Preserve joint calibration constraints

The completed contraction keeps every true generated parameter, but enclosing all feasible possibilities in one coordinate box loses important correlations. The shared training-error calculation is now complete as a separate component; it does not fix that geometric limitation.

Why a linear improvement alone is insufficient

In the first generated specified-field/no-removal case, the saved post-contraction nonlinear remainder allowances are about 210.64 m north, 156.78 m east and 144.16 m in height. Adding these symmetric allowances independently already contributes widths of roughly 421 / 314 / 288 m, before any remaining affine uncertainty. An exact solution of the affine constraints alone cannot remove that contribution from the current construction.

This is a limitation of the computed enclosure, not a lower bound on actual aircraft uncertainty. The next method must preserve joint constraints and reduce nonlinear overestimation. Narrowing a box around a fitted answer without proving that other possibilities are excluded is not acceptable.

First: certify affine support without trusting optimizer status

Implement a separate support calculation for the full parameter box intersected with necessary training inequalities. Keep all 27 columns. A numerical linear program may propose nonnegative inequality multipliers, but it does not certify the result. For any such multipliers lambda, the bound

c*x <= lambda*b + max_box((c - A.T*lambda)*x)

is valid whenever A*x <= b. Evaluate this certificate with exact rational arithmetic from the supplied binary inputs, then check outward endpoints. Use the opposite signed objective for a lower bound. A poor proposed multiplier can only loosen the bound; never label a region empty from an unverified solver status. Missing certificates fall back to the full box or explicitly abstain.

Qualify against independent small exact polytope optima, deliberately wrong or incomplete solver proposals, weak/contradictory constraints, zero columns and 27-coordinate correlated examples. Known feasible points must remain enclosed. Record finite software identities and arithmetic/runtime limits before launch. This mathematical component authorizes no aircraft fits.

Then: test a complete orientation cover on generated inputs

Prepare a separate finite feasibility study that partitions the original yaw interval into closed sectors covering the whole original interval. Recenter native expansions in each sector, retain every other calibration bound, and carry sector-specific training inequalities through to future support bounds. The union must include all sectors not rigorously excluded by necessary constraints. Never choose sectors using future truth or model preference.

Reuse the completed generated experiment's input definitions and all three physical candidates under both processing cases; create a new source/input freeze and work allowance. Preserve the old result. Compare truth containment, union widths, remainder widths and cost with the saved broad-box baseline. Time the new component before freezing the number of sectors and native calls. Stop at the finite allowance; a correct but still broad result fails usefulness.

No observed prediction fit follows until useful global propagation, numerical error treatment, training-only fit provenance and observational assumptions are qualified. Protected ESA outcomes remain untouched.

Completed contraction · Shared error-source assessment · Canonical roadmap.