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

Annotations already declare readOnlyHint=true, idempotentHint=true, destructiveHint=false, and openWorldHint=true, so the safety profile is well covered. The description adds useful behavioral context beyond annotations: zero modulus is rejected, n is bounded to 0–4096, and the call costs $0.001 USDC via x402, plus an HTTPS alternative. It does not discuss failure modes beyond zero rejection, but it meaningfully supplements the 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?

The description is front-loaded with the core computation and constraints, followed by pricing and an alternate endpoint. Every sentence carries relevant information, though the HTTPS endpoint sentence is somewhat operational rather than purely descriptive.

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 supplies the key constraints, the relationship between input and output ('residue is smaller than the modulus'), pricing, and an alternate endpoint. The only minor gap is the exact return type/format, but annotations already cover the tool's safety profile and the core behavior is sufficiently described.

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?

With 0% schema description coverage, the description must compensate, and it does: it explains that n runs from 0 to 4096 and that mod is a positive decimal integer with zero rejected. It also states that the residue is smaller than the modulus, adding semantic meaning beyond the raw schema constraints. It could mention why mod is a string up to 600 digits, 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 computation: 'T(n) mod m for the Tetranacci sequence.' This clearly distinguishes the tool from related siblings such as tetranacci (which likely returns the full term) and tetranacci_sum. It does not explicitly name alternatives, but the verb/resource is precise.

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?

The description gives no guidance on when to use this tool versus alternatives like tetranacci, tetranacci_step, or the many other *_mod tools. It states the computation and constraints but provides no when/when-not context or sibling routing.

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