Update BARouter submission

[zulk2002]

This PR updates the BARouter submission artifacts for RouterArena leaderboard evaluation.
BARouter is a budget-adaptive, cost-aware router. For this submission, the router selects among:

google/gemini-3.1-flash-lite
deepseek/deepseek-v4-flash
deepseek/deepseek-v4-pro

The submitted artifacts contain the final routing decisions and generated outputs. No local predictor artifacts or training files are included.

[zulk2002]

/evaluate

[zulk2002]

/evaluate

[github-actions]

Router Evaluation Results

Router: BARouter
Dataset Split: full

RouterArena Metrics

Metric	Value
RouterArena Score	0.7375
Accuracy	75.33%
Total Cost	$2.444208
Avg Cost per Query	$0.000291
Avg Cost per 1K Queries	$0.2910
Number of Queries	8400
Abnormal Entries	25
Robustness Score	0.8310

⚠️ 25 of 8400 queries (0.3%) had no valid generation (inference failed / empty answer) and were scored as incorrect (0). These queries still count toward the denominator, so accuracy and cost reflect the full query set. Please regenerate predictions for these queries and resubmit for a complete evaluation.

Optimality Metrics

Metric	Value
Opt.Sel (Optimal Selection)	0.7966
Opt.Cost (Cost Efficiency)	0.7207
Opt.Acc (Accuracy vs Optimal)	0.9245

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Evaluation completed by RouterArena automated workflow

[zulk2002]

/evaluate

[github-actions]

Router Evaluation Results

Router: BARouter
Dataset Split: full

RouterArena Metrics

Metric	Value
RouterArena Score	0.7379
Accuracy	75.72%
Total Cost	$3.058621
Avg Cost per Query	$0.000364
Avg Cost per 1K Queries	$0.3641
Number of Queries	8400
Abnormal Entries	21
Robustness Score	0.6881

⚠️ 21 of 8400 queries (0.3%) had no valid generation (inference failed / empty answer) and were scored as incorrect (0). These queries still count toward the denominator, so accuracy and cost reflect the full query set. Please regenerate predictions for these queries and resubmit for a complete evaluation.

Optimality Metrics

Metric	Value
Opt.Sel (Optimal Selection)	0.6441
Opt.Cost (Cost Efficiency)	0.6713
Opt.Acc (Accuracy vs Optimal)	0.9384

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Evaluation completed by RouterArena automated workflow