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

Annotations already establish that this is a safe, read-only, idempotent, non-destructive operation, so the description is not burdened with basic safety disclosure. It adds useful behavioral context beyond annotations: pricing, an HTTPS endpoint alternative, the valid input range, and the fact that a zero modulus is rejected. It does not discuss performance or output format in detail, but the examples cover the return concept.

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 front-loaded with the mathematical definition, then examples, then constraints, then operational details. It is appropriately sized for a two-parameter math function. The pricing and HTTPS endpoint sentences are useful but slightly operational; overall there is little waste.

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?

There is no output schema, so the description reasonably explains the return concept through the p(n) definition and examples. Both parameters are addressed: n via range and examples, mod via the reduction behavior and zero rejection. A mention of the exact return type (e.g., integer) would make it fully complete, but an agent can call the tool correctly from this description.

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 carry parameter meaning. It does this well for n by stating the 0–2000 range and giving p(0), p(5), and p(10) examples. For mod, it explains that an optional modulus reduces the count and that zero is rejected, though it does not restate the string-format detail already present in the schema pattern.

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 mathematical resource and algorithm: 'The number of integer partitions p(n), from the pentagonal recurrence.' It gives examples that make the meaning concrete. It does not differentiate itself from closely related siblings such as partition_distinct, partition_parts, partition_conjugate, or overpartition, so it falls 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 implied by the definition: call it to compute p(n). The description gives domain constraints (n from 0 to 2000) and a modulus behavior rule, but it does not say when to prefer this tool over partition_distinct, partition_parts, overpartition, or other partition-related siblings. No explicit exclusions or alternatives are named.

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