061d092874eeea6d7adf1dc59398c3c12999c49"},"incumbent_rank":{"component_ids":["mod_product.protected.case_000","mod_product.protected.case_001","mod_product.protected.case_002","mod_product.protected.case_003","mod_product.protected.case_004","mod_product.protected.case_005","mod_product.protected.case_006","mod_product.protected.case_007","mod_product.protected.case_008","mod_product.protected.case_009","mod_product.protected.case_010","mod_product.protected.case_011","mod_product.protected.case_012","mod_product.protected.case_013","mod_product.protected.case_014"],"components":[1,0,1,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:6ac950c9661dea9868fa486598b7ec23163b86e05da90c002af3a090fbc2b7b2"},"incumbent_state_id":"sha256:2301b3b5f1d8900ee1ebc59430c191dbc93eb83af2dc3688c1ff84e9e850f7d3","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 0}, {\"input\": 1, \"output\": 2}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 15}, {\"input\": -1, \"output\": 20}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    factor = (5, 2, 2, 5, 9)\n    return (x * factor[x % 5]) % 29\n```\n\nSanitized verifier feedback:\npassed_count=13\nfailed_count=2\nfailed_obligation_ids=[\"mod_product.protected.case_000\", \"mod_product.protected.case_002\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:dc6d8ae5d8cb36bc3481a25c1aa25c9e66ad03d8a89c6f90ffe223fe4716a9e6","sample_id":"sha256:d320facffca2c7d08dc011e041c3df6297a41bf29229de6cd30c0e76191c406e","source_transition_id":"sha256:da3de78339901cb53047e2e77b7b8cee94baae0f2ac39f51d96ac82d8efd6c65","split":"train","step_index":4,"target":"def transform(x):\n    factor = (2, 2, 2, 5, 9)\n    return (x * factor[x % 5]) % 29\n","task_id":"vlr-formal-v2-0000393","trajectory_id":"vlr-formal-v2-0000393-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:500029921a20fe08a5fe046be8c8baafaf589b14b4c33390bf58a2899dee6969","candidate_id":"sha256:8eca19b9fb7d7bcf83c3b18843e4077cdd87179f21dc63b58b5df758b7d51a84","certified":true,"rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"text":"def transform(state):\n    delta = (6, 4, 2, 5)\n    return (state + delta[state & 3]) % 17\n","verification_digest":"sha256:504d9d91405430f2340a4dd2aba53ade9bbe571f0f2968d370f04198064da9f4"},"incumbent_rank":{"component_ids":["fsm_delta.protected.case_000","fsm_delta.protected.case_001","fsm_delta.protected.case_002","fsm_delta.protected.case_003","fsm_delta.protected.case_004","fsm_delta.protected.case_005","fsm_delta.protected.case_006","fsm_delta.protected.case_007","fsm_delta.protected.case_008","fsm_delta.protected.case_009","fsm_delta.protected.case_010","fsm_delta.protected.case_011"],"components":[0,0,0,0,0,0,0,0,0,1,1,1],"schema_digest":"sha256:a5c3a1bd6a0fbc42c0f613624f889c21bf7b10dc53587ffc812fb2b18dab5cc1"},"incumbent_state_id":"sha256:f105ed33543f961eeae3f8796d9d25d1125e54d4e382c690afdc26dcb754e435","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(state) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 6}, {\"input\": 1, \"output\": 5}, {\"input\": 2, \"output\": 4}, {\"input\": 3, \"output\": 8}]\n\nCurrent certified implementation:\n```python\ndef transform(state):\n    delta = (6, 4, 2, 3)\n    return (state + delta[state & 3]) % 17\n```\n\nSanitized verifier feedback:\npassed_count=9\nfailed_count=3\nfailed_obligation_ids=[\"fsm_delta.protected.case_009\", \"fsm_delta.protected.case_010\", \"fsm_delta.protected.case_011\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:785c6eb5bc5912c37ad85ee73033aa314ac3aeed37b1aca431663d6f3f208f36","sample_id":"sha256:377b0fc29af89cbee55be75a313aa9348b8e6de4b6adc837a3308c13224639f3","source_transition_id":"sha256:626856090000da6ceeff1f0e007b4031dd387417cde530c5487069dcc77ea169","split":"train","step_index":1,"target":"def transform(state):\n    delta = (6, 4, 2, 5)\n    return (state + delta[state & 3]) % 17\n","task_id":"vlr-formal-v2-0000395","trajectory_id":"vlr-formal-v2-0000395-trajectory","view_type":"certified_generation","view_version":"1.0.0"}
{"accepted":{"artifact_digest":"sha256:66755d81646f19916a129c6d429e1156ced2f9478296f47861ef006171993f69","candidate_id":"sha256:48474b7f1c02d0ea9ad7a6b6877d29e257ff02c8318f2827efd877f51e513bf4","certified":true,"rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"text":"def transform(x):\n    delta = (8, 8, 5, 4, 2, 8)\n    return x + delta[abs(x) % 6]\n","verification_digest":"sha256:f61a710211878aae19e4f86ad350e1ab14dea40b3af18598f4d798252f2a3349"},"incumbent_rank":{"component_ids":["lookup_delta.protected.case_000","lookup_delta.protected.case_001","lookup_delta.protected.case_002","lookup_delta.protected.case_003","lookup_delta.protected.case_004","lookup_delta.protected.case_005","lookup_delta.protected.case_006","lookup_delta.protected.case_007","lookup_delta.protected.case_008","lookup_delta.protected.case_009","lookup_delta.protected.case_010","lookup_delta.protected.case_011","lookup_delta.protected.case_012","lookup_delta.protected.case_013","lookup_delta.protected.case_014","lookup_delta.protected.case_015","lookup_delta.protected.case_016","lookup_delta.protected.case_017"],"components":[0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0],"schema_digest":"sha256:76785d88257944536d18c179a321bfc1ca0f4274713239e1ee6540260a6e3422"},"incumbent_state_id":"sha256:2ef43cf8312d3067ace53007d4997fa0da96a9c1ac89aa155848fb47d5ac3b3c","prompt_messages":[{"content":"Use only the task, the current implementation, and the provided verification feedback. Return only a complete corrected Python implementation. Preserve already-passing requirements while addressing unresolved failures.","role":"system"},{"content":"Task:\nRepair the Python function transform(x) using the visible examples and the verifier feedback. A valid correction must improve unresolved protected obligations without regressing any already-satisfied protected obligation.\n\nVisible examples:\n[{\"input\": 0, \"output\": 8}, {\"input\": 1, \"output\": 9}, {\"input\": 2, \"output\": 7}, {\"input\": 3, \"output\": 7}, {\"input\": 4, \"output\": 6}, {\"input\": 5, \"output\": 13}]\n\nCurrent certified implementation:\n```python\ndef transform(x):\n    delta = (8, 8, -3, 4, 2, 8)\n    return x + delta[abs(x) % 6]\n```\n\nSanitized verifier feedback:\npassed_count=15\nfailed_count=3\nfailed_obligation_ids=[\"lookup_delta.protected.case_006\", \"lookup_delta.protected.case_007\", \"lookup_delta.protected.case_008\"]\n\nProduce the next complete implementation.","role":"user"}],"record_digest":"sha256:20316aea0539ec614af8674f51e2b59c5545c5e132a1b18a9f721d69b17489b4","sample_id":"sha256:89113c14c3a1d4be6500ebc037afb2a4a932e797aac6c06003b3fcf2c91f6c91","source_transition_id":"sha256:dc29757d95a366dc3629bb6112c7703175c4f97668d7db0768f2e9626fbd2eaf","split":"train","step_index":2,"target":"def transform(x):\n    delta = (8, 8, 5, 4, 2, 8)\n    return x + delta[abs(x) % 6]\n","task_id":"vlr-formal-v2-0000396","trajectory_id":"vlr-formal-v2-0000396-trajectory","view_type":"certified_generation","view_version":"1.0.0"}