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For a given orientation assignment, the induced symmetric communication graph (SCG) of P is the undirected graph that contains the edge (u,v) iff v lies in u's sector and vice versa. In this paper we ask what is the smallest angle a for which there exists an integer n=n(a), such that for any set P of n antennas of angle a and unbounded range, one can orient the antennas so that"},"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":"1108.0492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-08-02T06:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"a6307ab0e64e4dbe6c3e92f2d4736fd9d8242dfb14f6463e62e6456d71b45403","abstract_canon_sha256":"6f9bd9a84759305e43edeb7321eb81475e48890e912afbabe370daea26a3519a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:30.293098Z","signature_b64":"N+LzyP79GgWIsa7O7maToSqRK40NL45W7EWYaAIChzjeAfTMKfucTjP+U9Xj9lAIO6/ZaQjX5DU4OjUk+FiSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e98b98bc3385f32764156c152cfc5664cc210c217995152ee89bc4eb75b78cb2","last_reissued_at":"2026-05-18T04:16:30.292628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:30.292628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric Connectivity with Directional Antennas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Gila Morgenstern, Matthew J. 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