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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint and destructiveHint=false, so the safety profile is covered. The description adds genuinely useful non-schema context in '(cost: 1 credit)', but says nothing about the return value (boolean?), behavior on negative inputs, or how a string argument like '16' is handled despite the parameter accepting strings.

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?

A single sentence with an inline clarifying parenthetical and the credit cost appended. Nothing is redundant and the core meaning is front-loaded.

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 one-parameter predicate with full annotation coverage and full schema coverage, the description is nearly complete; the only meaningful gap is that with no output schema it does not say the result is a true/false answer, nor how edge cases (0, negatives, non-integer strings) are treated.

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% and the single parameter is fully documented as 'number to check, no unit, no default'. The description's parenthetical adds conceptual meaning to 'perfect square' but no syntax or input-handling detail beyond the schema, so the baseline 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 ('Checks') and a precise mathematical property, reinforced by the parenthetical definition 'the square of an integer'. It does not explicitly differentiate itself from adjacent predicate siblings such as is_prime or is_power, so it falls just short of a 5.

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 only implied by the name and the word 'Checks'; there is no statement of when to prefer this over is_power, is_prime, or a general calculate call, and no exclusions or prerequisites are given.

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