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

No annotations, so the description carries the full burden. It usefully discloses that state (variables, imports) persists across calls and that timeout caps at 300 seconds, but says nothing about error behavior, sandboxing, or how execution output is captured/returned.

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?

Four short lines, purpose front-loaded, with each remaining sentence adding a distinct operational fact (kernel source, state persistence, timeout cap). No filler or restated name text.

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?

No output schema exists, yet the description never describes what an execution returns (stdout, errors, result value), which is a meaningful gap for a code-execution tool. Kernel selection, persistence, and timeout behavior are covered, so the definition is workable but not complete.

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 0%, so the description must compensate, and it does for two of three params: kernel_id is explained as overriding the kernel established by select_backend, and timeout is defined in seconds with a max of 300. The 'code' param is left implicit but is self-evident from the tool purpose.

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+resource ('Execute Python code') and adds the key qualifier that it runs in the persistent solving kernel, which differentiates it from a one-shot execution. It references select_backend for kernel setup, but never contrasts itself with submit_code, so sibling distinction is only partial.

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?

Gives implied usage guidance: raise the timeout for long solver runs, and rely on state persisting across calls. However, it never says when to prefer this over submit_code or when to instead use python_interrupt/python_reset, so the caller must infer routing.

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 carries the full burden. It does disclose one meaningful trait — that state is preserved rather than discarded — but says nothing about what happens if nothing is running, whether interruption is cooperative, permissions, or the result of the call.

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?

A single front-loaded sentence with no filler; the verb and effect lead the reader immediately. It is efficient, though it is arguably too terse for the behavioral gaps it leaves.

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 one-parameter tool with no output schema and no annotations, the description covers purpose and one behavioral note. It omits how to target a specific kernel and what the caller observes after interrupting, leaving the agent to guess at invocation details.

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?

One parameter (kernel_id, nullable, default null) has 0% schema description coverage, and the description adds no meaning: it never explains what kernel_id identifies, that it is optional, or what the default targets. The 'solving kernel' phrasing hints at a default target but is not tied to the parameter.

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 ('interrupt') and resource ('running code in the solving kernel'), plus a scope qualifier ('state is preserved') that separates it from python_reset. It does not name siblings explicitly, so the differentiation is inferable rather than stated.

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 verb: call it when running code needs to be stopped without losing kernel state. There is no explicit guidance on when to prefer this over python_reset, nor any prerequisite or condition (e.g., only valid while execution is in flight).

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 behavioral burden. It usefully discloses that the created or reset kernel becomes the target of bare python_exec calls, but it does not mention that resetting may discard existing kernel state, nor does it explain the packages parameter's effect.

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 three short sentences with no wasted text. The main behavior is front-loaded, followed by the alternative tool guidance and the downstream effect on python_exec.

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 two-parameter, state-changing tool with no annotations, no output schema, and 0% schema description coverage, the description is incomplete. It covers purpose and one parameter but leaves packages undocumented and does not describe reset side effects or state loss.

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 0%, so the description must compensate for both parameters. It explains kernel_id's effect well by describing create-without vs reset-with, but it completely omits the packages parameter, leaving half the parameters undocumented.

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 gives a specific verb and resource, and it clearly distinguishes the two modes: no kernel_id creates a new kernel, while a provided kernel_id resets one. It also names the related sibling tool select_backend, so the tool's role is immediately identifiable.

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?

It explicitly says to prefer select_backend when solver packages are needed, which is useful routing guidance. The create-vs-reset condition is also clear, though the description does not explicitly state when not to use python_reset or what prerequisites exist.

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 behavioral disclosure. 'Check' implies a read-only operation, but it does not explicitly state that it is non-destructive, nor does it describe side effects, authorization needs, or rate limits. It only lists what is inspected, which is minimal 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.

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

A single, front-loaded sentence with no filler. It efficiently conveys the core purpose in one clause.

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 simple no-required-parameter tool with no output schema, the description gives an outline of what is returned (kernels, variables, packages). However, it omits usage context and parameter semantics, leaving gaps an agent must infer.

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 schema has 0% description coverage and the description never mentions the optional kernel_id parameter. It does not explain what the parameter does, when to supply it, or what the default behavior is when omitted.

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 a specific verb 'Check' and resource 'kernel state', and enumerates the inspected items (active kernels, variables, packages). It is clear but does not differentiate this tool from siblings like python_exec or python_interrupt.

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 when-to-use guidance is given. The description does not say when to prefer this over python_exec or python_interrupt, nor does it state any prerequisites like requiring an active kernel.

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 and delivers: persistent kernel lifetime, that re-invocation clears previous session state, that it returns modeling instructions, and that UNSAT is a legitimate terminal outcome. These are exactly the behavioral traits an agent needs and that the schema does not express.

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?

Front-loaded imperative first sentence, then setup behavior, then the backend list, then the workflow tail. The bulleted backend table is dense with information and every line earns its place; no filler.

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?

No output schema exists, but the description says what is returned (modeling instructions) and sketches the full three-stage workflow ending in submit_code. For a single-parameter entry-point tool, an agent has everything required to select and invoke it correctly.

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 0% and the single 'solver' parameter has no enum, so the description must supply the value domain — and it does, enumerating all six backends with a one-line semantic gloss each (e.g. 'z3: SMT — integers/reals/bitvectors, proofs, program verification'). It does not explicitly state that these strings are the accepted values of the solver argument, so the mapping is inferred rather than stated.

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?

Specific verb+resource: 'Start solving a constraint problem' and sets up a persistent IPython kernel preloaded with the backend solver library. It explicitly positions itself against siblings by naming the full workflow (python_exec to iterate, submit_code to finish), so an agent can place it without opening other schemas.

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?

Explicit when-to-use ('call this FIRST, once per problem'), re-use semantics ('Calling it again recycles the kernel for a new problem'), an escape hatch for uncertainty ('Unsure which backend fits? Read the resource mcp-solver://guide first'), and the follow-on tools. Nothing 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.

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

With no annotations, the description carries the full burden and does well: it discloses validation behavior (syntax-checked), the failure path, and what happens on success (stored and linked as a resource, server retains the last 50). It omits whether resubmission overwrites a prior submission and what an error response looks like.

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?

Three short sentences, front-loaded with the action and artifact, then the timing constraint, then the side effect. No filler and nothing repeated from the schema.

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 single-parameter submission tool with no annotations and no output schema, the description covers purpose, timing, validation, and persistence/retention. Remaining gaps (retry semantics, error format) are minor given the tool's simplicity.

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 0% and the schema itself only says 'code: string', so the description has to define the payload; it does so by specifying the code must be the final, verified, self-contained solver program. It stops short of stating language/format constraints, but the payload's required qualities are communicated.

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 (submit) plus the exact resource (the final, verified, self-contained solver program), which is distinct from the sibling execution/status tools. It does not explicitly name which sibling it is contrasted with, but the artifact it accepts is unambiguous.

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?

Gives explicit timing ('Call ONCE at the end'), an explicit prerequisite ('only after executing the program via python_exec and passing your verification'), and names the sibling tool involved. An agent cannot mistake when this should fire.

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