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The proof is more conceptual and simpler than the original one.\n  We also find a new sufficient condition for higher-dimensional normed spaces to share this characterization. In particular, a star $\\{op_i: i=1,...,k\\}$ in any CL-space is a Steiner minimal tree of its vertices $\\{o,p_1,...,p_k\\}$ if and only if all angles are absorbing, which in tur"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.5046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-08-25T09:26:22Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9060e973aba6599026a50a287827dd44d87b9594fb56a4ccdc7d33d3b45736fa","abstract_canon_sha256":"d91a8a16a9092915b7263494bcee8f6b5cd699a133f3f8715b91b4bc72e86bbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.509119Z","signature_b64":"eHWhZx3g1Qu2mRHSdJK+5sTfQiXS+NnvZ4GdMIxsEBJ0C1imW2aPwOpRZPlskaWxKgz70dNab9r9wdLxbGKiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63b11772cfcbf674803c964a247b1e7fbc780dd72f8163c10e97a78280085cf6","last_reissued_at":"2026-05-18T04:14:45.508689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.508689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Absorbing angles, Steiner minimal trees, and antipodality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Horst Martini, Konrad J. 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