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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false and openWorldHint, so the description is not expected to carry the safety profile. It adds genuinely useful operational context that annotations cannot express: each successful call costs $0.001 USDC via x402 on Solana, and the same computation is available over HTTPS. It doesn't state whether failed calls are charged.

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?

Front-loaded with the semantic definition, then range, then payment and transport details. Four compact clauses, though the HTTPS endpoint and price are commercial preamble, arguably essential for an x402 metered tool.

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 numeric tool with no output schema, the description supplies the definition, an index domain and concrete sample values, so an agent knows what to send and roughly what comes back (0 or 1). Only failure/payment-edge behavior is unaddressed, a minor gap at this complexity.

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 explain the single parameter, and it does: n is the bit index, it is the count whose bit parity is taken, and it must be 0..1000000. The examples t(0)=0, t(1)=1, t(2)=1 further pin down one-based versus zero-based indexing, a classic ambiguity.

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?

States a specific verb+resource: it returns the nth Thue-Morse bit and defines it as the parity of the 1-bits in n, with worked examples t(0)=0, t(1)=1, t(2)=1. That is enough to distinguish it from siblings from which it doesn't explicitly distinguish itself, such as thue_prefix, thue_sum and thue_weight, even though their names alone suggest they return other outputs.

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 use case is implicit: call this tool to get a single bit at index n, and 'n runs from 0 to 1000000' is stated. It never says when to prefer a sibling such as thue_prefix, which returns multiple bits, or what to do beyond the range, so there is context but no exclusions.

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