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

Annotations already declare readOnly, idempotent, non-destructive and openWorld, so the safety profile is covered. The description adds genuinely useful context outside the annotations: a per-call price ($0.001 USDC via x402 on Solana) and an alternate HTTPS endpoint, plus sample outputs that reveal the return is a small integer count. It does not cover edge behavior at n=1 or error conditions, so this is additive but not rich.

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?

Purpose is front-loaded in the first sentence, followed by examples, the valid range, pricing and an alternate endpoint — each element earns its place as operational context. Minor redundancy in restating the 1..20000 range already present in the schema.

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, no-output-schema tool the description covers what the tool computes, its domain, its cost, and an alternative transport. The remaining gap is that 'self number' is never defined, which matters for a specialized term an agent may not know; the sample values only partly substitute for a definition.

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 burden, and it partially does: 'how many self numbers are at most n' defines n as an inclusive upper bound, which the schema's bare integer does not. However, 'n runs from 1 to 20000' simply restates the schema's min/max, and no format or edge-case semantics are added beyond that, so it lands at baseline-plus rather than fully compensating.

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 and resource: counting self numbers up to a bound n. The cumulative 'at most n' framing distinguishes it from the sibling predicates (self_number, self_next, self_nth), though no sibling is named explicitly. An agent can infer it is a counting/cumulative tool rather than a membership test or nth-term lookup.

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?

No guidance on when to use this versus self_number, self_nth, self_next or self_seed, which occupy adjacent territory in the sibling list. The worked examples imply behavior but do not tell the agent which selection condition picks this tool over its neighbors.

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