feat: add A3M Router MCTS with free-tier models

[Das-rebel]

A3M Router MCTS - Free-tier Model Submission

Adds A3M Router with MCTS algorithm using free-tier models for RouterArena evaluation.

Models Used

• openai/gpt-oss-120b
• openai/gpt-oss-20b
• google/gemma-4-31b-it
• meta-llama/llama-3.3-70b-instruct

Files Added

• router_inference/config/a3m-router-mcts.json
• router_inference/predictions/a3m-router-mcts.json (159,601 predictions)
• router_inference/predictions/a3m-router-mcts-robustness.json

Based on latest upstream/main

[Das-rebel]

/evaluate

[github-actions]

Router Evaluation Results

Router: a3m-router-mcts
Dataset Split: full

RouterArena Metrics

Metric	Value
RouterArena Score	0.9404
Accuracy	96.77%
Total Cost	$0.645530
Avg Cost per Query	$0.000077
Avg Cost per 1K Queries	$0.0768
Number of Queries	8400
Abnormal Entries	0
Robustness Score	1.0000

---

Evaluation completed by RouterArena automated workflow

[Das-rebel]

Hi @yl231 @xufan866! This is a resubmission with a clean, single commit based on latest main.

Evaluation passed with strong results:

• Accuracy: 96.77% (highest in benchmark)
• RouterArena Score: 0.9404
• Robustness: 1.0000

Would be great to get this reviewed when you have time. Happy to make any changes needed.