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

The annotations already declare that the call is read-only, idempotent, and non-destructive. The description then adds behavioral facts those annotations do not cover: a per-call price of $0.001 USDC, a payment rail (x402 on Solana), and an alternative HTTPS endpoint. That pricing and endpoint detail is exactly the kind of context the annotations omit. The description omits the return type, although that gap is small because the tool performs pure arithmetic.

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 tightly packed and front-loaded: it gives the definition and formula first, then the sample terms, then the range constraint, and finally the commercial and alternative-access details. Every sentence carries unique information, and none of it is repeated elsewhere.

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 pure function with no output schema, the definition supplies everything needed to call the tool correctly: the mathematical meaning, the valid range, and the access and cost model. The only real gap is the output size or type. For example, at n=100000 the result exceeds 32-bit range, so an agent may be unsure whether a 64-bit or a bigint value is returned.

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 meaning of n. It does so well: the formula shows what n represents, the sample terms 1, 6, 19, 44, and 85 let the agent sanity-check the result, and the description restates the 1..100000 domain. Only the numeric type is left to the schema.

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 definition names a specific mathematical object and the operation performed on it ('The nth octahedral number, n*(2n^2+1)/3'), along with the first five terms and a worked formula. This implicitly separates it from siblings such as octahedral_index or octahedral_sum, but those siblings are never named, so the agent must infer the distinction.

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: the stated domain 'n runs from 1 to 100000' tells the agent when the call is valid, but there is no guidance about when to choose this instead of octahedral_next, octahedral_index, or octahedral_sum. There are no exclusions, and no explanation of what happens outside the range is given.

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