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

Annotations already declare readOnly, idempotent, and non-destructive, so the safety profile is covered. The description adds genuinely non-obvious behavior: the return format switches to a decimal string past 15 digits, and each successful call costs $0.001 USDC via x402 on Solana, plus an HTTPS fallback endpoint — all of which an agent needs before invoking.

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 and identity examples, then domain bounds, then output format, then payment/transport details — a sensible priority order with little waste. It reads as an efficient fact list rather than prose, but every sentence carries information.

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 correctly compensates by explaining that results are numeric until they exceed 15 digits, after which they become decimal strings. Combined with domain limits, pricing, and the HTTPS alternative, an agent has nearly everything needed to call and interpret the tool; only sibling disambiguation is missing.

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 carries the full burden and largely does: it defines n as permutation length (1..60) and k as ascent count (0..n-1), including the cross-parameter constraint the schema cannot express. Worked examples (A(4,1)=11, A(5,2)=66, A(n,0)=1) further anchor meaning, though individual parameters could be labeled more crisply.

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 verb and resource: 'The Eulerian number A(n, k), the number of permutations of n with k ascents,' which is precise and mathematical. It implicitly computes a single value, whereas siblings like eulerian_row/eulerian_poly produce rows or polynomials, but the definition never names those siblings so the agent must infer the distinction.

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?

Usable boundaries are stated ('k runs from 0 through n-1, n runs from 1 to 60'), which prevents invalid calls. However, there is no explicit guidance on when to use this tool versus eulerian_row, eulerian_poly, eulerian_sum, or eulerian_mod, 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.