Rigid Sphere Scattering

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

The description discloses that this is an exact closed-form computation (no solver), lists the underlying rigid-sphere Neumann boundary condition, and notes the series is truncated past convergence with fidelity='exact'. This adds meaningful behavioral detail beyond the `readOnlyHint` annotation without contradicting it.

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?

The description is dense but front-loads the tool's purpose and key distinction from the BEM solver. The formula and return-field list add necessary detail, though the length is near the upper bound and could be trimmed slightly without losing value.

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?

The description covers the physical model, formula, and usage context well, and lists return fields. However, with no output schema, it leaves return field meanings like `band_pct`, `valid_range_ok`, and `escalate_to` unexplained, and does not clarify valid input ranges or the meaning of `a_m`.

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?

The description gives meaningful semantics for `ka` and `theta_deg`, including the forward-direction reference and 180° backscatter, and embeds them in the formula. However, `a_m` is entirely unexplained despite appearing in the input schema, leaving an important parameter ambiguous.

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 description clearly states the tool computes the exact rigid-sphere plane-wave scattering far-field form function via the Mie series, and explicitly distinguishes it as the closed-form twin to the BEM scattering solve. This makes its purpose and resource unambiguous and differentiates it from `acoustic_radiation_submit`.

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?

It explicitly names `acoustic_radiation_submit` as the BEM alternative and says the BEM scattered far field must land on this analytic result, making the validation/reference use case explicit. The 'NO solver' statement clarifies when not to use it as a numerical simulation.

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