{"abstract":"Negative amplitudes cannot advance through magnitude segments.","category":"PCM sample encoding","checks":8,"contract":"Encode bounded PCM magnitude into an explicitly stipulated piecewise companding table: sign sideband, selected lower-bound segment and shifted residual mantissa.","contract_signature":"samples, edges, shifts","evaluation_group":"s3-pcm-pcm-companding-segment-code","failed_approach":"The first amplitude selects the segment of every later sample.","family":"s3-pcm-pcm-companding-segment-code-magnitude-selection","id":"FA-49961","implementations":{"attempt":{"sha256":"2099fd3dd047d9504d818856be90720ce02ea05e58bcb05fa6b193b962b12b8b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, edges, shifts):\n    out=[]\n    for sample in samples:\n        negative=sample<0\n        magnitude=abs(samples[0])\n        segment=0\n        while segment+1<len(edges) and magnitude>=edges[segment+1]:\n            segment+=1\n        residual=max(0,magnitude-edges[segment])\n        mantissa=residual>>shifts[segment]\n        out.append([negative,segment,mantissa])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])\ncheck('oracle 4', solve(*([], [0, 8], [1, 3])), [])\ncheck('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])\ncheck('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])\nif N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"43d7687a8698a80eac25192f7dca415be66adf4b2fc001f70eb7332af02c0d95","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, edges, shifts):\n    out=[]\n    for sample in samples:\n        negative=sample<0\n        magnitude=sample\n        segment=0\n        while segment+1<len(edges) and magnitude>=edges[segment+1]:\n            segment+=1\n        residual=max(0,magnitude-edges[segment])\n        mantissa=residual>>shifts[segment]\n        out.append([negative,segment,mantissa])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])\ncheck('oracle 4', solve(*([], [0, 8], [1, 3])), [])\ncheck('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])\ncheck('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])\ncheck('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])\nif N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nif N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Stipulated finite model; no claim of hardware timing or full file-format conformance. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-pcm-pcm-companding-segment-code-magnitude-selection","generated_at":"2026-09-29T14:45:04.807381+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Offline PCM interchange uses these exact bounded packet and sample representation decisions.","root_cause":"Negative amplitudes cannot advance through magnitude segments.","sha256":"44c978b8662d8121dacdd5246856f3dc8528450b0f34be84cc61048c018616ac","title":"Pcm companding segment code: magnitude selection · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.956,"exit_code":1,"observations":[{"actual":[[true,2,0],[true,2,0],[false,2,0],[false,2,0],[false,2,0]],"check":"oracle 1","expected":[[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0]],"passed":false},{"actual":[[false,0,0],[false,0,0],[false,0,0],[false,0,0]],"check":"oracle 2","expected":[[false,0,0],[false,0,2],[false,1,0],[false,2,0]],"passed":false},{"actual":[[false,0,0],[false,0,0],[false,0,0]],"check":"oracle 3","expected":[[false,0,0],[false,0,1],[false,0,1]],"passed":false},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[true,1,0],[false,1,0],[false,1,0]],"check":"oracle 5","expected":[[true,1,0],[false,1,0],[false,1,0]],"passed":true},{"actual":[[false,0,0],[false,0,0],[false,0,0]],"check":"oracle 6","expected":[[false,0,0],[false,1,0],[false,2,0]],"passed":false},{"actual":[[false,1,3],[true,1,3]],"check":"oracle 7","expected":[[false,1,3],[true,1,3]],"passed":true},{"actual":[[true,2,0],[true,2,0],[false,2,0],[false,2,0],[false,2,0],[true,2,0],[true,2,0],[false,2,0],[false,2,0],[false,2,0]],"check":"variant packet 1","expected":[[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0],[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[true, 2, 0], [true, 2, 0], [false, 2, 0], [false, 2, 0], [false, 2, 0]], \"expected\": [[true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[false, 0, 0], [false, 0, 0], [false, 0, 0], [false, 0, 0]], \"expected\": [[false, 0, 0], [false, 0, 2], [false, 1, 0], [false, 2, 0]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [[false, 0, 0], [false, 0, 0], [false, 0, 0]], \"expected\": [[false, 0, 0], [false, 0, 1], [false, 0, 1]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[true, 1, 0], [false, 1, 0], [false, 1, 0]], \"expected\": [[true, 1, 0], [false, 1, 0], [false, 1, 0]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [[false, 0, 0], [false, 0, 0], [false, 0, 0]], \"expected\": [[false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [[false, 1, 3], [true, 1, 3]], \"expected\": [[false, 1, 3], [true, 1, 3]], \"passed\": true}, {\"check\": \"variant packet 1\", \"actual\": [[true, 2, 0], [true, 2, 0], [false, 2, 0], [false, 2, 0], [false, 2, 0], [true, 2, 0], [true, 2, 0], [false, 2, 0], [false, 2, 0], [false, 2, 0]], \"expected\": [[true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0], [true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.96,"exit_code":1,"observations":[{"actual":[[true,0,0],[true,0,0],[false,0,0],[false,1,0],[false,2,0]],"check":"oracle 1","expected":[[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0]],"passed":false},{"actual":[[false,0,0],[false,0,2],[false,1,0],[false,2,0]],"check":"oracle 2","expected":[[false,0,0],[false,0,2],[false,1,0],[false,2,0]],"passed":true},{"actual":[[false,0,0],[false,0,1],[false,0,1]],"check":"oracle 3","expected":[[false,0,0],[false,0,1],[false,0,1]],"passed":true},{"actual":[],"check":"oracle 4","expected":[],"passed":true},{"actual":[[true,0,0],[false,1,0],[false,1,0]],"check":"oracle 5","expected":[[true,1,0],[false,1,0],[false,1,0]],"passed":false},{"actual":[[false,0,0],[false,1,0],[false,2,0]],"check":"oracle 6","expected":[[false,0,0],[false,1,0],[false,2,0]],"passed":true},{"actual":[[false,1,3],[true,0,0]],"check":"oracle 7","expected":[[false,1,3],[true,1,3]],"passed":false},{"actual":[[true,0,0],[true,0,0],[false,0,0],[false,1,0],[false,2,0],[true,0,0],[true,0,0],[false,0,0],[false,1,0],[false,2,0]],"check":"variant packet 1","expected":[[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0],[true,2,0],[true,1,0],[false,0,0],[false,1,0],[false,2,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [[true, 0, 0], [true, 0, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"expected\": [[true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [[false, 0, 0], [false, 0, 2], [false, 1, 0], [false, 2, 0]], \"expected\": [[false, 0, 0], [false, 0, 2], [false, 1, 0], [false, 2, 0]], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [[false, 0, 0], [false, 0, 1], [false, 0, 1]], \"expected\": [[false, 0, 0], [false, 0, 1], [false, 0, 1]], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [[true, 0, 0], [false, 1, 0], [false, 1, 0]], \"expected\": [[true, 1, 0], [false, 1, 0], [false, 1, 0]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [[false, 0, 0], [false, 1, 0], [false, 2, 0]], \"expected\": [[false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [[false, 1, 3], [true, 0, 0]], \"expected\": [[false, 1, 3], [true, 1, 3]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [[true, 0, 0], [true, 0, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0], [true, 0, 0], [true, 0, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"expected\": [[true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0], [true, 2, 0], [true, 1, 0], [false, 0, 0], [false, 1, 0], [false, 2, 0]], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}