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

Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower, yet the description adds genuinely non-schema information: a per-call price of $0.001 USDC via x402 on Solana and an alternate HTTPS endpoint. These are real operational facts an agent needs before calling a paid tool, though failure/refund behavior on a failed call is not stated.

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?

The mathematical definition is front-loaded, followed by a concrete example and then cost/transport details. Five short sentences, each carrying information; only the Catalan-sum remark is arguably decorative rather than operative.

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 one bounded integer parameter and no output schema, the description does the needed work by showing the exact return shape through the n = 4 example and disclosing payment and transport. The remaining gap is sibling differentiation among the narayana* tools, which would let an agent route confidently.

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 largely does: 'n runs from 1 to 60' plus the n = 4 example showing the row shape and the Catalan sum property. It stops short of explaining what happens at extremes (e.g., row length for large n) but the core semantics are covered.

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 mathematical object and its exact extent: 'Narayana numbers N(n,1) through N(n,n)', so an agent knows it returns a full row rather than a single term. It does not, however, distinguish itself from the sibling tools narayana, narayana_check, or narayana_cows, so the boundary is left to inference.

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 by the worked example (n = 4 yields 1, 6, 6, 1), with no statement of when to pick this over narayana (single value) or narayana_check. There are no exclusions, prerequisites, or alternative-routing guidance, so the agent must infer the choice from the name.

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