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

Beyond the readOnly/idempotent annotations, the description discloses the output encoding rule (values past 15 digits come back as a decimal string) and the payment/auth model ($0.001 USDC per successful call via x402 on Solana, plus an HTTPS alternative). That is real behavioral context an agent would otherwise not know, though failure modes beyond zero-rejection are not spelled out.

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 and examples before constraints, pricing, and the endpoint. Every sentence carries information, though the pricing/URL tail could be trimmed or split for scannability.

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 correctly supplies the return-format rule (decimal string past 15 digits), and annotations already cover safety and idempotency. Both parameters are addressed somewhere between schema and prose; only the ambiguity against lucas_mod keeps it from being fully self-sufficient.

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 load and largely succeeds: it defines what `n` indexes, its valid range and the fact zero is rejected, and explains that `mod` reduces the term. It does not explain why `mod` is a string with up to 600 digits, which is the one non-obvious schema trait left unaddressed.

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 names a specific resource (the nth Lucas number) and fully pins down the sequence with seeds L0=2, L1=1, the recurrence, and concrete examples (L5=11, L10=123). What it does not do is distinguish this from nearby siblings such as lucas_mod or lucas_sum, especially since this tool itself accepts a modulus.

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 stated (n from 0 to 4096, zero rejected, optional modulus reduces the term), so the agent knows when a call is valid. However there is no routing guidance against lucas_mod, lucas_index, or lucas_sum, and the presence of a `mod` parameter here makes the overlap with lucas_mod unaddressed.

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