{"abstract":"Accumulator silently wraps at a narrow width.","category":"Model quantization arithmetic","checks":6,"contract":"Accumulate integer products exactly without modular wrap; width is metadata and does not impose overflow in this toy contract. Inputs follow this explicit integer toy contract; ties use Python round-to-even where rounding is required.","contract_signature":"products, width","evaluation_group":"gradient-accumulation-remainder_window","failed_approach":"The attempted code avoids a single final mask but masks every product before summing, so high product bits are still lost.","family":"w3-model-quantization-arithmetic-accumulator-width-wrap","id":"FA-98711","implementations":{"attempt":{"sha256":"b6d47bfa8f7af42c7faf3a4194f8d22357e283e26cd366cf37a91ce59107acb6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(products, width):\n    mask=(1<<width)-1\n    return sum(p&mask for p in products)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive carry',solve([3*N,5*N],8),8*N)\ncheck('negative sum',solve([-N,-2*N],8),-3*N)\ncheck('empty',solve([],8),0)\ncheck('single',solve([N],8),N)\ncheck('large exact',solve([100*N],8),100*N)\ncheck('cancellation',solve([10*N,-10*N],8),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":"7f7a941282fcd198d40fab451a10ea6945e1b1de7b5acc8341af1d96354a9150","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(products, width):\n    mask=(1<<width)-1\n    return sum(products)&mask\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive carry',solve([3*N,5*N],8),8*N)\ncheck('negative sum',solve([-N,-2*N],8),-3*N)\ncheck('empty',solve([],8),0)\ncheck('single',solve([N],8),N)\ncheck('large exact',solve([100*N],8),100*N)\ncheck('cancellation',solve([10*N,-10*N],8),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":"Toy scalar/list arithmetic only; it does not model a production quantizer, hardware instruction, or accuracy/performance gain. 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":"w3-model-quantization-arithmetic-accumulator-width-wrap","generated_at":"2026-09-30T16:48:15.841772+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This deterministic model isolates one quantization arithmetic contract from tensor storage and runtime kernels.","root_cause":"Accumulate integer products exactly without modular wrap; width is metadata and does not impose overflow in this toy contract.","sha256":"b75c1acaf3744129b2aa2bc6efe2de4dba944ad6195d374fe8eff78b5607cdba","title":"Quantization: Accumulator silently wraps at a narrow width · case 01","variant":1,"variant_policy":"The fixture code references N, supplied as 1 through 5. Fixed boundary checks may repeat. These records share one mechanism and must remain together in evaluation splits.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":30.35,"exit_code":1,"observations":[{"actual":8,"check":"positive carry","expected":8,"passed":true},{"actual":509,"check":"negative sum","expected":-3,"passed":false},{"actual":0,"check":"empty","expected":0,"passed":true},{"actual":1,"check":"single","expected":1,"passed":true},{"actual":100,"check":"large exact","expected":100,"passed":true},{"actual":256,"check":"cancellation","expected":0,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive carry\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"negative sum\", \"actual\": 509, \"expected\": -3, \"passed\": false}, {\"check\": \"empty\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"single\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"large exact\", \"actual\": 100, \"expected\": 100, \"passed\": true}, {\"check\": \"cancellation\", \"actual\": 256, \"expected\": 0, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":26.437,"exit_code":1,"observations":[{"actual":8,"check":"positive carry","expected":8,"passed":true},{"actual":253,"check":"negative sum","expected":-3,"passed":false},{"actual":0,"check":"empty","expected":0,"passed":true},{"actual":1,"check":"single","expected":1,"passed":true},{"actual":100,"check":"large exact","expected":100,"passed":true},{"actual":0,"check":"cancellation","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive carry\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"negative sum\", \"actual\": 253, \"expected\": -3, \"passed\": false}, {\"check\": \"empty\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"single\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"large exact\", \"actual\": 100, \"expected\": 100, \"passed\": true}, {\"check\": \"cancellation\", \"actual\": 0, \"expected\": 0, \"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."}}