math.cos

Three distinct suites: educational examples on the calculator page, this legacy regression count (6/6 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 1.0.6 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 2026-10-28.meta-metrics-v2. Calculation version 1.0.6. CVP 1.0.0-proposed. 103/103 golden · 2/2 CVP boundary · 27/27 invalid · 3/3 property · 3/3 metamorphic · 4/4 round-trip · 18/18 O3 · 125/125 cross-interface · 8/8 cross-calculator · 4/4 URL→result→graph · 6/6 CVP contract. digest 176d7e8ae931. ≤2 ULP vs O3 applies to the 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros.

• Golden (oracle-backed) 103 / 103
• CVP boundary 2 / 2
• Invalid input 27 / 27
• Property 3 / 3
• Metamorphic 3 / 3
• Round-trip 4 / 4
• O3 high-precision 18 / 18
• Cross-interface 125 / 125
• Cross-calculator 8 / 8
• URL → result → graph 4 / 4
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP / URL→result→graph
• Interface claim Success 100/100. Error-path engine·REST·MCP 25/25 (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
• schema rejects incomplete input PASS
• rest success payload validates schema PASS

Fingerprint sha256:348d86f79bb60e8e2de13fb954db78409a100c70903ab38fbc86e02d8eaaa796

Input schema sha256:8533d44fa37a31f3772f9576730ec8bf3d8d630083f67b733f1228d6ee048842 · Output schema sha256:cb5c16fd5104b304380d3fec82b9db29daa5a348b30230ce908e3260f8f4b4fa · 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

cos

Engine

cos

Engine build

2026-10-27

Evidence core

2026-10-27T08:11:07.887Z

Rendered

2026-10-28T03:01:57.877Z

Last reviewed

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Assumptions

• Real cosine. The published engine supports angle and triangle-ratio modes. Adjacent/hypotenuse is a shared ratio mode (hypotenuse > 0, adjacent ≥ 0, adjacent ≤ hypotenuse). Use Arccos for the inverse API.
• Algebraic snap applies only when the reduced angle (mod 360°) is a listed identity such as 0°, 30°, 45°, 60°, 90°. Nearby degree floats keep their distinct reduced-quadrant binary64 evaluation; generic radians use Math.cos.

Limitations

• Angle mode: finite binary64 theta; deg(default) or rad. Degree reduction uses signed remainder before quadrant reduction; no add360 or angle-proximity epsilon. Listed common degree angles and 17 normalized binary64 radian tokens within ±2π use symbolic recognition, not mathematical exactness of floating-point radians.
• Ratio mode: finite adjacent≥0, hypotenuse>0 and adjacent≤hypotenuse; returns adjacent/hypotenuse. A nonzero ratio rounding tozero rejects RESULT_UNDERFLOW. Angle fields in ratio mode and side fields in angle mode reject UNEXPECTED_INPUT.
• Numeric aliases theta/t/angle/thetaInput, adjacent/adjInput and hypotenuse/hypInput must agree; unit/unitInput normalize degree(s)/°/radian(s), case/space accepted. Missing mode defaultsangle. Unknown keys reject. Explicit null/blank numeric fields reject; null/blank unit defaultsdeg.
• Strict decimal/scientific source text ≤512 characters; hexadecimal, booleans and grouped numbers reject. Nonzero text rounding tozero rejects NUMERIC_UNDERFLOW. RawJSON numbers are checked before lossy parse; finite subnormal accepted.
• Independent Decimal420/620 Taylor/Machin and Fraction references:2ULP fixed-vector ceiling; zero/sign/types strict. Legacy18 O3 samples retain2ULP budget; no whole-domain or cross-runtime bitwise guarantee. Radian generic path uses Math.cos; degrees reduced before conversion.
• Nearzeros relative conditioning is unbounded; large input spacing loses source angle information before computation. Cosine may legitimately round to±1. Display12significant digits falls back tofull binary64 if rounding changes a boundary. Native exports preserve full scalar and raw inputs.
• Graph omitted in ratio mode and for |theta|>1e6; diagram/derived angle is not independent verification. Typing local; sharedURLs/REST/MCP send inputs and may enter logs.