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Lingshu Solver

by io.github.genesis-plan
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verify

Check whether a claimed answer is correct. Give the equation plus a candidate value (a number for a single variable, {variable:value} pairs, or an array in variable order); the same certified kernel runs in a neighbourhood around the candidate. If a matching certified root is found the result is verified together with the error box; otherwise it is refuted and the nearest certified root is returned, so the calling agent immediately sees the correct value. Deterministic, not an LLM, reproducible across calls. Free to use: pass honorPaid:true to declare personal or evaluation use.

Input Schema

TableJSON 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

A4.3/5.0
Behavior4/5

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

No annotations exist, so the description carries the full burden, and it does well: it discloses the certified-kernel neighbourhood search, determinism and reproducibility, the refutation branch returning the nearest certified root, and a pricing/usage declaration via honorPaid. It omits failure modes such as malformed equation or non-convergence behaviour.

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?

The core behaviour and input forms are front-loaded in the first two sentences, and every sentence carries information. It runs slightly long, with the honorPaid pricing clause appended as a trailing sentence that is easy to skim past.

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?

For a 4-parameter tool with no annotations and no output schema, the description covers both outcomes (verified with error box vs refuted with nearest certified root) so the agent knows what it will receive. It stops short of describing invalid-input or timeout behaviour, which is a minor gap.

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

Parameters4/5

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

Schema description coverage is 100%, so baseline is 3, but the description adds meaning beyond the schema by explaining that the candidate is evaluated within a neighbourhood of the supplied value ('the same certified kernel runs in a neighbourhood around the candidate'), which contextualises what tolerance actually does.

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 object ('Check whether a claimed answer is correct') and frames the tool as a verifier of a supplied candidate rather than a solver, which cleanly separates it from siblings solve and poly_roots. An agent can select it without opening the 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 clear context for use: supply an equation plus a candidate value, and the tool certifies or refutes it. It does not explicitly say when not to use it (e.g. use solve/poly_roots when no candidate exists), so routing to alternatives is left to inference.

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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