CVP verified calculation capability
R²/R³ vector magnitude, normalize, add/subtract, dot/cross product, included angle, projection and scalar triple product. Finite normal binary64 components or zero; nine locked discovery entries.
Math Capability ID math.vector version 1.8.0 CVP VERIFIED CURRENT Core
Magnitude
|u| = √(ux² + uy² + uz²)u · v = ux vx + uy vy + uz vzu × vCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
ux | Finite decimal; zero or normal binary64 | — | input |
uy | Finite decimal; zero or normal binary64 | — | input |
uz | Finite decimal; zero or normal binary64 | — | input |
vx | Finite decimal; zero or normal binary64 | — | input |
vy | Finite decimal; zero or normal binary64 | — | input |
vz | Finite decimal; zero or normal binary64 | — | input |
wx | Finite decimal; zero or normal binary64 | — | input |
wy | Finite decimal; zero or normal binary64 | — | input |
wz | Finite decimal; zero or normal binary64 | — | input |
api_version | — | — | output |
api_contract_version | — | — | output |
spec_version | — | — | output |
page | Canonical calculator page URL | — | output |
links | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | R²/R³ exact dyadic intermediates for add/sub/dot/cross/triple/projection; scaled hypot/unit; atan2 exact cross/dot angle |
valid_domain | zero or finite normal binary64 components; required active x/y; absent z defaults0, explicit empty/null invalid |
singularity_policy | INVALID_INPUT on zero direction normalize/angle or zero projection target; zero source projection valid |
branch_policy | not applicable — real principal value only |
tolerance | relative2e-12 or8ULP; exact zero; cosine absolute2e-13; ordinary angle absolute2e-10 degrees |
convergence | not applicable — non-iterative |
conditioning | relative component error sensitive under cancellation; direction sensitive near zero |
rounding | ieee754_round_ties_to_even |
overflow | NUMERIC_RANGE for nonfinite/subnormal nonzero published fields or components; rescale; text-to-zero NUMERIC_UNDERFLOW |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.vector Python Fraction and mpmath100/180 independent fixtures plus benign O2 identities |
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.
magnitude (3,4,0) → 5
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 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/vector' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"magnitude","ux":3,"uy":4},"calculation_version":"1.8.0"}'{
"inputs": {
"mode": "magnitude",
"ux": 3,
"uy": 4
},
"calculation_version": "1.8.0"
}POST /api/v1/calc/vector. 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.vector"},"_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.vector","inputs":{"mode":"magnitude","ux":3,"uy":4},"calculation_version":"1.8.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.8.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.