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

Annotations already declare read-only, idempotent, non-destructive behavior; the description adds pricing ($0.001 per successful call), x402/Solana payment context, and an alternate HTTPS endpoint. It does not cover rate limits or error behavior, but the added payment/endpoint details are meaningful beyond annotations.

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 purpose and examples; price and endpoint follow. The sentence restating n/m bounds largely duplicates schema constraints, which keeps it from being maximally tight, but overall there is little waste.

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 math tool with no output schema, the description gives valid ranges, examples, pricing, and endpoint, but never states the return shape or defines a(n); an agent must infer the scalar integer result from examples. That leaves a real completeness gap.

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%, and the description only repeats the n/m bounds already present in the schema, plus examples that clarify n as the term index and m as the modulus. It does not define the underlying Narayana cow sequence or edge-case semantics.

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 that it computes Narayana's cow term a(n) modulo m and includes two worked examples, so the operation is unambiguous. However, it does not explicitly distinguish this from sibling modulo/sequence tools such as cows_index, cows_sum, or narayana_cows.

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?

No explicit when-to-use or when-not-to-use guidance is given; it lists bounds and examples but never routes the agent to or away from alternatives. The range limits imply valid inputs, not tool selection.

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