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

Annotations already cover readOnly, idempotent, non-destructive and open-world, so the safety bar is low. The description adds genuinely useful non-schema behavior: paid access at $0.001 USDC per successful call via x402 on Solana, plus an equivalent HTTPS endpoint, which matters for an agent's cost and fallback planning.

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 definition and recurrence, followed by worked examples, bounds, then access/pricing details. Dense but all sentences carry information; the recurrence notation is the only mildly costly part for an agent to parse.

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-integer, no-output-schema math tool this covers the definition, valid domain, sample values, and access cost. The only gap is that it never states the call returns a single integer F(n), which would close the loop on expected output.

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 parameter burden. It does name the range ('0 to 100000') and gives concrete sample outputs (F(1)=1, F(5)=3), which helps verify a call, but it never explicitly explains that the single parameter n is the index into the sequence, so it only partly compensates for the empty schema.

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?

Opens with a specific verb+resource: 'The nth Hofstadter female term', then defines it via the paired recurrence. It does not distinguish itself from near siblings such as hof_male, hof_pair, or hofstadter_f, which an agent scanning the tool list would plausibly confuse it with.

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?

Usage is implied by the domain statement ('n runs from 0 to 100000') and the pricing/transport note, so an agent knows the valid range and cost. There is no explicit statement of when to use this versus hof_male/hof_pair, nor any exclusion, leaving sibling routing to inference.

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