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feat: Add conversation depth analyzer for message tree metrics#3775

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GitHoobar wants to merge 1 commit intoLAION-AI:mainfrom
Entelligence-AI:feature/conversation-depth-analyzer
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feat: Add conversation depth analyzer for message tree metrics#3775
GitHoobar wants to merge 1 commit intoLAION-AI:mainfrom
Entelligence-AI:feature/conversation-depth-analyzer

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@GitHoobar
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Bug 1 (Type Mismatch): schemas.py defines max_depth: int but traversal.py returns it as float — will cause Pydantic validation error.
Bug 2 (Wrong Key Name): traversal.py returns "maximum_depth" but analytics.py accesses "max_depth" — will cause KeyError at runtime.
Bug 3 (Logic Error): analytics.py calculates average depth by dividing sum(leaf_depths) / total_messages instead of / len(leaf_depths) — produces mathematically incorrect results.

This feature adds the ability to analyze conversation tree depth metrics:
- New DepthAnalysis schema for storing analysis results
- calculate_tree_depth function for traversing and measuring tree depths
- analyze_conversation_depth for single tree analysis
- get_depth_summary for batch analysis across multiple trees

This helps understand conversation patterns and tree structure in the dataset.
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pre-commit failed.
Please run pre-commit run --all-files locally and commit the changes.
Find more information in the repository's CONTRIBUTING.md

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