CVP verified calculation capability
Right circular sphere, cylinder, cone, ring torus, conical frustum, right rectangular prism, right rectangular pyramid, regular tetrahedron, regular octahedron, regular icosahedron, regular dodecahedron, regular n-gon prism, regular n-gon pyramid, regular n-gon frustum, ellipsoid, spherical cap, spherical zone, spherical wedge, spherical lune, and spherical sector. Discovery /sphere, /cylinder, /cone, /torus, /frustum, /prism, /pyramid, /tetrahedron, /octahedron, /icosahedron, /dodecahedron, /regular-prism, /regular-pyramid, /regular-frustum, /ellipsoid, /spherical-cap, /spherical-zone, /spherical-wedge, /spherical-lune, /spherical-sector. Not the circle-only page, not a vector, not ISO 5167-5, not a sphere page, not CAS.
Math · Geometry Capability ID math.geometry.solid version 1.18.0 CVP VERIFIED CURRENT Core
Sphere
V = (4/3)πr³, A = 4πr²V = πr²h, A = 2πr(r+h)V = (1/3)πr²h, l = √(r²+h²)V = (1/3)πh(R² + Rr + r²)V = abh, A = 2(ab+ah+bh)V = abh/3V = a³√2/12, A = a²√3V = (√2/3)a³, A = 2√3 a²V = (5/12)(3+√5)a³, A = 5√3 a²V = (1/4)(15+7√5)a³, A = 3√(25+10√5) a²V = A h, A = (n s²)/(4 tan(π/n))V = A h/3, A = (n s²)/(4 tan(π/n))V = h/3 (A + a + √(Aa))V = 4/3 πabcV = (1/3)πh²(3r−h)V = (πh/6)(3a² + 3b² + h²)V = (2/3)r³θ (θ in radians)A = 2r²θ (θ in radians)V = (2/3)πr²hModes: sphere · cylinder · cone · torus · frustum · prism · pyramid · tetrahedron · octahedron · icosahedron · dodecahedron · regular prism · regular pyramid · regular frustum · ellipsoid · spherical cap · spherical zone · spherical wedge · spherical lune · spherical sector
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
r | — | — | input / output |
h | — | — | input / output |
R | — | — | input / output |
a | — | — | input / output |
b | — | — | input / output |
c | — | — | input / output |
n | — | — | input / output |
s | — | — | input / output |
t | — | — | input / output |
theta | — | — | input / output |
volume | — | — | output |
surface | — | — | output |
lateral | — | — | output |
slant | — | — | output |
diagonal | — | — | output |
cylinder | — | — | output |
cube | — | — | output |
slant_a | — | — | output |
slant_b | — | — | output |
square_base | — | — | output |
height | — | — | output |
face | — | — | output |
base | — | — | output |
cap | — | — | output |
apothem | — | — | output |
apothem_top | — | — | output |
prism | — | — | output |
sphere | — | — | output |
oblate | — | — | output |
prolate | — | — | output |
hemisphere | — | — | output |
symmetric | — | — | output |
theta_rad | — | — | output |
area | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | closed solid identities; ellipsoid surface uses spheroid / incomplete elliptic F,E |
valid_domain | positive dimensions as published (e.g. torus R > r) |
singularity_policy | INVALID_INPUT off the published solid domain; ellipsoid a=b=c uses 4πa² |
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 | not applicable — not a matrix κ product |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.geometry.solid 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.
sphere r=1 → V=4π/3
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/solid-geometry' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"sphere","r":1},"calculation_version":"1.18.0"}'{
"inputs": {
"mode": "sphere",
"r": 1
},
"calculation_version": "1.18.0"
}POST /api/v1/calc/solid-geometry. 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.geometry.solid"},"_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.geometry.solid","inputs":{"mode":"sphere","r":1},"calculation_version":"1.18.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.18.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.