CVP verified calculation capability
Unilateral Laplace table of causal elementary pairs: exp, sin, cos, step, ramp, t^n, damped sin/cos. Evaluate F(s) or f(t). Discovery /inverse-laplace. Not DFT, not Z, not Bromwich, not CAS.
Math · Transform Capability ID math.transform.laplace version 1.0.4 CVP VERIFIED CURRENT Core
Definition
F(s) = ∫₀^∞ e^{−s t} f(t) dtL{e^{a t}} = 1/(s−a), Re(s)>aCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
s | Finite decimal; nonzero underflow rejected before binary64 conversion | — | input / output |
t | Finite decimal; nonzero underflow rejected before binary64 conversion | — | input / output |
a | Blank uses default | — | input / output |
omega | Blank uses default | — | input / output |
w | Blank uses default | — | input |
n | Blank uses default | — | input / output |
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 |
integrand | 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 elementary table; scaled rational quotients and bounded phase/exponential evaluation |
valid_domain | exp, sin, cos, step, ramp, power n=0…8, exp_sin, exp_cos; finite real s strictly inside the stated ROC or finite t≥0; dimensionless parameters; omega is radians per unit t |
singularity_policy | INVALID_INPUT outside conservative ROC; NUMERICAL_RANGE_ERROR for unavailable finite nonzero output; NUMERICAL_RANGE_ERROR for bounded inverse phase/product or quantization exclusions |
branch_policy | causal unilateral with step(0)=1 and t^0=1 including t=0; inverse is table evaluation, no contour integration |
tolerance | 2e-11 relative per nonzero scalar in independent reference fixtures; mathematical zeros exact; not a uniform proof across all binary64 inputs |
convergence | not applicable — finite table evaluation |
conditioning | Near the ROC boundary reciprocal powers are sensitive to s−pole; trig zeros are sensitive to phase, exponentials to a*t. Input rounding is distinct 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; no false exact-zero or infinity output |
reproducibility | Capability@Version with approximate host transcendental functions; cross-runtime fixture checks do not establish bitwise portability for all inputs |
independent_oracle | cvp:math.transform.laplace O2 / private high-precision reference fixtures; public Evidence summaries and 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=laplace f=exp a=-1 s=1 → 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 5/5.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/laplace-transform' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"mode":"laplace","f":"exp","a":-1,"s":1},"calculation_version":"1.0.4"}'{
"inputs": {
"mode": "laplace",
"f": "exp",
"a": -1,
"s": 1
},
"calculation_version": "1.0.4"
}POST /api/v1/calc/laplace-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 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.laplace"},"_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.laplace","inputs":{"mode":"laplace","f":"exp","a":-1,"s":1},"calculation_version":"1.0.4"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.0.4) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.