math.arctan

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 1.0.9 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 2026-10-16.inverse-trig-discovery-pins-v8. Calculation version 1.0.9. CVP 1.0.0-proposed. 9/9 golden · 3/3 CVP boundary · 3/3 invalid · 8/8 property · 3/3 metamorphic · 4/4 round-trip · 21/21 O3 · 31/31 cross-interface · 4/4 cross-calculator · 4/4 URL→result→graph · 6/6 CVP contract. digest 4fb2a8fe2cc5.

• Golden (oracle-backed) 9 / 9
• CVP boundary 3 / 3
• Invalid input 3 / 3
• Property 8 / 8
• Metamorphic 3 / 3
• Round-trip 4 / 4
• O3 high-precision 21 / 21
• Cross-interface 31 / 31
• Cross-calculator 4 / 4
• URL → result → graph 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 21/21. Error-path engine·REST·MCP 5/5 (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:f4a509fca9e3c44178b7b8a02893b6156f9aef2de65b5802022df58076e59a83

Input schema sha256:2a41a9980f4d9dec9890f9c1211379bb434b0fe9d1a02110527337297ba1fa20 · Output schema sha256:ec1c6707934418696467e28589f6f5b47588c78046d7a9a47e2f9bf58f8a7d16 · 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

arctan

Engine

arctan

Engine build

2026-10-15

Evidence core

2026-10-15T07:33:30.941Z

Rendered

2026-10-19T06:49:24.323Z

Last reviewed

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Assumptions

• Real inverse tangent with principal branch (−π/2, π/2) (NIST DLMF §4.23(ii)). Infinity is not accepted as an input.
• Opposite/adjacent in the UI is a right-triangle length convenience (opposite ≥ 0, adjacent > 0, same unit). It is not atan2. The published engine remains single-argument arctan(x). Use Decimal for a signed ratio, and Tan for the forward map.
• When x is exactly a listed common value (0, ±1/√3, ±1, ±√3), the engine returns the exact algebraic angle such as 45° = π/4. Nearby floats are not snapped.

Limitations

• Missing x → MISSING_REQUIRED_INPUT
• Non-finite → INVALID_NUMBER
• 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.