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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, openWorld), and the description adds genuinely useful context the annotations do not: a $0.001 USDC per successful call charge via x402 on Solana, plus an equivalent HTTPS endpoint. The only gap is failure behavior (charge on invalid or out-of-range n).

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 predicate definition and contrasting examples are front-loaded in the first two sentences, with range, price, and the alternate endpoint trailing. No sentence is wasteful, though the range restatement duplicates the schema.

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?

With one parameter, no output schema, and full annotation coverage, an agent can call this correctly: it knows the input domain, that the result is a yes/no answer, the cost, and an HTTP fallback. Only error and out-of-range handling are unaddressed.

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 schema gives only a type and bounds. The description restates the 1..1,000,000,000,000 range already in the schema, but its examples do convey what n semantically is, partially compensating. Baseline 3 is appropriate.

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 gives a specific predicate ('Whether n is a Hamming number') and immediately defines it as 5-smooth, with positive and negative examples (1, 10, 30, 36 / 7, 14). It does not distinguish itself from the hamming_next, hamming_nth, or hamming_count siblings, 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?

Usage is only implied: this is a membership test, and the examples make that inference easy. There is no explicit statement of when to use this versus hamming_next or hamming_index, nor any note about what to do for out-of-range inputs.

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