CVP verified calculation capability
Solve ax² + bx + c = 0, or ax² + bx + c ○ rhs for ○ in {<,≤,>,≥}. Sign of a is the outside of the roots. Inequality discovery /quadratic-inequality. Not cubic, not CAS factoring.
Math Capability ID math.quadratic version 1.1.1 CVP VERIFIED CURRENT Core
Equation
ax² + bx + c = 0 (a ≠ 0)x = (−b ± √(b² − 4ac)) / (2a)Δ = b² − 4acxᵥ = −b/(2a), yᵥ = f(xᵥ)Modes: solve · inequality
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
a | Quadratic coefficient a ≠ 0 | — | input / output |
b | Linear coefficient | — | input / output |
c | Constant term | — | input / output |
op | Inequality operator for mode=inequality | — | input / output |
rhs | Right-hand side for mode=inequality | — | input / output |
delta | — | — | output |
x1 | — | — | output |
x2 | — | — | output |
real | — | — | output |
imag | — | — | output |
root_type | — | — | output |
xv | — | — | output |
yv | — | — | output |
op_symbol | — | — | output |
interval | — | — | output |
lo | — | — | output |
hi | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | exact + float64 |
algorithm | cancellation-safe quadratic roots; bounded optional exact radical simplification for discriminants ≤ 10^8 |
valid_domain | finite real a,b,c; a ≠ 0; discriminant products and published results must be representable |
singularity_policy | NOT_QUADRATIC when a = 0 (not the linear-equation page) |
branch_policy | real roots; complex conjugate pair reported as published, not a CAS |
tolerance | not applicable — exact radical when present; else IEEE-754 |
convergence | not applicable — closed form |
conditioning | discriminant cancellation is a known float64 risk; exact radical preferred when it exists |
rounding | exact radical string + IEEE-754 numeric |
overflow | NUMERICAL_RANGE_ERROR for discriminant product overflow/underflow or non-finite published results; rescale coefficients and rhs |
reproducibility | deterministic + Capability@Version |
independent_oracle | cvp:math.quadratic / Evidence published cases |
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.
x² − 5x + 6 = 0 → x = 2, x = 3
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.
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/quadratic' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"a":1,"b":-6,"c":8},"calculation_version":"1.1.1"}'{
"inputs": {
"a": 1,
"b": -6,
"c": 8
},
"calculation_version": "1.1.1"
}POST /api/v1/calc/quadratic. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Human-readable sources plus CVP reference evidence classes.
Sources
Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · 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.quadratic"},"_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.quadratic","inputs":{"a":1,"b":-6,"c":8},"calculation_version":"1.1.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.1.1) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.