Rotational Symmetry and Labeled Evidence in a Digital Heritage Registration Model

Abstract

Geometric alignment can be precise while absolute orientation remains unidentified. We construct an eightfold-symmetric, urn-like surface to separate these two issues in a yaw-only digital-heritage registration model. An original 1,920-point surface and a radial matching objective exhibit eight exactly equivalent orientation branches. An executed 400-trial branch-selection emulator compares a local branch chosen near the initialization with selection aided by a noisy labeled marker angle. Mean absolute yaw error is 90.22 degrees without branch evidence and 0.0985 degrees with marker selection; within-one-degree frequencies are 13.25% and 100%. These numbers arise from an explicit branch-and-noise model, not from running iterative closest point or a trained registration network. A three-dimensional surface rendering, polar symmetry orbit, repeated objective minima, and circular error distribution make the ambiguity visible. The analysis explains why geometric equivariance does not by itself identify an absolute branch and why extra labels change the information available to an estimator. No archaeological scan, artifact provenance, or full six-degree-of-freedom reconstruction is claimed.