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

Annotations already declare readOnlyHint, idempotentHint, openWorldHint, and destructiveHint=false, so the description does not need to repeat safety guarantees. It adds valuable behavioral context by stating the x402/Solana payment model, the per-call price, and an alternate HTTPS endpoint, which an agent would not know from the schema alone.

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 description is front-loaded with the core operation, followed by concrete examples, the input range, and practical payment/access details. Every sentence earns its place and there is no wasted wording.

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 simple one-parameter mathematical function with no output schema, the description covers the operation, input domain, examples, and access mechanics. It could explicitly state that the return value is an integer Narayana cow number, but that is strongly implied by the wording and examples.

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 compensate. It states the valid range 'n runs from 1 to 1000000' and gives four worked examples mapping inputs to outputs, but the range is also present in the schema's minimum/maximum constraints, and it does not explicitly define n as a positive integer beyond those bounds.

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 first sentence gives a specific verb-like operation and resource: 'The smallest Narayana cow number that is at least n.' The word 'next' and the 'at least n' semantics distinguish it from sibling tools like cows_index, cows_sum, and narayana_cows, though it does not explicitly name those alternatives.

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 implied by the definition and examples: call this when you need the least Narayana cow number greater than or equal to a given n. However, it does not explicitly state when to choose this over cows_index, cows_sum, or narayana_cows, nor does it mention exclusions or prerequisites.

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