CVP verified calculation capability
Exact n! for integers 0 ≤ n ≤ 5000 via BigInt arithmetic, with product expansion, digit count, and scientific notation for long integers.
Math Capability ID math.factorial version 1.0.2 CVP VERIFIED CURRENT Core
Definition
n! = n × (n − 1) × (n − 2) × … × 10! = 1n! = n × (n − 1)! (n ≥ 1)P(n,n) = n! (ordered arrangements of n distinct items)Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
n | Non-negative integer | — | input / output |
nInput | Share-URL alias for n | — | input |
value | Exact n! as a JSON number when it fits IEEE-754 safe integers; otherwise the exact decimal string | — | output |
digits | — | — | output |
expansion | — | — | output |
scientific | — | — | output |
max_n | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | integer |
exactness | exact |
algorithm | exact n! via successive integer product |
valid_domain | integer n ≥ 0 in the published bound |
singularity_policy | INVALID_INPUT for n < 0 (Γ is math.special) |
branch_policy | not applicable — integer domain |
tolerance | not applicable — exact integer identity |
convergence | not applicable — non-iterative Euclidean / combinatorial |
conditioning | not applicable — not a floating matrix |
rounding | none — BigInt / exact integer |
overflow | coded error or stringified BigInt when exceeding JSON number |
reproducibility | deterministic exact integer + Capability@Version |
independent_oracle | Evidence published cases (n! table) |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
5! = 120; 10! = 3,628,800; 100! has 158 digits; 5000! has 16,326 digits
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.
Human page, REST, and MCP share the same engine and calculation_version.
Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json
and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 5/5.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/factorial' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"n":0},"calculation_version":"1.0.2"}'{
"inputs": {
"n": 0
},
"calculation_version": "1.0.2"
}POST /api/v1/calc/factorial. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Human-readable sources plus CVP reference evidence classes.
Sources
Derived identities
Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Inspect, then execute. Same engine as REST and the human calculator.
curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: inspect_capability' \
-d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.factorial"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'curl -sS -X POST 'https://www.calculatorx.com/mcp' \
-H 'Content-Type: application/json' \
-H 'MCP-Protocol-Version: 2026-07-28' \
-H 'Mcp-Method: tools/call' \
-H 'Mcp-Name: execute_calculation' \
-d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.factorial","inputs":{"n":0},"calculation_version":"1.0.2"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.0.2) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.