Public evidence

math.modulo

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

Verification

9/9 calculation tests · Production surface contract 4/4

Golden tests 2 / 2
Boundary tests 2 / 2
Property tests 5 / 5
Production surface contract 4 / 4
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract PASS
Evidence attested at 2026-09-16T06:44:24.203Z
Last production check 2026-09-16T06:44:24.203Z
Public / cache —
Origin —
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
schema rejects incomplete input PASS

Fingerprint sha256:5ba3a81dd04037965fc6b23d197c431682f90dc6c960dd3d5db6d516b6d5828f

Input schema sha256:19372bdf1fd728b662c50bf812d7e8aa118d70ce261d2d2631e0ae8e010ac866 · Output schema sha256:1b4650313a5147e01abd108983a2ef1a1df66e3f5eee1a782caf14785a16d623 · 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: modulo
Engine: modulo
Engine build: 2026-09-16
Evidence core: 2026-09-16T14:30:31.968Z
Rendered: 2026-09-16T14:39:28.358Z
Last reviewed: —

Assumptions

Euclidean remainder
Not JavaScript truncated %
Integers only

Limitations

Euclidean remainder, not truncated or floored remainder toward −∞ of the quotient only
Not IEEE remainder or floating-point fmod
modulus = 0 → DIVISION_BY_ZERO
Share URLs use modulus, not m (m is reserved elsewhere)

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 (integer division / remainder)
Knuth, The Art of Computer Programming, Euclidean division (remainder ≥ 0)

Published checks

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

ID	Kind	Status	Detail
`golden-mod`	golden	pass	Expected remainder=2 · quotient=3 · Actual a=17 · modulus=5 · remainder=2 · quotient=3 · identity=17 = (3)·(5) + 2 · convention=euclidean
`golden-mod-negative`	golden	pass	Expected remainder=3 · quotient=-4 · Actual a=-17 · modulus=5 · remainder=3 · quotient=-4 · identity=-17 = (-4)·(5) + 3 · convention=euclidean
`boundary-mod-zero`	boundary	pass	Expected DIVISION_BY_ZERO · Actual DIVISION_BY_ZERO
`boundary-mod-missing`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`property-mod-pos`	property	pass	17 = 3·5 + 2
`property-mod-neg`	property	pass	−17 = (−4)·5 + 3
`property-mod-range`	property	pass	0 ≤ r < \|m\|
`property-mod-identity`	property	pass	a = q·m + r
`property-mod-neg-m`	property	pass	r still in [0,\|m\|)