math.numerical.root

Three distinct suites: educational examples on the calculator page, this legacy regression count (19/19 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.

STALE · Build schema 1.1.6 matches page · production binding STALE · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · CVP STALE · attestation STALE — Production CURRENT withheld · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-06.polynomial-value-underflow. Calculation version 1.1.3. CVP 1.0.0-proposed. 7/7 golden · 6/6 CVP boundary · 13/13 invalid · 1/1 property · 5/5 cross-interface · 1/1 cross-calculator · 5/5 CVP contract. digest 9e6c673d4478.

• Golden (oracle-backed) 7 / 7
• CVP boundary 6 / 6
• Invalid input 13 / 13
• Property 1 / 1
• Cross-interface 5 / 5
• 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 4/4 (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 sha256:27514fc845e8b051722e679d184b7a27afc81935570a4d4d3fd7293d702676ae

Input schema sha256:402fe8fce2315f92fc3e206e4fbc665cdbf852fdf067954b2e2b81c309a55629 · Output schema sha256:d9ba55faf7e861d2f5e7555c1689d63f2e610a27afa176297a835eb9342eb76c · 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

2026-10-06

Evidence core

2026-10-06T08:56:18.911Z

Rendered

2026-10-07T13:43:02.517Z

Last reviewed

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Assumptions

• The Result Card includes an engine-linked figure of f around the published root (marker is pack.root on y=0; 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 solving normalizes finite coefficients before evaluating signs, steps, and scaled residuals. The published signed residual remains the raw binary64 evaluation. A zero scale at x=0 with c₀=0 is an exact root; an underflowed zero elsewhere is not accepted 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