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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), and the description adds genuinely new behavioral context the annotations cannot express: a per-call price, the x402/Solana payment rail, billing only on success, and an equivalent HTTPS endpoint. It does not describe output format or error modes, keeping it short of a 5.

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 and formula are front-loaded, examples are minimal but maximally informative, and the logistics (range, price, endpoint) are packed into two short trailing sentences. No sentence is wasted.

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 one-parameter pure-computation tool with no output schema, everything an agent needs to call it correctly is present: what it computes, indexing convention, valid domain, and cost. Only the return type/format is left implicit.

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 the most important part by establishing that n is zero-based (0th=0, 1st=2, 5th=30), which the schema's min/max alone cannot convey. It restates the range already in the schema rather than adding new detail there.

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 defines the exact mathematical object via its closed form (n*(n+1)) plus concrete example values, which unambiguously separates it from the many sequence siblings (polygonal, triangular-adjacent, etc.). An agent knows precisely what this returns without opening the schema.

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 valid domain (n from 0 to 10000000) and the cost model give useful preconditions, but there is no guidance on when to pick this over a sibling sequence tool, nor any note on failure behavior outside the range. Usage is implied rather than stated.

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