Public evidence

math.numerical.interpolate

Machine-checked verification for calculation version 1.1.0 · tier engine_tested

Open calculator API Capability Download JSON MCP Review policy

Verification

13/13 calculation tests · Production surface contract 4/4

Golden tests 4 / 4
Boundary tests 2 / 2
Property tests 7 / 7
Production surface contract 4 / 4
Engine tested Yes
Source checked Yes
Artifact integrity PASS
Production attestation Embedded snapshot: unpublished · Build schema 1.1.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT)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 —
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 sha256:04761ef110e87c6f4f6ebc725d35dd25017d0474ed8a93ffe43a1f4d7e448d72

Input schema sha256:520b91ca6f72fd59f598a333ae26f1e3266f9c3f01da970ae68e3ced324ccba0 · Output schema sha256:d6e80d7818c522dea0dd306929f1b4d5ac7c85ec5f6fda46d0659e96eb245cff · 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: numerical-interpolation
Engine: numerical-interpolation
Engine build: 2026-09-19
Evidence core: 2026-09-19T01:46:58.355Z
Rendered: 2026-09-19T02:14:29.321Z
Last reviewed: —

Assumptions

Unique x; sorted internally
Natural spline ends, not clamped
Not Akima / PCHIP / regression / CAS

Limitations

Not Akima, PCHIP, clamped spline, or statistical regression
Linear/spline x outside the table without extrapolate → VALUE_OUT_OF_RANGE
Lagrange limited to 9 points (degree ≤ 8); linear/spline table ≤ 100
Not a second interpolator and not CAS

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-linear-mid`	golden	pass	Expected y=10 · Actual n=2 · method=linear · x=5 · y=10 · x_min=0 · x_max=10 · in_range=true · extrapolated=false
`golden-lagrange-x2`	golden	pass	Expected y=2.25 · Actual n=3 · method=lagrange · x=1.5 · y=2.25 · x_min=0 · x_max=2 · in_range=true · extrapolated=false
`golden-spline-mid`	golden	pass	Expected y=0.6875 · Actual n=3 · method=spline · x=0.5 · y=0.6875 · x_min=0 · x_max=2 · in_range=true · extrapolated=false
`golden-spline-2pt`	golden	pass	Expected y=10 · Actual n=2 · method=spline · x=5 · y=10 · x_min=0 · x_max=10 · in_range=true · extrapolated=false
`boundary-out-of-range`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-akima`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-lerp-mid`	property	pass	linear midpoint
`property-lerp-node`	property	pass	linear at x0
`property-lagrange-2pt`	property	pass	lagrange 2-pt = linear
`property-lagrange-x2`	property	pass	P(x)=x² at 1.5
`property-extrapolate`	property	pass	linear extrapolate
`property-spline-mid`	property	pass	natural spline (0,0)(1,1)(2,0) at 0.5
`property-spline-line`	property	pass	collinear spline = linear