mathlas

by Archerkattri

Overview Schema Related Servers Score Discussions

Python

Local

Server Quality Checklist

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Latest release: v1.4.1
Disambiguation5/5
Each tool has a distinct purpose: different types of search (existing math, formal math, web directive), identification (constants, sequences, conjectured relations), verification (formal and numeric), and support (add finding, checklist, scaffold, program search). No two tools appear to do the same thing; descriptions clarify boundaries.
Naming Consistency4/5
Most tool names follow a verb_noun pattern (e.g., add_finding, identify_constant, search_existing_math). A few deviate: applicability_checklist (adjective_noun), conjecture_relation (noun_noun), funsearch (blend), and mapping_scaffold (gerund_noun). This is mostly consistent with minor exceptions that do not hinder understanding.
Tool Count5/5
With 12 tools, the server is well-scoped for a mathematical assistant. Each tool covers a necessary operation (search, identification, verification, support) without being excessive or sparse. The count feels appropriate for the domain.
Completeness5/5
The tool set covers the full workflow: searching for existing results (both natural language and formal), identifying unknowns (constants, sequences), conjecturing relations, verifying claims (formally and numerically), and applying results (checklist, scaffold). There are no obvious gaps; it provides a comprehensive surface for mathematical problem-solving.
Average 4.5/5 across 12 of 12 tools scored.
See the Tool Scores section below for per-tool breakdowns.
- No community issues in the last 6 months
- 23 commits in the last 12 weeks
- Last stable release on July 2, 2026
- No critical vulnerability alerts
- No high-severity vulnerability alerts
- No code scanning findings
- CI is passing
This repository is licensed under Apache 2.0.
This repository includes a README.md file.
No tool usage detected in the last 30 days. Usage tracking helps demonstrate server value.
Tip: use the "Try in Browser" feature on the server page to seed initial usage.
This repository includes a glama.json configuration file.
If you are the author, simply .
If the server belongs to an organization, first add glama.json to the root of your repository:
```
{
  "$schema": "https://glama.ai/mcp/schemas/server.json",
  "maintainers": [
    "your-github-username"
  ]
}
```
Then . Browse examples.
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How to sync the server with GitHub?

Servers are automatically synced at least once per day, but you can also sync manually at any time to instantly update the server profile.

To manually sync the server, click the "Sync Server" button in the MCP server admin interface.

How is the quality score calculated?

The overall quality score combines two components: Tool Definition Quality (70%) and Server Coherence (30%).

Tool Definition Quality measures how well each tool describes itself to AI agents. Every tool is scored 1–5 across six dimensions: Purpose Clarity (25%), Usage Guidelines (20%), Behavioral Transparency (20%), Parameter Semantics (15%), Conciseness & Structure (10%), and Contextual Completeness (10%). The server-level definition quality score is calculated as 60% mean TDQS + 40% minimum TDQS, so a single poorly described tool pulls the score down.

Server Coherence evaluates how well the tools work together as a set, scoring four dimensions equally: Disambiguation (can agents tell tools apart?), Naming Consistency, Tool Count Appropriateness, and Completeness (are there gaps in the tool surface?).

Tiers are derived from the overall score: A (≥3.5), B (≥3.0), C (≥2.0), D (≥1.0), F (<1.0). B and above is considered passing.

Tool Scores

Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint=true and idempotentHint=true, so the tool is safe and idempotent. The description adds that the tool decomposes statements into preconditions and conclusion for the agent to verify, disclosing that the tool outputs a checklist rather than performing verification itself.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two sentences with no extraneous information. The core action is front-loaded, followed by a concise usage instruction. Every sentence serves a clear purpose.
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?
Given that an output schema exists, the description does not need to explain return values. It covers purpose, usage context, and parameter semantics adequately for a simple tool with one parameter.
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%, and the description reiterates the parameter's meaning as 'the candidate result's statement text', adding no extra semantic context beyond what the schema already provides. Baseline of 3 is appropriate.
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?
The description clearly states the verb 'Decompose' and the resource 'candidate theorem's statement into atomic preconditions + conclusion'. It distinguishes the tool from siblings by specifying its role in checking applicability after search, before relying on a candidate, which sets it apart from search and verification tools.
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?
Explicitly says 'Use after search, before relying on any candidate,' providing clear when-to-use guidance. It does not explicitly mention alternatives or when not to use, but the context is sufficiently clear for an agent to select this tool appropriately.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint and idempotentHint. The description adds important behavioral traits: it produces a plan only, no web call is made, and the user must perform the search and feed results back via add_finding. This is valuable context beyond annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two sentences: first provides the core functionality and output structure; second gives usage guidance. No redundant words, front-loaded, every sentence earns its place.
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?
Given the existence of an output schema (not shown but present), the description adequately covers the tool's process, constraints (no web call), and integration with other tools (add_finding). Complete for a planning tool, though some might want more detail on output interpretation.
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?
Only one parameter 'problem' with schema description already present. The description adds minimal extra meaning ('Args: problem (description)'), which doesn't significantly enhance understanding beyond the schema. Schema coverage is 100%, so baseline 3 is appropriate.
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?
The description clearly states it provides a structured web-search plan, listing specific components (arXiv query strings, sub-fields, named results, other tools). It distinguishes itself by noting mathlas makes no web call and directs the user to use add_finding, differentiating it from sibling tools.
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?
States 'Use when the local index missed' which is a clear context for use. Does not explicitly list when not to use or alternatives beyond that, but the context is clear enough. Could be more explicit about exclusions.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations are neutral (no readOnly/destructive/idempotent hints). Description adds behavioral context: sandbox (no-network, timeout, rlimit), MAP-Elites DB storage, few-shot context retrieval. This goes beyond structured fields.
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?
Description is 4 sentences, well-structured, front-loaded with purpose. Could be slightly more concise but effectively communicates key workflow.
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?
Given complexity (7 params, 3 actions) and presence of output schema (not shown), description covers core workflow and returns. Might miss edge cases (e.g., error handling on invalid program_src), but sufficient for iterative evolution use case.
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 coverage is 100%, but description adds action-specific context (e.g., 'program_src — YOU write it', 'behavior — selects MAP-Elites cell'). Clarifies conditional parameters per action.
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?
Description clearly states tool is a sandboxed program-search harness with three explicit actions (evaluate, register, status) and problem IDs. Distinct from sibling tools like verify_formal or search_directive.
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?
Provides guidance 'Use to iteratively evolve programs — YOU are the generator, mathlas is the deterministic scorer.' Implicitly suggests when to use (evolution loop) and mentions sandbox constraints, but doesn't explicitly list when not to use or compare to siblings.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations indicate readOnlyHint and idempotentHint, which the description does not contradict. The description adds context that the tool builds a scaffold and does not make judgments, complementing the annotations without repeating them.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two concise sentences with no wasted words. The first sentence states the purpose; the second gives usage guidance. Well-structured and front-loaded.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool has an output schema, the description appropriately explains the output as 'structured questions + fill-in template.' It covers usage context and parameter roles, providing sufficient completeness for a two-parameter tool.
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 coverage is 100% with clear descriptions for both parameters. The description mentions the parameter names in context but adds minimal new meaning beyond what the schema already provides, so baseline 3 is appropriate.
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?
The description clearly states the tool builds a 'needs<->guarantees scaffold' with structured questions and a fill-in template. The verb 'build' and specific resource distinguish it from siblings like applicability_checklist and search tools.
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?
The description explicitly says 'Use when applicability is non-obvious' and clarifies the judging is done by the user. It provides clear context but does not explicitly mention when not to use or suggest alternatives, though the sibling list helps differentiate.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations indicate readOnly and idempotent; description adds algorithms used (PSLQ, CF), verification threshold (>=25 digits), and provenance status (conjectured). No contradictions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two efficient sentences, front-loaded with action and key information. Every sentence adds value without redundancy.
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?
Covers purpose, usage condition, algorithm, verification state, and parameter hints. Could mention potential for no results or runtime cost, but overall sufficient given output schema exists.
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 coverage is 100% but description adds useful context: 'MANY digits', 'cost grows fast' for max_terms, default values. Enhances understanding beyond schema.
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?
Clearly states the tool's purpose: finding conjectured relations via PSLQ and continued-fraction methods, with numerical verification but not proof. Usage condition 'when identify_constant returns UNIDENTIFIED' distinguishes it from sibling identify_constant.
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?
Explicitly states when to use: after identify_constant returns UNIDENTIFIED. Does not explicitly mention when not to use or alternatives, but context implies other sibling tools for different tasks.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior4/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations declare readOnlyHint and idempotentHint, which align with the description. The description adds value beyond annotations by detailing the index fusion method, optional corpus_dir behavior, and the effect of source_filter/source_weights (e.g., down-weighting hurts queries targeting that source). No contradictions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is concise (5 sentences) and efficiently structured: core purpose first, then usage guidance, then parameter explanations with examples. No redundant or irrelevant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the complexity (5 parameters, nested objects, output schema exists), the description covers all necessary aspects: index composition, usage pattern, parameter nuances, and follow-up tool. Output schema is present so return values need not be described.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema coverage is 100%, and the description adds significant context: explains omit for corpus_dir uses prebuilt index, provides example for source_filter, and notes important behavior about source_weights. This adds meaningful meaning beyond the schema.
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?
The description clearly states it finds existing theorems/results from the mathlas index, specifying the index composition (dense + BM25 + RRF, fused with web_added findings). It distinguishes itself from the sibling applicability_checklist by advising to use this tool first for 'does known math solve this?' and then follow up with applicability_checklist.
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?
The description explicitly tells when to use: 'Use FIRST for any does known math solve this? question.' It also provides follow-up guidance (applicability_checklist). While it doesn't explicitly state when not to use, it implies the primary use case clearly.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Disclosures beyond annotations: states 'REAL Lean 4 kernel (NO LLM)', rejects 'sorry'/'admit', promises honest results (never fake), lists three outcome categories with meaning. Annotations (readOnlyHint, idempotentHint) are consistent and description adds significant behavioral context.
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?
Description is front-loaded with 'Run the REAL Lean 4 kernel (NO LLM)', then clearly splits modes with examples and outcomes. Slightly long but every sentence serves a purpose; structured for quick parsing. Minor redundancy could be trimmed.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given tool complexity (two modes, multiple outcomes, constraints), description covers all aspects: parameter combinations, expected behavior, error handling, and guidance to use sibling tool. No gaps for agent invocation. Output schema presence implied but not needed due to description of outcomes.
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 coverage is 100% with descriptions, but description adds value by explaining the two usage modes, clarifying that 'proof' must be a Lean 4 proof of 'statement', and noting that omitting both 'lean' and 'proof' results in UNDETERMINED. Adds context not in schema.
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?
Description clearly states it runs the real Lean 4 kernel, distinguishes two modes (typecheck and proof-check), and emphasizes it never writes proofs. Specific verbs like 'typecheck', 'proof-check', and 'returns proof_status' make purpose unambiguous. Differentiates from sibling verify_numeric.
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?
Explicitly describes when to use each mode: pass 'lean' for typechecking, pass 'proof' for proof-checking. Advises to find declaration names first with search_formal_math. Explains how to handle REFUTED outcome. Does not explicitly exclude cases like using for numeric verification, but context implies alternatives.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
The description discloses important behavioral traits beyond annotations: it mentions provenance 'web_added', that BM25 is always used, that dense retrieval is optional if dense_vec is provided, and that no model is loaded by mathlas. This adds value beyond the annotations which only give readOnlyHint, destructiveHint, etc.
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 description is relatively concise, fitting the purpose and usage into one sentence. It is front-loaded with the main purpose. However, the technical details about dense_vec and BM25 could be slightly more structured, but overall it is efficient.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (5 parameters, 3 required, optional dense_vec, and outcome of immediate searchability), the description covers all essential aspects: purpose, when to use, parameter meanings, and behavioral consequences. The output schema presumably documents the return value, so the description is complete.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Parameters5/5
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 100%. The description adds meaning beyond the schema by clarifying each parameter: 'statement (the real text)', 'slogan (short natural-language denotation)', 'source (URL/arXiv/citation)', and explains dense_vec in detail (must match model, omit for BM25-only). This compensates fully for any ambiguity.
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?
The description clearly states the tool's purpose: 'Ingest a web-found result into the live mathlas corpus so search_existing_math returns it immediately'. It specifies the verb (ingest), resource (live corpus), and the effect (immediate searchability). This makes it distinct from sibling tools, which focus on searching or other operations.
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?
The description explicitly guides usage: 'Use after web-searching per search_directive.' This provides clear context for when to invoke the tool. It doesn't explicitly list when not to use, but the context implies it is for web-found results, and sibling tools cover other scenarios.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already indicate readOnly and idempotent. Description adds valuable behavioral details: PSLQ algorithm, 50+ digit reevaluation, honest UNIDENTIFIED output. No contradictions.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Single paragraph, front-loaded with purpose, then method, usage, and parameter hints. Every sentence adds value with no redundancy.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 2 params, 100% schema coverage, and detailed annotation, the description fully covers inputs, process, and output behavior (closed form or UNIDENTIFIED).
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 coverage is 100% (baseline 3). Description adds extra guidance: 'give many digits, >16' for value, and example constant names for basis, enhancing usability beyond schema.
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?
Explicitly states 'Identify a real number's closed form', with method details (PSLQ, closed-form search) and honesty condition. Clearly distinguishes from sibling 'identify_sequence' and other tools.
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?
Provides explicit when-to-use: 'Use when you have a numeric constant and want to know what it IS.' Does not explicitly state when not to use or mention alternatives, but context is clear enough.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Description adds behaviors beyond annotations: exact match, no fuzzy scoring, and honest UNDETERMINED if data absent. Annotations already indicate read-only and idempotent, which description aligns with.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two concise sentences: first states core behavior and constraints, second gives usage guidance and parameter summary. No redundant information.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the presence of an output schema, the description adequately covers purpose, usage, behavior, and parameter hints. It is complete for the tool's complexity.
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 coverage is 100%, but description adds the key constraint that terms should have >=4 integers and mentions default for max_results, providing extra context beyond the schema.
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?
The description clearly states the tool matches an integer sequence against a local OEIS copy using exact contiguous term-match. It distinguishes from sibling 'identify_constant' by focusing on sequences, and includes specific verbs and resources.
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?
Explicitly states when to use: when having >=4 integer terms wanting the named sequence. The condition of data file absence leading to UNDETERMINED is mentioned. Does not explicitly exclude alternatives, but the context is clear.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnlyHint, idempotentHint, openWorldHint. Description adds honest 'service unavailable' behavior and cached response labeling with age, providing rich behavioral context beyond annotations.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Compact description with no wasted words. Front-loads purpose, covers caching, usage context, and parameter details efficiently.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
For a tool with 3 parameters and an output schema, the description is comprehensive: explains caching, service availability, usage scenario, and all parameters. No gaps.
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 coverage is 100%, baseline 3. Description adds value by giving example patterns for query, default for k, and explanations for backend options, exceeding schema info.
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?
The description clearly states it finds mathlib declarations via Loogle/LeanSearch, specifying query types and services. It distinguishes itself from siblings as the 'ONE tool that itself calls the web', setting it apart clearly.
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?
Explicitly states when to use: 'when you need the formal Lean name/type of a result, e.g. before writing a verify_formal snippet'. Provides backend guidance but does not explicitly state when not to use it.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Behavior5/5
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already indicate readOnly and idempotent. The description adds key behavioral details: independent sympy re-evaluation, higher precision, 20-digit threshold, and 'airtight' nature. No contradiction.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Conciseness5/5
Is the description appropriately sized, front-loaded, and free of redundancy?
Two concise sentences plus an Args line, all front-loaded. No redundancy, every sentence adds value.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Completeness5/5
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Output schema exists, so return values need no explanation. Description covers purpose, method, prerequisites, and usage context. Complete for a numeric verification tool.
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 coverage is 100% with descriptions for both parameters. The description adds examples for closed_form and clarifies value as decimal string, enhancing understanding beyond schema.
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?
The description clearly states the verb 'verify' and the resource 'numeric claim', with precise method (sympy re-evaluation, >=20 digits). It distinguishes from siblings like 'verify_formal' and 'identify_constant' by focusing on numeric identity.
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?
Explicitly says 'Use BEFORE asserting any numeric identity', providing clear when-to-use guidance. However, no mention of when not to use or alternatives, but the context is sufficient.
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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