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

Annotations already cover read-only, idempotent, non-destructive behavior, and the description adds real value beyond them: the valid domain of n (0–100000), a per-successful-call price of $0.001 USDC via x402 on Solana, and an equivalent HTTPS endpoint. It does not describe what happens on an out-of-range n, which is the one behavioral gap.

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 mathematical definition is front-loaded in the first sentence, examples follow as compact confirmation, then boundary and payment details. Every sentence carries information, with the possible exception of the fully redundant range restatement already present in the schema's minimum/maximum.

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 single-parameter deterministic math tool with no output schema, this is complete: the operation is defined rigorously, the domain is bounded, the return value is demonstrated by example (a count), and payment/auth requirements are disclosed. An agent has everything needed to call it correctly.

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?

With schema description coverage at 0%, the description must carry the meaning of n, and it does: n is the integer whose two-cube representation count is returned, cubes must be positive (so 0 is not a cube in this context), and the range is 0–100000. Only the range part repeats the schema's min/max; the definition of the counting rule is genuine added meaning.

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 the exact computation: counting representations of n as a sum of two positive cubes with order ignored and equal cubes allowed. The worked examples (2→1, 9→1, 91→1, 1729→2) pin down the semantics precisely. It does not, however, distinguish itself from near-neighbors in the sibling list such as taxicab, taxicab_count, cube_ways, or cube_sum.

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: an agent can infer this is the tool for a two-cube representation count, and the examples show valid inputs. There is no explicit when-to-use statement, no exclusions, and no routing to overlapping siblings like taxicab or cube_ways that could compute similar quantities.

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