CVP verified calculation capability
Exact P(n,k) and C(n,k) for integers 0 ≤ k ≤ n ≤ 1000 via the multiplicative formula. Not a factorial product page.
Math Capability ID math.combinatorics version 1.0.3 CVP VERIFIED CURRENT Core
Permutation
P(n,k) = n! / (n − k)!C(n,k) = n! / (k!(n − k)!)P(n,k) = C(n,k) × k!Modes: combination · c · ncr · binomial · binomial coefficient · binomial-coefficient · permutation · p · npr · nPr · nCr
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
n | Population0 | — | input / output |
nInput | — | — | input |
k | Selection0 | — | input / output |
kInput | — | — | input |
symbol | — | — | output |
value | — | — | output |
digits | — | — | output |
max_n | — | — | output |
algorithm | — | — | output |
numeric_domain | — | — | output |
exactness | — | — | output |
numeric_backend | — | — | output |
work | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | integer |
exactness | exact |
algorithm | Exact BigInt multiplicative product for P(n,k), divide-at-each-step ratio for C(n,k) |
valid_domain | Distinct items without replacement;0<=k<=n<=1000, including C(0,0)=P(0,0)=1. Safe JSON integers or integer strings,4digits/512characters; matching n/nInput and k/kInput aliases. |
singularity_policy | Reject k>n, out-of-bound/negative/fractional inputs, unknown keys and modes, null values, conflicting aliases and raw nonzero-to-zero underflow. This product does not extend C(n,k)=0 for k>n. |
branch_policy | not applicable — integer domain |
tolerance | not applicable — exact integer identity |
convergence | not applicable — non-iterative Euclidean / combinatorial |
conditioning | Counts are discrete and exact for accepted normalized integers; there is no floating conditioning/measurement model. Above18digits, preview is explicitly approximate8-significant-digit rounding; complete exact counts and working are exported. |
rounding | none — BigInt / exact integer |
overflow | coded error or stringified BigInt when exceeding JSON number |
reproducibility | deterministic exact integer + Capability@Version |
independent_oracle | Independent CPython stdlib math.comb/math.perm full-pack comparison, exact equality; not an IUT-generated expected value. |
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.
mode=combination n=10 k=3 → 120
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes. 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/combinatorics' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"combination","n":10,"k":3},"calculation_version":"1.0.3"}'{
"inputs": {
"mode": "combination",
"n": 10,
"k": 3
},
"calculation_version": "1.0.3"
}POST /api/v1/calc/combinatorics. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Declared calculation modes for this capability.
combinationpermutationHuman-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · 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.combinatorics"},"_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.combinatorics","inputs":{"mode":"combination","n":10,"k":3},"calculation_version":"1.0.3"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.0.3) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.