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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds non-obvious operational context: $0.001 USDC per successful call via x402 on Solana, and an equivalent HTTPS endpoint. That pricing and transport detail is exactly what an agent needs before invoking. It does not say what is returned on a miss, which keeps it from 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?

Two compact sentences front-load the semantics, then examples, then constraints and pricing — every element (including the HTTPS mirror) is information the caller needs for an x402-paid tool, with no filler.

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?

There is no output schema, so the description must convey the return value, and it does: a found/not-found determination plus the smallest index. The only gap is the exact shape/representation when the value is absent within the limit.

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 carries the burden. It does clarify that 'value' is searched against terms a(0)..a(limit) and that 'limit' bounds the search, but the stated range 0–100000 merely restates the schema's min/max, and the value ceiling (1e12) is unmentioned.

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 precise query: does a value occur in Recamán's sequence over a(0)..a(limit), and if so at what smallest index. That verb+resource framing is far more specific than the title. It does not explicitly separate itself from the sibling 'recaman' (presumably the sequence generator), so it falls short of a 5.

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 worked examples (2 → index 4; 4 not present by index 20) plus the 0–100000 limit range imply when the tool is useful, but there is no explicit 'use this instead of recaman when…' routing or statement about how large a limit to pick before a miss is conclusive.

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