{"abstract":"Zero embeddings become a fabricated unit vector.","category":"Embedding vector normalization","checks":6,"contract":"Normalize by L2 length while preserving input dimensionality; zero and empty inputs remain unchanged.","contract_signature":"v","evaluation_group":"embedding-zero-preserving-l2","failed_approach":"Replacing zero by a vector of ones still invents a direction.","family":"w3-embedding-vector-normalization-zero-vector-policy","id":"FA-99356","implementations":{"attempt":{"sha256":"25634a07759f7c62cce526fb8c89ce681811db3439ba4fbfe59158dcc9b64f9d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v):\n    return [x/(sum(y*y for y in v)**0.5) for x in v] if any(v) else ([0.0] if len(v)==1 else [1.0]*len(v))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero pair', solve([0,0]), [0,0])\ncheck('empty', solve([]), [])\ncheck('ordinary', solve([3,4]), [0.6,0.8])\ncheck('signed zero', solve([0,0,0]), [0,0,0])\ncheck('single zero', solve([0]), [0])\ncheck('direction retained', solve([-N,N]), [-N/(2*N*N)**0.5,N/(2*N*N)**0.5])\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":"487fe7e5ef0c4837cded3768934a23b16146e613db7d06a1141b8f6281e34859","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v):\n    return [x/(sum(y*y for y in v)**0.5) for x in v] if any(v) else [1.0]*len(v)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('zero pair', solve([0,0]), [0,0])\ncheck('empty', solve([]), [])\ncheck('ordinary', solve([3,4]), [0.6,0.8])\ncheck('signed zero', solve([0,0,0]), [0,0,0])\ncheck('single zero', solve([0]), [0])\ncheck('direction retained', solve([-N,N]), [-N/(2*N*N)**0.5,N/(2*N*N)**0.5])\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":"Inputs are finite toy vectors or token rows; this contract makes no claim about model quality or production embedding behavior. 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-embedding-vector-normalization-zero-vector-policy","generated_at":"2026-09-30T16:48:23.078999+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A small embedding preparation contract can be checked without a model or retrieval system.","root_cause":"The zero norm fallback inserts a coordinate value that is not in the input direction.","sha256":"53670f3c5f6d552f3171057aa13cebe1b96a32515d14c3deb854fc8ae3e14c92","title":"Zero embeddings become a fabricated unit vector · 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":28.111,"exit_code":1,"observations":[{"actual":[1.0,1.0],"check":"zero pair","expected":[0,0],"passed":false},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.6,0.8],"check":"ordinary","expected":[0.6,0.8],"passed":true},{"actual":[1.0,1.0,1.0],"check":"signed zero","expected":[0,0,0],"passed":false},{"actual":[0.0],"check":"single zero","expected":[0],"passed":true},{"actual":[-0.7071067811865475,0.7071067811865475],"check":"direction retained","expected":[-0.7071067811865475,0.7071067811865475],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero pair\", \"actual\": [1.0, 1.0], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"ordinary\", \"actual\": [0.6, 0.8], \"expected\": [0.6, 0.8], \"passed\": true}, {\"check\": \"signed zero\", \"actual\": [1.0, 1.0, 1.0], \"expected\": [0, 0, 0], \"passed\": false}, {\"check\": \"single zero\", \"actual\": [0.0], \"expected\": [0], \"passed\": true}, {\"check\": \"direction retained\", \"actual\": [-0.7071067811865475, 0.7071067811865475], \"expected\": [-0.7071067811865475, 0.7071067811865475], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":24.614,"exit_code":1,"observations":[{"actual":[1.0,1.0],"check":"zero pair","expected":[0,0],"passed":false},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.6,0.8],"check":"ordinary","expected":[0.6,0.8],"passed":true},{"actual":[1.0,1.0,1.0],"check":"signed zero","expected":[0,0,0],"passed":false},{"actual":[1.0],"check":"single zero","expected":[0],"passed":false},{"actual":[-0.7071067811865475,0.7071067811865475],"check":"direction retained","expected":[-0.7071067811865475,0.7071067811865475],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"zero pair\", \"actual\": [1.0, 1.0], \"expected\": [0, 0], \"passed\": false}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"ordinary\", \"actual\": [0.6, 0.8], \"expected\": [0.6, 0.8], \"passed\": true}, {\"check\": \"signed zero\", \"actual\": [1.0, 1.0, 1.0], \"expected\": [0, 0, 0], \"passed\": false}, {\"check\": \"single zero\", \"actual\": [1.0], \"expected\": [0], \"passed\": false}, {\"check\": \"direction retained\", \"actual\": [-0.7071067811865475, 0.7071067811865475], \"expected\": [-0.7071067811865475, 0.7071067811865475], \"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."}}