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.

STALE · Build schema 1.1.0 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 2026-10-13.inverse-angle-dual-field. Calculation version 1.0.7. 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 · 23/23 cross-interface · 4/4 cross-calculator · 4/4 URL→result→graph · 5/5 CVP contract. digest ba9dc359a496.

• 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 23 / 23
• Cross-calculator 4 / 4
• URL → result → graph 4 / 4
• CVP contract 5 / 5
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 21/21. Error-path engine·REST·MCP 2/2 (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
• rest success payload validates schema PASS

Fingerprint sha256:0eaafa4c30359dbfbc594b53963d9dd2ce079214d9aa5fcbf726f51021fa6e6e

Input schema sha256:eb99846613ffc2031fb1fb7e3d0ef7531e2552f60dd8f21d62cb80e22f3dfa10 · Output schema sha256:54220fdceb1754d56c53f6099fbeaac0fc5a15fec4e2ef7fcc4b045ddd694e1c · 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

2026-10-14

Evidence core

2026-10-14T02:50:33.742Z

Rendered

2026-10-14T09:26:08.345Z

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