CVP verified calculation capability
Direct DFT / IDFT and radix-2 FFT / IFFT of a length-N sequence, N≤64. FFT requires N=2^k. Numpy backward: unnormalized forward, 1/N inverse. Discovery /dft, /inverse-dft, /fft, /ifft. Not Laplace, not Z, not CAS.
Math · Transform Capability ID math.transform.dft version 1.2.1 CVP VERIFIED STALE Core
Forward DFT
X[k] = Σ_n x[n] e^{−2πi kn/N}x[n] = (1/N) Σ_k X[k] e^{2πi kn/N}Modes: dft · idft · fft · ifft
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
samples | — | — | input |
x | — | — | input |
re | — | — | input / output |
im | — | — | input / output |
n | — | — | output |
algorithm | — | — | output |
normalization | — | — | output |
x_re | — | — | output |
x_im | — | — | output |
mag | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | complex |
exactness | float64 |
algorithm | direct O(N²) DFT and radix-2 Cooley–Tukey; Numpy backward convention; 12-digit publication preserves nonzero small components |
valid_domain | N ≤ 64; FFT requires N = 2^k |
singularity_policy | INVALID_INPUT when N is off-bound or FFT length is not a power of two; NUMERICAL_RANGE_ERROR on nonfinite published input, output or magnitude |
branch_policy | complex bins; no continuous-Fourier branch |
tolerance | note: reconstruction residual vs Evidence; no global default |
convergence | not applicable — finite DFT, not an iterative solver |
conditioning | not applicable — unitary-scale is Numpy backward, not orthonormal 1/√N as a product |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic + Capability@Version |
independent_oracle | cvp:math.transform.dft 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=dft samples=1,0,0,0 → X=[1,1,1,1]
CVP VERIFIED · production STALE · 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/discrete-fourier-transform' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"dft","samples":[1,0,0,0]},"calculation_version":"1.2.1"}'{
"inputs": {
"mode": "dft",
"samples": [
1,
0,
0,
0
]
},
"calculation_version": "1.2.1"
}POST /api/v1/calc/discrete-fourier-transform. 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.transform.dft"},"_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.transform.dft","inputs":{"mode":"dft","samples":[1,0,0,0]},"calculation_version":"1.2.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.2.1) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.