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

Annotations already cover read-only/idempotent/non-destructive, so the description correctly spends its words elsewhere: per-call pricing ($0.001 USDC via x402 on Solana) and an alternate HTTPS endpoint. That billing and transport detail is exactly the kind of context annotations cannot convey; it only misses stating the return shape (presumably a single integer).

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?

Front-loaded with the definition, then examples, then constraints, then commercial details. Every element is useful (the pricing and endpoint matter for actually invoking the paid x402 service), though four illustrative examples are slightly more than strictly needed.

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, no-output-schema math tool, this covers semantics, edge behavior, domain limits, cost, and an alternate transport. The only gap is an explicit statement of the return value, which the examples make inferable but not stated.

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% (the n property has only numeric bounds, no description), so the description must carry semantics. It does: it explains that n is the lower bound queried against, restates the range 1..10^12, and the examples demonstrate the inclusive behavior when n is itself a Hamming number.

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?

States a precise verb+resource: 'The smallest Hamming number that is at least n'. The worked examples (7->8, 10->10) make the 'at least' semantics unambiguous and distinguish it from the sibling hamming_nth, which selects the nth Hamming number rather than the next one at or above a value.

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 examples effectively define the use case, and the stated domain (n from 1 to 10^12) signals the valid operating range. It does not explicitly name alternatives like hamming_nth or hamming_index for the agent to route between, so it stops just short of a 5.

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