Angular uncertainty of local disparity planes

Pre-registered 2026-10-30. Use the same27 analytic frame conditions and compare all-valid patches, the prior disparity/depth gate and that gate plus angular confidence radius<=15 degrees. No ICP/real-data run or tuned alternate windows.

For a 5x5 centered affine disparity design [dx,dy,1], independent .5px Gaussian noise gives coefficient covariance diag(.25/50,.25/50,.25/25). Map coefficients [a,b,c] to unnormalized normal [fxa,fyb,c-a(u-cx)-b(v-cy)]. Covariance maps by A C A^T. Enclose the95% chi-square3 coefficient ellipsoid by a normal-space ball R=sqrt(chi2_3(.95)*lambda_max(A C A^T)). Conservative unsigned angular radius is asin(min(1,R/||normal_hat||)), capped90 degrees. Invalid patches explicitly90. Assume .5px even on clean controls, as before. This bound is exact for the stated linear affine-disparity Gaussian model, but curved/cross-surface patches violate that model; no blanket95% guarantee is made for those measurements.

First unit-test Monte Carlo coverage on20000 independent coefficient realizations (seed20261030), fixed tilted plane [.3,-.1,24] at principal point: require >=95% coverage. This is a code/model sanity check, not validation on real stereo noise. Then run prior27 scene/frame/noise conditions; retain exact source/depth hashes. Truth normals are analytic and scoring-only. Report radius quantiles, actual angular coverage and joint XYZ/normal precision for all populations, retention, spatial cells and normal spectrum. No normal-plane smoothing of scored XYZ.

Keep the prior necessary continuation screen: all18 noisy frames must have

=80% joint precision, >=10% domain retention, >=8 occupied cells and normal singular ratio>=.05. Empty selections fail support, with precision/coverage null. No post-result tuning, transfer or registration if screen fails. Preserve all cases and clean controls. Source/protocol/baseline hashes frozen before execution.