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

With no annotations, the description carries the full burden, and it delivers: it states the computation is total and deterministic ('closes for every A'), the discrete-log case returns NOT_KNOWN rather than MISS, x(Q) is public and never a private face, the court never backfills requested faces, and floats are refused. These are meaningful behavioral disclosures beyond the bare 'projection' label.

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 information-dense but delivered as long run-on sentences with parenthetical asides ('scalar multiplication, total, no search'; 'not MISS, because nothing was graded'), making it harder to scan. It does front-load the core purpose, and every clause carries meaningful content, but structure could be improved with clear mode bullets.

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 complex 4-parameter tool with no output schema and no annotations, the description covers the mathematical semantics and the NOT_KNOWN boundary case well. But it never describes the actual return payload shape or error behavior for invalid inputs beyond floats refused, and it leaves the Q/q_hex relationship implicit, so an agent may not know exactly what response to expect.

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%, but the description explains A as the private face, k as accepted for the same face, q_hex as the public-face input, and Q as the computed/public affine projection. It also specifies decimal/64-hex for A and the general decimal-or-hex string rule. However, the exact relationship between Q and q_hex and the precise accepted encoding for q_hex (e.g., compressed/uncompressed) remain ambiguous.

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 'Affine key projection on secp256k1' then enumerates three concrete behaviors: scalar multiplication from the private face, bond verification when both faces are posted, and discrete-log rejection when only the public face is posted. This is a specific verb+resource with explicit input modes, so an agent can distinguish it from unrelated siblings like verify_grover or noaa_goes_r_weather.

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?

It gives clear conditions for how to use the tool: post A alone, post A and q_hex, or post q_hex alone, with a precise explanation of what will happen in each case. It does not name alternative tools to use instead, but the input-mode guidance is explicit enough to route invocation.

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