Preserve shared nonlinear reference errors

The saved constraint audit shows that further linear projection cannot repair the retained nonlinear width. Build a separate mathematical enclosure that preserves two common error vectors across all epochs. Keep the original physical model, all 27 calibration directions and their bounds. No observed fits follow from component tests.

Initial velocity and the common clock

Track velocity changes from the uncertain initial velocity directly, rather than subtracting two independently widened velocity bounds. The Cayley update has the exact identity (C(a)-I)v = -2 (I+[a]x)^-1 (a x v), permitting an incremental-velocity recurrence with the existing bounded primitives.

Use a fixed initial coordinate metric. Split coordinate rates into that metric times the uncertain initial velocity, a term for velocity change and a term for metric change. Combine the reference velocity with the correlated prefix clock. Its nonlinear product contains one shared physical vector

gamma_v = delta_initial_velocity * delta_time_offset.

Bound it componentwise from the original domain and represent it once, with the appropriate known metric/time-slope coefficient at each epoch. Keep all remaining clock error, dynamic motion, metric variation and cross terms. Internal state bounds must include the full shared error; only the final factored observation may separate it from the unshared remainder.

Initial lever and attitude

For the initial body-to-navigation rotation R0 and lever L, define

gamma_L = R0(p)L(p) - R0(c)L(c) - D(R0 L)_c (p-c).

The existing rotation/lever bounds supply a common vector-radius bound. A zero lever expansion center is allowed without setting the actual lever to zero: the complete original lever domain remains. Nonzero centers need the full derivative and bound, not a zero-center shortcut.

Separate Rt L = R0 L + (Rt-R0)L. Bound the latter as genuine motion: rotation product telescoping bounds ||Rt-R0|| by accumulated body/navigation angular motion, capped at two. The geographic metric's uncertainty and the first-order lever contribution must remain in the dynamic remainder. It is invalid simply to subtract the old initial-lever radius from a completed total bound.

Joint representation and gates

One joint expansion definition binds the shared vectors to all epochs. Retain the original 27 columns plus six bounded auxiliary error coordinates. Coefficients may change with known metric/time slopes; the underlying shared variables cannot be independently reselected per epoch. Zero or unidentified columns stay present. An inconsistent binding or missing shared block must abstain.

First test the exact product/rotation decomposition and its bounds, including nonzero centers and actual nonzero levers. Then connect it to a new native candidate, preserving all field, transport, calibration and packet-boundary terms. Qualify all candidates/processing cases against the unchanged engine and independent known-motion controls. Save every native/Jacobian, shared binding, inequality, error contribution and certificate. Future truth is unavailable to the enclosure/region calculation.

Freeze a separate finite source/input/environment/call allowance before any new study. Keep at most four numerical threads; no retries, expansions or signals. A native qualification and a distinct usefulness comparison precede any observed prediction work. Global numerical treatment, actual receiver-error adequacy and independent confirmation remain additional gates. Existing data, completed results and protected ESA groups remain untouched.

Saved constraint outcome · Native decomposition · Canonical roadmap.