math.root

Three distinct suites: educational examples on the calculator page, this legacy regression count (24/24 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 1.0.6 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 2026-10-26.root-complete-contract-v2. Calculation version 1.0.6. CVP 1.0.0-proposed. 108/108 golden · 14/14 CVP boundary · 17/17 invalid · 4/4 property · 2/2 metamorphic · 3/3 round-trip · 19/19 O3 · 1/1 cross-interface · 5/5 cross-calculator · 4/4 URL→result→graph · 6/6 CVP contract. digest e1f0a9ed78e2. Path-specific ULP vs O3 applies only to the 19 published tabulated vectors: identity n=1 (0 ULP); Math.sqrt including tiny/huge (≤2); Math.cbrt including odd-negative and tiny/huge (≤2); moderate Math.pow including odd-negative, ⁸√15, and max safe n (≤2); extreme Math.pow at |a|=1e±300 (≤64). It is not a whole-domain guarantee. Even roots of a<0 and illegal n are contract errors (NOT_REAL / INVALID_INDEX), not ULP claims.; plus103 independently generated Decimal250 reference vectors with path-specific0/2/64ULP, scalar type strict and identity exact; not whole-domain.

• Golden (oracle-backed) 108 / 108
• CVP boundary 14 / 14
• Invalid input 17 / 17
• Property 4 / 4
• Metamorphic 2 / 2
• Round-trip 3 / 3
• O3 high-precision 19 / 19
• Cross-interface 1 / 1
• Cross-calculator 5 / 5
• URL → result → graph 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
• Assurance Core

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

Fingerprint sha256:42ed01a2478e858d10cd94807092abfcabc582dec8bda81812d9e92850549df2

Input schema sha256:4e390513efa70a86d1eb766085e865373966b168a9c105b772c9b697816e9719 · Output schema sha256:47b2dc74f1d8ce5c453fee82059224736347ee808d745cbdb670258b2b4ab21e · 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

root

Engine

root

Engine build

2026-10-26

Evidence core

2026-10-26T07:42:21.186Z

Rendered

2026-10-28T03:01:57.875Z

Last reviewed

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Assumptions

• Real principal root only. This engine does not return complex values.
• Index n is a positive safe integer (1st, square, cube, 4th, …, nth root). Generalized powers a^(1/n) with non-integer, negative, or non-safe-integer n belong on the Exponent calculator.
• Even n requires a ≥ 0 and returns b ≥ 0. Odd n allows a < 0 (for example ∛(−8) = −2).
• n = 2 uses Math.sqrt. n = 3 uses Math.cbrt, returning an implementation-approximated binary64 result (including negatives). Other n use a^(1/n) for a ≥ 0, or −(|a|)^(1/n) for odd n and a < 0.
• The Square Root calculator is a different contract: √(x<0) returns the principal imaginary. This page rejects that case as NOT_REAL.

Limitations

• Principal real nth root only. Even index requires a≥0 (NOT_REAL otherwise); odd-negative uses the real negative branch, distinct from complex principal powers.
• Strict decimal/scientific text up to512 characters; reject unknown keys, nonfinite, null, hex, comma, mismatching aliases, nonzero text rounded to zero. Exact positive safe-integer index; omitted index defaults to2, explicit blank/null rejects. Semantic cross-field and exact-text rules run after Schema shape validation.
• Binary64 identity for n=1, Math.sqrt for n=2, Math.cbrt for n=3, signed Math.pow for higher indices. Declared fixed references have≤64 ULP overall; existing path-specific O3 vectors retain0/2/64 ULP. Not a whole-domain guarantee or exact-decimal result.
• Relative condition number in radicand is1/n away from zero; derivative singular at zero for n>1. Input rounding, reciprocal-exponent error and root rounding are distinct. Raising rounded output to n can overflow or amplify error.
• 12 significant digit display; exports keep full binary64 scalar, raw inputs and calculation version. Bounded real graph; typing computes locally, shared URLs and REST/MCP send inputs and may enter logs.