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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive), so the description's job is to add operational context: it discloses the input ceiling (8192), the modulus reduction behavior, the large-value representation switch to a decimal string past 15 digits, and the $0.001 x402 payment plus an alternative HTTPS endpoint. That is meaningful detail beyond the annotations, though 'zero is rejected' is ambiguous about whether it means n=0, mod=0, or a zero result.

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?

Five short sentences, front-loaded with the mathematical definition before constraints, output format, and pricing. No sentence is filler; even the endpoint line carries actionable routing information.

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 two-parameter pure arithmetic function with no output schema, the description covers domain, modulus behavior, return-value formatting for large results, and payment mechanics. The gaps are the ambiguous 'zero is rejected' clause and the exact return type/format for small non-modular values.

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 carries the full burden. It partially compensates: it explains that `mod` is optional and 'reduces the term', and restates n's 0..8192 domain (which merely duplicates schema min/max). It does not clarify that `mod` is supplied as a digit string, what happens to the return type under modulus, or which parameter the zero rejection applies to.

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 states a specific verb and resource ('The nth Jacobsthal-Lucas number') and pins down the sequence by its seeds L0=2, L1=1 plus the recurrence, which cleanly separates it from the sibling `jacobsthal` and the various `jacobsthal_*` aggregate tools. It never explicitly names a sibling, so the differentiation is implicit through mathematical identity rather than routing language.

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 constraints are present (n bounded to 0..8192, optional modulus, zero rejected), but there is no statement of when to prefer this over `jacobsthal`, `jacobsthal_sum`, or `lucas`, and no prerequisites or exclusions. An agent can infer the domain from the math, but nothing routes it deliberately.

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