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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, openWorld), so the description's extra value is real: it discloses the $0.001 USDC x402 payment per successful call and an equivalent HTTPS endpoint. It doesn't state failure behavior for invalid n or whether payment is charged on error, which keeps it 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?

Front-loaded with the operation and definition, followed by worked values, domain, then pricing/transport. Every sentence adds either semantics or operational facts; nothing 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?

For a single-parameter computational tool with no output schema, the description covers definition, domain, samples, cost, and an alternate transport. The only omission is an explicit statement that the result is a single integer term (and behavior for out-of-range n).

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 coverage is 0% with one property, so the description must carry the meaning of n - and it does, defining n as the index of the term, restating the 0..100000 bound, and anchoring values via G(0)=0, G(1)=1, G(10)=6. That is solid semantic anchoring beyond a bare integer.

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 (the nth Hofstadter G term) and gives the defining recurrence G(n) = n - G(G(n-1)) with base cases, which uniquely identifies this sequence among the many sibling Hofstadter tools (hof_q, hof_h, hof_female, hof_male). An agent can discriminate it without opening the schema.

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 supplies the valid domain (n from 0 to 100000) and the cost per call, which frames when it's callable, but it never says when to prefer this over sibling sequence tools or what to do if n is out of range. Usage is implied rather than guided.

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