Public evidence

math.vector

Machine-checked verification for calculation version 1.6.1 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.6.1 · engine_tested · 11/11 tests. It is not the current published claim. Current evidence is 1.7.1 (11/11 tests) · latest.

CVP status

Not a matrix, not coordinate geometry, not CAS, not /add, not /angle-between-lines. Discovery pages lock one mode.

Declared partition coverage: PASS · 10/10 declared partitions (magnitude, normalize, add, sub, dot, cross, angle, projection, triple, invalid-domain)
Versions: Calculation 1.6.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-29.cross-product-hardening-iface2
Verification revision: 2026-09-29.cross-product-hardening-iface2 · 7/7 property · digest 3e840b22dc12

Verification

Legacy regression suite: 11/11 calculation tests · Production surface contract 5/5

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.

STALE · Build schema 1.7.1 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 2026-09-29.cross-product-hardening-iface2. Calculation version 1.6.1. CVP 1.0.0-proposed. 10/10 golden · 4/4 CVP boundary · 9/9 invalid · 7/7 property · 6/6 cross-interface · 2/2 cross-calculator · 5/5 CVP contract. digest 3e840b22dc12.

Golden (oracle-backed) 10 / 10
CVP boundary 4 / 4
Invalid input 9 / 9
Property 7 / 7
Cross-interface 6 / 6
Cross-calculator 2 / 2
CVP contract 5 / 5
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
rest success payload validates schema PASS

Fingerprint sha256:ac32314f62ded5a898784c2f40399ab969489b6d6f6b031d6e29d3d45d860e06

Input schema sha256:c3b0a52d9ad70c13d4218478382853570277d3da941c09450b5ff6939e1bd78b · Output schema sha256:ce4391db313211e8fe668eab2a2fd0927ee72392981b21a44b5dc428ab879690 · 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: vector
Engine: vector
Engine build: 2026-10-14
Evidence core: 2026-10-14T05:05:51.930Z
Rendered: 2026-10-19T05:16:54.635Z
Last reviewed: —

Assumptions

Euclidean R²/R³
uz/vz/wz default to 0
Not a matrix
Not coordinate geometry
Not CAS

Limitations

R²/R³ only; uz/vz/wz default to 0
Not a matrix — det / inverse / eigen stay on math.linear_algebra
Not coordinate geometry (two-point line / intersection / angle between lines)
Angle is the vector included angle in [0°, 180°], not the acute line angle
Zero vector: magnitude 0 is valid; normalize / angle / projection → INVALID_INPUT
unknown mode (including cas, eigen, matrix) → INVALID_MODE

Sources

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

ISO 80000-2:2019 Quantities and units — Mathematics
Supports: Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.
CRC Standard Mathematical Tables — vector algebra in R³
Supports: u·v, u×v, proj_v u, and the scalar triple product u·(v×w)
Gilbert Strang, Calculus — Chapter 11: Vectors and Matrices (MIT OpenCourseWare) — §§11.1–11.3 Vectors, Dot Products, Projections and Cross Products
Supports: Vector components and magnitudes, dot product and angle/projection relations, and cross product/determinant orientation and area. Projecting a point displacement onto the unit normal to Ax+By+C=0 gives distance |Ax₀+By₀+C|/sqrt(A²+B²); this planar expression is derived from the projection formula. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Verification disclosure

Aggregate outcomes, scope and artifact commitments are public. Complete test inputs, expected values, execution records and oracle infrastructure are retained privately. This summary does not independently reproduce the full verification run.