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

Annotations only assert readOnly/idempotent/no-side-effects, and the description adds far more: the mathematical theorems that produce proven_impossible, the multi-start L-BFGS + FEM shape-derivative method, 5-16 vertex design space, three-mesh reanalysis, uncertainty being estimates 'not rigorous bounds,' and that not_achieved is 'never an impossibility proof.' The stated 'ideal membrane only' assumption and resolution warnings are exactly the behavioral caveats an agent needs.

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?

Purpose is front-loaded and nearly every clause carries necessary information for a genuinely complex inverse-geometry tool, so the length is warranted. However, it is delivered as one dense run-on paragraph with no grouping, which costs some readability.

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?

Given an output schema already exists, the description need not restate return values, and instead goes beyond by explaining the epistemic status of each outcome (proof vs. bounded search), the idealization assumptions, and uncertainty limits. For a tool of this mathematical complexity, nothing an agent needs to call it correctly 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 coverage is 100% and the schema already defines tolerance_cents semantics ('success when |error| + uncertainty ≤ tolerance'), the 5-16 vertex range, and every other parameter. The description restates the vertex range and tolerance-based acceptance rather than adding new parameter meaning, so it sits at the documented baseline for full schema coverage.

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?

The first sentence states a precise verb and resource: 'design a polygonal drumhead whose lowest tones play requested frequency ratios,' with concrete examples (fifth, triad, pentatonic scale). It also implicitly distinguishes itself from the sibling hear_the_shape by naming it as the shared forward solver reused for verification, so an agent can separate the inverse-design tool from the analysis tool.

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?

Usage is implied rather than stated: the description clarifies the relationship to hear_the_shape (this tool designs, then reanalyses with the forward solver) but never gives an explicit 'use this when / use hear_the_shape instead when' rule or states prerequisites. It does define outcome conditions (proven_impossible vs. not_achieved), which helps set expectations but is not routing guidance.

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