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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false. The description adds useful context beyond that: pricing ($0.001 USDC per successful call via x402 on Solana) and an equivalent HTTPS endpoint. It does not cover failure behavior, rate limits, or wallet/auth setup, but it meaningfully supplements the annotations.

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 description front-loads the mathematical definition and then adds range, examples, pricing, and endpoint information compactly. It is appropriately sized for the tool, with only minor redundancy between the stated range and the schema's min/max.

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 deterministic one-parameter math tool with no output schema, the description covers the output definition, input range, illustrative examples, pricing, and HTTPS equivalent. That is enough for an agent to understand what is returned and how to invoke the paid endpoint.

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?

There is one required integer parameter, n, and the schema already supplies its type and range. The description repeats the range and gives illustrative bit values for 0, 2, and 4, plus the base-3 digit condition, which adds some semantic meaning. However, it does not add much invocation detail beyond the schema for this single simple parameter.

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 names a specific function and gives an exact predicate: it returns 1 when every base-3 digit of n is 0 or 1, and 0 when any digit is 2. That makes the computed resource clear. It does not explicitly distinguish itself from related siblings such as cantor_count or ternary_digit.

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 explicit when-to-use or when-not-to-use guidance, and no comparison to alternatives like cantor_count or ternary_digit. The mathematical definition implies what the tool computes, but an agent gets no routing guidance among the many number-theory siblings.

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