CVP verified calculation capability

Percent error Calculation Capability

Absolute/signed percent error, complete inverse branches and per-branch diagnostics; binary64 range and resolution policy.

Math Capability ID math.percent_error version 1.1.5 CVP VERIFIED STALE Engineering

Model

Percent error (lab convention)

Percent error (lab convention): % error = |O − T| / |T| × 100% [2][4]
Measurement error: ε = O − T [1]
Absolute error: |ε| = |O − T| [1][4]
Relative error: relative = |O − T| / |T| [3]
Signed (optional): % error = (O − T) / T × 100% [4]

Modes: p · o · t

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`abs`	—	—	input / output
`observed`	—	—	input / output
`true`	—	—	input / output
`percent`	—	—	input / output
`percent_error`	—	—	input / output
`absolute`	—	—	input / output
`solution_type`	—	—	input / output
`value`	—	—	input / output
`absolute_error`	—	—	input / output
`relative_error`	—	—	input / output
`signed_percent_error`	—	—	input / output
`achieved_percent_error`	—	—	input / output
`direction`	—	—	input / output
`resolution_limited`	—	—	input / output
`rounding`	—	—	input / output
`code`	—	—	input / output
`constraint`	—	—	input / output
`entered_percent_error`	—	—	input / output
`candidates`	—	—	input / output
`branches`	—	—	input / output
`omitted_branches`	—	—	input / 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`	Absolute or signed laboratory percent error; exact rational algebra of normalized binary64 inputs, one ties-even rounding per field; complete inverse branches with per-branch diagnostics.
`valid_domain`	Finite decimal binary64 numbers/strings up to512 characters, matching aliases, T≠0; every published result/branch/secondary field must be representable.
`singularity_policy`	TRUE_VALUE_ZERO at T=0; exact P=100 absolute or P=−100 signed yields infinite T only at O=0, otherwise no/unique/two solutions; NUMERIC_RANGE rejects any nonzero under/overflow: rescale.
`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`	Near T=0 or inverse P=±100, input perturbations are amplified.8ULP same-sign nonzero triple consistency, strict zero. Requested P preserved; achieved P/branch resolution_limited disclose inverse output rounding.
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	Private independent CPython Fraction/float; public summary Evidence, no third-party certification.
`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

Interactive evaluation runs locally in the browser. Shared URLs and REST may evaluate the same versioned engine on the server (query SSR).
Accepted value T ≠ 0.
Default formula uses absolute value so % error ≥ 0.
Two active fields solve the selected third; all three supplied values check consistency before solving, even with explicit solve_for. Consistency allows8 ULP for same-sign nonzero P and strict zero.
Inverse P is the requested percentage. Candidates are rounded to binary64, so achieved_percent_error and resolution_limited disclose any discrepancy; two mathematical branches may round to the same float.
All aliases must agree. Unknown inputs and invalid absolute/signed policies are rejected.

Example

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

|101.5 − 100| / 100 × 100% = 1.5%

Open this example in the calculator

Trust

CVP VERIFIED · production STALE · CVP protocol 1.0.0-proposed · Engineering 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 · production STALE · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (forward, inverse-observed, inverse-true, verify, invalid-domain)
Calculation version: 1.1.5
Verification: 14/14 calculation tests · 10/10 legacy golden · 4/4 legacy boundary
Production surface contract: 6/6
Versions: Calculation 1.1.5 · CVP protocol 1.0.0-proposed · Evidence 2026-10-22.percent-error-complete-contract-v3
Verification revision: 2026-10-22.percent-error-complete-contract-v3 · 3/3 property · digest 6f7189188a89
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: Private independent CPython Fraction/float checks complete primary, secondary and inverse branch sets on sampled normalized binary64 inputs; arithmetic comparison0 ULP, triple consistency8 ULP for same-sign nonzero percentages with strict zero. Public disclosure is summary-only, not the private full corpus.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 4/4 (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: 151/151 golden · 4/4 CVP boundary · 37/37 invalid · 3/3 property · 1/1 metamorphic · 7/7 round-trip · 26/26 cross-interface · 3/3 cross-calculator · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.1.5 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

STALE · Build schema 1.1.5 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · 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/percent-error' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"experimental":101.5,"theoretical":100},"calculation_version":"1.1.5"}'

{
  "inputs": {
    "experimental": 101.5,
    "theoretical": 100
  },
  "calculation_version": "1.1.5"
}

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

Full REST contract: REST API docs.

Tool id: percent-error
Engine: percent-error
REST: POST /api/v1/calc/percent-error
MCP: execute_calculation with capability_id: "math.percent_error"
Agent input schema: Canonical (MCP / Agent)
REST input schema: Compatibility (tol[] / tol1…)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.1.5)
Versioned output schema: Immutable pin (1.1.5)

Operations

Declared calculation modes for this capability.

References

Human-readable sources plus CVP reference evidence classes.

Sources

Derived identities

CalculatorX laboratory convention — Absolute-value percent error, signed opt-in, and reverse-solve states

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.percent_error"},"_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.percent_error","inputs":{"experimental":101.5,"theoretical":100},"calculation_version":"1.1.5"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.1.5) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.