CVP verified calculation capability
Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS.
Math Capability ID math.complex version 1.3.0 CVP VERIFIED CURRENT Core
Modulus
r = √(re² + im²)(re₁re₂ − im₁im₂) + (re₁im₂ + im₁re₂)iz^n = r^n (cos nθ + i sin nθ)z = r e^{iθ}Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
re | — | — | input / output |
im | — | — | input / output |
re2 | — | — | input |
im2 | — | — | input |
r | — | — | input / output |
arg_deg | scalar plane angle | — | input / output |
n | — | — | input / output |
from | — | — | input |
re1 | — | — | input |
im1 | — | — | input |
arg | scalar plane angle | — | input |
exponent | — | — | input |
euler | — | — | output |
cis | — | — | output |
k | — | — | output |
n_roots | — | — | output |
roots | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | complex |
exactness | float64 |
algorithm | scaled rectangular arithmetic/division and integer powers; reduced-degree trigonometry and De Moivre roots |
valid_domain | finite normal nonzero components or zero; r≥0; integer power |n|≤1000 and root2≤n≤64 |
singularity_policy | DIVISION_BY_ZERO on 0+0i divisor |
branch_policy | arg in (−180°,180°], negative real axis +180 even signed zero; origin0 convention; k=0 principal then all distinct roots |
tolerance | vector norm relative2e-11; argument absolute2e-9 degrees on well-conditioned cases; exact cardinal polar directions |
convergence | not applicable — non-iterative |
conditioning | relative component error can grow with cancellation; direction sensitive at origin and discontinuous on negative-real cut |
rounding | ieee754_round_ties_to_even |
overflow | NUMERIC_RANGE on nonfinite, subnormal nonzero or underflowed intermediate/result; rescale |
reproducibility | deterministic + Capability@Version |
independent_oracle | cvp:math.complex O2 / 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.
mode=add re=1 im=2 re2=3 im2=4 → 4+6i
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.
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 5/5.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/complex' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"add","re":1,"im":2,"re2":3,"im2":4},"calculation_version":"1.3.0"}'{
"inputs": {
"mode": "add",
"re": 1,
"im": 2,
"re2": 3,
"im2": 4
},
"calculation_version": "1.3.0"
}POST /api/v1/calc/complex. 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 · 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.complex"},"_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.complex","inputs":{"mode":"add","re":1,"im":2,"re2":3,"im2":4},"calculation_version":"1.3.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.3.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.