Fix NameError, improve logging and UUID handling

Capture errors and stabilize LLM output

perf: optimize token usage and context window for K2 engine (10k context, 8k response)

chore: major reliability overhaul - added result_data storage, auto-migrations, and fixed JSON parsing

fix: align ReasoningTrace fields with database schema

fix: reliable ArXiv ID lookup and uniformized paper ID prefixes

fix: validate ScientificDocument schema with authors and document_type

fix: resolve UnboundLocalError for logger in AnalysisService

fix: automatic paper persistence, qdrant index fix, and JSON output hardening for K2 Think

docs: finalize architecture documentation and ensure exclusive K2 Think model integration

fix: resolve InFailedSqlTransaction by adding db.rollback() in background task and adding detailed error logging

fix: correct internal schema import in AnalysisService background task

fix: actually start background analysis task and implement process_analysis in AnalysisService

Initial clean backend deployment