{"paper":{"title":"Operator-norm bounds and a quadratic lower-growth example for the special Euclidean algebra se(3)","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sooraj K.C, Vivek Mishra","submitted_at":"2026-05-29T09:44:52Z","abstract_excerpt":"We prove operator-norm and gradient Lipschitz bounds for exponential-map parameterizations on the special Euclidean algebra se(3), providing an explicit example of intermediate polynomial growth behavior. Using the contraction property of the SO(3) left Jacobian, we show that\n  ||exp(theta)||_op <= 1 + ||theta||_F\n  for all theta in se(3). We then derive a self-contained O(R^2) upper bound for the gradient Lipschitz constant, with explicit constant 4.02, and construct an objective J* satisfying\n  L_J*(R; se(3)) >= 0.0505 R^2\n  for R >= 2.\n  These results place se(3) between compact Lie algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31076","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31076/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}