QC-005 HHL. n<=2 integer A and rational b,x. Checks A x = b exactly. Does not invert. Floats refused.
| Name | Required | Description | Default |
|---|---|---|---|
| b | Yes | right-hand side b as comma-separated rationals, one per row, e.g. 2,4 | |
| x | Yes | the presented solution x as comma-separated rationals, e.g. 1,2; the court checks A x = b exactly and never inverts | |
| matrix | Yes | integer matrix A, 1x1 or 2x2: rows separated by '|', entries by ',', e.g. 2,0|0,2 |
Changes observed during successful MCP inspections.
Input schema / properties / b / descriptionAdded value: +"right-hand side b as comma-separated rationals, one per row, e.g. 2,4"Input schema / properties / matrix / descriptionAdded value: +"integer matrix A, 1x1 or 2x2: rows separated by '|', entries by ',', e.g. 2,0|0,2"Input schema / properties / x / descriptionAdded value: +"the presented solution x as comma-separated rationals, e.g. 1,2; the court checks A x = b exactly and never inverts"Input schema / requiredPrevious value: -[]New value: +[
+ "b",
+ "matrix",
+ "x"
+]Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
With no annotations, the description carries the full burden and does meaningful work: it discloses that the check is exact, that the tool never inverts (so it verifies a presented solution rather than solving), that floats are refused, and that n<=2. It stops short of describing what a failed check returns or how errors surface, but the non-obvious behavioral traits are covered.
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?
Extremely compact and front-loaded, with the identifier first and constraints after; every fragment carries information. The telegraphic style edges toward cryptic, but there is no filler to cut.
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?
It covers input domain and the core operation, but with no output schema and no annotations it should say what a verification returns (pass/fail, witness, error on refusal). For a 3-parameter verifier the return contract is left unspecified, which is a real gap.
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 the schema already documents the format of b, x, and matrix in detail. The description only restates the type constraints (integer A, rational b/x), adding nothing beyond the schema. Baseline 3 is appropriate when the schema does the heavy lifting.
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?
States a specific verb and resource: it checks A x = b exactly for the HHL algorithm (QC-005). The 'HHL' tag does differentiate it from the many other verify_* quantum-algorithm siblings. However, the acronym is undocumented jargon, so an agent unfamiliar with HHL gets less differentiation value than a plain-language statement would give.
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?
Usage is implied and bounded: 'n<=2 integer A and rational b,x' along with 'Floats refused' tells the agent the accepted input domain, so it knows when the call is valid. But it never says when to reach for this tool versus a sibling verifier, nor names any alternative. Implied usage rather than explicit routing.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
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