Research question. Which interpolation claims survive when a query crosses a knot or leaves the tabulated domain?
Predict¶
Predict exact recovery of affine data inside a cell. Separately predict the observable results of clamp, fill, and reject policies outside the grid. Do not extend an interior derivative prediction across a discrete cell or policy change.
Compute¶
uv run --no-sync python -m examples.investigations.interpolation_boundary_policiesThe example evaluates public one-dimensional and regular-grid APIs on analytic affine fixtures and records interior value/derivative errors and boundary events.
Audit¶
Compare values and derivatives with the analytic affine map. Exercise all three boundary policies deliberately. Then follow the callable contracts in Scientific contract registry to their validation targets and limitations.
Misconception check¶
Smooth interpolation within a selected cell does not imply differentiability of the cell selection or the clamp/fill/reject boundary.
State the warranted claim¶
The affine fixtures validate branch-stable interior values and derivatives plus explicit boundary policy behavior. They make no derivative claim at knots or policy transitions.