VibeMath demonstrates solid definition quality with complete input schemas, clear descriptions, and well-structured parameters. All 6 tools have explicit JSON Schema definitions with type constraints and enums. Descriptions are concise (50-150 chars) and action-oriented. However, output schemas are not documented in the tool definitions themselves, only inferred from implementation. Parameter descriptions are present but could be more prescriptive about use cases and dependencies. No tool annotations (readOnlyHint, destructiveHint) despite all tools being read-only. Error handling is minimal, no recovery guidance or actionable error messages visible in tool definitions.

• Add explicit output schema documentation to each tool definition. Example: 'Returns: {problem: Problem, events: SolutionEvent[], attempts: Attempt[], verifications: Verification[], methods: MethodFamily[], source_assertions: SourceAssertion[], replay: ReplayCandidate | null}'
• Add readOnlyHint: true to all 6 tool definitions in create-server.ts to signal to agents that these tools are safe to call without side effects.
• Enhance parameter descriptions with use-case guidance. E.g., 'verification: Filter by verification level. Use this to find only peer-reviewed or mechanically-verified problems when high confidence is required.'
• Rename 'export_low_hanging_fruit_handoff' to 'build_lhf_handoff' to clarify that it constructs a handoff object, not exports data to a file.
• Add error recovery hints to tool descriptions. E.g., 'If problem not found, try search_math_frontier() with a partial name or field filter.'