{"abstract":"Block-floating PCM disallows the valid most-negative mantissa.","category":"PCM sample encoding","checks":8,"contract":"Bounded block-floating PCM: choose the smallest shared right shift fitting signed mantissas, cap exponent, saturate residual overflow and report reconstructed amplitudes.","contract_signature":"samples, mantissa_bits, max_shift","evaluation_group":"s3-pcm-pcm-block-exponent","failed_approach":"Unsigned clamping destroys all negative block values.","family":"s3-pcm-pcm-block-exponent-negative-bound","id":"FA-49321","implementations":{"attempt":{"sha256":"4efb5b10ec838cd74ed8764516468bfd4183c81a98641f9881d770211b70ab8d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, mantissa_bits, max_shift):\n    shift=0\n    low=0\n    high=(1<<(mantissa_bits-1))-1\n    while shift<max_shift and any((x>>shift)<low or (x>>shift)>high for x in samples):\n        shift+=1\n    mantissas=[max(low,min(high,x>>shift)) for x in samples]\n    restored=[x<<shift for x in mantissas]\n    return [shift,mantissas,restored]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 8, -9], 4, 3)), [1, [0, 4, -5], [0, 8, -10]])\ncheck('oracle 2', solve(*([7, -8], 4, 3)), [0, [7, -8], [7, -8]])\ncheck('oracle 3', solve(*([0, 100, -100], 4, 2)), [2, [0, 7, -8], [0, 28, -32]])\ncheck('oracle 4', solve(*([], 4, 3)), [0, [], []])\ncheck('oracle 5', solve(*([-17, 3], 4, 4)), [2, [-5, 0], [-20, 0]])\ncheck('oracle 6', solve(*([1, 2], 3, 0)), [0, [1, 2], [1, 2]])\ncheck('oracle 7', solve(*([16, -16], 4, 1)), [1, [7, -8], [14, -16]])\nif N == 1: check('variant packet 1', solve(*[[1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10]])\nif N == 2: check('variant packet 2', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 3: check('variant packet 3', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 4: check('variant packet 4', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 5: check('variant packet 5', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\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":"12a34475d8c4b50249cf557ecd2b9d9ed2c407f74d545f7b4f69c885da3a32bd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(samples, mantissa_bits, max_shift):\n    shift=0\n    low=-((1<<(mantissa_bits-1))-1)\n    high=(1<<(mantissa_bits-1))-1\n    while shift<max_shift and any((x>>shift)<low or (x>>shift)>high for x in samples):\n        shift+=1\n    mantissas=[max(low,min(high,x>>shift)) for x in samples]\n    restored=[x<<shift for x in mantissas]\n    return [shift,mantissas,restored]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('oracle 1', solve(*([1, 8, -9], 4, 3)), [1, [0, 4, -5], [0, 8, -10]])\ncheck('oracle 2', solve(*([7, -8], 4, 3)), [0, [7, -8], [7, -8]])\ncheck('oracle 3', solve(*([0, 100, -100], 4, 2)), [2, [0, 7, -8], [0, 28, -32]])\ncheck('oracle 4', solve(*([], 4, 3)), [0, [], []])\ncheck('oracle 5', solve(*([-17, 3], 4, 4)), [2, [-5, 0], [-20, 0]])\ncheck('oracle 6', solve(*([1, 2], 3, 0)), [0, [1, 2], [1, 2]])\ncheck('oracle 7', solve(*([16, -16], 4, 1)), [1, [7, -8], [14, -16]])\nif N == 1: check('variant packet 1', solve(*[[1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10]])\nif N == 2: check('variant packet 2', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 3: check('variant packet 3', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 4: check('variant packet 4', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\nif N == 5: check('variant packet 5', solve(*[[1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9, 1, 8, -9], 4, 3]), [1, [0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10, 0, 8, -10]])\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-block-exponent-negative-bound","generated_at":"2026-09-29T14:44:59.030407+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":"Block-floating PCM disallows the valid most-negative mantissa.","sha256":"55113a3b350b155a4223c21e368ce87b63090aead442945889a1db5f90d24d2c","title":"Pcm block exponent: negative bound · 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":45.936,"exit_code":1,"observations":[{"actual":[3,[0,1,0],[0,8,0]],"check":"oracle 1","expected":[1,[0,4,-5],[0,8,-10]],"passed":false},{"actual":[3,[0,0],[0,0]],"check":"oracle 2","expected":[0,[7,-8],[7,-8]],"passed":false},{"actual":[2,[0,7,0],[0,28,0]],"check":"oracle 3","expected":[2,[0,7,-8],[0,28,-32]],"passed":false},{"actual":[0,[],[]],"check":"oracle 4","expected":[0,[],[]],"passed":true},{"actual":[4,[0,0],[0,0]],"check":"oracle 5","expected":[2,[-5,0],[-20,0]],"passed":false},{"actual":[0,[1,2],[1,2]],"check":"oracle 6","expected":[0,[1,2],[1,2]],"passed":true},{"actual":[1,[7,0],[14,0]],"check":"oracle 7","expected":[1,[7,-8],[14,-16]],"passed":false},{"actual":[3,[0,1,0,0,1,0],[0,8,0,0,8,0]],"check":"variant packet 1","expected":[1,[0,4,-5,0,4,-5],[0,8,-10,0,8,-10]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [3, [0, 1, 0], [0, 8, 0]], \"expected\": [1, [0, 4, -5], [0, 8, -10]], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [3, [0, 0], [0, 0]], \"expected\": [0, [7, -8], [7, -8]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [2, [0, 7, 0], [0, 28, 0]], \"expected\": [2, [0, 7, -8], [0, 28, -32]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [0, [], []], \"expected\": [0, [], []], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [4, [0, 0], [0, 0]], \"expected\": [2, [-5, 0], [-20, 0]], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [0, [1, 2], [1, 2]], \"expected\": [0, [1, 2], [1, 2]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [1, [7, 0], [14, 0]], \"expected\": [1, [7, -8], [14, -16]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [3, [0, 1, 0, 0, 1, 0], [0, 8, 0, 0, 8, 0]], \"expected\": [1, [0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.652,"exit_code":1,"observations":[{"actual":[1,[0,4,-5],[0,8,-10]],"check":"oracle 1","expected":[1,[0,4,-5],[0,8,-10]],"passed":true},{"actual":[1,[3,-4],[6,-8]],"check":"oracle 2","expected":[0,[7,-8],[7,-8]],"passed":false},{"actual":[2,[0,7,-7],[0,28,-28]],"check":"oracle 3","expected":[2,[0,7,-8],[0,28,-32]],"passed":false},{"actual":[0,[],[]],"check":"oracle 4","expected":[0,[],[]],"passed":true},{"actual":[2,[-5,0],[-20,0]],"check":"oracle 5","expected":[2,[-5,0],[-20,0]],"passed":true},{"actual":[0,[1,2],[1,2]],"check":"oracle 6","expected":[0,[1,2],[1,2]],"passed":true},{"actual":[1,[7,-7],[14,-14]],"check":"oracle 7","expected":[1,[7,-8],[14,-16]],"passed":false},{"actual":[1,[0,4,-5,0,4,-5],[0,8,-10,0,8,-10]],"check":"variant packet 1","expected":[1,[0,4,-5,0,4,-5],[0,8,-10,0,8,-10]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 1\", \"actual\": [1, [0, 4, -5], [0, 8, -10]], \"expected\": [1, [0, 4, -5], [0, 8, -10]], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [1, [3, -4], [6, -8]], \"expected\": [0, [7, -8], [7, -8]], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [2, [0, 7, -7], [0, 28, -28]], \"expected\": [2, [0, 7, -8], [0, 28, -32]], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [0, [], []], \"expected\": [0, [], []], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [2, [-5, 0], [-20, 0]], \"expected\": [2, [-5, 0], [-20, 0]], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [0, [1, 2], [1, 2]], \"expected\": [0, [1, 2], [1, 2]], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [1, [7, -7], [14, -14]], \"expected\": [1, [7, -8], [14, -16]], \"passed\": false}, {\"check\": \"variant packet 1\", \"actual\": [1, [0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10]], \"expected\": [1, [0, 4, -5, 0, 4, -5], [0, 8, -10, 0, 8, -10]], \"passed\": true}], \"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."}}