{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:3BSAIAH5WFY5L7RZC4H4M5Z2D7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f2a0f39c95d779217bd8ec58c0999682ef6d229f74247e554a99887453bad26","cross_cats_sorted":["cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2009-07-16T07:10:17Z","title_canon_sha256":"47fd35c6e17f70aab47b8ff068b14175731f23aabf64199254172a3da5d93d94"},"schema_version":"1.0","source":{"id":"0907.2759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2759","created_at":"2026-07-04T15:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2759v1","created_at":"2026-07-04T15:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2759","created_at":"2026-07-04T15:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"3BSAIAH5WFY5","created_at":"2026-07-04T15:46:13Z"},{"alias_kind":"pith_short_16","alias_value":"3BSAIAH5WFY5L7RZ","created_at":"2026-07-04T15:46:13Z"},{"alias_kind":"pith_short_8","alias_value":"3BSAIAH5","created_at":"2026-07-04T15:46:13Z"}],"graph_snapshots":[{"event_id":"sha256:e7b9123696c07bf016b8df8e8d8437312a8ed24503274c90d22642fa358ccdb6","target":"graph","created_at":"2026-07-04T15:46:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0907.2759/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss certain types of cyclic and nearly cyclic interactions among N \"point\"-agents in the plane, leading to formations of interesting limiting geometric configurations. Cyclic pursuit and local averaging interactions have been analyzed in the context of multi-agent gathering. In this paper, we consider some nearly cyclic interactions that break symmetry leading to factor circulants rather than circulant interaction matrices.","authors_text":"Alfred Bruckstein, Frederique Oggier","cross_cats":["cs.RO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2009-07-16T07:10:17Z","title":"On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2759","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5ad0ac19cdb0310521935172e0cf99774f3a5719f8d4c432f5a80b29e7d9ef36","target":"record","created_at":"2026-07-04T15:46:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f2a0f39c95d779217bd8ec58c0999682ef6d229f74247e554a99887453bad26","cross_cats_sorted":["cs.RO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MA","submitted_at":"2009-07-16T07:10:17Z","title_canon_sha256":"47fd35c6e17f70aab47b8ff068b14175731f23aabf64199254172a3da5d93d94"},"schema_version":"1.0","source":{"id":"0907.2759","kind":"arxiv","version":1}},"canonical_sha256":"d8640400fdb171d5fe39170fc6773a1fcde822cac6b367e2318281fc718115ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8640400fdb171d5fe39170fc6773a1fcde822cac6b367e2318281fc718115ec","first_computed_at":"2026-07-04T15:46:13.774809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:46:13.774809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ltRy2ul7qkWzkJR3Zk1s/iGgHXvUJyvx/A3ZmAgzQzqKoZR2HqmELswy9QH1P1qN2p8eO833iQ+nzMbq8PU1Cw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:46:13.775203Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad0ac19cdb0310521935172e0cf99774f3a5719f8d4c432f5a80b29e7d9ef36","sha256:e7b9123696c07bf016b8df8e8d8437312a8ed24503274c90d22642fa358ccdb6"],"state_sha256":"75ab9b2e1b5628248fae6bdca27c079704552ff9e15b31a625413379e2d4b5aa"}