Calibration-aware channel controls

This local-calibration design is implemented and its 72-case matrix is complete. The subsequent nonlinear study does not qualify the whole diagnostic for observed use. Current pending work is collated under C02/C03/C04 in the authoritative roadmap.

The constant-gain control rules out treating fixed-calibration scalar separation as sufficient information. The calculation below measures the part of a force-magnitude difference outside a local calibration tangent space.

Defined calculation

For a constructed recording, keep one calibration vector across all epochs: three dimensionless acceleration gains, three acceleration offsets in m/s², and one gravity adjustment in m/s². Use the existing exploratory bounds unchanged (±0.15 gain, ±0.25 m/s² offset and ±0.05 m/s² gravity).

At zero corrections, the residual is measured body-force magnitude minus the candidate's required-force magnitude. Differentiate the scalar residual with respect to all seven coordinates, scale columns by their bounds, and report the complete singular spectrum. Keep all seven columns, including dependent ones. Project the residual onto the orthogonal complement with an explicit relative SVD tolerance of 10⁻¹⁰. No covariance or calibrated information/power is implied.

Report the local projected residual, minimum-norm linear correction, whether that correction lies within the bounds, and its actual nonlinear residual when feasible. A projection can remove more than a bounded nonlinear calibration can realize. A surviving local residual likewise does not rule out another nonlinear solution. Both limitations must accompany the numbers.

Verification before any new study

Ordinary deterministic unit tests check independent finite-difference derivatives, exact affine projection, rank deficiency, bound checks, invalid inputs and failure at zero force. Constructed straight and changing-motion examples are mathematical controls, not observed fits. They use no archive files, native integration, fused attitude or optimizer.

This step introduces no observational budget and does not alter completed freezes. A later trajectory matrix needs its own finite frozen allowance. A recorded-data comparison still requires nonlinear calibration ambiguity, quantization, timing, averaging, shared uncertainty and a motion-selected support policy to be addressed.