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

With no annotations provided, the description carries the full burden. It discloses several behavioral traits: alias resolution (k equals A, q_hex equals Q), parsing rules ('Hex A legally contains e; a decimal point is the float'), edge-case handling ('Empty on BOTH faces is REFUSED_EMPTY'), and boundaries ('Does not invent a third scalar. Does not ECDLP'). It doesn't describe the return value or success condition, but still provides substantive behavioral context.

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 description is compact and has no obvious fluff, but it is also cryptic and front-loads a fragment ('QC-021 Presented two-way affine pair') instead of a clear action sentence. Unpacked abbreviations and jargon (REFUSED_EMPTY, ECDLP, WINs) make it harder for an agent to parse quickly.

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?

There is no output schema or annotation, and the description leaves important questions unanswered: what does a successful verification return, what does REFUSED_EMPTY mean operationally, what does 'WINs as two faces' mean, and when should this tool be selected over verify_* or project_affine_key siblings? The tool is under-specified for reliable 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 100%, but the description adds significant meaning beyond it: it maps k and q_hex as alias labels, defines what counts as a private vs public face, gives parsing nuance for hexadecimal vs decimal, and explains co-presented CSV handling. This goes well beyond the schema's brief descriptions.

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 opens with a noun phrase ('Presented two-way affine pair') rather than an explicit verb. It gives details about the roles of A/k and Q/q_hex, but never clearly states what the tool does (e.g., checks correspondence, returns a status) beyond what the tool name implies. The purpose remains vague.

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?

There is no guidance on when to use this tool vs alternatives. It doesn't mention any sibling tool or exclusion condition. Usage is only implied by the tool name and the cryptic description.

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