NOTE ON GEOMETRIC ALGEBRAS AND CONTROL PROBLEMS WITH SO(3)–SYMMETRIES

Jaroslav Hrdina, Aleš Návrat, Petr Vašík, Lenka Zalabová

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves and algorithmically sketches that two oriented bases with identical Gram matrices can be connected by a rotor, proceeding via a flag-alignment scheme and using the rotor formula Rxy = 1 + yx (normalized) to align successive hyperplanes (their eq. (26)) , culminating in Theorem 3.6 and an explicit flag-based algorithm . The model solution independently constructs the same object: it builds a product of simple rotors that align the complete flags and ensures previously aligned subspaces are fixed—conceptually the same strategy. The model adds explicit handling of 180° cases and normalization details, which the paper’s pseudocode glosses over, but these are minor implementation clarifications rather than substantive differences. Net: both are correct, following substantially the same proof idea.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The core theorem and construction are sound and align with standard GA rotor techniques. The flag-alignment strategy is clearly motivated and well-suited to the control applications presented. To improve robustness and reproducibility, the authors should explicitly mention normalization and address the 180° case in the pseudocode. These are small but important clarifications that will help practitioners implement the method without ambiguity.