math.arccos

Three distinct suites: educational examples on the calculator page, this legacy regression count (10/10 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 1.1.0 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 2026-10-29.math-uuce-fields-v1. Calculation version 1.1.0. CVP 1.0.0-proposed. 9/9 golden · 5/5 CVP boundary · 5/5 invalid · 8/8 property · 4/4 metamorphic · 5/5 round-trip · 30/30 O3 · 42/42 cross-interface · 4/4 URL→result→graph · 6/6 CVP contract. digest 9dd654d8b9fb.

• Golden (oracle-backed) 9 / 9
• CVP boundary 5 / 5
• Invalid input 5 / 5
• Property 8 / 8
• Metamorphic 4 / 4
• Round-trip 5 / 5
• O3 high-precision 30 / 30
• Cross-interface 42 / 42
• URL → result → graph 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 30/30. Error-path engine·REST·MCP 7/7 (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 (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session. Raw HTTP REST/JSON-RPC transport rejection 5/5; raw-number source and conflicting pins are transport-only checks, not engine/SSR input-source parity.
• 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 sha256:3b072caa15812e2cccc80c32c73f36086fa09a84592e6b85b5a1babbe961e884

Input schema sha256:18e0ece6d572ff8c71d1bbbe42abcb61fb6d86428ddcd7bea19f872ff495ce75 · Output schema sha256:146a751dcdf4193e8e9fa445879572f56639d8141d389a4a1cc7af426c468344 · 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

arccos

Engine

arccos

Engine build

2026-10-29

Evidence core

2026-10-29T08:55:15.563Z

Rendered

2026-10-29T17:04:55.713Z

Last reviewed

—

Assumptions

• Real inverse cosine with principal branch [0, π] (NIST DLMF §4.23(ii)). Complex arccos is not returned.
• When x is exactly a listed common value (0, ±1/2, ±√2/2, ±√3/2, ±1), the engine returns the exact algebraic angle such as 60° = π/3. Nearby floats are not snapped.

Limitations

• x outside [−1, 1] → NOT_REAL
• Missing x → MISSING_REQUIRED_INPUT
• Near-common-value hint is display metadata; it does not replace the canonical deg/rad or assert mathematical exactness.
• Raw input accepts finite JSON numbers or decimal strings; normalized inputs contain numeric x only. Nonzero text rounded to zero is NUMERIC_UNDERFLOW.
• Unknown inputs are UNKNOWN_INPUT; x/xInput conflicts are AMBIGUOUS_INPUT.
• Legacy engine test counts are separate from the CVP Manifest suite. CVP identity is included; production status requires the linked report matched by version, revision and digest.