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

Annotations already declare this a read-only, idempotent, non-destructive operation, so the bar is lower. The description adds genuinely useful context beyond them: the per-call price ($0.001 USDC on Solana via x402) and an equivalent HTTPS endpoint, which matter for an agent deciding whether and how to call it.

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?

It is front-loaded with the definition and a concrete example, then adds bounds and payment details. Three sentences with essentially no filler, though the HTTPS/pricing sentence is somewhat ancillary to the computation itself.

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 pure, single-step computation with no output schema, the definition plus worked example sufficiently conveys the return value (a 4-element integer array). The bounds and payment model are disclosed; only error behavior is left implicit, which is minor for this operation.

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 the parameter meaning, and it does: it explains that each argument is a 4-element [a,b,c,d] encoding and demonstrates the ordering with a worked example ([1,1,0,1] x [1,0,1,1] = [2,1,1,1]). The integer range is restated from the schema rather than adding new information.

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 operation (matrix product) on a specific resource (two integer 2x2 matrices in [a,b,c,d] form). It is clearly distinguishable from siblings like sl2_det, sl2_trace, sl2_inv and sl2_pow, though it never names them explicitly.

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 purpose makes the 'when' largely self-evident (multiply two 2x2 matrices), but there is no explicit guidance on when to prefer this over sl2_pow, matrix_ops or poly_mul, and no stated preconditions beyond the entry bounds.

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