Certified erf envelope

Beacon vendors the Chelis WI-13 certified erf envelope artifact for sound bounding of erf operations in WireDag graphs.

Artifact location and integrity

The certified envelope lives at:

data/erf_envelope.json

Its SHA-256 hash is pinned:

2470666bfb3b57ed85043fd2d0498fd9da2cf3cce61a2db9639d5f20c61b1d43

Beacon verifies this hash at load time. If the artifact has been modified, Beacon refuses to proceed.

How it works

The erf envelope is a piecewise representation of the error function, composed of:

• Polynomial segments: certified polynomial approximations valid over specific subintervals of the real line.
• Saturation segments: regions where erf(x) is close enough to ±1 that a tight constant bound suffices.

When Beacon encounters an erf node in the WireDag, it:

1. Computes the propagated argument range (the interval flowing into the erf node).
2. Looks up which envelope segments overlap that argument range.
3. Evaluates the certified polynomial or saturation bound over each overlapping segment.
4. Takes the union of the resulting output intervals.

The result is a sound enclosure of all values erf(x) can take for x in the propagated argument range.

Why a vendored artifact

The erf function has no closed-form expression in elementary functions. Bounding it soundly requires either arbitrary-precision evaluation (expensive) or a pre-certified approximation. The WI-13 envelope provides the latter: a fixed, auditable artifact whose correctness is established once and reused across all Beacon invocations.