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

Goes well beyond the annotations by disclosing the payment model ($0.001 USDC per successful call via x402), an alternate HTTPS endpoint, the return-type switch to a decimal string past 15 digits, and the zero-modulus rejection. These are material behaviors an agent could not derive from readOnlyHint/idempotentHint alone, and nothing contradicts them.

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 constraints, then payment details — a sensible ordering with little waste. The pricing/endpoint sentence is somewhat dense but genuinely decision-relevant, so it earns its place.

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 usefully states the return representation (integer vs decimal string past 15 digits) and the error case, plus cost and alternate transport. What remains unstated (exact response envelope, error code for zero modulus) is minor for a pure computation tool.

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 carry the load — and it does: n is explained via the recurrence, the 0–4096 range, and a worked example (T(10)=56), while mod is described as an optional reduction with a stated rejection rule for zero. Only the string-format nature of mod is left to the schema pattern.

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?

Opens with a specific verb+resource (the nth Tetranacci number) and defines the recurrence, so there is no ambiguity about the computation. It does not explicitly distinguish itself from nearby siblings like tetranacci_mod, tetranacci_step, or tetranacci_sum, though the mention of an optional modulus implicitly covers the mod variant.

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 constraints are given (n from 0 to 4096, modulus of zero rejected), which tells the agent when a call is valid. However, there is no explicit guidance on choosing this tool over tetranacci_mod/tetranacci_sum/tetranacci_index, so sibling routing is left to inference.

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