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

Annotations already declare readOnly, idempotent, openWorld and non-destructive, so the safety profile is covered. The description adds genuinely non-obvious behavior: a $0.001 USDC per-call charge via x402 on Solana and an equivalent HTTPS endpoint, which materially affects how an agent should budget and route the call.

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?

Four short sentences: definition first, then concrete samples, then the valid domain, then access/pricing. Nothing is padded and the most decision-relevant fact (what the tool computes) is front-loaded.

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 one-parameter pure-math tool with no output schema, the description supplies the definition, examples, domain bound and payment/transport details, which is close to everything needed. The only gap is that the return representation (plain integer index?) is left implicit.

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 burden, and it does: it explains that k is a Golomb value and that the range is 1..5000, matching the schema's min/max. It stops short of stating the return value is the index n explicitly enough to be a full specification, but the examples fill that gap.

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 first sentence gives a precise mathematical definition: the smallest index n where Golomb a(n) = k, which unambiguously identifies this as the inverse of the Golomb sequence. It does not, however, name the sibling golomb/golomb_sum as the forward direction, so an agent must infer that relationship from the names alone.

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 worked examples ('index 1 holds 1, index 4 holds 3, index 6 holds 4') and the stated domain k = 1..5000 give strong implied guidance on when the tool applies. But there is no explicit statement of when to use golomb (forward) versus this inverse, and no mention of error behavior outside the range.

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