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

Annotations already cover the safety profile (readOnly, idempotent, non-destructive, openWorld), so the description's job is incremental — and it delivers genuinely useful non-schema facts: a $0.001 per-successful-call price via x402 on Solana, and an equivalent HTTPS endpoint. That cost/access information is exactly the kind of context annotations cannot express. Purity of function is implied by the exact formula.

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-loads the mathematical definition, then examples, then the domain limit, then cost/endpoint. Every sentence contributes; the pricing sentence is slightly commercial in tone but is actionable operational information. Tight overall 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?

With a single undocumented parameter, no output schema, and a trivial return value, the definition-plus-examples is sufficient to call it correctly and predict the result. The one real gap is sibling disambiguation in a corpus dense with wythoff_* variants, which the description does not address.

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 must carry the parameter's meaning — and it does: n is the index, it runs 1 to 1,000,000 (matching the schema bounds), and four worked examples map inputs to outputs, making the semantics unambiguous. It stops short of 5 only because it doesn't discuss invalid input or why the upper bound exists.

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 verb-less but exact mathematical operation: 'the lower Wythoff number floor(n*phi)', and backs it with concrete input/output examples (n=1→1, n=2→3, n=5→8, n=10→16). An agent knows exactly what value comes back. It does not, however, distinguish itself from sibling tools like wythoff_upper, wythoff, or wythoff_pair, which is the only thing keeping it off a 5.

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?

The description defines the computation but never says when to pick this over wythoff_upper, wythoff, wythoff_pair, or wythoff_sum — all of which appear in the sibling list and would be easy to confuse. There are no exclusions or selection criteria; an agent must infer routing from the word 'lower' alone.

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