CVP verified calculation capability
Minimize a polynomial, sin, or exp on [a, b] by golden-section search or Brent. Not multivariate, not maximization, not CAS.
Math · Numerical Capability ID math.numerical.optimize_1d version 1.0.5 CVP VERIFIED CURRENT Core
Golden
c = b − φ̂(b−a), d = a + φ̂(b−a)golden section + inverse parabolic interpolationCanonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
method | golden/golden_section/gss/golden_section_search; brent/brents/fminbound/bounded; case insensitive; hyphen/space normalize | — | input / output |
integrand | poly/polynomial, sin, exp/e^x; case insensitive | — | input / output |
f | Alias of integrand; supplied aliases must agree | — | input |
a | Finite decimal; conversion underflow is rejected before computation | — | input / output |
lo | Finite decimal; conversion underflow is rejected before computation | — | input |
xmin | Finite decimal; conversion underflow is rejected before computation | — | input / output |
b | Finite decimal; conversion underflow is rejected before computation | — | input / output |
hi | Finite decimal; conversion underflow is rejected before computation | — | input |
xmax | Finite decimal; conversion underflow is rejected before computation | — | input |
coeffs | Constant-first2–9 decimal coefficients; constants use c0,0 | — | input / output |
tol | Positive absolute bracket tolerance at most1; default1e-8 only absent | — | input / output |
max_iter | Integer1–100, default100 only absent | — | input / output |
coefficients | Alias of coeffs; supplied arrays/lists must agree after decimal normalization | — | input |
fmin | — | — | output |
bracket_width | — | — | output |
exact_xmin | — | — | output |
exact_fmin | — | — | output |
abs_err_x | — | — | output |
abs_err_f | — | — | output |
iterations | — | — | output |
n_eval | Numerical search objective calls including two endpoint checks; analytic baseline work excluded | — | output |
converged | Only the internal bracket width met tol; not a global optimality or certified error guarantee | — | output |
termination | — | — | output |
bracket | Final internal search bracket; a selected original endpoint can lie outside this smaller search interval | — | output |
reference_available | — | — | output |
search_scope | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | golden-section / Brent 1-D minimizer on a published unimodal f; stationary-point coefficients are normalized and zero-tested; cubic references use cancellation-safe quadratic roots and finite outputs use 12 significant digits |
valid_domain | finite bracket; published f family |
singularity_policy | INVALID_INPUT on a degenerate bracket; NUMERICAL_RANGE_ERROR on nonfinite interval width, function evaluation/output overflow, exp underflow to zero, or unsafe sin phase indices; NO_CONVERGENCE when unpublished |
branch_policy | not applicable — real iterate |
tolerance | note: interval width vs Evidence; no global default |
convergence | max_iter: engine published bound; criterion: interval / Brent step |
conditioning | multimodal f is out of seed scope |
rounding | ieee754_round_ties_to_even |
overflow | ieee754_nonfinite_or_coded_error |
reproducibility | deterministic algorithm + Capability@Version |
independent_oracle | cvp:math.numerical.optimize_1d 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.
golden poly 0,0,1 on [-1,2] → xmin=0
CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published methods. 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/one-dimensional-optimization' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"method":"golden","integrand":"poly","coeffs":[0,0,1],"a":-1,"b":2},"calculation_version":"1.0.5"}'{
"inputs": {
"method": "golden",
"integrand": "poly",
"coeffs": [
0,
0,
1
],
"a": -1,
"b": 2
},
"calculation_version": "1.0.5"
}POST /api/v1/calc/one-dimensional-optimization. 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.numerical.optimize_1d"},"_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.numerical.optimize_1d","inputs":{"method":"golden","integrand":"poly","coeffs":[0,0,1],"a":-1,"b":2},"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.