Carry direction through the calculation

The previous static-bound replacement did not improve complete predictions. The next component keeps separate horizontal and vertical bounds as values move through the calculation. It does not discard the tighter training-derived information already available.

The prototype now supports vector and matrix arithmetic, matrix actions, scalar reciprocals and square roots. It keeps separate coordinate-change and reference-linearization error bounds. Operations use exact rational bound arithmetic, outward export and explicit reference-value rounding allowances. Singular or ambiguous domains are rejected.

Forty local tests cover exact polynomial curves, matrix actions, rounding, immutable inputs, source-prefix support and rotation controls. A separate rotation-length identity can tighten vertical departure when the learned force direction is known. Its norm and linearization premises must be established from the source; an interval box alone cannot prove them. These are mathematical controls, not aircraft findings or measurements of the cause of the current prediction widths.

What remains

The six-source preflight now passes against the actual saved source and its training-conditioned bounds. A value-range improvement is insufficient for replacing a Taylor remainder: all reference coefficients must agree or their differences must be bounded explicitly. Rotation updates, inverse-skew operations, time and lever-arm terms also need compatible bounds. Preserve every physical/shared-error column and test improvement against the actual baseline before another complete comparison.

The prototype is separate from all frozen engines. It has not produced new aircraft fits or qualified full-recording prediction ranges.

Implementation · Operator derivation · Matrix operations · Scalar and rotation identity · Tests · Previous diagnosis · Roadmap.