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.

This calculator CURRENT · Public schema 1.0.4 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.square-root-complete-contract-v1. Calculation version 1.0.4. CVP 1.0.0-proposed. 80/80 golden · 7/7 CVP boundary · 11/11 invalid · 4/4 property · 2/2 metamorphic · 3/3 round-trip · 7/7 cross-interface · 5/5 URL→result→graph · 6/6 CVP contract. digest 767ce88755a9. 80 fixed and seeded complete results including both signs, zero, subnormal, max finite and rounding neighbors; not exhaustive

• Golden (oracle-backed) 80 / 80
• CVP boundary 7 / 7
• Invalid input 11 / 11
• Property 4 / 4
• Metamorphic 2 / 2
• Round-trip 3 / 3
• Cross-interface 7 / 7
• URL → result → graph 5 / 5
• CVP contract 6 / 6
• 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 covered in the current full review; Core ui-ssr is not a 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:c5f09468ffa8ad03d95114a4a2621da17c7336834988fca78c1bfad2f9f3b341

Input schema sha256:69b9b78cd467274524000030ed067a5c87391b85c6af4b7d168f00914a774f79 · Output schema sha256:dfb5553c678fd2ff8916c23d13c5350a0fde5ceadb85438461be5492923fc37f · 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

2026-10-26

Evidence core

2026-10-26T05:34:16.140Z

Rendered

2026-10-28T03:01:57.873Z

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

• Principal branch on finite real radicands: x≥0 gives real=principal=√x,imag=0; x<0 gives real=0,imag=√|x|,principal=null. Both real/imag/principal are always present.
• Numbers or strict decimal/scientific strings of at most512 characters; x and xInput must agree. Unknown keys, nonfinite values, null, booleans, hex, commas and nonzero-to-zero underflow reject.
• Binary64 input rounding and Math.sqrt output rounding are distinct; at most2 ULP on declared independent Decimal2000 reference vectors, not an exhaustive or exact-decimal guarantee. Relative condition number1/2 away from zero; derivative unbounded at zero.
• 12 significant digit display. Perfect-square claims require safe-integer radicands and roots. Scaled Babylonian working is an illustration, not the engine algorithm.
• Live graph shows the real branch in a bounded window; negative radicands have no real point. Typing computes locally; shared URLs and REST/MCP send inputs and may enter logs.