Public evidence

math.arctan

Machine-checked verification for calculation version 1.0.7 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· any finite real x; mathematical principal range (−90°, 90°); binary64 may round to ±90° · Protocol · Schema · Production report

Declared partition coverage: PASS · 3/3 declared partitions (arctan, invalid-domain, xcal)
Versions: Calculation 1.0.7 · CVP protocol 1.0.0-proposed
CVP identity: 8/8 property · digest cf317536e8dd

Verification

Legacy regression suite: 10/10 calculation tests · Production surface contract 3/3

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 1.0.7 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. 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 · 1/1 cross-interface · 4/4 cross-calculator · 4/4 URL→result→graph · 1/1 CVP contract. digest cf317536e8dd.

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 1 / 1
Cross-calculator 4 / 4
URL → result → graph 4 / 4
CVP contract 1 / 1
Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
Interface claim Success 1/1. 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 valid input executes PASS
engine success output 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.

Build & scope

Engine identity and declared limitations.

Tool: arctan
Engine: arctan
Engine build: 2026-09-10
Evidence core: 2026-09-10T22:48:17.762Z
Rendered: 2026-09-16T22:03:43.780Z
Last reviewed: —

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

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

NIST Digital Library of Mathematical Functions, Chapter 4 — Elementary Functions
Supports: Inverse trigonometric functions as elementary inverses of sine, cosine, and tangent
NIST DLMF §4.23 — Inverse trigonometric functions; principal values
Supports: Principal arctan on the real line with range (−π/2, π/2); degree output is θ × 180/π
CalculatorX mathematical conventions — Principal branch; exact-value recognition; ratio mode is UI-only
Supports: Published engine is arctan(x) of one real argument (not atan2).

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`one`	golden	pass	Expected deg=45 · Actual deg=45 · rad=0.7853981633974483 · exact=true
`sqrt3`	golden	pass	Expected deg=60 · Actual deg=60 · rad=1.0471975511965976 · exact=true
`inv-sqrt3`	golden	pass	Expected deg=30 · Actual deg=30 · rad=0.5235987755982988 · exact=true
`zero`	golden	pass	Expected deg=0 · rad=0 · Actual deg=0 · rad=0 · exact=true
`neg`	golden	pass	Expected deg=-45 · Actual deg=-45 · rad=-0.7853981633974483 · exact=true
`missing-x`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`x-abc`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`x-infinity`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`x-1e20`	golden	pass	Expected deg=90 · Actual deg=90 · rad=1.5707963267948966
`x-tiny`	golden	pass	Expected deg=5.729577951308233e-19 · Actual deg=5.729577951308233e-19 · rad=1e-20