Public evidence

math.complex

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

Verification

18/18 calculation tests · Production surface contract 3/3

Golden tests 6 / 6
Boundary tests 4 / 4
Property tests 8 / 8
Production surface contract 3 / 3
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: STALE · Last attested schema matched 1.1.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract PASS
Evidence attested at 2026-09-18T21:41:55.460Z
Last production check 2026-09-18T21:41:55.460Z
Public / cache PASS
Origin PASS
Supplemental domain review Not performed
Named expert review Not performed

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS

Fingerprint sha256:933db0a6c85a1e68a54041b715593b584d20e12d4a85bc25db3f0509e2896082

Input schema sha256:9e89cd81a307dbc4761ec4a28c1ba4ee64806b285173cebcc467c2200b0b2c7b · Output schema sha256:1dc06d14d1da7351eb9d111c65babe633cc9932dea8fa623c3e97a86e67cf623 · 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: 2026-09-19
Evidence core: 2026-09-19T01:23:52.320Z
Rendered: 2026-09-19T02:14:29.319Z
Last reviewed: —

Assumptions

atan2 argument in degrees
Not a CAS

Limitations

Not symbolic simplify or complex analysis
Division by 0+0i → DIVISION_BY_ZERO
Integer n only for power/root; not i^i
Argument uses atan2, degrees

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

Published checks

Golden, boundary, and property cases included in this evidence build.

ID	Kind	Status	Detail
`golden-add`	golden	pass	Expected re=4 · im=6 · Actual mode=add · re=4 · im=6 · r=7.21110255093 · arg_deg=56.309932474 · euler=7.21110255093 e^{i 56.309932474°} · cis=7.21110255093 (cos 56.309932474° + i sin 56.309932474°) · formula=(re₁+re₂) + (im₁+im₂)i
`golden-polar`	golden	pass	Expected r=5 · Actual mode=rect_to_polar · re=3 · im=4 · r=5 · arg_deg=53.1301023542 · euler=5 e^{i 53.1301023542°} · cis=5 (cos 53.1301023542° + i sin 53.1301023542°) · formula=r = \|z\|, θ = atan2(im, re)
`golden-mul-i`	golden	pass	Expected re=-1 · im=0 · Actual mode=mul · re=-1 · im=0 · r=1 · arg_deg=180 · euler=1 e^{i 180°} · cis=1 (cos 180° + i sin 180°) · formula=(re₁re₂ − im₁im₂) + (re₁im₂ + im₁re₂)i
`boundary-complex-div0`	boundary	pass	Expected DIVISION_BY_ZERO · Actual DIVISION_BY_ZERO
`boundary-complex-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`golden-i-squared`	golden	pass	Expected re=-1 · im=0 · Actual n=2 · mode=power · re=-1 · im=0 · r=1 · arg_deg=180 · euler=1 e^{i 180°} · cis=1 (cos 180° + i sin 180°)
`golden-cube-roots-unity`	golden	pass	Expected n_roots=3 · re=1 · Actual n=3 · mode=root · k=0 · re=1 · im=0 · r=1 · arg_deg=0 · euler=1 e^{i 0°}
`golden-euler-identity`	golden	pass	Expected re=-1 · im=0 · Actual mode=euler · re=-1 · im=0 · r=1 · arg_deg=180 · euler=1 e^{i 180°} · cis=1 (cos 180° + i sin 180°) · formula=z = r e^{iθ} = r (cos θ + i sin θ)
`boundary-complex-zero-pow0`	boundary	pass	Expected INVALID_INPUT · Actual INVALID_INPUT
`boundary-complex-root-n1`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`property-cx-add`	property	pass	sum
`property-cx-i2`	property	pass	i²=-1
`property-cx-mod`	property	pass	\|3+4i\|=5
`property-cx-roundtrip`	property	pass	polar round-trip
`property-cx-conj`	property	pass	conjugate
`property-cx-i2-power`	property	pass	power i²
`property-cx-roots3`	property	pass	cube roots of 1
`property-cx-euler`	property	pass	e^{iπ}=-1