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

Annotations already cover read-only, idempotent, non-destructive, and open-world behavior, so the description adds the non-obvious operational facts: a $0.001 USDC x402/Solana charge per successful call and an equivalent HTTPS endpoint. That payment requirement materially changes how an agent should invoke it. It does not describe the return value's type or failure modes, which keeps it below 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 definition, then examples, then domain, then price and endpoint — a sensible ordering with no filler. The five example pairs are slightly more than needed but they demonstrate the non-monotonic mapping that an agent cannot guess.

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 pure-math tool with annotations and no output schema, the description covers semantics, valid domain, cost, and transport. The only missing piece is what 'complexity' formally means (minimal count of 1s under +/*), which matters for a model unfamiliar with the term.

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%, so the description must carry the param; it does so by defining k as the target complexity and giving concrete input->output pairs (k=6 -> 7, k=12 -> 41). The stated range duplicates the schema's min/max but reinforces it. It never spells out the underlying 'integer complexity' definition, which is the one substantive gap.

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 precise verb+resource: the smallest positive integer of a given integer complexity, with worked examples showing the k -> value mapping. An agent can tell it is not complexity_max/complexity_sum/complexity_count, though those siblings are never named explicitly.

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 through the worked examples and the stated domain 'k runs from 1 to 19', but there is no explicit statement of when to prefer this over the sibling tools (complexity, complexity_max, complexity_sum, complexity_count). The agent must infer the distinction from the math alone.

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