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 1.0.5 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 2026-09-09.root-cvp. Calculation version 1.0.5. CVP 1.0.0-proposed. 5/5 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 · 1/1 CVP contract. digest a3f7a7bfcb95. 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.

• Golden (oracle-backed) 5 / 5
• 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 1 / 1
• 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 valid input executes PASS
• engine success output validates schema PASS

Fingerprint sha256:7faeb383ad7c423d84a64781f249bee383d3304f8f97e3f173f7801b0286e088

Input schema sha256:d0ef74fe6f7704d12f423072babe01e3271217e5bcd4efcca488f5a5cce6a060 · Output schema sha256:926b0e5761c82a91c0fea6146365eeacd6097d2ded3d7162df787ec7cd73c31a · 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

2026-09-10

Evidence core

2026-09-10T22:48:17.762Z

Rendered

2026-09-16T22:03:43.777Z

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

• n must be a positive safe integer → INVALID_INDEX
• Even roots of a < 0 → NOT_REAL (unlike square-root imaginary)
• Missing a → MISSING_REQUIRED_INPUT