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

With no annotations supplied, the description carries the full burden and does disclose the key trait: stateless, no side effects, plus a concrete return-shape contract. Gaps remain around failure behavior (what happens with non-square matrices or vectors that are not valid probability distributions) and what 'strict boundary verification' changes. Those are material for a calculation tool but secondary to the stateless/no-side-effects disclosure.

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 routing and return-shape facts are front-loaded and genuinely useful, but the text is dense with capitalized bracket tags, an inline JSON block, and promotional phrasing like 'high-order' and '(100% [ref:cell_id] rate)'. Several tokens could be trimmed without losing meaning.

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 two-parameter dispatcher with four operations, no output schema, and no annotations, the description supplies the operation set, the return shape, the side-effect profile, and the routing rule — enough to call it correctly. It stops short of explaining error modes and the semantics of 'strict', which is the main remaining hole.

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 description coverage is 100%, so every nested property already documents itself, which sets the baseline at 3. The description adds mapping value by linking each operation name to its purpose, but adds nothing about the 'strict' flag or how target_cells interacts with output_text. It neither compensates for nor undermines the schema.

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 names concrete operations (symbolic matrix solving, 1D Wasserstein distance, Shannon entropy gain, groundedness citation verification), which maps directly onto the four enum values, so an agent knows what the tool computes. It also distinguishes itself from a named sibling via the ROUTING sentence. It loses a point only because the bracketed '[PUBLIC READ - STATELESS CALCULATOR]' framing is noisier than a plain verb+resource statement.

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 ROUTING clause is explicit: use logic_analyze for stateless math/logic verification, and use causal_checkpoint for stateful session persistence. That is a real when-to-use rule with a named alternative. What is missing is when NOT to use it among the other 18 siblings (e.g., which tool handles groundedness checks that need stored cells).

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