Verified calculation capability

Sum / addition Calculation Capability

Exact decimal sum of a list of values (comma/space/newline separated), with optional long-addition work. · Math

Capability ID math.sum · version 1.0.2

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

Model

Sum

Sum: Sum = Σᵢ₌₁ⁿ xᵢ
Mean: x̄ = (1/n) Σᵢ₌₁ⁿ xᵢ
Mean from the sum: Mean = Sum / n

Solve modes: sum · long

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`values`	Array of numbers to add	—	input
`sumInput`	Share-URL / text list of values	—	input
`input`	Alias for sumInput	—	input
`value`	—	—	output
`sum`	—	—	output
`count`	—	—	output
`algorithm`	—	—	output
`mean`	JSON binary64 of Sum/n. Not claimed exact; see mean_numeric_approximate.	—	output
`mean_rational_exact`	true when mean_num/mean_den is an exact rational mean (exact-decimal algorithm).	—	output
`mean_numeric_approximate`	true when the JSON mean number or displayed mean must not be treated as exact.	—	output
`mean_exact`	Compatibility alias of mean_rational_exact (exact rational source). Does not mean the JSON mean number is exact. Prefer mean_rational_exact and mean_numeric_approximate.	—	output
`chart`	Running totals for visualization. Last point matches published sum when chart_model is exact-decimal.	—	output
`chart_model`	Numeric model of chart[]. exact-decimal: Number(exact prefix sumStr). binary64: IEEE-754 visualization only (scientific-notation lists).	—	output

Assumptions / Validity

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

Assumptions

Tokens are parsed as decimal numbers; scientific notation is allowed in Sum mode only.
Units are not parsed. 5 kg + 3 kg is treated as 5 + 3; the sum keeps whatever unit the inputs shared.
Thousands separators are not supported. A comma in 7,890 is a value separator (7 + 890), with a non-blocking warning.
Long addition pads decimal places with zeros so columns align.
Plain decimal tokens are summed in base-10 (exact). Any scientific-notation token switches the list to Neumaier compensated IEEE-754 summation.

Example

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

937 + 129 + 2248 = 3314

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 (sum-exact-decimal, sum-scientific, long-integer, long-decimal, invalid-domain)
Calculation version: 1.0.2
Verification: 31/31 calculation tests · 24/24 legacy golden · 7/7 legacy boundary
Production surface contract: 3/3
Versions: Calculation 1.0.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 3/3 property · digest a295d54714a4
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: Plain-decimal and long-addition goldens: exact sumStr identity vs independent BigInt rationals. Scientific-notation goldens: ≤2 ULP on value vs the same exact rational rounded to binary64. Tabulated vectors only — not a whole-domain ≤2 ULP guarantee, including unlisted cancellation or mixed-format lists.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
CVP suite: 10/10 golden · 6/6 CVP boundary · 9/9 invalid · 3/3 property · 1/1 metamorphic · 6/6 cross-interface · 3/3 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: add
Engine: sum
REST: POST /api/v1/calc/add
MCP: execute_calculation with capability_id: "math.sum"
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

OpenStax Prealgebra 2e — Add Whole Numbers — 1.2 Place-value addition
OpenStax Prealgebra 2e — Add Integers — 3.2 Signed addition
CalculatorX mathematical conventions — Neumaier compensated summation for scientific-notation lists

Reference evidence classes: O1 model · 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.sum"}}}'

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