{"abstract":"Feature standardization divides by variance.","category":"Embedding vector normalization","checks":6,"contract":"Standardize each column with population mean and standard deviation; zero-variance columns become zeros.","contract_signature":"rows","evaluation_group":"embedding-population-standardization","failed_approach":"Using sample variance changes the scale contract for small batches.","family":"w3-embedding-vector-normalization-variance-standardization","id":"FA-99411","implementations":{"attempt":{"sha256":"012537b43f3e2f95ba9b97d190a45de68bf0489177319ed17887e01bd4fa9bbe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(rows):\n    return [[(x-sum(r[j] for r in rows)/len(rows))/(max((sum((r[j]-sum(q[j] for q in rows)/len(rows))**2 for r in rows)/max(len(rows)-1,1))**0.5,1)) for j,x in enumerate(row)] for row in rows] if rows else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('population scale', solve([[0],[2]]), [[-1.0],[1.0]])\ncheck('offset feature', solve([[N,10],[N+2,14]]), [[-1.0,-1.0],[1.0,1.0]])\ncheck('constant column', solve([[1,5],[3,5]]), [[-1.0,0],[1.0,0]])\ncheck('singleton', solve([[N,N]]), [[0,0]])\ncheck('empty', solve([]), [])\ncheck('three points', solve([[0],[3],[6]]), [[-3/(6**0.5)],[0],[3/(6**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":"b682a43e8415ddbdbdc396267924a643481be7f182f3d553779cf4ece06c76d9","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(rows):\n    return [[(x-sum(r[j] for r in rows)/len(rows))/max(sum((r[j]-sum(q[j] for q in rows)/len(rows))**2 for r in rows)/len(rows),1) for j,x in enumerate(row)] for row in rows] if rows else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('population scale', solve([[0],[2]]), [[-1.0],[1.0]])\ncheck('offset feature', solve([[N,10],[N+2,14]]), [[-1.0,-1.0],[1.0,1.0]])\ncheck('constant column', solve([[1,5],[3,5]]), [[-1.0,0],[1.0,0]])\ncheck('singleton', solve([[N,N]]), [[0,0]])\ncheck('empty', solve([]), [])\ncheck('three points', solve([[0],[3],[6]]), [[-3/(6**0.5)],[0],[3/(6**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-variance-standardization","generated_at":"2026-09-30T16:48:24.023910+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 feature residual is divided by variance rather than standard deviation.","sha256":"c061b6b12edd61b311774e7daf25e17fe8c4b48c0a19204d9317ccb37ae70a14","title":"Feature standardization divides by variance · 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":29.782,"exit_code":1,"observations":[{"actual":[[-0.7071067811865475],[0.7071067811865475]],"check":"population scale","expected":[[-1.0],[1.0]],"passed":false},{"actual":[[-0.7071067811865475,-0.7071067811865475],[0.7071067811865475,0.7071067811865475]],"check":"offset feature","expected":[[-1.0,-1.0],[1.0,1.0]],"passed":false},{"actual":[[-0.7071067811865475,0.0],[0.7071067811865475,0.0]],"check":"constant column","expected":[[-1.0,0],[1.0,0]],"passed":false},{"actual":[[0.0,0.0]],"check":"singleton","expected":[[0,0]],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[[-1.0],[0.0],[1.0]],"check":"three points","expected":[[-1.2247448713915892],[0],[1.2247448713915892]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"population scale\", \"actual\": [[-0.7071067811865475], [0.7071067811865475]], \"expected\": [[-1.0], [1.0]], \"passed\": false}, {\"check\": \"offset feature\", \"actual\": [[-0.7071067811865475, -0.7071067811865475], [0.7071067811865475, 0.7071067811865475]], \"expected\": [[-1.0, -1.0], [1.0, 1.0]], \"passed\": false}, {\"check\": \"constant column\", \"actual\": [[-0.7071067811865475, 0.0], [0.7071067811865475, 0.0]], \"expected\": [[-1.0, 0], [1.0, 0]], \"passed\": false}, {\"check\": \"singleton\", \"actual\": [[0.0, 0.0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"three points\", \"actual\": [[-1.0], [0.0], [1.0]], \"expected\": [[-1.2247448713915892], [0], [1.2247448713915892]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.171,"exit_code":1,"observations":[{"actual":[[-1.0],[1.0]],"check":"population scale","expected":[[-1.0],[1.0]],"passed":true},{"actual":[[-1.0,-0.5],[1.0,0.5]],"check":"offset feature","expected":[[-1.0,-1.0],[1.0,1.0]],"passed":false},{"actual":[[-1.0,0.0],[1.0,0.0]],"check":"constant column","expected":[[-1.0,0],[1.0,0]],"passed":true},{"actual":[[0.0,0.0]],"check":"singleton","expected":[[0,0]],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[[-0.5],[0.0],[0.5]],"check":"three points","expected":[[-1.2247448713915892],[0],[1.2247448713915892]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"population scale\", \"actual\": [[-1.0], [1.0]], \"expected\": [[-1.0], [1.0]], \"passed\": true}, {\"check\": \"offset feature\", \"actual\": [[-1.0, -0.5], [1.0, 0.5]], \"expected\": [[-1.0, -1.0], [1.0, 1.0]], \"passed\": false}, {\"check\": \"constant column\", \"actual\": [[-1.0, 0.0], [1.0, 0.0]], \"expected\": [[-1.0, 0], [1.0, 0]], \"passed\": true}, {\"check\": \"singleton\", \"actual\": [[0.0, 0.0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"three points\", \"actual\": [[-0.5], [0.0], [0.5]], \"expected\": [[-1.2247448713915892], [0], [1.2247448713915892]], \"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."}}