{"abstract":"Epsilon normalization adds epsilon to every coordinate divisor.","category":"Embedding vector normalization","checks":6,"contract":"Divide a vector by max(L2 norm, positive epsilon); zero and empty vectors return all-zero shape.","contract_signature":"v, epsilon","evaluation_group":"embedding-epsilon-stabilized-unit","failed_approach":"Adding epsilon to the norm changes every ordinary vector even when no stabilization is needed.","family":"w3-embedding-vector-normalization-epsilon-denominator","id":"FA-99396","implementations":{"attempt":{"sha256":"f9d8ff1835cc761d3ffdb6cb4d6aec5a7f1c416383d7647f828b6078cce493f8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v, epsilon):\n    length=sum(x*x for x in v)**0.5\n    return [x/(length+epsilon) for x in v]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('ordinary norm', solve([3,4],0.1), [0.6,0.8])\ncheck('small vector', solve([0.03,0.04],0.1), [0.3,0.39999999999999997])\ncheck('zero shape', solve([0,0],0.1), [0,0])\ncheck('empty', solve([],0.1), [])\ncheck('single above epsilon', solve([N],0.1), [1.0])\ncheck('negative coordinate', solve([-3,4],0.1), [-0.6,0.8])\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":"b62995c073064e8e5d80dd61517d77d02cc225743a4f395edaf7e1303bd94226","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(v, epsilon):\n    return [x/(abs(x)+epsilon) for x in v]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('ordinary norm', solve([3,4],0.1), [0.6,0.8])\ncheck('small vector', solve([0.03,0.04],0.1), [0.3,0.39999999999999997])\ncheck('zero shape', solve([0,0],0.1), [0,0])\ncheck('empty', solve([],0.1), [])\ncheck('single above epsilon', solve([N],0.1), [1.0])\ncheck('negative coordinate', solve([-3,4],0.1), [-0.6,0.8])\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-epsilon-denominator","generated_at":"2026-09-30T16:48:23.554898+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 stabilizer is added to each coordinate magnitude instead of to the vector norm.","sha256":"19143646de68a8fbc14b01ca0444ae5fdc8bbfb4104a9552f0b37dd8a0edbc47","title":"Epsilon normalization adds epsilon to every coordinate divisor · 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":32.54,"exit_code":1,"observations":[{"actual":[0.5882352941176471,0.7843137254901962],"check":"ordinary norm","expected":[0.6,0.8],"passed":false},{"actual":[0.19999999999999996,0.2666666666666666],"check":"small vector","expected":[0.3,0.39999999999999997],"passed":false},{"actual":[0.0,0.0],"check":"zero shape","expected":[0,0],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.9090909090909091],"check":"single above epsilon","expected":[1.0],"passed":false},{"actual":[-0.5882352941176471,0.7843137254901962],"check":"negative coordinate","expected":[-0.6,0.8],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"ordinary norm\", \"actual\": [0.5882352941176471, 0.7843137254901962], \"expected\": [0.6, 0.8], \"passed\": false}, {\"check\": \"small vector\", \"actual\": [0.19999999999999996, 0.2666666666666666], \"expected\": [0.3, 0.39999999999999997], \"passed\": false}, {\"check\": \"zero shape\", \"actual\": [0.0, 0.0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"single above epsilon\", \"actual\": [0.9090909090909091], \"expected\": [1.0], \"passed\": false}, {\"check\": \"negative coordinate\", \"actual\": [-0.5882352941176471, 0.7843137254901962], \"expected\": [-0.6, 0.8], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":30.636,"exit_code":1,"observations":[{"actual":[0.9677419354838709,0.9756097560975611],"check":"ordinary norm","expected":[0.6,0.8],"passed":false},{"actual":[0.23076923076923075,0.2857142857142857],"check":"small vector","expected":[0.3,0.39999999999999997],"passed":false},{"actual":[0.0,0.0],"check":"zero shape","expected":[0,0],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[0.9090909090909091],"check":"single above epsilon","expected":[1.0],"passed":false},{"actual":[-0.9677419354838709,0.9756097560975611],"check":"negative coordinate","expected":[-0.6,0.8],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"ordinary norm\", \"actual\": [0.9677419354838709, 0.9756097560975611], \"expected\": [0.6, 0.8], \"passed\": false}, {\"check\": \"small vector\", \"actual\": [0.23076923076923075, 0.2857142857142857], \"expected\": [0.3, 0.39999999999999997], \"passed\": false}, {\"check\": \"zero shape\", \"actual\": [0.0, 0.0], \"expected\": [0, 0], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"single above epsilon\", \"actual\": [0.9090909090909091], \"expected\": [1.0], \"passed\": false}, {\"check\": \"negative coordinate\", \"actual\": [-0.9677419354838709, 0.9756097560975611], \"expected\": [-0.6, 0.8], \"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."}}