{"abstract":"Infinity normalization divides by total magnitude.","category":"Embedding vector normalization","checks":6,"contract":"Scale a finite vector so its largest absolute coordinate is one; zero or empty input returns empty.","contract_signature":"v","evaluation_group":"embedding-linf-unit-vector","failed_approach":"Adding a constant to the total magnitude still leaves the largest coordinate below one.","family":"w3-embedding-vector-normalization-infinity-unit-length","id":"FA-99351","implementations":{"attempt":{"sha256":"df3929122fb300aece883b8e501761a9ba89421e5ef917984e5c0044c221cb0f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v):\n    return [x/(sum(abs(y) for y in v)+1) for x in v] if v and any(v) else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('dominant coordinate', solve([N,3*N]), [1/3,1.0])\ncheck('negative maximum', solve([-N,2]), [-N/max(N,2),2/max(N,2)])\ncheck('single value', solve([-(N+1)]), [-1.0])\ncheck('zero', solve([0,0]), [])\ncheck('empty', solve([]), [])\ncheck('ties', solve([N,-N]), [1.0,-1.0])\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":"a95304168c5017e1abbd3d371ec683c372ae9599ca35f20cb173b19efef21cbf","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v):\n    return [x/sum(abs(y) for y in v) for x in v] if v and any(v) else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('dominant coordinate', solve([N,3*N]), [1/3,1.0])\ncheck('negative maximum', solve([-N,2]), [-N/max(N,2),2/max(N,2)])\ncheck('single value', solve([-(N+1)]), [-1.0])\ncheck('zero', solve([0,0]), [])\ncheck('empty', solve([]), [])\ncheck('ties', solve([N,-N]), [1.0,-1.0])\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":"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-infinity-unit-length","generated_at":"2026-09-30T16:48:23.079377+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 sum of coordinate magnitudes is used instead of the largest magnitude.","sha256":"eb80727a03d0dfd92224816aee29c5e3f900d8d0cf2ce3eb81929d213759cccd","title":"Infinity normalization divides by total magnitude · 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":26.322,"exit_code":1,"observations":[{"actual":[0.2,0.6],"check":"dominant coordinate","expected":[0.3333333333333333,1.0],"passed":false},{"actual":[-0.25,0.5],"check":"negative maximum","expected":[-0.5,1.0],"passed":false},{"actual":[-0.6666666666666666],"check":"single value","expected":[-1.0],"passed":false},{"actual":[],"check":"zero","expected":[],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.3333333333333333,-0.3333333333333333],"check":"ties","expected":[1.0,-1.0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"dominant coordinate\", \"actual\": [0.2, 0.6], \"expected\": [0.3333333333333333, 1.0], \"passed\": false}, {\"check\": \"negative maximum\", \"actual\": [-0.25, 0.5], \"expected\": [-0.5, 1.0], \"passed\": false}, {\"check\": \"single value\", \"actual\": [-0.6666666666666666], \"expected\": [-1.0], \"passed\": false}, {\"check\": \"zero\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"ties\", \"actual\": [0.3333333333333333, -0.3333333333333333], \"expected\": [1.0, -1.0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":26.297,"exit_code":1,"observations":[{"actual":[0.25,0.75],"check":"dominant coordinate","expected":[0.3333333333333333,1.0],"passed":false},{"actual":[-0.3333333333333333,0.6666666666666666],"check":"negative maximum","expected":[-0.5,1.0],"passed":false},{"actual":[-1.0],"check":"single value","expected":[-1.0],"passed":true},{"actual":[],"check":"zero","expected":[],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.5,-0.5],"check":"ties","expected":[1.0,-1.0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"dominant coordinate\", \"actual\": [0.25, 0.75], \"expected\": [0.3333333333333333, 1.0], \"passed\": false}, {\"check\": \"negative maximum\", \"actual\": [-0.3333333333333333, 0.6666666666666666], \"expected\": [-0.5, 1.0], \"passed\": false}, {\"check\": \"single value\", \"actual\": [-1.0], \"expected\": [-1.0], \"passed\": true}, {\"check\": \"zero\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"ties\", \"actual\": [0.5, -0.5], \"expected\": [1.0, -1.0], \"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."}}