{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GXC7QK42FGWSCBBGXIL6SV2CZG","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":"6ce1fe54a9b0f329bc5efdb5ff4570af1dd73e03b11ec4fc9542681ae2df26a7","cross_cats_sorted":["math.CA","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2022-03-02T19:32:01Z","title_canon_sha256":"9e040141bd7eb58b7a6883c0195048237a94bc6d8630b13e1612b8e9c8b7c2f4"},"schema_version":"1.0","source":{"id":"2203.01367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.01367","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"2203.01367v1","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01367","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"GXC7QK42FGWS","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_16","alias_value":"GXC7QK42FGWSCBBG","created_at":"2026-07-05T04:01:47Z"},{"alias_kind":"pith_short_8","alias_value":"GXC7QK42","created_at":"2026-07-05T04:01:47Z"}],"graph_snapshots":[{"event_id":"sha256:9544f9f5e495d1faff16e44fb64535d018a0985543f01b2579d8cb603b56052c","target":"graph","created_at":"2026-07-05T04:01:47Z","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/2203.01367/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the solutions under consideration. Using an appropriate metric, with respect to which the distance is contracting, one can show convergence to a unique equilibrium or, if attraction only occurs in certain directions, to a periodic orbit. Contraction analysis was originally considered for ordinary differential equations, but has been extended to discrete-time systems, c","authors_text":"Christoph Kawan, Peter Giesl, Sigurdur Hafstein","cross_cats":["math.CA","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2022-03-02T19:32:01Z","title":"Review on contraction analysis and computation of contraction metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01367","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":"sha256:42d52c5b4eba6d19b0dcb9d7b6f20b4a5dbcb8afbeeae83c4daf888f8a3aaba3","target":"record","created_at":"2026-07-05T04:01:47Z","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":"6ce1fe54a9b0f329bc5efdb5ff4570af1dd73e03b11ec4fc9542681ae2df26a7","cross_cats_sorted":["math.CA","math.OC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2022-03-02T19:32:01Z","title_canon_sha256":"9e040141bd7eb58b7a6883c0195048237a94bc6d8630b13e1612b8e9c8b7c2f4"},"schema_version":"1.0","source":{"id":"2203.01367","kind":"arxiv","version":1}},"canonical_sha256":"35c5f82b9a29ad210426ba17e95742c9b7772fa44863fdeb4c6ec4f234b76b14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35c5f82b9a29ad210426ba17e95742c9b7772fa44863fdeb4c6ec4f234b76b14","first_computed_at":"2026-07-05T04:01:47.027657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:01:47.027657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yfN7QerVsfwNfJoHX1J+UJzugM14VnphijOJhgARDzjg1nZMdf4hYFz1YuADfZsG77rj/BoHV2Oe5/i05Wr1BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:01:47.028171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.01367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42d52c5b4eba6d19b0dcb9d7b6f20b4a5dbcb8afbeeae83c4daf888f8a3aaba3","sha256:9544f9f5e495d1faff16e44fb64535d018a0985543f01b2579d8cb603b56052c"],"state_sha256":"352aaedae09c22157b85aaad36efe60c3dacd963533c06ef15d0d75ba41e174e"}