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

Annotations cover readOnly/idempotent/no-destruction, and the description adds genuinely useful context beyond them: the accepted domain n in [0,4096], rejection of zero modulus, the residue-bound invariant, and a per-call x402 USDC price plus an equivalent HTTPS endpoint. These payment and constraint disclosures are not derivable from annotations.

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 formula, then constraints, then pricing/endpoint. Sentences are short and largely earn their place, though the copy-pasted pricing/endpoint boilerplate is auxiliary to the core operation.

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?

With no output schema, the description usefully states the return invariant (residue smaller than modulus) and covers the full input domain plus the payment model. Adequate for an agent to call correctly; only the meaning of L(n) itself is left implicit.

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 compensate, and it does: it states n's range and that the modulus is a positive decimal integer with zero rejected. The zero-rejection is especially valuable since the schema pattern '^[0-9]{1,600}$' alone would accept 0. It doesn't clarify that n is an index into the Lucas sequence or the string-vs-integer representation nuance.

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?

The description opens with the explicit operation 'L(n) mod m', which is a specific compute verb and resource. It distinguishes itself from Lucas siblings (lucas, lucas_sum, lucas_index) by the mod component, though it never states that L(n) denotes a Lucas number, leaving a small inference gap.

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 and the n<=4096 constraint, but there is no explicit when-to-use guidance and no mention of when to pick this over lucas_sum or other *_mod siblings. The agent must infer applicability from the formula alone.

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