math.square_root

Three distinct suites: educational examples on the calculator page, this legacy regression count (18/18 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 1.0.4 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 2026-09-09.o3-boundary. Calculation version 1.0.3. CVP 1.0.0-proposed. 7/7 golden · 7/7 CVP boundary · 7/7 invalid · 4/4 property · 2/2 metamorphic · 3/3 round-trip · 21/21 O3 · 7/7 cross-interface · 5/5 URL→result→graph · 1/1 CVP contract. digest aa716638904c. ≤2 ULP vs O3 applies to the published tabulated Square Root vectors, including non-negative named and seeded values, principal imaginary of -9 and -2, IEEE-754 min-subnormal, and max-finite. It is not a guarantee over the entire input domain.

• Golden (oracle-backed) 7 / 7
• CVP boundary 7 / 7
• Invalid input 7 / 7
• Property 4 / 4
• Metamorphic 2 / 2
• Round-trip 3 / 3
• O3 high-precision 21 / 21
• Cross-interface 7 / 7
• URL → result → graph 5 / 5
• CVP contract 1 / 1
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 4/4. 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. Integration: URL → SSR result → Live graph current point (5/5). Hydration/slider/history are URL-canonical contracts, not a live browser session. Live-browser hydration, slider, Copy JSON, and Overview/Focus are not Core CVP. They are covered by npm run test:math-graph-e2e (MATH_GRAPH_E2E_ONLY=square_root).
• 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 sha256:01a95214633a22c075abfe506188cc7661a6d663cf51ab4754c55d1807615663

Input schema sha256:ff1cf6b2f9ee1b970abddef0da1ea9f8523f33da2149c3b96c0f0cd1ca3b6aec · Output schema sha256:5d98f7f033a8be30482d03b3180c7f013da86b33a56a0b85893efef90e0bee63 · 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

square-root

Engine

square-root

Engine build

2026-10-14

Evidence core

2026-10-14T02:50:33.742Z

Rendered

2026-10-26T04:58:53.676Z

Last reviewed

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Assumptions

• Principal branch: nonnegative real root when x ≥ 0.
• Unlike Log / Ln, this engine does not reject x < 0. It returns the principal imaginary √|x| i, not a real error.
• The other real root for x > 0 is −√x; the other imaginary root for x < 0 is −√|x| i. The published value is the principal one.

Limitations

• x ≥ 0 → principal = √x, imag = 0
• x < 0 → real = 0, imag = √|x|, principal = null (unlike math.root NOT_REAL)
• Missing x → MISSING_REQUIRED_INPUT