{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OBYYWS7O2B3BW4MS6EQ6R5WWFC","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":"84ae228c51f06f8430a351354629f731d0ba9e6f49b9b8b5b91de9d4e8b2e96c","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-23T05:15:31Z","title_canon_sha256":"9f67c8b8b4e5c2f18131b424bd03d39bc7a6bb89e76912127de17d3cd5e41439"},"schema_version":"1.0","source":{"id":"1105.4404","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4404","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4404v3","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4404","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"OBYYWS7O2B3B","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OBYYWS7O2B3BW4MS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OBYYWS7O","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:9750355aed0f614344719d6d22c031380d2bbbeabc900c80b2b94dd634214054","target":"graph","created_at":"2026-05-18T03:13:46Z","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"},"paper":{"abstract_excerpt":"A less studied numerical characteristic of periodic orbits of area preserving twist maps of the annulus is the twist or torsion number, called initially the amount of rotation. It measures the average rotation of tangent vectors under the action of the derivative of the map along that orbit, and characterizes the degree of complexity of the dynamics. The aim of this paper is to give new insights into the definition and properties of the twist number, and to relate its range to the order properties of periodic orbits. We derive an algorithm to deduce the exact value or a demi--unit interval con","authors_text":"Emilia Petrisor","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-23T05:15:31Z","title":"Twist number and order properties of periodic orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4404","kind":"arxiv","version":3},"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:ca5a77daf8512e8a85d492ca55e7a3225c92137df0323c76b59809edbc649c0c","target":"record","created_at":"2026-05-18T03:13:46Z","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":"84ae228c51f06f8430a351354629f731d0ba9e6f49b9b8b5b91de9d4e8b2e96c","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-23T05:15:31Z","title_canon_sha256":"9f67c8b8b4e5c2f18131b424bd03d39bc7a6bb89e76912127de17d3cd5e41439"},"schema_version":"1.0","source":{"id":"1105.4404","kind":"arxiv","version":3}},"canonical_sha256":"70718b4beed0761b7192f121e8f6d628873d876571bfbaca3a534e52143664f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70718b4beed0761b7192f121e8f6d628873d876571bfbaca3a534e52143664f0","first_computed_at":"2026-05-18T03:13:46.597145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:46.597145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n3pr/1c9QrsVtrW+p02tfUAC4IMdzx/VtiTC5oi0b4c04EWhkW11RuKnljkSMeJv0zg7g9c6H3Ldv3RjrB6fAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:46.597770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4404","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca5a77daf8512e8a85d492ca55e7a3225c92137df0323c76b59809edbc649c0c","sha256:9750355aed0f614344719d6d22c031380d2bbbeabc900c80b2b94dd634214054"],"state_sha256":"e20ab0e84399595fe4f328e6be86d2e938a2eb70415e31b9ab69f1322b0b30a4"}