Bound the actual midpoint local step
The completed component study covers reciprocal calibration, rotations and
fixed-time body preintegration. Continue with the actual local step in
ilvis0_native.c and ilvis0_tangent.cpp, without changing either frozen kernel.
No observed-data prediction starts follow from the component pass.
Local dynamics
For skew matrix S(a), the native velocity update uses
B(a) = (I + S(a))^-1 and T(a) = B(a)*(I - S(a)) = 2*B(a)-I.
B has operator norm at most one; T is orthogonal. The resolvent identity
gives global first-derivative/Taylor constants of 1/1 for B and 2/2 for T.
Include vector-product remainders, rather than treating these factors as fixed.
The midpoint force rotation is
Exp(-win*dt/2) * attitude * Exp(theta/2) * dv, while final attitude uses
full rotations. Propagate both rotation products with their orthogonality intact.
The local velocity update combines T(a)*v with B(a)*(force + gravity*dt).
Preserve the native processing distinction:
win = physical_background + transport - removal*standard_background;a = (2*physical_background + transport)*dt/2.
Removal changes the logged-rate interpretation, not the physical Coriolis term. The conventional standard vector is the same for every candidate, including the stationary disc. Do not replace it with a candidate-specific field.
Qualification and remaining closure
Start with independent linear algebra/exponential references and supplied global vector/matrix input bounds. Test large attitude changes, joint force/ rate uncertainty, both hemispheres, all three candidate field assignments, zero/profiled removal and nearly zero rates. Check every nominal value and directional derivative before qualifying a separately frozen finite matrix.
Then construct global geographic-rate/context bounds from a supported state region and propagate the predictor/corrector step as actually coded. Domain crossings must be unsupported, not clipped. Receiver-time uncertainty across packet boundaries and long-record floating-point effects remain separate.
These are prerequisites to a complete native global bound. Local software success cannot itself calibrate the receiver error family or authorize a new observed prediction study.