{"abstract":"Gradient style clipping expands a vector already under the norm bound.","category":"Embedding vector normalization","checks":6,"contract":"Return v scaled by min(1, bound/L2(v)); zero vectors stay zero and bound is positive.","contract_signature":"v, bound","evaluation_group":"embedding-l2-clipping","failed_approach":"Clipping only the maximum coordinate ignores the Euclidean norm across coordinates.","family":"w3-embedding-vector-normalization-norm-clipping","id":"FA-99391","implementations":{"attempt":{"sha256":"7b416b2eca214ba745c2d198ceef84bf13a1c72b5ee7f8eeba8576ce61407415","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v, bound):\n    return [max(-bound,min(bound,x)) for x in v]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('inside bound', solve([N,0],2*N), [N,0])\ncheck('outside bound', solve([3*N,4*N],N), [3*N*(N/(5*N)),4*N*(N/(5*N))])\ncheck('boundary', solve([N,0],N), [N,0])\ncheck('zero', solve([0,0],N), [0,0])\ncheck('coordinate cap insufficient', solve([N,N],N), [N*(N/(2*N*N)**0.5),N*(N/(2*N*N)**0.5)])\ncheck('empty', solve([],N), [])\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":"c81d8236896183bed0b65a65c7f5f530709dec7ad09c4139de0831f02b04888f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v, bound):\n    length=sum(x*x for x in v)**0.5\n    return [x*bound/length for x in v] if length else list(v)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('inside bound', solve([N,0],2*N), [N,0])\ncheck('outside bound', solve([3*N,4*N],N), [3*N*(N/(5*N)),4*N*(N/(5*N))])\ncheck('boundary', solve([N,0],N), [N,0])\ncheck('zero', solve([0,0],N), [0,0])\ncheck('coordinate cap insufficient', solve([N,N],N), [N*(N/(2*N*N)**0.5),N*(N/(2*N*N)**0.5)])\ncheck('empty', solve([],N), [])\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-norm-clipping","generated_at":"2026-09-30T16:48:23.555372+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":"Every vector is rescaled to the bound, including vectors whose norm is already smaller.","sha256":"d408c9ed91839cfd7dba12d6a4e3ba9e7c7fce3c1e26e50670ecadce0a903191","title":"Gradient style clipping expands a vector already under the norm bound · 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":32.701,"exit_code":1,"observations":[{"actual":[1,0],"check":"inside bound","expected":[1,0],"passed":true},{"actual":[1,1],"check":"outside bound","expected":[0.6000000000000001,0.8],"passed":false},{"actual":[1,0],"check":"boundary","expected":[1,0],"passed":true},{"actual":[0,0],"check":"zero","expected":[0,0],"passed":true},{"actual":[1,1],"check":"coordinate cap insufficient","expected":[0.7071067811865475,0.7071067811865475],"passed":false},{"actual":[],"check":"empty","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"inside bound\", \"actual\": [1, 0], \"expected\": [1, 0], \"passed\": true}, {\"check\": \"outside bound\", \"actual\": [1, 1], \"expected\": [0.6000000000000001, 0.8], \"passed\": false}, {\"check\": \"boundary\", \"actual\": [1, 0], \"expected\": [1, 0], \"passed\": true}, {\"check\": \"zero\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"coordinate cap insufficient\", \"actual\": [1, 1], \"expected\": [0.7071067811865475, 0.7071067811865475], \"passed\": false}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":30.301,"exit_code":1,"observations":[{"actual":[2.0,0.0],"check":"inside bound","expected":[1,0],"passed":false},{"actual":[0.6,0.8],"check":"outside bound","expected":[0.6000000000000001,0.8],"passed":false},{"actual":[1.0,0.0],"check":"boundary","expected":[1,0],"passed":true},{"actual":[0,0],"check":"zero","expected":[0,0],"passed":true},{"actual":[0.7071067811865475,0.7071067811865475],"check":"coordinate cap insufficient","expected":[0.7071067811865475,0.7071067811865475],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"inside bound\", \"actual\": [2.0, 0.0], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"outside bound\", \"actual\": [0.6, 0.8], \"expected\": [0.6000000000000001, 0.8], \"passed\": false}, {\"check\": \"boundary\", \"actual\": [1.0, 0.0], \"expected\": [1, 0], \"passed\": true}, {\"check\": \"zero\", \"actual\": [0, 0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"coordinate cap insufficient\", \"actual\": [0.7071067811865475, 0.7071067811865475], \"expected\": [0.7071067811865475, 0.7071067811865475], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"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."}}