CVP verified calculation capability
Unilateral Z table of causal elementary pairs: a^n, step, ramp, n a^n, sin, cos, damped sin/cos. Evaluate X(z) or x[n]. Discovery /inverse-z. Not DFT, not Laplace, not residue, not CAS.
Math · Transform Capability ID math.transform.z version 1.0.5 CVP VERIFIED CURRENT Core
Definition
X(z) = Σ_{n=0}^∞ x[n] z^{−n}Z{a^n} = z/(z−a), |z|>|a|Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
z | — | — | input / output |
n | — | — | input / output |
a | Absent or blank uses default | — | input / output |
omega | Absent or blank uses default | — | input / output |
w | Absent or blank uses default | — | input |
method | Named table token; case/space/hyphen normalized; aliases must agree | — | input |
f | Named table token; case/space/hyphen normalized; aliases must agree | — | input / output |
pair | Named table token; case/space/hyphen normalized; aliases must agree | — | input |
sequence | Named table token; case/space/hyphen normalized; aliases must agree | — | input |
value | — | — | output |
algorithm | — | — | output |
roc | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | floating-point approximation |
algorithm | unilateral causal table; scaled rational and stable half-angle forward quotients, bounded inverse phase and logarithmic geometric evaluation |
valid_domain | geom, step, ramp, n_geom, sin, cos, geom_sin, geom_cos; finite real z with |z| strictly above stated ROC radius or integer n0…64; dimensionless a and z, omega radians per sample |
singularity_policy | INVALID_INPUT outside conservative ROC or integer domain; NUMERICAL_RANGE_ERROR for nonfinite/nonzero range, inverse phase/product or quantization exclusions |
branch_policy | causal unilateral, u[0]=1 and a^0=1 including a=0; negative a alternates by integer parity; inverse is named sequence evaluation |
tolerance | 2e-11 relative per nonzero scalar in independent reference fixtures; mathematical zeros exact; no uniform all-binary64 accuracy theorem |
convergence | not applicable — finite table evaluation |
conditioning | Near |z|=radius rational quotients are sensitive to distance/phase. Trig zeros and exponential geometric scales can be sensitive; input rounding differs from evaluation error. |
rounding | binary64 evaluation; publish12 significant decimal digits without clamping nonzero values |
overflow | Coded range/precision refusal; decimal input underflow is NUMERIC_UNDERFLOW before conversion; inverse tiny subnormal quantization can be refused even when representable |
reproducibility | Capability@Version and approximate host transcendental functions; cross-runtime fixtures do not establish universal bitwise portability |
independent_oracle | cvp:math.transform.z O2 / private independent high-precision fixtures; public Evidence summaries and digest commitments |
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=z f=geom a=0.5 z=1 → 2
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/z-transform' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"z","f":"geom","a":0.5,"z":1},"calculation_version":"1.0.5"}'{
"inputs": {
"mode": "z",
"f": "geom",
"a": 0.5,
"z": 1
},
"calculation_version": "1.0.5"
}POST /api/v1/calc/z-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 expected_values · 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.transform.z"},"_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.z","inputs":{"mode":"z","f":"geom","a":0.5,"z":1},"calculation_version":"1.0.5"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.0.5) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.