Public evidence

math.arcsin

Machine-checked verification for calculation version 1.0.5 · 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· x ∈ [−1, 1]; principal range [−90°, 90°] · Protocol · Schema · Production report

Declared partition coverage: PASS · 2/2 declared partitions (arcsin, invalid-domain)
Versions: Calculation 1.0.5 · CVP protocol 1.0.0-proposed
CVP identity: 5/5 property · digest 2ccf13f932a9

Verification

Legacy regression suite: 11/11 calculation tests · Production surface contract 3/3

Three distinct suites: educational examples on the calculator page, this legacy regression count (11/11 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 1.0.5 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 1.0.5. CVP 1.0.0-proposed. 6/6 golden · 5/5 CVP boundary · 5/5 invalid · 5/5 property · 3/3 metamorphic · 5/5 round-trip · 19/19 O3 · 1/1 cross-interface · 4/4 URL→result→graph · 1/1 CVP contract. digest 2ccf13f932a9.

Golden (oracle-backed) 6 / 6
CVP boundary 5 / 5
Invalid input 5 / 5
Property 5 / 5
Metamorphic 3 / 3
Round-trip 5 / 5
O3 high-precision 19 / 19
Cross-interface 1 / 1
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 sha256:4953573189c37b0f083d599a9bb748776f1bccdfcf9ad01a1848131122926ea0

Input schema sha256:641160f19a9efb5244e923b248dfcb154664532e49d7513a9c76395b68579fa5 · Output schema sha256:a4feb150689f71cbdce87fc4184f3fb38209adf430ce4fe41b93d7cdd4ed69d0 · 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: arcsin
Engine: arcsin
Engine build: 2026-09-10
Evidence core: 2026-09-10T22:48:17.762Z
Rendered: 2026-09-16T22:03:43.779Z
Last reviewed: —

Assumptions

Real inverse sine with principal branch [−π/2, π/2] (NIST DLMF §4.23(ii)). Complex arcsin is not returned.
Opposite/hypotenuse in the UI is a local triangle convenience (hypotenuse > 0, opposite ≥ 0, opposite ≤ hypotenuse). The published engine is arcsin(x). Use Decimal for a signed ratio, and Sin for the forward map.
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 30° = π/6. Nearby floats are not snapped.

Limitations

x outside [−1, 1] → NOT_REAL
Missing x → MISSING_REQUIRED_INPUT

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 arcsin on [−1, 1] with range [−π/2, π/2]; degree output is θ × 180/π
CalculatorX mathematical conventions — Principal branch; exact-value recognition; triangle mode is UI-only
Supports: Published engine is arcsin(x). Opposite/hypotenuse is a local triangle convenience (positive sides, opposite ≤ hypotenuse). Inputs outside [−1, 1] are NOT_REAL.

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
`half`	golden	pass	Expected deg=30 · rad=0.5235987755982988 · Actual deg=30 · rad=0.5235987755982988 · exact=true
`one`	golden	pass	Expected deg=90 · Actual deg=90 · rad=1.5707963267948966 · exact=true
`zero`	golden	pass	Expected deg=0 · rad=0 · Actual deg=0 · rad=0 · exact=true
`neg`	golden	pass	Expected deg=-90 · Actual deg=-90 · rad=-1.5707963267948966 · exact=true
`sqrt2-over-2`	golden	pass	Expected deg=45 · Actual deg=45 · rad=0.7853981633974483 · exact=true
`out-of-domain`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL
`neg-out-of-domain`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL
`missing-x`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`x-abc`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`x-object`	boundary	pass	Expected INVALID_NUMBER · Actual INVALID_NUMBER
`oddness`	golden	pass	Expected deg=-30 · Actual deg=-30 · rad=-0.5235987755982988 · exact=true