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

Annotations already declare readOnly/idempotent/non-destructive, and the description adds genuinely non-obvious behavior: values past 15 digits are returned as a decimal string, modulus behavior, zero rejection, and the paid x402 pricing model with an HTTPS fallback. That pricing and return-format disclosure is meaningfully beyond what the annotations carry.

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 numeric constraints, then return-format caveat, then the payment/endpoint details. Every sentence carries operational value and nothing is redundant.

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 steps in to explain the return format (decimal string past 15 digits) and the modulus-reduced result, plus pricing for the paid endpoint. All inputs are characterized, so an agent can call it correctly and predict the shape of the response.

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, and it largely does: it explains that 'mod' reduces the term, states the n range, and clarifies that zero is rejected — the latter a constraint not derivable from the schema (which permits n=0 and a '0' mod string). The rejection note is slightly ambiguous about which parameter it applies to, keeping this from a 5.

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 names a specific mathematical resource ('the nth Padovan number') and even supplies the defining recurrence (P0=P1=P2=1, term = two back + three back), so an agent knows exactly what is computed. It implicitly separates itself from siblings padovan_step/padovan_sum by being the single-term evaluator, though it never names those siblings explicitly.

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 through constraints ('n runs from 0 to 8192', 'zero is rejected'), which help an agent avoid invalid calls. There is no explicit guidance on when to prefer this over padovan_step or padovan_sum, so the agent must infer the distinction.

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