Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.
A Representation--Optimization Trichotomy for Objectives Parameterized via Matrix Exponential Maps
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Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)
Proves ||exp(theta)||_op <= 1 + ||theta||_F on se(3) and constructs J* with L_J*(R; se(3)) >= 0.0505 R^2 for R >= 2, showing intermediate quadratic growth.