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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds genuinely new behavioral facts beyond them: a per-call price ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint. That payment/endpoint disclosure is exactly the kind of context annotations cannot carry.

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-loaded with the definition, then recurrence, then examples, then range and cost — every sentence carries information. The telegraphic style ('Odd n copies b(n-1)') is dense but not padded.

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-integer-input pure math tool with no output schema, the definition + recurrence + examples + range + price/endpoint covers everything an agent needs to decide and invoke correctly. Missing only an explicit statement of what shape the response takes.

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 coverage is 0%, so the description has to carry the meaning of 'n' itself, and it does: it defines n as the partition index, bounds it to 0–1000, and anchors it with worked values (b(0)=1, b(1)=1, b(4)=4, b(10)=14). Only the return-value wording ('b(n) is the answer') is left implicit.

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 ('the number of binary partitions of n, partitions into powers of two') and backs it with the full recurrence, so the agent knows exactly what is being computed. It does not, however, distinguish itself from the sibling binary_partition_sum, which an agent could easily confuse it with.

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?

The n range (0 to 1000) and the pricing model give implicit boundaries for when the call is valid and what it costs, but there is no explicit when-to-use/when-not guidance and no routing away from binary_partition_sum.

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