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, and the description still adds real context: the 0 sentinel semantics, the input domain bound, and the pricing/metadata of a paid x402 call plus the HTTPS endpoint equivalent. The only omission is whether paid calls fail or charge on invalid input, which matters for an agent budgeting calls.

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 sentinel rule, then examples, then range and pricing/endpoint metadata — nothing is wasted. The example list is dense ('1 is 1, 2 is 4, 4 is 6, 28 is 11, and 5 is 0') and slightly terse in phrasing, but each pair earns its place by disambiguating the direction of the mapping.

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 no output schema, the description does its job by explaining the return value (a 1-based index, or 0 when n is absent) and the valid input domain. It is complete enough to call correctly; only the paid-call edge cases (invalid n, failure charging) are left unaddressed.

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 carries the full burden, and it does: it defines n's range (1–1,000,000) and pins the semantics through concrete value mappings including the 0 'not a term' case. That is materially more than the raw schema's minimum/maximum integers convey.

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/resource: the first index where Narayana's cow sequence equals n, with the 0 sentinel for non-terms. This clearly distinguishes it from the sibling sequence generators/accessors like cows_next, cows_sum, narayana_cows, and narayana_check. Worked examples (1→1, 2→4, 4→6, 28→11, 5→0) let an agent confirm the intended mapping without opening anything.

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?

It gives clear operational context: n runs from 1 to 1,000,000 and non-terms return 0, which tells the agent exactly when the tool applies and what an out-of-domain answer looks like. It stops short of naming alternatives (cows_next, narayana_cows) or an explicit when-not-to-use, so it is strong but not complete routing guidance.

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