CVP verified calculation capability

Ratio Calculation Capability

Simplify, scale, and compare ratios; solve proportions; split a total; convert part-to-part ratios to fraction, decimal, and part-of-whole percent using exact rationals.

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

Model

Simplify

Simplify: r₁:⋯:rₙ → exact rationals; L=LCM(d₁,…,dₙ); rᵢ′=L·rᵢ; g=GCF(|r₁′|,…,|rₙ′|); (r₁′÷g):⋯:(rₙ′÷g)
Proportion: A/B = C/D → A·D = B·C
Scale: r₁:⋯:rₙ → (k·r₁):⋯:(k·rₙ)
Split total: partᵢ = total × (termᵢ / Σ terms) with every term ≥ 0 and Σ terms > 0

Modes: simplify · proportion · scale · split · compare · convert · simp · reduce · prop · solve · multiply · divide · share · allocate · eq · equivalent · fraction · percent · pct

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`a`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`aInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`A`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input / output
`b`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`bInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`B`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input / output
`c`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`cInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`C`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input / output
`d`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`dInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`D`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input / output
`k`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input / output
`kInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`factor`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`total`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`totalInput`	Exact strings:48 decimal digits per integer/decimal or numerator/denominator; total token≤128 characters	—	input
`terms`	—	—	input / output
`termCount`	—	—	input
`scaleOp`	—	—	input / output
`scale_op`	—	—	input
`op`	—	—	input
`value`	—	—	output
`ratio`	—	—	output
`terms_exact`	—	—	output
`gcf`	—	—	output
`clearing_factor`	—	—	output
`shares`	—	—	output
`solved`	—	—	output
`solved_for`	—	—	output
`equivalent`	—	—	output
`part_to_part`	—	—	output
`part_of_whole`	—	A	output
`part_of_whole_B`	—	—	output
`simplified`	—	—	output
`viz_terms`	—	—	output
`viz_labels`	—	—	output

Trusted Math contract

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

Field	Declaration
`numeric_domain`	rational
`exactness`	exact
`algorithm`	Six exact-rational modes; denominator clearing/GCF, cross multiplication, scaling, allocation, comparison and conversion
`valid_domain`	Integer, decimal or fraction tokens,48 digits per component,128 characters;2/3 terms. JSON unsafe integers rejected; exact relative to accepted normalized tokens.
`singularity_policy`	ALL_ZERO for simplify; proportion requires exactly one blank and nonzero B,D, unique solution; scale factor nonzero; split nonnegative terms and total, positive sum; convert marks undefined fractions/percentages null.
`branch_policy`	Six explicit modes; signed rationals reduced to positive denominators;2/3 terms where supported; undefined quotients and nonunique proportions rejected
`tolerance`	not applicable — exact rational identity; approximate graphical percentages are presentation only
`convergence`	not applicable — finite rational algebra; Euclidean reduction terminates, no iterative numeric solver
`conditioning`	Rational arithmetic adds no roundoff, but small divisors amplify perturbations in quotients and solved proportions. Exactness does not recover input information lost during JSON parsing.
`rounding`	none for exact accepted rational tokens; binary64 JSON numbers may already round; bars and percent labels are explicitly approximate
`overflow`	bounded48-digit input components; BigInt rational results serialized as exact strings or safe integers
`reproducibility`	deterministic exact rational arithmetic relative to accepted normalized tokens + Capability@Version
`independent_oracle`	cvp:math.ratio / 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

Finite rationals: integers, terminating decimals, or simple fractions a/b.
Proportion denominators in A/B or C/D must be nonzero when used.
Simplify / proportion / compare allow negative terms. Split does not.

Example

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

12:18 → 2:3; 1.5:2.25 → 2:3; 3/4:5/6 → 9:10; 4:7 = x:21 → x=12

Open this example in the calculator

Trust

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.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Verified scope: all published modes
Assurance: Core
Declared partition coverage: PASS · 8/8 declared partitions (simplify, proportion, scale, split, compare, convert, three-term, invalid-domain)
Calculation version: 1.0.3
Verification: 26/26 calculation tests · 11/11 legacy golden · 7/7 legacy boundary · 8/8 legacy property
Production surface contract: 10/10
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-10-21.ratio-complete-contract-v3
Verification revision: 2026-10-21.ratio-complete-contract-v3 · 7/7 property · digest 980fb61ebf20
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: All six published Ratio modes (simplify, proportion, scale, split, compare, convert), including A:B:C where those modes support it. Independent O2 expected values; exact rational BigInt; Node is runtime host only.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 19/19 golden · 7/7 CVP boundary · 7/7 invalid · 7/7 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 10/10 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. Production surface contract 10/10.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/ratio' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"mode":"simplify","a":12,"b":18},"calculation_version":"1.0.3"}'

{
  "inputs": {
    "mode": "simplify",
    "a": 12,
    "b": 18
  },
  "calculation_version": "1.0.3"
}

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

Full REST contract: REST API docs.

Tool id: ratio
Engine: ratio
REST: POST /api/v1/calc/ratio
MCP: execute_calculation with capability_id: "math.ratio"
Agent input schema: Canonical (MCP / Agent)
REST input schema: Compatibility (tol[] / tol1…)
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

Derived identities

CalculatorX split convention — Nonnegative parts only

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.ratio"},"_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.ratio","inputs":{"mode":"simplify","a":12,"b":18},"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.