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

Annotations already establish that this is a read-only, idempotent, non-destructive operation. The description adds useful behavioral context beyond annotations: bit 0 is on the right, output is padded to exactly width bits, invalid widths are rejected, and calls have a stated x402/USDC price and HTTPS alternative.

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 core purpose and output format are front-loaded, and most details earn their place. Pricing and HTTPS endpoint information add length but are materially useful for invocation; the rejection sentence is slightly redundant with the preceding constraint.

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 simple two-parameter computation tool with no output schema and no parameter descriptions, the definition covers the essential output semantics, validation rule, and payment/access detail. It is complete enough to call correctly, though it could be slightly more explicit about the return type being a bit string.

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 parameter meaning. It explains both n and width semantically and gives the key constraint n < 2^width, but it does not clarify why n is a string or its arbitrary-precision encoding, leaving some schema-level nuance unexplained.

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 operation — returning the binary reflected Gray code of n written in exactly width bits — and includes output orientation. It is clear what the tool does, but it does not differentiate itself from sibling tools such as gray_encode, gray_decode, gray_flip, or gray_next.

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 description provides validity constraints for n and width, but does not say when to use this tool versus the many related Gray-code sibling tools. There are no explicit alternatives or when-not conditions to guide tool selection.

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