121 machine-proven math facts, plus 49 real-world claims with machine-checked arithmetic
Scored across 3 tools
The three tools have clearly distinct targets: checking claims in text, looking up machine-checked facts, and searching past P vs NP attempts. An agent can easily choose between checking a text, retrieving a library fact, or warning against known attempts.
All three names follow a consistent snake_case verb_noun pattern: check_claim, lookup_fact, search_attempts. There are no mixed conventions or vague standalone verbs.
Three tools is a tight, well-scoped surface for a claim-checking server, and each tool earns its place. There is no obvious redundancy or missing sibling operation that would justify adding more tools.
The surface covers the core lifecycle of checking claims, retrieving supporting facts, and warning about known P vs NP attempts. Minor gaps exist around explaining labels or browsing supported fact domains, but agents can work around these.
Find the claims in a text and check the ones plain code can: arithmetic (PROVEN or FALSIFIED), primes, unit conversions. A famous unsolved problem (P vs NP, the Riemann hypothesis) is OPEN. Anything else is NOT CHECKED, which never means false, with a next step.
| Name | Required | Description | Default |
|---|---|---|---|
| text | Yes | The sentence or answer to check, e.g. "2+2=5" |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnly/idempotent/non-destructive, so the bar is lower; the description still adds real value by defining the four verdict labels and warning that NOT CHECKED never means false. That is exactly the misuse it needs to prevent. It stops short of describing the actual response payload or what the 'next step' field contains.
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?
Two dense sentences, front-loaded with the action and immediately followed by the verdict taxonomy; no filler. The phrase 'with a next step' is cryptic and slightly undermines an otherwise tight statement.
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 one parameter and a read-only, idempotent profile covered by annotations, the main remaining burden is return semantics, which the description handles by naming all four verdicts. Since no output schema exists, the description should also sketch the response shape and explain the 'next step', which it does not.
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% with a single documented 'text' parameter, so the baseline is 3. The description contributes one useful nuance — that the input may contain multiple claims to be found — but adds no format or length guidance beyond the schema's maxLength.
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 (find and check) and resource (claims), and bounds the scope precisely: arithmetic, primes, unit conversions. The boundary 'the ones plain code can' implicitly separates it from lookup_fact, but no sibling is named, so sibling differentiation is left to inference.
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 scope statement implies when to use it (computable claims only) and the OPEN/NOT CHECKED outcomes imply when it won't answer. However, it never says 'for factual/world knowledge use lookup_fact' or any other explicit routing, leaving the agent to infer the alternative.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Search the library of machine-checked facts. Compact by default (claim start, label, receipt link); set detail true for the full wording.
| Name | Required | Description | Default |
|---|---|---|---|
| query | Yes | Words about the fact, e.g. "root theorem" | |
| detail | No | Full claim, what checked it and what is not proven | |
| max_results | No | How many matches, at most 25 |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare readOnly/idempotent/non-destructive/closed-world, so the bar is lower; the description adds real behavioral context by disclosing the compact-by-default response shape (claim start, label, receipt link) and what the full mode surfaces. It stops short of describing match ranking or result-count behavior beyond the schema's max_results.
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?
Two tight sentences with zero filler; the default behavior is front-loaded and the mode toggle follows immediately. Nothing repeats the schema verbatim.
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, the description usefully characterizes both return modes, which is the main gap it needed to fill. It is slightly incomplete on sibling routing (when this beats check_claim) and on what a 'receipt link' actually points to.
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 baseline is 3; the description earns a bump by explaining the practical consequence of the detail flag — compact versus full wording — which is more actionable than the schema's 'Full claim, what checked it and what is not proven'. It says nothing extra about query or max_results.
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: "Search the library of machine-checked facts" tells the agent exactly what corpus is being queried, which the name alone ('lookup_fact') does not. It does not, however, differentiate itself from siblings check_claim or search_attempts, so an agent must infer the boundary.
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 second sentence implies usage via the detail toggle (compact for scanning, detail for full wording), but there is no explicit statement of when to choose lookup_fact over check_claim or search_attempts, and no exclusions or prerequisites.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Search the list of past attempts at P vs NP. Rows are labeled SOURCED, GUESS or NOT TRACED. A match is a warning sign, never a verdict.
| Name | Required | Description | Default |
|---|---|---|---|
| query | Yes | Words about your idea, e.g. "linear programming TSP" | |
| max_results | No | How many matches, at most 25 |
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
Annotations already declare read-only, idempotent, non-destructive, closed-world behavior. The description adds useful context about result labels and the caution that matches are not verdicts, but it does not explain what SOURCED, GUESS, or NOT TRACED actually mean, so the added behavioral value is moderate.
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 only two sentences and is front-loaded with the core action. Both sentences earn their place: the first states the tool's purpose, and the second adds essential interpretive context about result labels and significance.
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 search tool with no output schema, the description should explain return values more fully. It names the row labels but does not define them or describe the shape of results, leaving a meaningful gap for an agent trying to interpret matches.
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%, so both the query and max_results parameters are fully documented in the schema. The description does not add syntax, formatting, or semantic detail beyond the structured fields, making the baseline score of 3 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 states a clear verb and resource: searching past attempts at P vs NP. It does not explicitly differentiate this tool from siblings check_claim or lookup_fact, so it falls short of 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 offers interpretive guidance ('a match is a warning sign, never a verdict') but does not say when to use this search versus check_claim or lookup_fact. There is no explicit when-to-use or when-not-to-use instruction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
Recent tool additions, removals, and schema changes observed during successful MCP inspections.
check_claimlookup_factsearch_attemptsDeterministic claim verification with receipts across ~60 domains. No model in the loop.
Cite the claim, not the paper: 5,033 assertions, each hash-verifiable against its source PDF
Deterministic signed verification of numeric & financial claims for AI agents & spreadsheets.
Architecture compiler for AI code. 11 tools, 92 actions, 872 Lean4 proofs, 100/100 self-cert.
Add one secure layer between your agents and this server.
