beam_modal

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 that there is no solver, that only up to 5 modes are supported per boundary, the material alternatives, and the accuracy domain of slender-beam theory. It does not state numeric limits (min slenderness ratio) for when the result becomes unreliable, so not a 5.

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?

Front-loads the identity and formula, then physical caveats, then return shape. Dense but nearly every clause earns its place; the formula and symbol-heavy phrasing make it slightly heavier than strictly necessary for an agent.

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 physics oracle with no output schema, the description compensates fully by listing the return object's fields and explaining the underlying model, units, and applicability limits. An agent has everything needed to call and interpret it.

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%, so the description must compensate, and it does: it enumerates all five valid `boundary` values (which the schema does not), explains `n_modes` (up to 5 each), the `youngs_gpa`+`density_kg_m3` vs `material` alternatives, and the bending direction tied to `height_mm` (I = width·height³/12). It adds little on the sheer `length_mm`/`width_mm`/`height_mm` units, but the physics context is strong.

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+resource+method: 'Exact Euler-Bernoulli natural frequencies of a uniform rectangular beam' and explicitly identifies itself as the closed-form modal oracle that fem_modal is gated against, cleanly separating it from that sibling.

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?

Establishes when this tool is appropriate (closed-form, no solver, slender beams) and when it is not ('thick beams need a Timoshenko correction'), and names the gating relationship to fem_modal. It does not spell out an explicit either/or selection rule with fem_modal, so it stops short of a 5.

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