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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive). Beyond that, the description discloses validation behavior (non-terms and leading zeros are rejected), a 600-digit input ceiling, and an x402 payment requirement with per-successful-call pricing plus an alternate HTTPS endpoint — genuinely useful operational context an agent cannot get from structured fields.

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 core definition, then the index anchors, then the failure conditions, then pricing/transport. Each sentence carries information. Slightly dense in a single block rather than separated, but no wasted content.

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 read-only math tool with no output schema, the description supplies the return semantics (the index n), the input domain, and the payment/transport details needed to actually call it. Only the format of the returned payload is left implicit, which is a small gap.

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% (the only field has just a pattern and maxLength), so the description must carry the load, and it does: value is a decimal integer, max 600 digits, no leading zeros, must be an actual Pentanacci term. That adds real meaning over the regex. Minor tension: the pattern ^[0-9]{1,600}$ would accept leading zeros, which the description says are rejected.

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 operation: the inverse of the Pentanacci sequence, returning the smallest index n such that P(n) = value. The concrete anchors ('0 is index 0, and 1 is index 4') make the mapping unambiguous. It doesn't explicitly contrast with the sibling 'pentanacci' (which presumably returns the term), but the verb+resource is specific enough to infer the split.

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?

Rejection conditions ('a number that is not a Pentanacci term, or a leading zero, is rejected') implicitly tell the agent the valid input domain. However, there is no explicit when-to-use statement or named alternative (e.g. use pentanacci to go index→term, this to go term→index). Usage must be inferred from the semantics.

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