Next component: keep calibration errors mutually consistent

The complete common-transform comparison passes correctness but misses its fixed improvement target. Its saved-only audit passes. Further duration expansion is deferred while the remaining conservatism is investigated.

The reference acceleration and the force-transform matrix depend on the same physical orientation, accelerometer gain and bias. The current relaxation allows their remainder coordinates to vary separately. Add only necessary consistency constraints, with no tighter physical bounds, new drift process, discarded orientation sector or extra fitted information.

Mathematical candidate

Let the common matrix be M, reference specific force f, constant accelerometer bias b and gravity g. Reference acceleration satisfies

A = M (f - b) + g e_D.

Write M = M_c + J_M δp + E_M and A = A_c + J_A δp + E_A. With b = b_c + J_b δp, the exact relation is

E_A - E_M (f - b_c)
  = d_0 + (J_M (f - b_c) - M_c J_b + e_D J_g - J_A) δp
    - (M - M_c) J_b δp.

Here d_0 = M_c (f - b_c) + g_c e_D - A_c. Preserve centre and Jacobian mismatches explicitly; do not assume different floating-point constructions cancel exactly. Bound the final product over the entire original physical region. Express the result as six outward necessary inequalities on the existing 51 coordinates. Keep force/clock/reference bindings explicit.

Qualification before use

First test the relation independently: exact affine controls, full rotations, sector and point domains, gain boundaries, signs and every affected coordinate. Use an independent rotation/force oracle and exact rational inequality checks. Verify finite input validation, stale bindings, zero caps, outward coefficient conversion and preservation of known physical calibrations. No sampled test alone establishes the global bound.

Freeze finite identities, evaluations, environment and sources before the component qualification. Only after it passes, prepare a separate saved-only 48-case comparison using the sealed training and future artifacts. It should need no new native integration or observed fitting. Compare complete sector unions, preserve every failure and keep correctness separate from narrowing. Future truth remains unavailable until the revised prediction is saved.

If the candidate is invalid or unhelpful, publish that result rather than relaxing the earlier target. Recording-scale usefulness, numerical enclosure and observational-error adequacy remain prerequisites for new aircraft fits.