Public evidence

math.arccos

Machine-checked verification for calculation version 1.0.4 · 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 [0, π] · Protocol · Schema · Production report

Declared partition coverage: PASS · 2/2 declared partitions (arccos, invalid-domain)
Versions: Calculation 1.0.4 · CVP protocol 1.0.0-proposed
CVP identity: 8/8 property · digest 2dd501560e45

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 1.0.4 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 1.0.4. 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 · 1/1 cross-interface · 4/4 URL→result→graph · 1/1 CVP contract. digest 2dd501560e45.

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 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 sha256:1890c7f33424a5c6968c5c448278070d5b3816f29f87fb2a418f4ea08e9e4f00

Input schema sha256:a665d5e441cdb6e1663dc0061225e8eabd385666b93278cc174877e3601d2355 · Output schema sha256:87cf516bf6b5a568747eba4fe89a0a8937987da9f414d549dea687bfa8223aa5 · 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: arccos
Engine: arccos
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 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

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 arccos on [−1, 1] with range [0, π]; degree output is θ × 180/π
CalculatorX mathematical conventions — Principal branch; exact algebraic values only for exact inputs
Supports: Published engine is arccos(x). Direct inputs outside [−1, 1] are NOT_REAL with no domain clamp.

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=60 · Actual deg=60 · rad=1.0471975511965976 · exact=true
`zero`	golden	pass	Expected deg=90 · Actual deg=90 · rad=1.5707963267948966 · exact=true
`one`	golden	pass	Expected deg=0 · rad=0 · Actual deg=0 · rad=0 · exact=true
`neg-one`	golden	pass	Expected deg=180 · Actual deg=180 · rad=3.141592653589793 · exact=true
`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
`no-domain-clamp`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL
`no-near-exact-snap`	golden	pass	Expected deg=59.99999994045648 · Actual deg=59.99999994045648 · rad=1.0471975501573674
`boundary-acos-oor`	boundary	pass	Expected NOT_REAL · Actual NOT_REAL