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

Annotations already declare readOnly/idempotent/non-destructive, so the description doesn't need to restate safety; instead it adds the non-obvious cost model ($0.001 USDC per successful call via x402 on Solana) and an alternative HTTPS endpoint, which an agent cannot infer from annotations. It doesn't discuss overflow or output behavior, but the examples effectively cover the return shape.

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 definition is front-loaded with the semantic core, then the domain, then examples, then cost/endpoint. Slightly repetitive examples (two fifth powers) add demonstration value but the second could be trimmed.

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's examples do double duty by showing the return value as a flat 4-integer array. For a small pure-computation tool with two parameters, that is nearly everything an agent needs; only the array-ordering convention 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 coverage is 0%, so the description carries the load; it defines the exponent domain (0 to 64) and, more importantly, the worked examples reveal that the 4-element array is a row-major flattening ([1,1,0,1]^5 = [1,5,0,1]), which the bare schema does not make explicit. It omits the ±1,000,000 element bounds and never states the ordering in words.

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 operation (matrix exponentiation) on a precisely defined resource (2x2 integer matrix), which cleanly separates it from siblings sl2_mul, sl2_det, sl2_inv and sl2_trace. The worked examples make the operation unambiguous even before reading the schema.

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 implied by the math (raise this matrix to this exponent), but there is no explicit statement of when to pick this over matrix_ops or the other sl2_* siblings, and no prerequisites or exclusions are given.

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