math.numerical.root

Three distinct suites: educational examples on the calculator page, this legacy regression count (39/39 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 1.1.6 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 2026-10-16.root-input-share-contract-v5. Calculation version 1.1.6. CVP 1.0.0-proposed. 107/107 golden · 6/6 CVP boundary · 19/19 invalid · 2/2 property · 21/21 cross-interface · 1/1 cross-calculator · 5/5 CVP contract. digest a3a919f46dd8.

• Golden (oracle-backed) 107 / 107
• CVP boundary 6 / 6
• Invalid input 19 / 19
• Property 2 / 2
• Cross-interface 21 / 21
• 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 11/11 (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. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity.
• 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 sha256:2a2b71febdaea1c0115e11315a1c6ace4274f1fcecc8cc0d5c16563f187da68d

Input schema sha256:1e6fd5072a02870c9be3ed64267c58a58a88d2c89ea715da66131a9cc294238f · Output schema sha256:a337266d5e0e3647cf43e5eb80bf222a5559ce23ced3a333f64099934284387d · 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

numerical-root

Engine

numerical-root

Engine build

2026-10-16

Evidence core

2026-10-16T12:29:44.098Z

Rendered

2026-10-23T01:27:11.649Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of f around the published root (marker locates the candidate at pack.root on y=0; its label includes the signed residual and does not certify a zero; Newton/secant seeds and the bisection bracket are read from inputs, not REST fields). Same fnValue as REST/MCP. Iterate history is not a REST field.
• Not CAS / not complex roots listed
• Not a system of equations
• Not all-roots of a polynomial
• Not ⁿ√a
• Polynomial degree ≤ 8
• Polynomial convergence uses |f(x)| divided by Σ|cᵢ||x|ⁱ; sin uses |sin x|. A small residual alone does not prove a nearby root for every polynomial.
• Polynomial values, derivatives, and residual stopping tests use exact dyadic intermediates for the supplied binary64 coefficients and iterate. Solver values use power-of-two scaling; published signed and scaled residuals are projected to binary64. An underflowed solver value is not treated as an exact root.

Limitations

• Not ⁿ√a — that remains /calc/math/root
• Not three independent Newton/bisection/secant product pages
• Not CAS / not a nonlinear system
• Degree > 8 → INVALID_INPUT
• No convergence → NO_CONVERGENCE