math.vector

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

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-10-19.vector-full-review-v8. Calculation version 1.7.1. CVP 1.0.0-proposed. 387/387 golden · 4/4 CVP boundary · 28/28 invalid · 7/7 property · 6/6 cross-interface · 2/2 cross-calculator · 6/6 CVP contract. digest ce42f17d98f9.

• Golden (oracle-backed) 387 / 387
• CVP boundary 4 / 4
• Invalid input 28 / 28
• Property 7 / 7
• Cross-interface 6 / 6
• Cross-calculator 2 / 2
• CVP contract 6 / 6
• Interfaces PASS · UI (SSR) / REST / MCP
• Interface claim ui-ssr is query-result HTML, not a live browser session. 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.
• Verified scope all published modes
• 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:ca9fc104c4c1d96f54eea8621842b545f839b6d8448d8c52b12cc1ad6418cb3b

Input schema sha256:424f2494bbe9b9bae719a6bb04a7904dc69995f7cc398a3f46c715be3bef0c4d · Output schema sha256:d0ed0cc129b88ebb9d65abf827900664f6a174aaf18f3cd4c5e54f18ce6248fa · 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

vector

Engine

vector

Engine build

2026-10-19

Evidence core

2026-10-19T06:48:56.530Z

Rendered

2026-10-23T01:27:11.640Z

Last reviewed

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Assumptions

• Euclidean R²/R³
• Absent z defaults to 0; explicit empty/null is invalid
• Not a matrix
• Not coordinate geometry
• Not CAS

Limitations

• R²/R³; required x/y for each active vector; optional z defaults to zero only when absent. Explicit empty or null is invalid.
• Nonzero inputs and published fields must be finite normal binary64 (at least 2^-1022); NUMERIC_RANGE requires rescaling. Decimal text that rounds to zero is NUMERIC_UNDERFLOW.
• Dot/cross/triple, addition and projection use exact dyadic intermediate arithmetic; published values are binary64, not arbitrary precision. Magnitude, normalization and angle are approximate.
• Zero u is valid for magnitude and projection; zero direction is invalid for normalize/angle and zero v is invalid for projection.
• Included angle is atan2(|u×v|,u·v) in [0°,180°], with radians and cosine. Direction becomes sensitive near zero; relative component accuracy can deteriorate under cancellation.
• Consistent component units: magnitude/add/sub/projection retain units, dot/cross square units, triple cubes units, normalized components and projection scale dimensionless.
• Figures show only exact z=0 modes other than cross/triple. A shared linear scale can hide subpixel arrows; those are labeled, never changed to zero.
• Not matrices, coordinate geometry or CAS. Unknown mode is INVALID_MODE; unsupported input keys are rejected.