Native reference-acceleration construction
The component qualification is complete. This plan specifies the next candidate; it permits no observed fits. Add a separate module rather than editing completed shared-reference sources. Keep all 27 physical bounds and the native midpoint equations. A new finite native qualification must be frozen before execution.
Preserve relative attitude, including its derivative
A coarse bound on (R_mid-R_initial)*f_reference is insufficient: subtracting
two independently bounded attitudes loses their common initial rotation. Because
the reference force is near gravity in magnitude, that lost cancellation can
recreate the original broad remainder.
Preserve the exact factors R=Q*R_initial*P, where Q accumulates the left
navigation rotations and P the right body rotations. Track E_Q=Q-I and
E_P=P-I directly. For a small left increment E_step=exp(-win*dt)-I,
E_Q_new=E_Q+E_step+E_step*E_Q.
For a right body increment E_body=exp(theta)-I,
E_P_new=E_P+E_body+E_P*E_body.
An exponential-minus-identity has the same derivative/remainder as the original
exponential, but a small center norm. Reconstruct complete rotation matrices
with the known rotation norm when required. At a half step, build the analogous
Q_mid/P_mid from the same old state and the native half increments. Then
force_rest=E_Q_mid*R_initial*P_mid*f_reference
+R_initial*E_P_mid*f_reference
+R_mid*(f_current-f_reference).
This exact identity keeps relative-attitude changes small without declaring aircraft motion zero. Common force-bias cancellation must be algebraic, as in the component plan. Every calibration column stays present.
Accumulate departures from the reference velocity
Maintain v=v_initial+A*S+u, where S is the common accumulated period and
u contains all departures. For the native skew argument
a=(dt/2)*(2*earth+transport) and B=(I+[a]x)^-1, the exact residual increment is
du=B*(dt*force_rest-2*(a cross v)-dt*(a cross A)).
The complete increment is A*dt+du. The last term follows from
(B-I)A=-B*(a cross A); omitting it changes the model. Gravity is already in
the reference A; do not add it a second time. Field removal affects the same
navigation-rate terms as in the unchanged engine.
Follow the existing two-context midpoint construction: first estimate an increment using transport at the provisional midpoint, then derive revised coordinate rates from the midpoint of the old velocity and that estimate. Use those revised rates for the final transport/increment. Do not substitute an average involving the final corrected velocity.
At that midpoint, use the reference velocity
v_initial+A*(S_previous+dt/2) and residual u_previous+du_estimate/2.
For fixed initial metric m0 and current midpoint metric m, split rates into
m0*v_initial + m0*A*S_mid
+ m*u_mid + (m-m0)*(v_initial+A*S_mid).
Integrate only the last two terms as departures. The constant-reference terms
sum exactly to m0*(v_initial*S + A*S*S/2). Use the correlated prefix clock;
do not accumulate independent quadratic time errors. Initial-velocity scalar
bounds retain their per-axis domains, as in the previous candidate.
Intermediate position/velocity/metric bounds must include the complete common errors. Their indirect influence on transport, gravity-frame rotation and geographic denominators cannot be removed by final observation factorization.
Factor only the final observation
Use the qualified acceleration component's three common vectors and the clock
center s, native slope q, and remainder e. The acceleration polynomial's
unshared allowance retains
A_max*((abs(s)+abs(q)*delta_tau_max)*e_max + e_max*e_max/2).
Its nine coefficients are the known fixed metric times q*q, s*q and
s*s/2, with the component's normalization radii. Keep the prior six
velocity/time and initial-lever columns. All epochs use one source-bound
15-vector; no block can be dropped or independently reselected per epoch.
The lever can use the same relative factors:
(R-R_initial)L=E_Q*R_initial*P*L+R_initial*E_P*L.
Retain metric/lever cross terms and the existing initial-lever common error. This also avoids bounding a small attitude departure by the sum of two large initial-attitude uncertainties.
Tests and next gate
First use independent constant-force/constant-velocity controls where the reference polynomial is exact, including nonzero actual levers, offset signs and calibration centers. Compare centers and all 27 tangent columns against the unchanged native engine for every model/processing case. Check actual known control common vectors against the new unshared remainder at corners and fixed interior points. Include packet boundaries and clock slopes other than one.
Retain the existing 1 micrometre center/pose, 20 micrometre tangent-column and 10 micrometre arithmetic comparison limits unless a separate justified method specifies a genuinely different question. Do not relax them to obtain success. No complete floating-point enclosure follows from numerical agreement alone.
Next qualify a typed 42-column joint interface with complete source/domain/ expansion bindings and future-truth isolation, then freeze a matched complete orientation-cover comparison. Short correctness and usefulness do not establish recording-scale uncertainty, receiver-error adequacy or independent confirmation.