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Lingshu Solver

by io.github.genesis-plan
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verify

Check whether a claimed answer is actually correct — call this on any number you computed yourself before passing it downstream. verdict=verified means it is a certified real root; verdict=refuted_or_unverified means it is NOT, and nearestCertifiedRoot then carries the correct value so you can self-correct in the same turn. Deterministic and reproducible.

Input Schema

NameRequiredDescriptionDefault
equationYesA single equation containing an equals sign, e.g. "x^2 = 4".
candidateYesThe claimed answer: a number (single variable, default variable x), {variable:value} for multiple variables, or an array in variables order.
toleranceNoNeighbourhood radius (optional, default 1e-3) within which a matching certified root is searched.
variablesNoVariable names (required for multiple variables or array candidates), e.g. ["x","y"].

Schema Changelog

Changes observed during successful MCP inspections.

  1. Changed4 schema fields changed
    • changedInput schema / properties / candidate / description
      Previous value: -"声称的答案：数字（单变量，默认变量 x）、{变量:值}（多变量）、或按 variables 顺序的数组。"New value: +"The claimed answer: a number (single variable, default variable x), {variable:value} for multiple variables, or an array in variables order."
    • changedInput schema / properties / equation / description
      Previous value: -"含 \"=\" 的方程，如 \"x^2 = 4\"。"New value: +"A single equation containing an equals sign, e.g. \"x^2 = 4\"."
    • changedInput schema / properties / tolerance / description
      Previous value: -"邻域半径（可选，默认 1e-3），在该邻域内寻找匹配的认证根。"New value: +"Neighbourhood radius (optional, default 1e-3) within which a matching certified root is searched."
    • changedInput schema / properties / variables / description
      Previous value: -"变量名（多变量或数组候选时必填），如 [\"x\",\"y\"]。"New value: +"Variable names (required for multiple variables or array candidates), e.g. [\"x\",\"y\"]."
  2. First observed

TDQS

A4.1/5.0
Behavior4/5

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 names the verdict values (verified / refuted_or_unverified), explains what they mean, and exposes the self-correction field (nearestCertifiedRoot) and determinism. It does not describe tolerance behavior or any failure/error modes, which keeps it below a 5.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

One tight paragraph, front-loaded with the core action and followed by the outcome semantics an agent needs. Sentences are long but every clause (verdict meanings, nearestCertifiedRoot, determinism) earns its place; no filler.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

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 must explain return values, and it does explain verdict and nearestCertifiedRoot. Combined with 100% schema coverage on inputs, an agent has what it needs to call and interpret the tool, though tolerance semantics remain unexplained.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so every parameter including tolerance and variables is already documented in the schema. The description reinforces the 'claimed answer' intent but adds no format or syntax detail beyond what the schema provides. Baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Check whether a claimed answer is actually correct') in the first clause, and contrasts with the solving siblings (solve, poly_roots) by framing it as verification rather than computation. An agent can distinguish it from any sibling without opening a schema.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives explicit when-to-use guidance: 'call this on any number you computed yourself before passing it downstream.' That is a clear trigger condition. It does not name or exclude the alternative siblings (solve, poly_roots), so it stops short of full routing guidance.

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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