math.numerical.optimize_1d

Three distinct suites: educational examples on the calculator page, this legacy regression count (11/11 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-18.optimization-input-convergence-contract-v4. Calculation version 1.0.5. CVP 1.0.0-proposed. 163/163 golden · 2/2 CVP boundary · 22/22 invalid · 1/1 property · 7/7 cross-interface · 1/1 cross-calculator · 5/5 CVP contract. digest 30e09aefa76f.

• Golden (oracle-backed) 163 / 163
• CVP boundary 2 / 2
• Invalid input 22 / 22
• Property 1 / 1
• Cross-interface 7 / 7
• Cross-calculator 1 / 1
• CVP contract 5 / 5
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 3/3 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
• Verified scope all published methods
• Assurance Core

• release artifacts aligned PASS
• schema output required declared PASS
• schema valid input executes PASS
• engine success output validates schema PASS
• rest success payload validates schema PASS

Fingerprint sha256:c05b3eb8e55fe3912f5947141e2e5922a729096d866e7eb3492bd93edd4fcdd8

Input schema sha256:199aa93bda804129d175b60146d9bfe9ee976de0f7cdc20a60266b2fb0446d87 · Output schema sha256:0d22b3f9be4f6eef8c87f5a0a2dea980fa970e99e4bb8916bc858dfe2e1d93cd · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Tool

one-dimensional-optimization

Engine

one-dimensional-optimization

Engine build

2026-10-18

Evidence core

2026-10-18T12:13:53.001Z

Rendered

2026-10-23T01:27:11.652Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of f on [a, b] (marker is published xmin, fmin; full polynomial coefficients are returned in the result). Curve samples are illustrative binary64 evaluations; primary polynomial ordering uses exact dyadic intermediates. Iterate history is not a REST field.
• Minimize only; f treated as unimodal on [a, b]
• Not multivariate and not CAS
• Polynomial degree ≤ 8

Limitations

• Minimize only; not multivariate, Nelder-Mead, gradient descent, maximization or CAS.
• Unimodal assumption; arbitrary multimodal intervals can yield local candidates, not a guaranteed global minimum. Original closed interval endpoints are compared.
• a<b; finite interval width; decimal scalars, matching aliases, degree<=8, positive tol<=1, integer max_iter1..100.
• converged indicates only requested internal bracket width; max_iter and resolution_limit return an explicit candidate. Inspect termination and bracket_width.
• Polynomial comparison uses exact dyadic intermediates of binary64 inputs. Coordinates retain binary64 precision; objective values/signed analytic-baseline differences publish12 significant digits. Required endpoint/final nonzero underflow or overflow rejects.
• Legacy exact_xmin/exact_fmin are optional binary64 analytic baselines when available; signed abs_err_x/abs_err_f are comparisons, not certified bounds. Tied minima may differ in location; figures are illustrative.