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

readOnlyHint=true already tells the agent this is a safe read, so the description only needs to add context. It does add one meaningful behavioral trait — determinism plus a 'zero hallucination' claim, implying stable, reproducible output rather than generative variance — but the d^2 = 0 notation is unexplained jargon and there is no mention of return format, latency, or limits on input.

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?

Two sentences, front-loaded with the domain scope, and no filler prose. It is dense with unexplained acronyms and mathematical notation, which costs some clarity, but it wastes no space.

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, so the description carries the burden of explaining what a 'solve' returns — a CPA alignment table, a Middot classification, a chiastic structure? None of that is stated. For a multi-mode deterministic solver with three interacting parameters, an agent cannot predict the response shape or judge a correct invocation from this text alone.

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%, and the schema itself documents all three parameters including enumerated example values for 'pair' and action strings for 'action'. The description adds no syntax, constraints, or interplay guidance (e.g. whether 'query' overrides 'pair'/'action'), so the baseline 3 is appropriate.

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 a domain (CPA, Middot, chiastic folding) and asserts a deterministic solver, but never states operationally what the tool does with a query — it reads more like a marketing abstract than a verb+resource statement. It is clearly distinct from the icx_* knowledge-graph siblings, so there is no confusion risk, but the core action is left to inference from the name.

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 statement of when to use this versus alternatives, no prerequisites, and no exclusions. The presence of an 'ask' action inside the schema hints at a question-answering mode, but the description never explains when to pick that over cpa/middot/fold, nor when an agent should reach for this tool at all.

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