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 1.0.6 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 2026-10-15.inverse-trig-input-provenance-v6. Calculation version 1.0.6. 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 · 37/37 cross-interface · 4/4 URL→result→graph · 6/6 CVP contract. digest 24ff68017009.

• 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 37 / 37
• 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.
• 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:e4934d43b5d94755afcbc9c5121de55f4cb8ca0159bb912f3c04fe59324f9219

Input schema sha256:9a8481028d4f07154adb403fd0defab4c0c750877a85ed9632b4b6d2806c8f6f · Output schema sha256:5f74dc67a8255889feda2a9c4475d706c36d9e5ebc64211e94faf752ca5e206e · 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

2026-10-15

Evidence core

2026-10-15T07:33:30.941Z

Rendered

2026-10-15T08:30:11.022Z

Last reviewed

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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.