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

Annotations already declare readOnly, idempotent, non-destructive, openWorld. The description adds genuinely new behavioral facts: a per-call price of $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint. That is real value beyond structured fields, though it says nothing about response shape or failure behavior on invalid n.

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 predicate is front-loaded in the first sentence, examples follow immediately as evidence, then the domain, price, and alternate endpoint in tight sequence. No sentence is filler.

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-integer predicate tool with no output schema, the description covers what is computed, what in-range inputs look like, positive and negative examples, cost, and a transport alternative. That is sufficient for correct invocation.

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 coverage is 0%, so the description must carry meaning — and it does clarify that n is the integer whose divisors are examined and that it runs 1 to 2000, plus worked examples of the predicate's outcome. It adds little beyond duplicating the schema's min/max bounds, but it is enough to call the tool correctly with a single integer.

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?

States a specific decision problem (do the divisors of n partition into two equal-sum sets) and supports it with positive and negative examples (6, 12, 20, 945 vs 1, 10, 18). It does not distinguish itself from close siblings like zumkeller_count, zumkeller_half, zumkeller_odd, or zumkeller_subset, so an agent must infer the boundary.

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 domain of n (1 to 2000) is stated, which implicitly tells the agent when the tool is applicable, and the pricing line signals it is a paid call. However, there is no guidance on when to prefer the sibling variants (count, subset, half, odd) or what to do for n outside range, leaving the choice to inference.

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