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

Annotations already declare readOnly, idempotent, non-destructive, open-world behavior, so the safety profile is covered. The description adds genuinely new behavioral context beyond that: a price of $0.001 USDC per successful call settled via x402 on Solana, the fact that only successful calls are charged, and an equivalent HTTPS endpoint. It does not describe latency or failure modes for out-of-range input beyond the n=0 rejection.

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 short sentences, front-loaded with the definition and edge cases, with the commercial/payment details compressed into one trailing clause. Nothing is redundant and no sentence is padding.

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, but the description fully specifies the return domain (0 or +/-1, with mu(1)=1), so the agent knows what comes back without one. For a one-parameter pure-math tool with annotations already covering safety, the addition of pricing and an alternate transport leaves nothing material missing.

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 the semantic load, and it largely does: it defines the domain by rejecting n = 0 and pins down mu(1) = 1, which are exactly the edge values an agent would otherwise guess wrong on. It does not mention the schema's upper bound of 10^12, so one boundary is left to the schema alone.

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?

Names the exact mathematical object (the Mobius function mu(n)) and defines it operationally: 0 if n has a squared prime factor, otherwise (-1)^k for k distinct primes. This is a specific verb+resource that separates it from the dozens of nearby number-theoretic siblings such as liouville, mertens, or squarefree, since the defining rule is spelled out rather than assumed.

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 implied by the definition – an agent that needs mu(n) knows this is the tool – and one boundary condition is stated ('n = 0 is rejected'). However, no sibling is named as the alternative (e.g. liouville for the closely related lambda(n), or mertens for prefix sums), and no guidance is given about when this is preferable to the HTTPS endpoint variant beyond the bare URL.

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