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

Annotations already declare readOnly/idempotent/non-destructive, so the description's added value is the x402 pay-per-call pricing ($0.001 USDC per successful call on Solana) and the equivalent HTTPS endpoint — real operational context an agent cannot get from the annotations. It stops short of stating error behavior for out-of-range n or the exact return shape.

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, then the indexing convention, a worked example, the domain, and the pricing/endpoint — each sentence adds distinct information with no filler.

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 pure function whose result is fully determined by the stated formula, the description supplies domain, convention, example, and cost/access details. The only gap is what happens for invalid input and the concrete return type (integer 4 or -4), which an agent can infer but is not told.

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 carry the parameter meaning, and it does: it fixes the domain (n from 0 to 4096), pins the Fibonacci base cases (F0=0, F1=1) that determine the result, and gives a worked example (n=5 yields -4). Only the integer type is left to the schema.

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 gives the exact quantity computed (L(n)^2 - 5*F(n)^2), the closed form 4*(-1)^n, and the Fibonacci indexing convention, which unambiguously separates it from siblings like lucas, lucas_sum, and lucas_mod. It reads as a definition rather than a verb-led statement of what the tool returns, but the mathematical scope is unmistakable.

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 only implied: an agent must infer that this tool is the one to call when it needs the Lucas discriminant specifically. There is no explicit when-to-use/when-not guidance or named alternative among the many lucas_* siblings, though the cost and alternate HTTPS endpoint give useful operational context.

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