Feasible scalar matches resolve the calibration-control gate

The new candidate passes all 12 known-answer identities and all 72 matched three-start comparisons. It uses the same constructed histories, seven calibration bounds and repeat tolerances as the earlier nonlinear study. That study's failed outcomes remain unchanged.

The batch completed 228 charged identities in 11.57 seconds: 147 algebraic certificates and 81 actual mathematical optimizer starts, using 4,950 counted residual/Jacobian calls. It read no aircraft originals, ran no observed fit and performed no native integration.

Why this works

Before optimizing, the new candidate asks whether one feasible constant gain already matches the complete scalar history. It checks every epoch, all gain bounds, fresh residuals and the full seven-column Jacobian. A matching mean alone is insufficient; a gain outside the bounds is rejected without clipping.

Forty-eight of the 72 constructed histories have such a near-zero scalar match. Their three requested starts therefore return explicitly labeled feasible constructions, not three claims of independent optimizer convergence. Across all certificate identities, maximum RMS is about 1.35 × 10⁻¹⁴ m/s². The largest feasible objective is 1.11 × 10⁻²⁶, against a nonnegative lower bound of zero. This does not claim unique calibration or an exact global optimum.

The other 24 histories are wrong-model changing-direction and climbing controls. They use the unchanged bounded solver from each requested start and pass all repeat checks. The construction does not force a model difference or require one for software qualification.

What this establishes

The scalar-calibration software now handles both informative and nearly uninformative controls without asking a nonlinear optimizer to rediscover an already available feasible solution. The unit checks also reject temporal disagreements hidden by a mean match and physically inadmissible gains.

This qualifies C02's mathematical diagnostic, not an observational error model or independent detection of curvature. A scalar match supplies only a necessary constraint: it does not identify orientation or demonstrate a complete motion history without gyroscopes. Actual observations may remain ambiguous.

C03's quantization, synchronization, integration-period, within-packet motion, receiver-differentiation and combined uncertainty gates still precede recorded-data channel comparisons. C04 remains blocked by those gates. The main result remains 53 globe / zero flat / zero unresolved, and the separate IMU21 horizontal-only sensitivity outcome remains unresolved.

Every identity · Completed report · Frozen plan · Earlier failed method · Roadmap.