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

Annotations already cover safety (readOnly, idempotent, non-destructive), so the description wisely spends its space on things annotations can't convey: big values past 15 digits are returned as decimal strings rather than floats, out-of-domain k returns 0 instead of erroring, and each call costs $0.001 USDC. The pricing and overflow-format disclosure are exactly the kind of context an agent needs before invoking.

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 covering definition, example, edge case, ranges, output format, price, and alternate endpoint with zero filler. Behavioral facts an agent needs before calling are front-loaded and the operational details (cost, URL) trail.

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 integer function with no output schema, the description supplies definition, domain, out-of-range semantics, and return formatting, which is nearly everything needed to invoke correctly. The remaining gap is sibling disambiguation against narayana_row and narayana_check.

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, and it largely does: it names both parameters, gives their domains (n from 1 to 60, k from 0 to 60), and defines the out-of-range behavior for k. It stops short of explaining the combinatorial meaning of k (peak position), so an agent still can't reason about which k to request without outside knowledge.

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 the exact computation ('The Narayana number N(n,k)') with a worked example N(5,3)=20, so an agent knows precisely what it returns. It does not, however, distinguish itself from close siblings like narayana_row, narayana_check, or narayana_cows, which an agent scanning the list could easily confuse it with.

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?

There is no explicit guidance on when to pick this over narayana_row (which presumably returns a full row) or narayana_check. The range and edge-case notes describe input behavior rather than tool-selection context, leaving the choice between siblings to inference.

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