Candidate: preserve a common reference acceleration

This is a proposed continuation if the duration screen confirms that position propagation dominates the remaining allowance. It authorizes no new observed fits. Preserve the completed shared-reference comparison and its source freeze.

Exact physical split

At the fixed joint expansion, choose one recorded reference specific-force sample. For a physical calibration vector p, define a constant navigation-frame reference acceleration

A(p) = R_initial(p) * f_reference(p) + g(p) * e_down.

This is an algebraic reference term, not an additional measured force or an assumption of constant actual aircraft acceleration. Keep every departure from it. In particular,

R_mid f_current = R_initial f_reference + (R_mid - R_initial) f_reference + R_mid (f_current - f_reference).

For a common bias/gain calibration, the force difference has exact cancellation of the common additive bias:

f_current - f_reference = (raw_rate_current - raw_rate_reference) / (1 + gain).

Do not bound two independent bias terms and subtract their radii. Differences must use the declared incremental-velocity periods without interpolating data. Bound the attitude difference by accumulated physical rotation, retaining field, transport and calibration effects. Preserve supported gain domains.

The midpoint velocity equation also contains B=(I+[a]x)^-1. Splitting off A * period requires retaining (B-I) A, using the exact identity (B-I) A = -B (a cross A), and the existing force, gravity, Coriolis and transport remainders. Keep the native predictor's estimate-based midpoint; substituting a midpoint of the final corrected velocity changes its model.

Accumulate velocity departures from v_initial + A*S directly. Split coordinate rates with a fixed reference metric, retaining every changing-metric term. The constant-acceleration contribution to position is A*S*S/2; do not independently widen the same time/acceleration at every packet. Intermediate state bounds must retain the complete common errors and their indirect effects on geographic metrics and dynamics.

One polynomial of common errors

Let c be the fixed expansion, delta_tau=tau(p)-tau(c), A_c=A(c) and gamma_A=A(p)-A_c-J_A*(p-c). At a query the correlated clock is S=s+q*delta_tau+e, with known center s, known native slope q and a separately bounded clock remainder e. The exact nonlinear part of A*(s+q*delta_tau)^2/2 after its physical tangent is

(s*s/2) * gamma_A + (s*q) * ((A-A_c)*delta_tau) + (q*q) * (A*delta_tau*delta_tau/2).

These are three common three-vectors, shared across every epoch, with known query-dependent coefficients. Do not force q=1 at packet boundaries. Retain the full extra clock contribution; a norm bound is

A_max * ((abs(s) + abs(q)*delta_tau_max)*e_max + e_max*e_max/2).

The previous velocity/time and initial-lever error blocks remain. A direct construction therefore has 27 physical plus 15 auxiliary enclosure coordinates. These auxiliaries are conservative mathematical error variables, not new sensor freedoms; one fixed source/domain/expansion binding must link all epochs.

Obtain bounds for the three new vectors from the original complete calibration domain: the reference acceleration's Taylor remainder, its full change times the time-offset radius, and half its full norm times the squared time-offset radius. Use outward arithmetic and independently validate the actual nonlinear vectors, including nonzero force/attitude/gain/bias/time centers. An unknown aircraft calibration is never supplied to the region calculation as an oracle.

Qualification sequence

1. Independently test the polynomial identity and conservative radii, including packet slopes zero/one/two, negative offsets and clock remainder.
2. Build a separate native candidate from the algebra above. Keep original physical models, parameter bounds, packet handling and reference source.
3. Qualify native values, every physical tangent column and factored probe residuals on all candidates/processing cases, independent constant-motion controls, nonzero centers and genuine nonzero levers.
4. Qualify the expanded joint interface: all columns and one common block across training/future, exact support certificates, binding/domain rejection and future-truth isolation.
5. Freeze a matched usefulness comparison separately. A shorter or correct bound alone cannot qualify recording-scale prediction or observational uncertainty.

Every new numerical study needs its own finite frozen allowance. No retries, completed-budget reuse, altered acceptance limits, process signals or protected ESA evaluation. Whole-program floating-point enclosure and receiver-error adequacy remain separate requirements.

Duration screen · Completed short comparison · Canonical roadmap.