CVP verified calculation capability

Multiplication Calculation Capability

Exact decimal product of multiplicand × multiplier, with optional long-multiplication work.

Math Capability ID math.multiplication version 1.0.3 CVP VERIFIED CURRENT Core

Model

Product

Product: product = multiplicand × multiplier
Repeated addition — for non-negative integer multiplier: a × n = a + a + … + a (n times), n ∈ ℤ≥0
Commutative: a × b = b × a
Distributive: a × (b + c) = a×b + a×c

Modes: product · long

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Multiplicand	—	input
`b`	Multiplier	—	input
`product`	—	—	output
`productStr`	—	—	output
`work`	—	—	output
`gridTruncated`	—	—	output
`warning`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	float64 a × b
`valid_domain`	finite reals a, b
`singularity_policy`	not applicable — multiplication has no pole
`branch_policy`	not applicable — real principal value only
`tolerance`	not applicable — closed form; capability Evidence owns comparison, no global default
`convergence`	not applicable — non-iterative
`conditioning`	not applicable — not a matrix κ product
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	cvp:math.multiplication / Evidence published cases
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

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

Assumptions

Real decimal inputs parsed as exact decimal strings (integer mantissa × 10^−scale), not binary floating-point.
Product mode and Long multiplication mode use the same exact mantissa multiplication; Long adds partial-product steps.

Example

One numerical check. The calculator page holds worked steps and FAQ.

2552 × 64 = 163328

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 · 5/5 declared partitions (product, long, long-grid, digit-bound, invalid-domain)
Calculation version: 1.0.3
Verification: 15/15 calculation tests · 10/10 legacy golden · 5/5 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 6/6 property · digest 7a9319794cf7
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: Exact decimal-string identity (productStr) vs O2 mantissa×BigInt dual-checked against per-digit BigInt partials. Long vectors also require IUT work to contain those partials, or LONG_GRID_TRUNCATED at 25 digits. 48 significant digits per factor; 49-digit factors are rejected. This is not a whole-domain proof beyond the published vectors.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 12/12 golden · 5/5 CVP boundary · 4/4 invalid · 6/6 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 4/4 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.3 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.3 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/multiplication' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"a":8,"b":6},"calculation_version":"1.0.3"}'

{
  "inputs": {
    "a": 8,
    "b": 6
  },
  "calculation_version": "1.0.3"
}

POST /api/v1/calc/multiplication. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: multiplication
Engine: multiplication
REST: POST /api/v1/calc/multiplication
MCP: execute_calculation with capability_id: "math.multiplication"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.3)
Versioned output schema: Immutable pin (1.0.3)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Margaret Stevens — The Maths Workbook (University of Oxford) — Chapter 1, §1: Algebraic Expressions and Fractions; §3: Equations

Derived identities

CalculatorX mathematical conventions — Exact decimal place-count multiplication

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

Try with an agent

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.multiplication"},"_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.multiplication","inputs":{"a":8,"b":6},"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.