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

Annotations already cover read-only, idempotent, non-destructive, and open-world behavior. The description adds useful context: pricing ($0.001 USDC per successful call), x402/Solana payment context, an HTTPS alternative endpoint, and rejection behavior for invalid values. It does not mention rate limits or error response format, so it stops short of a 5.

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?

It is front-loaded with the core definition and examples, followed by validation, parameter format, then payment/access details. No redundant sentences; every part serves selection or correct invocation.

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 math tool with no output schema, the description supplies the return meaning ('smallest n'), input domain constraints, examples, cost, and alternate transport. An agent has enough information to decide whether and how to call it correctly.

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?

With one parameter and 0% schema description coverage, the description compensates by stating that value must be a decimal integer of at most 12 digits, that leading zeros are rejected, that non-Landau values are rejected, and by giving example mappings. It does not exhaustively define the accepted Landau value set, but it adds substantial domain meaning beyond the schema pattern.

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?

Defines the inverse of Landau's function precisely: it returns the smallest n such that g(n) equals value, with examples (1 is index 0, 6 is index 5). This clearly distinguishes it from sibling tools like landau, landau_mod, and landau_sum.

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 implies the use case by defining the inverse operation and states invalid inputs are rejected, but it never explicitly routes the agent between this and siblings such as landau or landau_sum. There is no explicit when-to-use/when-not guidance beyond the operation itself.

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