Training information may narrow the prediction region
The affine contractor is implemented and all 10 component tests pass, including exact-rational feasible-point checks, signed/zero columns, near-touching bounds and overflow rejection. A separately frozen finite qualification is next; no native uncertainty box has been narrowed by these tests.
The connected native source passes all 24 frozen interface controls. Useful recording-scale nonlinear bounds remain the limiting requirement. A small calibration box chosen around a fitted answer is not automatically a valid replacement for the full declared parameter region.
The next mathematical prerequisite contracts a box using necessary training
constraints while retaining every nuisance coordinate. For an approximation
f(theta) = f0 + J*(theta-center) + remainder, observations y, componentwise
measurement allowances e and valid global remainder bounds r imply
Each row provides conservative bounds for a coordinate by allowing every other coordinate to vary over its entire current interval. Intersect those bounds with the old box and repeat a finite number of times. Use outward arithmetic; preserve zero/unidentified columns. A contradiction may exclude a box only when its entire outward row interval misses the necessary constraint. Lack of contraction is a valid outcome, not a reason to delete a parameter.
Implementation and qualification
lll.ilvis0_training_boxis a pure affine-constraint component. It accepts a full box, matrix and lower/upper row constraints. It reads no archive, performs no native integration or fitting, and makes no scientific decision.- Check exact known intervals, contradictory rows, all 27 columns, signed and zero coefficients, nearly touching boundaries and finite iteration limits. Compare retained feasible points with an independent exact-rational oracle.
- An outward overflow or unsupported domain must fail, not silently clip away possibilities. Return unresolved width honestly when the constraints are weak.
- After these tests, freeze a finite generated qualification before applying any contraction to a native prediction uncertainty construction.
What this does not supply
This calculation cannot establish the measurement allowances, global nonlinear remainders or native floating-point error. Those must be valid over each input box. Any statistical coverage comes from a separately justified training-noise event and shared scale, not from interval contraction itself. If every true parameter satisfies the input inequalities on that event, conservative repeated intersection preserves that same event; it does not create another independent confidence claim.
If the full-box remainder makes the inequalities uninformative, this step may leave the box unchanged. Supported short-prefix constraints, separate branches or tighter global propagation would then be needed. No observed fit or protected ESA outcome is authorized by a successful affine software control.