Preserve source derivatives in the remainder

The six-source screen completes under the original limits. All height bounds improve, but all horizontal bounds widen. No complete prediction comparison or aircraft fit follows directly from this result.

Develop a separate conservative interval calculation of the physical body sources and their calibration derivatives over the declared parameter box. Keep the literal recorded inputs, mounting matrix, all 27 physical columns and both packet phases. Include the reference point in the convex domain used for the derivative proof. Do not reuse an unrelated saved body Taylor radius.

For a physical source component f, supplied numerical center c, supplied row j, reference z0 and box displacement limits w, the mean-value bound is

remainder <= |f(z0) - c| + sum(w[k] * sup_box |df/dz[k] - j[k]|).

Each supremum must have an outward enclosure. Bound the ideal source value at the reference independently of the rounded native center. Treat clipped packet fractions as continuous, piecewise differentiable functions and include both one-sided slopes where the domain crosses a boundary. No hidden clock-column drop is permitted.

First check the rotation value and derivative enclosures against independent exact-rational references, then the source stream against independent known answers. Only after that may a separately frozen candidate intersect these Taylor bounds with the existing physical/training norm closures and qualify native propagation. Preserve every center, matrix, domain binding and existing acceptance criterion. A fresh complete comparison is required before observed prediction work can proceed.

This development uses generated data only. It does not authorize new aircraft starts, confirmation-data inspection, cap expansion or a claim of calibrated coverage.