Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, closed-world), yet the description adds valuable behavioral context: results are bounded upper bounds and extrapolated estimates rather than exact values, finite spectral agreement does not prove isospectrality, damping is excluded, and execution is CPU/direct-only with 'no planner binding'. These caveats materially shape how an agent should trust and use the output.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Three dense sentences, front-loaded with the core operation before moving to caveats and execution profile. Every clause carries information, though the sentences are somewhat packed and the 'no planner binding' fragment is slightly terse relative to its importance.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

An output schema exists, so return-value documentation is unnecessary, yet the description still names the outputs (upper bounds, extrapolated estimates, optional frequencies/shapes) helpfully. Combined with the accuracy and execution caveats, it is nearly complete; only explicit usage/precondition guidance for a six-parameter numerical tool is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so the schema already documents modes, polygon, boundary, wave_speed, compare_polygon, and include_mode_shapes. The description reinforces the physical meaning of fixed/free boundary and the frequency/shape outputs but adds no syntax or constraint details beyond what the schema provides, so the baseline of 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb (compute), resource (ideal fixed/free membrane modes), scope (1–12), and method (bounded P1 finite elements) for a simple polygon in metres. No sibling tool in the list covers spectral geometry, so the naming as an acoustic/membrane solver plus the 'drum' framing makes its purpose unmistakable.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides interpretive context – fixed/free physical mappings, the isospectrality caveat, and 'no damping' – but never states when to call this tool versus another or what preconditions the caller must satisfy. Usage is implied by the physics framing rather than explicitly routed, which is adequate but leaves gaps.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.