Public evidence

math.complex

Machine-checked verification for calculation version 1.2.2 · tier engine_tested

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

Historical evidence. This page is version 1.2.2 · engine_tested · 18/18 tests. It is not the current published claim. Current evidence is 1.3.0 (18/18 tests) · latest.

CVP status

Not a CAS, not contour integrals, not i^i. Discovery /complex-polar, /complex-power, /complex-roots, /complex-euler lock one mode.

Declared partition coverage: PASS · 12/12 declared partitions (add, sub, mul, div, rect-to-polar, polar-to-rect, conjugate, modulus, power, root, euler, invalid-domain)
Versions: Calculation 1.2.2 · CVP protocol 1.0.0-proposed · Evidence 2026-10-28.metric-scope-v3
Verification revision: 2026-10-28.metric-scope-v3 · 3/3 property · digest ad3c9713cff3

Verification

Legacy regression suite: 18/18 calculation tests · Production surface contract 5/5

Three distinct suites: educational examples on the calculator page, this legacy regression count (18/18 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 1.3.0 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.metric-scope-v3. Calculation version 1.2.2. CVP 1.0.0-proposed. 643/643 golden · 5/5 CVP boundary · 9/9 invalid · 3/3 property · 2/2 metamorphic · 5/5 cross-interface · 2/2 cross-calculator · 5/5 CVP contract. digest ad3c9713cff3.

Golden (oracle-backed) 643 / 643
CVP boundary 5 / 5
Invalid input 9 / 9
Property 3 / 3
Metamorphic 2 / 2
Cross-interface 5 / 5
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 1/1 (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:e0739588fe355615b0398bc84f6fb87c24353b515be6f2cb1ea442f6934ef49b

Input schema sha256:881a73654cc9b89d5c84225f9e9f7849260395cb6ebdde68432bfdd41593064b · Output schema sha256:f58ab55516f5f61e19df35f10232422cd2e96d09251072dde28295f3102dec91 · 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: complex
Engine: complex
Engine build: 2026-10-19
Evidence core: 2026-10-19T05:16:22.549Z
Rendered: 2026-10-29T07:58:56.678Z
Last reviewed: —

Assumptions

atan2 argument in degrees
Not a CAS

Limitations

Finite decimal inputs; matching aliases only. Missing rectangular components default0; explicit empty inputs are errors.
Power integer |n|≤1000; roots integer2≤n≤64; zero has one distinct root;0^0 undefined.
Argument in degrees (−180,180]; negative real axis assigned+180 including signed zero; origin0 by convention (undefined mathematically).
Nonzero input/output components and modulus must be normal finite binary64; unrepresentable scaling/intermediates return NUMERIC_RANGE.
Vector error budget2e-11 times modulus, argument2e-9 degrees away from ill-conditioned origin/cut; cancellation can lose relative component accuracy.
No symbolic CAS or complex noninteger powers.

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 — De Moivre and Euler form
Supports: z^n = r^n (cos nθ + i sin nθ); z = r e^{iθ}; nth roots equally spaced on a circle
NIST DLMF — 4.2 Definitions: Logarithm and Exponential
Supports: Complex exponential and logarithm definitions, including the exponential’s trigonometric representation and branch conventions. Mathematical reference only; not validation or endorsement of this implementation.
Gilbert Strang, Calculus — Chapter 9: Polar Coordinates and Complex Numbers (MIT OpenCourseWare) — §9.4 Complex Numbers
Supports: Complex arithmetic, conjugates, modulus and argument, polar/exponential multiplication and division, de Moivre’s formula and complex roots. Noninteger powers require a specified branch; those branch and numerical policies remain CalculatorX’s own contract. 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.