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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It merely says 'perform computations' without stating whether the operation is read-only, what output to expect, or that the only supported operation is count_points. This leaves significant ambiguity for an agent deciding whether to call it.

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?

The description is a single sentence, front-loaded with the action and resource. It contains no filler or redundancy, earning a high conciseness score despite the 'etc.' being slightly lazy.

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?

With no output schema and no annotations, the description should clarify return values and limitations. It only gives a vague 'etc.' and doesn't explain what the result of 'curve point counting' looks like. The tool appears simple, but the missing return/behavior details leave the description incomplete.

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%—all three parameters (curve, field, operation) have clear descriptions. The tool description adds no parameter-specific meaning, so the baseline score of 3 applies per the rubric.

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 states the tool performs algebraic geometry computations, with a concrete example (curve point counting). This clearly identifies the resource domain and distinguishes it from sibling math tools (number theory, finite fields, representation theory). However, the verb 'perform' is generic and 'etc.' introduces vagueness.

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 by the domain name and description—this tool is for algebraic geometry problems—but there is no explicit guidance about when to use it versus siblings, nor any exclusions or prerequisites. The description relies on the user to infer fit from the tool name and example.

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

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

No annotations are provided, so the description must disclose behavioral traits. It indicates this is a computation/analysis tool, implying a read-only, non-destructive operation, but it does not explain what the output looks like, whether it can fail, or any side effects. This is minimal transparency.

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?

The description is a single short sentence and is front-loaded, but it is under-specific and generic. While it is not verbose, the words 'computations and analysis' do not add meaningful detail, making the brevity a drawback rather than a strength.

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?

With only two parameters and no output schema, the description still does not explain what the tool returns or how to interpret the result. It also lacks usage context. For a mathematical computation tool, an agent needs more context to rely on it correctly, so completeness is insufficient.

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?

The input schema provides 100% coverage with descriptions for both parameters, including an example for the required 'field' parameter and an enum with default for 'operation'. The description itself adds no parameter information beyond the schema, so the baseline of 3 applies.

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 'Perform finite field computations and analysis' identifies the domain (finite fields) and a generic verb, but it does not specify what kinds of computations or analyses are available. It is not a tautology, but it lacks the specificity needed to distinguish it from broader problem-solving tools, and it does not mention the actual operations (analyze, compute_structure) from the schema.

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 guidance on when to use this tool versus its siblings such as frontiermath_solve_problem or frontiermath_number_theory. The description does not state use cases, prerequisites, or exclusions, so an agent receives no help in selecting between alternatives.

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

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

No annotations are provided, so the description must carry the burden of behavioral disclosure. 'List' implies a read-only operation, but it does not explicitly state that it has no side effects or how it behaves regarding output size or pagination. The behavior is simple and mostly clear, but lacks explicit safety assurances.

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?

The description is a single concise sentence that front-loads the main action and resource. Every word earns its place, with no redundant or vague phrasing.

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?

For a zero-parameter listing tool with no output schema, this description fully conveys what the tool does: it lists all problems and their descriptions. It is complete for the tool's simplicity, covering the essential return content without over-specifying.

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?

The tool has zero parameters, so the schema coverage is vacuously 100% and the baseline is 4. The description does not need to explain parameters, and there is no ambiguity about inputs.

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 uses the specific verb 'List' with a clear resource ('all available FrontierMath problems') and specifies that descriptions are included. This clearly distinguishes it from sibling tools like frontiermath_solve_problem, which focuses on solving rather than listing.

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?

The description implies usage for enumerating available problems, but it does not explicitly state when to use this tool versus alternatives like the topic-specific tools or solve_problem. No explicit when-to-use or exclusions are provided, so guidance is only implied.

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

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

With no annotations, the description carries the full burden of disclosing behavior. It only states that computations are performed, omitting details about return format, side effects, or safety. For a pure computation tool, it does not confirm whether it is read-only or mention any prerequisites.

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?

The description is a single concise sentence, front-loaded with the verb 'Perform' and only includes essential clarifying examples. Every word earns its place, with no redundancy or fluff.

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?

The tool has no output schema and no annotations, so the description should explain return values and any constraints. It does not mention what the computation returns, how results are formatted, or any limitations on primeLimit. This leaves significant gaps for the agent.

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%, so the baseline is 3. The description adds context by naming the specific computation types (multiplicative orders, density) that map to the operation parameter, but it does not clarify primeLimit beyond its schema description. Thus, it provides modest added meaning.

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 clearly states the tool performs number theory computations, with specific examples (multiplicative orders, density calculations) that give concrete meaning. It distinguishes from sibling tools by naming a distinct mathematical subfield, though 'computations' remains somewhat broad.

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?

No guidance is provided for when to use this tool versus alternatives. The description does not mention any exclusions or reference sibling tools, leaving the agent to infer usage solely from the tool name and general description.

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

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

There are no annotations, so the description carries the full burden of behavioral disclosure. It only says 'perform computations' and does not mention what the tool returns, whether it has side effects, error behavior, or any other runtime characteristics. This is a significant gap for a computational tool.

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?

The description is a single, front-loaded sentence with no unnecessary words. It efficiently conveys the purpose, though 'etc.' is a minor filler and could have been replaced with more specificity.

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?

With no output schema and no annotations, the description is minimal and does not explain the return value, capabilities, or limitations. The tool name and schema provide structure, but the description lacks enough context for an agent to fully understand what 'representation theory computations' entails in practice.

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% (all three parameters have descriptions, including an enum for groupType), so the baseline is 3. The description does not add any extra meaning beyond the schema, but the schema already provides adequate parameter semantics.

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 clearly states the tool performs representation theory computations and gives examples (Coxeter groups, Braid groups), which distinguishes it from sibling math tools like algebraic geometry or number theory. It is a specific verb+resource but uses 'etc.' which adds slight vagueness, so it doesn't earn a 5.

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?

The description implies usage for representation theory tasks by naming the topic, but does not explicitly state when to use this tool over alternatives or exclude other cases. No alternatives or exclusions are mentioned, so it falls short of providing clear guidance.

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

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

With no annotations, the description must carry the full burden of behavioral disclosure. It only says 'solve' without stating what the tool returns (e.g., the solution), whether it is read-only, or any prerequisites. This is a significant gap for a compute tool.

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?

The description is one sentence and front-loaded with the verb, but it redundantly lists the IDs that are already in the schema enum. Still concise with no filler beyond that redundant list.

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?

For a tool with no output schema and no annotations, the description should at least mention what the tool returns (e.g., the solution). It only describes the action. Given the simple parameter, more context about output or workflow is needed.

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?

The input schema fully describes the single required parameter problemId with an enum of the same five IDs listed in the description. The description adds no semantic value beyond the schema, so 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 clearly states the tool solves specific FrontierMath problems by ID and even lists the valid IDs. This distinguishes it from sibling tools that are topic-specific or list problems.

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?

The description implies usage when a specific problem ID is already known, but it does not explicitly mention alternatives like using list_problems to find IDs or topic-specific tools. Clear context yet no exclusions or alternative names.

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

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

With no annotations, the description carries the transparency burden. It implies a read-only, safe operation ('Get documentation'), but doesn't disclose return format, potential size, or any caveats. For a simple help tool, this is adequate but not rich.

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?

The description is a single, clear sentence with no wasted words. It is front-loaded with the action and resource, earning a perfect score.

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?

For a help tool with no parameters and no output schema, the description is mostly complete. It could specify what kind of documentation (e.g., examples, return values) but is sufficient for the tool's simple purpose.

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?

There are no parameters, so the baseline of 4 applies. The description doesn't need to explain parameters, and it correctly omits them.

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 clearly states the action ('Get') and the resource ('comprehensive documentation for all frontiermath functions'). It distinguishes this tool from its siblings, which are math solvers, by focusing on documentation.

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?

The usage is implied by the tool's name and description: use it to obtain documentation for the other frontiermath tools. However, it does not explicitly state when to use it vs. alternatives or provide any exclusions.

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