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

Annotations already declare readOnlyHint, idempotentHint and destructiveHint=false, so the safety profile is covered. The description adds genuinely new operational context: a per-call price of $0.001 USDC via x402 on Solana and an equivalent HTTPS endpoint, both of which matter to an agent deciding whether to spend a call.

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 definition is front-loaded in the first clause, followed by examples, range, price and endpoint in a compact block with no filler sentences. The pricing and URL sentences are boilerplate but each carries decision-relevant information.

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 single-parameter, annotation-covered, no-output-schema math tool, the description supplies everything needed to call it correctly: what it computes, the valid domain, sample values and the cost of a call. Only the relation to the sibling sum variant is missing.

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 the parameter meaning, and it does: it anchors the index with concrete values (n=5 -> 24, n=9 -> 282, n=10 -> 500) which let an agent sanity-check its input and output. It restates the 0-80 bound already in the schema, but the worked values add real semantic content.

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 first sentence names a specific computed quantity (the number of plane partitions of n), so an agent knows exactly what value it returns. It does not, however, distinguish itself from the sibling plane_partition_sum, which an agent scanning the tool list would likely confuse with it.

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?

There is no guidance on when to pick this tool over plane_partition_sum or related partition tools (partition, overpartition, binary_partition). The domain constraint (n from 0 to 80) is stated, but that is a validity limit rather than a usage recommendation.

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