Verified calculation capability

Ordinary factorial 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

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Definition

Definition: n! = n × (n − 1) × (n − 2) × … × 1
Zero: 0! = 1
Recurrence: n! = n × (n − 1)! (n ≥ 1)
Permutations: P(n,n) = n! (ordered arrangements of n distinct items)

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`n`	Non-negative integer. Share-URL alias: nInput	—	input / output
`nInput`	Share-URL alias for n (SSR and page hydrate accept both)	—	input
`value`	Exact n! as a JSON number when it fits IEEE-754 safe integers; otherwise the exact decimal string	—	output
`exact`	Exact decimal digits of n!	—	output
`digits`	—	—	output
`expansion`	—	—	output
`scientific`	—	—	output
`max_n`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

n is an integer satisfying 0 ≤ n ≤ 5000.
Ordinary (single) factorial only — not multifactorial and not the real Gamma function for non-integers.

Example

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

Open this example in the calculator

Trust

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.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
Assurance: Core
Declared partition coverage: PASS · 2/2 declared partitions (factorial, invalid-domain)
Calculation version: 1.0.2
Verification: 24/24 calculation tests · 8/8 legacy golden · 7/7 legacy boundary · 9/9 legacy property
Production surface contract: 3/3
Versions: Calculation 1.0.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-08.exact-integer-profile
Verification revision: 2026-09-08.exact-integer-profile · 19/19 property · digest b7065c58307c
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: Exact decimal-string identity vs Python math.factorial on the 23 published tabulated vectors (named 0,1,5,10,20,100,5000 plus 16 seeded n in 0–4999). 5000! is verified as the full 16,326-digit value and as SHA-256 of those ASCII digits. This is not a whole-domain proof beyond the published table.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 6/6 golden · 7/7 CVP boundary · 6/6 invalid · 19/19 property · 5/5 metamorphic · 23/23 O3 · 1/1 cross-interface · 1/1 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.2 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

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 3/3.

Tool id: factorial
Engine: factorial
REST: POST /api/v1/calc/factorial
MCP: execute_calculation with capability_id: "math.factorial"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.2)
Versioned output schema: Immutable pin (1.0.2)

References

Human-readable sources plus CVP reference evidence classes.

Sources

NIST Digital Library of Mathematical Functions, Chapter 5 — Gamma Function
NIST DLMF §5.4 — Special values and extrema
CalculatorX mathematical conventions — Domain 0 ≤ n ≤ 5000; exact BigInt n!

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

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"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.2) when reproducibility matters. Full protocol notes: MCP docs.