Public evidence

math.prime_factorization

Machine-checked verification for calculation version 1.0.0 · tier engine_tested

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Verification

11/11 calculation tests · Production surface contract 3/3

Golden tests 3 / 3
Boundary tests 2 / 2
Property tests 6 / 6
Production surface contract 3 / 3
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Production attestation Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status PASS (0 stale; 164 CURRENT) @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

Fingerprint sha256:b89c30b7ff14bba3f4754488b02426f6bed77fbe3e83717d726c89b4d580672e

Input schema sha256:87cce1a3541796472731ab489ebec577a891fa572e053d23bc4123c56d289420 · Output schema sha256:03cb63458fd0dc6ded0829e175d96b9c62c227a6e33a5ffed917dde071a6145f · 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: prime-factorization
Engine: prime-factorization
Engine build: 2026-09-16
Evidence core: 2026-09-16T14:30:31.968Z
Rendered: 2026-09-16T14:39:28.358Z
Last reviewed: —

Assumptions

Unique factorization (fundamental theorem of arithmetic)
Trial division
n = 1 is neither prime nor composite

Limitations

Trial division only — not a primality-proving sieve for cryptographic sizes
n = 1 is neither prime nor composite (empty factorization)
Domain 1 ≤ n ≤ 10^12
n < 1 → VALUE_MUST_BE_POSITIVE
unknown mode → 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 (primes / factorization)
Fundamental theorem of arithmetic

Published checks

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

ID	Kind	Status	Detail
`golden-factor-12`	golden	pass	Expected canonical=2^2 × 3 · is_prime=false · omega=2 · big_omega=3 · Actual n=12 · mode=factorize · is_prime=false · canonical=2^2 × 3 · omega=2 · big_omega=3 · max_n=1000000000000
`golden-prime-13`	golden	pass	Expected is_prime=true · canonical=13 · Actual n=13 · mode=factorize · is_prime=true · canonical=13 · omega=1 · big_omega=1 · max_n=1000000000000
`golden-one`	golden	pass	Expected canonical=1 · is_prime=false · omega=0 · Actual n=1 · mode=factorize · is_prime=false · canonical=1 · omega=0 · big_omega=0 · max_n=1000000000000
`boundary-prime-zero`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-prime-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-factor-12`	property	pass	12=2^2×3
`property-prime-13`	property	pass	13 prime
`property-one`	property	pass	1 not prime
`property-product`	property	pass	∏ p^e = n
`property-square`	property	pass	49=7^2
`property-composite-mode`	property	pass	9 not prime