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

Annotations already cover safety (readOnly, idempotent, non-destructive), and the description adds commercially meaningful facts annotations cannot express: a $0.001 USDC charge per successful call via x402 on Solana, plus an equivalent HTTPS endpoint for the same operation. It does not disclose failure behavior for out-of-range input, but the cost and transport disclosure is substantive.

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?

Four tight sentences: definition first, then the closed-form characterization, then examples, then domain and commercial terms. Every clause is load-bearing and the core purpose is front-loaded.

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 single-parameter pure function with no output schema, the description supplies definition, formula, sanity-check examples, input domain, price, and an alternate endpoint — enough to call it correctly. The only mild gap is that the return type (a positive integer) is implied rather than 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 description coverage is 0%, so the description carries the burden for the single parameter and does state its domain explicitly ('n runs from 1 to 1000000000000'), matching the schema's min/max. It also makes clear n is the integer whose unitary divisor count is computed, though it doesn't say anything about large-input performance.

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 mathematical definition (count of unitary divisors), reinforced by the formula 2^omega(n) and worked examples (7→2, 12→4, 30→8). This is far more than a restatement of the name, though it never explicitly distinguishes itself from near-neighbors like biunitary_count or unitary_sigma in the sibling list.

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?

There is no statement of when to use this tool versus alternatives, and no guidance on how it differs from related siblings such as biunitary_count, unitary_sigma, divisor_count, or unit_sum. The worked examples implicitly confirm the mathematical interpretation but provide no selection guidance.

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