{"abstract":"Worker variances omit between-worker spread.","category":"Distributed training aggregation","checks":6,"contract":"Each worker supplies [count,sum,sumsq]; return the global population variance rounded to 12 decimals, or None when total count is zero.","contract_signature":"stats","evaluation_group":"w3-dta-distributed-variance","failed_approach":"Weighting local variances by worker count still omits the between-worker mean contribution.","family":"w3-distributed-training-aggregation-distributed-variance","id":"FA-99321","implementations":{"attempt":{"sha256":"a0c3e7827307832b5e5638f3744ac0f1734f5483c73ce6b205e7bb4b50ca22ae","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(stats):\n    n=sum(c for c,s,q in stats); return sum((q/c-(s/c)**2)*c for c,s,q in stats if c)/n if n else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('between-worker spread',solve([[1,0,0],[1,2,4]]),1)\ncheck('unequal workers with within variance',solve([[2,2*N,4*N*N],[1,5*N,25*N*N]]),round(38*N*N/9,12))\ncheck('one constant worker',solve([[N,3*N,9*N]]),0)\ncheck('empty',solve([]),None)\ncheck('zero observations',solve([[0,0,0]]),None)\ncheck('zero worker excluded',solve([[0,99*N,999*N],[1,N,N*N]]),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":"0624690b97f6c823a0f7ca71106e9651425762979aef416e3e29c937eb0d30bd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(stats):\n    return sum(q/c-(s/c)**2 for c,s,q in stats if c)/sum(1 for c,s,q in stats if c) if any(c for c,s,q in stats) else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('between-worker spread',solve([[1,0,0],[1,2,4]]),1)\ncheck('unequal workers with within variance',solve([[2,2*N,4*N*N],[1,5*N,25*N*N]]),round(38*N*N/9,12))\ncheck('one constant worker',solve([[N,3*N,9*N]]),0)\ncheck('empty',solve([]),None)\ncheck('zero observations',solve([[0,0,0]]),None)\ncheck('zero worker excluded',solve([[0,99*N,999*N],[1,N,N*N]]),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 already materialized Python values from a fixed toy collective; no transport, failure recovery, optimizer state, or real model behavior is represented. 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-distributed-training-aggregation-distributed-variance","generated_at":"2026-09-30T16:48:23.078722+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A toy distributed-training contract makes replica and shard contribution rules explicit without claiming framework compatibility or performance.","root_cause":"Averaging worker-local variances discards differences between their means.","sha256":"898f1dd8f17ee02c57e6e7392a0c64fdd5a2be492a3cb4794076b88d0ca59fb9","title":"Worker variances omit between-worker spread · 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":28.83,"exit_code":1,"observations":[{"actual":0.0,"check":"between-worker spread","expected":1,"passed":false},{"actual":0.6666666666666666,"check":"unequal workers with within variance","expected":4.222222222222,"passed":false},{"actual":0.0,"check":"one constant worker","expected":0,"passed":true},{"actual":null,"check":"empty","expected":null,"passed":true},{"actual":null,"check":"zero observations","expected":null,"passed":true},{"actual":0.0,"check":"zero worker excluded","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"between-worker spread\", \"actual\": 0.0, \"expected\": 1, \"passed\": false}, {\"check\": \"unequal workers with within variance\", \"actual\": 0.6666666666666666, \"expected\": 4.222222222222, \"passed\": false}, {\"check\": \"one constant worker\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"empty\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"zero observations\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"zero worker excluded\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.37,"exit_code":1,"observations":[{"actual":0.0,"check":"between-worker spread","expected":1,"passed":false},{"actual":0.5,"check":"unequal workers with within variance","expected":4.222222222222,"passed":false},{"actual":0.0,"check":"one constant worker","expected":0,"passed":true},{"actual":null,"check":"empty","expected":null,"passed":true},{"actual":null,"check":"zero observations","expected":null,"passed":true},{"actual":0.0,"check":"zero worker excluded","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"between-worker spread\", \"actual\": 0.0, \"expected\": 1, \"passed\": false}, {\"check\": \"unequal workers with within variance\", \"actual\": 0.5, \"expected\": 4.222222222222, \"passed\": false}, {\"check\": \"one constant worker\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"empty\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"zero observations\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"zero worker excluded\", \"actual\": 0.0, \"expected\": 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."}}