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

Annotations already cover read-only, idempotent, non-destructive, and open-world, so the safety profile is settled. The description adds real behavioral context those annotations cannot convey: a per-call price ($0.001 USDC via x402 on Solana) and an equivalent HTTPS endpoint. It omits what the response actually looks like for a paid call (e.g., payment failure behavior).

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 computation, then bounds, then pricing and transport. The bounds sentence duplicates the schema, but the rest earns its place and there is no filler.

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?

One parameter and no output schema, yet two things an agent needs remain unresolved: the definition of t(n) and the shape of the return (two values? an object with weight and bit?). The pricing disclosure is a genuine plus, but the mathematical target stays under-specified.

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 meaning of n, and it only restates the bound ('n runs from 0 to 1000000') that the schema's minimum/maximum already encode. It never explains that n is the index into the sequence nor whether the range is inclusive.

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?

It names a concrete quantity ('the number of 1s in t(0) through t(n), and the bit t(n) itself'), which is more than a restatement of the title, but the notation 't(n)' is never defined — an agent must infer Thue-Morse from the tool name alone. It also does not distinguish itself from near-siblings like thue_sum, thue_prefix, or thue_morse, which plausibly compute overlapping quantities.

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 pick this over thue_sum/thue_prefix, and no exclusions. The only call-context information is the n range and the payment/transport details, which are operational facts rather than selection guidance.

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