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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), so the description correctly spends its words on non-obvious behavior: a $0.001 USDC per-call x402 payment on Solana and an equivalent HTTPS endpoint. The range bound and sample outputs also let an agent sanity-check results. It stops short of describing the return shape or failure/refund behavior on error.

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?

Three compact sentences: definition first, then calibration examples, then range/payment/endpoint. Every element is useful, though the range is stated twice (prose and schema) and the examples are slightly verbose.

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 pure math function with a read-only annotation set and no output schema, the description covers definition, valid domain, expected values, cost, and a fallback transport. An agent has everything needed to call it correctly.

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 must carry the load — and it does: 'n' is defined as the count of terms summed, bounded to 1–5000, with four concrete input/output pairs that pin down the meaning precisely. The bound repeats the schema's minimum/maximum, which is mildly redundant but reinforces it.

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 verb and resource — 'the sum of the first n octahedral numbers' — and the worked examples (n=1→1, n=3→26, n=10→2035) make the operation unambiguous. It does not, however, explicitly distinguish itself from the sibling octahedral/octahedral_next/octahedral_index tools, so an agent must infer that this is the cumulative-sum variant.

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 use this versus octahedral (single term), octahedral_next, or octahedral_index, despite those siblings existing. The only constraints given ('n runs from 1 to 5000' and the price) are preconditions, not usage routing.

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