{"abstract":"Coordinate power pooling averages before applying sign.","category":"Embedding vector normalization","checks":6,"contract":"For equal-width vectors, return sign(mean)*sqrt(abs(mean)) per coordinate; empty input returns empty.","contract_signature":"vectors","evaluation_group":"embedding-signed-power-mean-pooling","failed_approach":"Taking the square root of absolute mean loses the sign of a negative pooled coordinate.","family":"w3-embedding-vector-normalization-coordinate-power-pooling","id":"FA-99421","implementations":{"attempt":{"sha256":"4bf5b6c93451e0037b5a30fe28be8fa5f2c2ce1a49eadc1d26e7bbd8a02ddaa7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(vectors):\n    return [abs(sum(v[j] for v in vectors)/len(vectors))**0.5 for j in range(len(vectors[0]))] if vectors else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('signed negative', solve([[-N],[-N]]), [-N**0.5])\ncheck('cancellation first', solve([[N],[-N]]), [0.0])\ncheck('nonzero mean', solve([[N],[3*N]]), [(2*N)**0.5])\ncheck('empty', solve([]), [])\ncheck('mixed coords', solve([[N,0],[3*N,-4*N]]), [(2*N)**0.5,-(2*N)**0.5])\ncheck('singleton', solve([[-N,N]]), [-N**0.5,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":"faabf0633fdd7a5471ef58f280d6bdf4c3efa488d7d45cfa339411da936438fe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(vectors):\n    return [sum((1 if v[j]>=0 else -1)*abs(v[j])**0.5 for v in vectors)/len(vectors) for j in range(len(vectors[0]))] if vectors else []\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('signed negative', solve([[-N],[-N]]), [-N**0.5])\ncheck('cancellation first', solve([[N],[-N]]), [0.0])\ncheck('nonzero mean', solve([[N],[3*N]]), [(2*N)**0.5])\ncheck('empty', solve([]), [])\ncheck('mixed coords', solve([[N,0],[3*N,-4*N]]), [(2*N)**0.5,-(2*N)**0.5])\ncheck('singleton', solve([[-N,N]]), [-N**0.5,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-coordinate-power-pooling","generated_at":"2026-09-30T16:48:24.023684+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":"Signed coordinate roots are computed on individual values, discarding cancellation semantics.","sha256":"cd5d604677a9ab927a62ca8c22a739864280d4508848c761549a224094281fa5","title":"Coordinate power pooling averages before applying sign · 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":29.453,"exit_code":1,"observations":[{"actual":[1.0],"check":"signed negative","expected":[-1.0],"passed":false},{"actual":[0.0],"check":"cancellation first","expected":[0.0],"passed":true},{"actual":[1.4142135623730951],"check":"nonzero mean","expected":[1.4142135623730951],"passed":true},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[1.4142135623730951,1.4142135623730951],"check":"mixed coords","expected":[1.4142135623730951,-1.4142135623730951],"passed":false},{"actual":[1.0,1.0],"check":"singleton","expected":[-1.0,1.0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"signed negative\", \"actual\": [1.0], \"expected\": [-1.0], \"passed\": false}, {\"check\": \"cancellation first\", \"actual\": [0.0], \"expected\": [0.0], \"passed\": true}, {\"check\": \"nonzero mean\", \"actual\": [1.4142135623730951], \"expected\": [1.4142135623730951], \"passed\": true}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"mixed coords\", \"actual\": [1.4142135623730951, 1.4142135623730951], \"expected\": [1.4142135623730951, -1.4142135623730951], \"passed\": false}, {\"check\": \"singleton\", \"actual\": [1.0, 1.0], \"expected\": [-1.0, 1.0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.412,"exit_code":1,"observations":[{"actual":[-1.0],"check":"signed negative","expected":[-1.0],"passed":true},{"actual":[0.0],"check":"cancellation first","expected":[0.0],"passed":true},{"actual":[1.3660254037844386],"check":"nonzero mean","expected":[1.4142135623730951],"passed":false},{"actual":[],"check":"empty","expected":[],"passed":true},{"actual":[1.3660254037844386,-1.0],"check":"mixed coords","expected":[1.4142135623730951,-1.4142135623730951],"passed":false},{"actual":[-1.0,1.0],"check":"singleton","expected":[-1.0,1.0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"signed negative\", \"actual\": [-1.0], \"expected\": [-1.0], \"passed\": true}, {\"check\": \"cancellation first\", \"actual\": [0.0], \"expected\": [0.0], \"passed\": true}, {\"check\": \"nonzero mean\", \"actual\": [1.3660254037844386], \"expected\": [1.4142135623730951], \"passed\": false}, {\"check\": \"empty\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"mixed coords\", \"actual\": [1.3660254037844386, -1.0], \"expected\": [1.4142135623730951, -1.4142135623730951], \"passed\": false}, {\"check\": \"singleton\", \"actual\": [-1.0, 1.0], \"expected\": [-1.0, 1.0], \"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."}}