rigid_sphere_scattering

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

With no annotations, the description carries the full burden and does well: it discloses this is a closed-form analytic computation with 'NO solver', truncation 'past convergence', fidelity='exact', and the physical behavior of the backscatter limit. It also signals diagnostics surface via returned fields (valid_range_ok, warnings, escalate_to), though permission/auth or range-limit behavior is not spelled out.

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 purpose and the sibling relationship are front-loaded, but the large inline LaTeX Neumann-series formula does little to help an agent select or invoke the tool, and the prose is dense. The formula and physical-limit sentences occupy space that does not earn its place for tool-selection purposes.

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?

For a complex analytic physics tool with no output schema and no annotations, the description is fairly complete: it lists the returned fields, states the exactness/truncation guarantee, and exposes diagnostics like warnings and escalate_to. Minor gaps remain around valid ranges and the unexplained `a_m` input.

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 0% across 3 params, so the description must compensate. It explains `theta_deg` well (measured from the forward direction, 180° is backscatter) and implies `ka` is the size parameter, but `a_m` is only visible in the return list and never defined as an input, leaving one of three parameters unexplained.

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 states a specific verb+resource — computing the exact rigid-sphere plane-wave scattering far-field form function via the Mie series — and explicitly positions it as the closed-form twin the BEM solve (`acoustic_radiation_submit`, problem='scattering') is gated against. An agent can tell this apart from the solver-based sibling without opening either schema.

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 establishes the relationship to the BEM scattering solve ('the ... twin the ... BEM solve is gated against') and notes that 'A BEM scattered far field must land on |f∞(θ)|', which implies the verification use case. However, it never states when an agent should call this versus `acoustic_radiation_submit`, or any exclusions — the guidance is implied rather than explicit.

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